U.S. patent application number 11/487571 was filed with the patent office on 2007-12-13 for techniques for using chirped fields to reconfigure a medium that stores spectral features.
This patent application is currently assigned to Montana State University. Invention is credited to William R. Babbitt, Tiejun Chang, Kristian D. Merkel, Mingzhen Tian.
Application Number | 20070285762 11/487571 |
Document ID | / |
Family ID | 38792883 |
Filed Date | 2007-12-13 |
United States Patent
Application |
20070285762 |
Kind Code |
A1 |
Chang; Tiejun ; et
al. |
December 13, 2007 |
TECHNIQUES FOR USING CHIRPED FIELDS TO RECONFIGURE A MEDIUM THAT
STORES SPECTRAL FEATURES
Abstract
Techniques for reconfiguring spectral features stored in a
medium based on a two-state atomic system with transition dipole
moment .mu. includes causing a chirp to pass into the medium. The
chirp includes a monochromatic frequency that varies in time by a
chirp rate .kappa. over a frequency band B.sub.R during a time
interval T.sub.R. The amplitude A.sub.R of the chirp is constant
over B.sub.R and equal to A.sub.R=(hbar/.mu..pi.) {square root over
((.kappa. ln [2/.epsilon.]))}, The term hbar is reduced Plank's
constant, ln is a natural logarithm function, and .pi. is a ratio
of a circumference of a circle to a diameter of the circle. For
.epsilon.<<1, the atomic-state populations in the two states
are inverted. For .epsilon.=1, prior atomic-state populations are
erased, with final populations equal in the two states, regardless
of populations before erasure.
Inventors: |
Chang; Tiejun; (Bozeman,
MT) ; Tian; Mingzhen; (Bozeman, MT) ; Babbitt;
William R.; (Bozeman, MT) ; Merkel; Kristian D.;
(Bozeman, MT) |
Correspondence
Address: |
EVANS & MOLINELLI, PLLC
U.S. POST OFFICE BOX 7024
FAIRFAX STATION
VA
22039
US
|
Assignee: |
Montana State University
|
Family ID: |
38792883 |
Appl. No.: |
11/487571 |
Filed: |
July 14, 2006 |
Related U.S. Patent Documents
|
|
|
|
|
|
Application
Number |
Filing Date |
Patent Number |
|
|
60699477 |
Jul 15, 2005 |
|
|
|
Current U.S.
Class: |
359/326 |
Current CPC
Class: |
G11C 13/04 20130101;
G01R 33/28 20130101; G02F 1/17 20130101 |
Class at
Publication: |
359/326 |
International
Class: |
G02F 1/35 20060101
G02F001/35 |
Goverment Interests
STATEMENT OF GOVERNMENTAL INTEREST
[0002] This invention was made with Government support under
Contract Nos. MDA-972-03-1-0002 awarded by the Defense Advanced
Research Projects Agency and NRO-DII-000-03-C-0312 awarded by the
National Reconnaissance Office. The Government has certain rights
in the invention.
Claims
1. A method for erasing spectral features stored in a medium based
on a two-state atomic system having a transition dipole moment of
.mu., in which an atom transitions between a first state and a
second state, comprising the step of causing a chirped
electromagnetic field to pass into the medium, wherein: the chirped
electromagnetic field includes a monochromatic frequency that
varies in time by a chirp rate .kappa. over an erasure frequency
band of bandwidth B.sub.E during an erasure time interval T.sub.E;
and an amplitude A.sub.E of the electromagnetic field oscillations
in the chirped electromagnetic field over the erasure frequency
band is substantively constant and substantively specified by an
equation of form A.sub.E=(hbar/.mu..pi.) {square root over
((.kappa. ln 2))}, in which hbar is Plank's constant, ln is a
natural logarithm function, and .pi. is a ratio of a circumference
of a circle to a diameter of the circle, whereby substantively
fifty percent of the two-state atomic system responsive in the
erasure frequency band exposed to the chirped electromagnetic field
is in the first state after erasure regardless of a percentage in
the first state before erasure.
2. A method as recited in claim 1, wherein: the chirped
electromagnetic field further includes a start edge in a start time
interval T.sub.S adjacent before the erasure time interval T.sub.E;
and an amplitude A.sub.S of the electromagnetic field oscillations
during the start time interval T.sub.S increases with a
substantively continuous first derivative from substantively zero
at a start of the start time interval T.sub.S to A.sub.E and a
substantively zero rate of change at an end of the start time
interval T.sub.S.
3. A method as recited in claim 2, wherein a frequency .omega.(t)
of the electromagnetic field oscillations at a time t during the
start time interval T.sub.S changes with a substantively continuous
first derivative to match a start frequency .omega..sub.0 and start
frequency rate of change .kappa.s at a start of the erasure time
interval T.sub.E.
4. A method as recited in claim 2, wherein a phase of the
electromagnetic field oscillations during the start time interval
T.sub.S changes with a substantively continuous first derivative to
match a start phase and start phase rate of change at a start of
the erasure time interval T.sub.E.
5. A method as recited in claim 2, wherein A.sub.S is substantively
specified by an equation of form A.sub.S(t)={cosine
[.pi.(t-t.sub.0)/T.sub.S]+1}A.sub.E/2, in which t is time and
t.sub.0 is time at a start of the erasure time interval
T.sub.E.
6. A method as recited in claim 3, wherein .omega.(t) during the
start time interval T.sub.S is substantively specified by an
equation of form d.omega.(t)/dt={cosine
[.pi.(t-t.sub.0)/T.sub.S]+1}.kappa.s/2, in which t is time, t.sub.0
is time at a start of the erasure time interval T.sub.E,
d.omega.(t)/dt is time rate of change of frequency at a time t, and
.kappa.s is the start frequency rate of change at time t.sub.0.
7. A method as recited in claim 1, wherein: the chirped
electromagnetic field further includes a finish edge in a finish
time interval T.sub.F adjacent after the erasure time interval
T.sub.E; and an amplitude A.sub.F of the electromagnetic field
oscillations during the finish time interval T.sub.F decreases with
a substantively continuous first derivative from a value
substantively equal to A.sub.E with a substantively zero rate of
change at a start of the finish time interval T.sub.F to zero at an
end of the finish time interval T.sub.F.
8. A method as recited in claim 7, wherein a frequency .omega.(t)
of the electromagnetic field oscillations at a time t during the
finish time interval T.sub.F changes with a substantively
continuous first derivative to match an end-erase frequency
.omega.e and an end-erase frequency rate of change .kappa.e at an
end of the erasure time interval T.sub.E.
9. A method as recited in claim 7, wherein a phase of the
electromagnetic field oscillations during the finish time interval
T.sub.F changes with a substantively continuous first derivative to
match an end-erase phase and an end-erase phase rate of change at
an end of the erasure time interval T.sub.E.
10. A method as recited in claim 7, wherein A.sub.F is
substantively specified by an equation of form A.sub.F(t)={cosine
[.pi.(t-t.sub.0-T.sub.E)/T.sub.F]+1}A.sub.E/2, in which t is time
and t.sub.0 is time at a start of the erasure time interval
T.sub.E.
11. A method as recited in claim 8, wherein .omega.(t) during the
finish time interval T.sub.F is substantively specified by an
equation of form d.omega.(t)/dt={cosine
[.pi.(t-t.sub.0-T.sub.E)/T.sub.F]+1}.kappa.e/2, in which t is time,
t.sub.0 is time at a start of the erasure time interval T.sub.E,
d.omega.(t)/dt is time rate of change of frequency at a time t, and
.kappa.e is the end-erase frequency rate of change at the end of
the erasure time interval T.sub.E.
12. A method as recited in claim 1, wherein the chirp rate .kappa.
is substantively constant over the erasure frequency band and
substantively equal to B.sub.E/T.sub.E.
13. A method as recited in claim 2, wherein: the chirped
electromagnetic field further includes a finish edge in a finish
time interval T.sub.F adjacent after the erasure time interval
T.sub.E; and an amplitude A.sub.F of the electromagnetic field
oscillations during the finish time interval T.sub.F decreases with
a substantively continuous first derivative from a value
substantively equal to A.sub.E with a substantively zero rate of
change at a start of the finish time interval T.sub.F to zero at an
end of the finish time interval T.sub.F.
14. A method as recited in claim 13, wherein a duration of the
start time interval T.sub.S is substantively equal to a duration of
the finish time interval T.sub.F.
15. A method as recited in claim 1, wherein the amplitude A.sub.E
of the electromagnetic field oscillations over the bandwidth
B.sub.E is substantively constant and substantively specified by
the equation for a particular portion less than all of the medium,
in which portion spectral features are to be erased.
16. A method as recited in claim 1, wherein the medium is an
inhomogeneously broadened transition (IBT) material and the
amplitude A.sub.E and dipole moment .mu. are for an electric
field.
17. A method as recited in claim 1, wherein the medium is a
material subjected to a magnetic field for nuclear magnetic
resonance (NMR) measurements and the amplitude A.sub.E and dipole
moment .mu. are for a magnetic field.
18. A method as recited in claim 1, further comprising the step of
causing a different chirped electromagnetic field to pass into the
medium, wherein: the different chirped electromagnetic field has a
monochromatic frequency that varies in time by a chirp rate
.kappa.2 over a different erasure frequency band of bandwidth
B.sub.E2 during the same erasure time interval T.sub.E; and an
amplitude A.sub.E2 of the electromagnetic field oscillations in the
different chirped electromagnetic field over the bandwidth B.sub.E2
is substantively constant and substantively specified by an
equation of form A.sub.E2=(hbar/.mu..pi.) {square root over
((.kappa.2 ln 2))} whereby substantively fifty percent of the
two-state atomic system responsive in the different erasure
frequency band exposed to the different chirped electromagnetic
field is in the first state after erasure regardless of a
percentage in the first state before erasure.
19. A method as recited in claim 1, further comprising: in response
to causing the chirped electromagnetic field to pass into the
medium, receiving a readout electromagnetic field from the medium;
and determining the spectral features stored in the medium within
the erasure frequency band before erasure based on the readout
electromagnetic field
20. A method as recited in claim 1, wherein: interactions of the
chirped electromagnetic field and the medium are coherent over a
time scale up to time T.sub.2; and the chirp rate .kappa. within
the erasure frequency band satisfies an inequality given by
.kappa.>>ln 2/(.pi.T.sub.2).sup.2, whereby erasure is
effective even at small values for T.sub.2.
21. A method as recited in claim 1, wherein: the medium is an
optical absorption medium with frequency-dependent absorption based
on the two state atomic system; the two-state atomic system has a
population decay time that describes a rate of return of a
population of atoms in the two-state atomic system to a ground
state of the two state atomic system; and the method further
comprises waiting a particular time based on a target absorption
value and the population decay time, whereby absorption over the
erasure frequency band attains the target absorption value.
22. A method as recited in claim 3, wherein .omega.(t) during the
start time interval T.sub.S is substantively specified by an
equation of form d.omega.(t)/dt=.kappa.s in which t is time,
d.omega.(t)/dt is time rate of change of frequency at a time t, and
.kappa.s is the start frequency rate of change at a start of the
erasure time interval T.sub.E.
23. A method as recited in claim 22, wherein: .kappa. is a constant
substantively equal to B.sub.E/T.sub.E; and .kappa.s is
substantively equal to .kappa..
24. A method as recited in claim 8, wherein .omega.(t) during the
finish time interval T.sub.F is substantively specified by an
equation of form d.omega.(t)/dt=.kappa.e in which t is time,
d.omega.(t)/dt is time rate of change of frequency at a time t, and
.kappa.e is the end-erase frequency rate of change at the end of
the erasure time interval T.sub.E.
25. A method as recited in claim 24, wherein: .kappa. is a constant
substantively equal to B.sub.E/T.sub.E; and .kappa.e is
substantively equal to .kappa..
26. A method for inverting non-uniform spectral features stored in
a medium based on a two-state atomic system having a transition
dipole moment of .mu., in which an atom transitions between a first
state and a second state, comprising the step of causing a chirped
electromagnetic field to pass into the medium, wherein: the chirped
electromagnetic field includes a monochromatic frequency that
varies in time by a chirp rate .kappa. over an inversion frequency
band of bandwidth B.sub.1 during an inversion time interval
T.sub.1; and an amplitude A.sub.1 of the electromagnetic field
oscillations in the chirped electromagnetic field over the
inversion frequency band is substantively constant and
substantively specified by an equation of form
A.sub.1=(hbar/.mu..pi.) {square root over ((.kappa. ln
[2/.epsilon.]))}, in which hbar is Plank's constant, ln is a
natural logarithm function, .pi. is a ratio of a circumference of a
circle to a diameter of the circle, and .epsilon. is a non-zero
fractional difference from complete inversion, whereby a particular
relative population (r) of the excited state of the two-state
atomic system, responsive at a particular frequency in the
inversion frequency band exposed to the chirped electromagnetic
field, is substantively equal to X*(1-.epsilon.) after inversion
when the relative population of the excited state is -X before
inversion, wherein r is +1 to indicate all atoms are in the excited
state and r is -1 to indicate all atoms are in the ground
state.
27. A method as recited in claim 26, wherein: the chirped
electromagnetic field further includes a start edge in a start time
interval T.sub.S adjacent before the inversion time interval
T.sub.1; and an amplitude A.sub.S of the electromagnetic field
oscillations during the start time interval T.sub.S increases with
a substantively continuous first derivative from substantively zero
at a start of the start time interval T.sub.S to A.sub.1 and a
substantively zero rate of change at an end of the start time
interval T.sub.S.
28. A method as recited in claim 27, wherein a frequency .omega.(t)
of the electric field oscillations at a time t during the start
time interval T.sub.S changes with a substantively continuous first
derivative to match a start frequency .omega..sub.S and start
frequency rate of change .kappa.s at a start of the inversion time
interval T.sub.1.
29. A method as recited in claim 27, wherein a phase of the
electromagnetic field oscillations during the start time interval
T.sub.S changes with a substantively continuous first derivative to
match a start phase and start phase rate of change at a start of
the inversion time interval T.sub.1.
30. A method as recited in claim 27, wherein A.sub.S is
substantively specified by an equation of form
A.sub.S(t)={sech[(t-t.sub.0)/(T.sub.S/2)]}A.sub.I, in which t is
time and t.sub.0 is time at a start of the erasure time interval
T.sub.1 and sech is the hyperbolic secant function.
31. A method as recited in claim 28, wherein .omega.(t) during the
start time interval T.sub.S is substantively specified by an
equation of form .omega.(t)=.omega..sub.0+{T.sub.S tanh
[(t-t.sub.0)/(T.sub.S/2)]-T.sub.1}.kappa.s/2, in which t is time,
t.sub.0 is time at a start of the inversion time interval T.sub.1,
.omega..sub.0 is frequency at time t.sub.0, .kappa.s is the start
frequency rate of change at time t.sub.0, and tanh is the
hyperbolic tangent function.
32. A method as recited in claim 26, wherein: the chirped
electromagnetic field further includes a finish edge in a finish
time interval T.sub.F adjacent after the inversion time interval
T.sub.1; and an amplitude A.sub.F of the electromagnetic field
oscillations during the finish time interval T.sub.F decreases with
a substantively continuous first derivative from a value
substantively equal to A.sub.1 with a substantively zero rate of
change at a start of the finish time interval T.sub.F to zero at an
end of the finish time interval T.sub.F.
33. A method as recited in claim 32, wherein a frequency .omega.(t)
of the electromagnetic field oscillations at a time t during the
finish time interval T.sub.F changes with a substantively
continuous first derivative to match an end-invert frequency
.omega..sub.0+B.sub.1 and an end-invert frequency rate of change
.kappa.e at an end of the inversion time interval T.sub.1.
34. A method as recited in claim 32, wherein a phase of the
electromagnetic oscillations during the finish time interval
T.sub.F changes with a substantively continuous first derivative to
match an end-invert phase and an end-invert phase rate of change at
an end of the inversion time interval T.sub.1.
35. A method as recited in claim 32, wherein A.sub.F is
substantively specified by an equation of form
A.sub.F(t)={sech[(t-t.sub.0-T.sub.1)/(T.sub.F/2)]}A.sub.1, in which
t is time and t.sub.0 is time at a start of the inversion time
interval T.sub.1.
36. A method as recited in claim 33, wherein .omega.(t) during the
finish time interval T.sub.F is substantively specified by an
equation of form
.omega.(t)=.omega..sub.0+{T.sub.Stanh[(t-t.sub.0T.sub.1)/(T.sub.S/2)]+T.s-
ub.1}.kappa.e/2, in which t is time, t.sub.0 is time at a start of
the inversion time interval T.sub.1, .omega..sub.0 is frequency at
time t.sub.0, and .kappa.e is the end-invert frequency rate of
change at the end of the inversion time interval T.sub.1.
37. A method as recited in claim 26, wherein the chirp rate .kappa.
is substantively constant over the inversion frequency band and
substantively equal to B.sub.1/T.sub.1.
38. A method as recited in claim 27, wherein: the chirped
electromagnetic field further includes a finish edge in a finish
time interval T.sub.F adjacent after the inversion time interval
T.sub.1; and an amplitude A.sub.F of the electromagnetic field
oscillations during the finish time interval T.sub.F decreases with
a substantively continuous first derivative from a value
substantively equal to A.sub.1 with a substantively zero rate of
change at a start of the finish time interval T.sub.F to zero at an
end of the finish time interval T.sub.F.
39. A method as recited in claim 38, wherein the start time
interval T.sub.S is substantively equal to the finish time interval
T.sub.F.
40. A method as recited in claim 26, wherein the amplitude A.sub.1
of the electromagnetic field oscillations over the inversion
frequency band is substantively constant and substantively
specified by the equation for a particular portion less than all of
the medium in which portion spectral features are to be
inverted.
41. A method as recited in claim 26, wherein the medium is an
inhomogeneously broadened transition (IBT) material and the
amplitude A.sub.1 and dipole moment .mu. are for an electric
field.
42. A method as recited in claim 26, wherein the medium is a
material subjected to a magnetic field for nuclear magnetic
resonance (NMR) measurements and the amplitude A.sub.1 and dipole
moment .mu. are for a magnetic field.
43. A method as recited in claim 26, further comprising the step of
causing a different chirped electromagnetic field to pass into the
medium, wherein: the different chirped electromagnetic field has a
monochromatic frequency that varies in time by a chirp rate
.kappa.2 over a different inversion frequency band of bandwidth
B.sub.I2 during the same inversion time interval T.sub.1; and an
amplitude A.sub.I2 of the electromagnetic field oscillations in the
different chirped electromagnetic field over the bandwidth B.sub.I2
is substantively constant and substantively specified by an
equation of form A.sub.I2=(hbar/.mu..pi.) {square root over
((.kappa.2 ln [2/.epsilon.2]))} in which .epsilon.2 is a non-zero
fractional difference from complete inversion whereby a particular
relative population (r) of the excited state of the two-state
atomic system, responsive at a particular frequency in the
inversion frequency band exposed to the chirped electromagnetic
field, is substantively equal to X*(1-.epsilon.) after inversion
when the relative population of the excited state is -X before
inversion, wherein r is +1 to indicate all atoms are in the excited
state and r is -1 to indicate all atoms are in the ground
state.
44. A method as recited in claim 26, wherein: interactions of the
chirped electromagnetic field and the medium are coherent over a
time scale up to time T.sub.2; and the chirp rate .kappa. within
the inversion frequency band satisfies an inequality given by
.kappa.>>ln [2/.epsilon.]/(.pi.T.sub.2).sup.2, whereby
inversion is effective even at small values for T.sub.2.
45. A method as recited in claim 26, wherein: the medium is an
optical absorption medium with frequency-dependent absorption based
on the two state atomic system; the two-state atomic system has a
population decay time that describes a rate of return of a
population of atoms in the two-state atomic system to a ground
state of the two state atomic system; and the method further
comprises waiting a particular time based on a target absorption
value and the population decay time, whereby absorption over the
inversion frequency band attains the target absorption value.
46. A method as recited in claim 28, wherein .omega.(t) during the
start time interval T.sub.S is substantively specified by an
equation of form d.omega.(t)/dt=.kappa.s in which t is time,
d.omega.(t)/dt is time rate of change of frequency at a time t, and
.kappa.s is the start frequency rate of change at a start of the
inversion time interval T.sub.1.
47. A method as recited in claim 46, wherein: .kappa. is a constant
substantively equal to B.sub.1/T.sub.1; and .kappa.s is
substantively equal to .kappa..
48. A method as recited in claim 33, wherein .omega.(t) during the
finish time interval T.sub.F is substantively specified by an
equation of form d.omega.(t)/dt=.kappa.e in which t is time,
d.omega.(t)/dt is time rate of change of frequency at a time t, and
.kappa.e is the end-erase frequency rate of change at the end of
the inversion time interval T.sub.1.
49. A method as recited in claim 48, wherein: .kappa. is a constant
substantively equal to B.sub.1/T.sub.1; and .kappa.e is
substantively equal to .kappa..
50. An apparatus for reconfiguring spectral features stored in a
medium based on a two-state atomic system having a transition
dipole moment of .mu., in which an atom transitions between a first
state and a second state, comprising: means to form a chirped
electromagnetic field wherein the chirped electromagnetic field
includes a monochromatic frequency that varies in time by a chirp
rate .kappa. over a reconfiguration frequency band of bandwidth
B.sub.R during a reconfiguration time interval T.sub.R, and an
amplitude A.sub.R of the electromagnetic field oscillations in the
chirped electromagnetic field over the reconfiguration frequency
band is substantively constant and substantively specified by an
equation of form A.sub.R=(hbar/.mu..pi.) {square root over
((.kappa. ln [2/.epsilon.]))} in which hbar is Plank's constant, ln
is a natural logarithm function, .pi.is a ratio of a circumference
of a circle to a diameter of the circle; and means for passing the
chirped electromagnetic field into the medium, whereby for
.epsilon.<<1, a particular relative population (r) of the
excited state of the two-state atomic system, responsive at a
particular frequency in the inversion frequency band exposed to the
chirped electromagnetic field, is substantively equal to
X*(1-.epsilon.) after inversion when the relative population of the
excited state is -X before inversion, wherein r is +1 to indicate
all atoms are in the excited state and r is -1 to indicate all
atoms are in the ground state, and for .epsilon.=1, substantively
fifty percent of the two-state atomic system responsive in the
erasure frequency band exposed to the chirped electromagnetic field
is in the first state after erasure regardless of a percentage in
the first state before erasure.
51. An apparatus for reconfiguring spectral features stored in a
medium based on a two-state atomic system having a transition
dipole moment of .mu., in which an atom transitions between a first
state and a second state, comprising: a controller to form a
chirped electromagnetic field wherein the chirped electromagnetic
field includes a monochromatic frequency that varies in time by a
chirp rate .kappa. over a reconfiguration frequency band of
bandwidth B.sub.R during a reconfiguration time interval T.sub.R,
and an amplitude A.sub.R of electromagnetic field oscillations in
the chirped electromagnetic field over the reconfiguration
frequency band is substantively constant and substantively
specified by an equation of form A.sub.R=(hbar/.mu..pi.) {square
root over ((.kappa. ln [2/.epsilon.]))}, in which hbar is Plank's
constant, ln is a natural logarithm function, .pi.is a ratio of a
circumference of a circle to a diameter of the circle; an
electromagnetic modulator for modulating an electromagnetic carrier
frequency with the chirped electromagnetic field to form a
reconfiguration beam; and an electromagnetic coupler for passing
the reconfiguration beam into the medium, whereby for
.epsilon.<<1, a particular relative population (r) of the
excited state of the two-state atomic system, responsive at a
particular frequency in the inversion frequency band exposed to the
chirped electromagnetic field, is substantively equal to
X*(1-.epsilon.) after inversion when the relative population of the
excited state is -X before inversion, wherein r is +1 to indicate
all atoms are in the excited state and r is -1 to indicate all
atoms are in the ground state, and for .epsilon.=1, substantively
fifty percent of the two-state atomic system responsive in the
erasure frequency band exposed to the chirped electromagnetic field
is in the first state after erasure regardless of a percentage in
the first state before erasure.
52. A computer-readable medium carrying one or more sequences of
instructions for forming chirped electromagnetic field to
reconfigure spectral features stored in a medium based on a
two-state atomic system having a transition dipole moment of .mu.,
in which an atom transitions between a first state and a second
state, wherein execution of the one or more sequences of
instructions by one or more processors causes the one or more
processors to perform the steps of: determining a temporal
frequency form for a chirped electromagnetic field that includes a
monochromatic frequency that varies in time by a chirp rate ic over
a reconfiguration frequency band of bandwidth B.sub.R during a
reconfiguration time interval T.sub.R; and determining an amplitude
A.sub.R of electromagnetic field oscillations in the chirped
electromagnetic field over the reconfiguration frequency band that
is substantively constant and substantively specified by an
equation of form A.sub.R(hbar/.mu..pi.) {square root over ((.kappa.
ln [2/.epsilon.]))} in which hbar is reduced Plank's constant, ln
is a natural logarithm function, .pi. is a ratio of a circumference
of a circle to a diameter of the circle; and driving an
electromagnetic modulator to impose the chirped electromagnetic
field onto an electromagnetic carrier frequency, whereby for
.epsilon.<<1, a particular relative population (r) of the
excited state of the two-state atomic system, responsive at a
particular frequency in the inversion frequency band exposed to the
chirped electromagnetic field, is substantively equal to
X*(1-.epsilon.) after inversion when the relative population of the
excited state is -X before inversion, wherein r is +1 to indicate
all atoms are in the excited state and r is -1 to indicate all
atoms are in the ground state, and for .epsilon.=1, substantively
fifty percent of the two-state atomic system responsive in the
erasure frequency band exposed to the chirped electromagnetic field
is in the first state after erasure regardless of a percentage in
the first state before erasure.
Description
CROSS-REFERENCE TO RELATED APPLICATIONS
[0001] This application claims benefit of Provisional Appln.
60/699,477, filed Jul. 15, 2005, the entire contents of which are
hereby incorporated by reference as if fully set forth herein,
under 35 U.S.C. .sctn.119(e).
BACKGROUND OF THE INVENTION
[0003] 1. Field of the Invention
[0004] The present invention relates to configuring a medium with a
two-state atomic system that stores spectra at electromagnetic
frequencies, and, in particular, to the use of a chirped field to
erase or invert spectra already stored in the medium.
[0005] 2. Description of the Related Art
[0006] Information processing based on optical analog signal
processing promises to provide advantages in speed, size and power
over current information processing systems. Many versatile optical
coherent transient (OCT) processing devices have been proposed. An
OCT device relies on broadband complex spatial-spectral grating
formed in the optical properties of a material, such as an
inhomogeneously broadened transition (IBT) material, also called a
spatial-spectral (S2) material. A spatial-spectral grating has the
ability to generate a broadband optical output signal that depends
on an optical probe waveform impinging on that grating and the one
or more interacting optical signals that formed the grating. The
optical properties of the spatial-spectral grating at any
electromagnetic frequency are determined by the population of atoms
in each electron quantum level state of a two-state atomic
system.
[0007] In optical analog signal processing, the medium is used to
store particular spectral features of interest, such as the result
of the interaction of one or more optical beams carrying
information. See for example, published International Patent
application WO 2003/098384 entitled "Techniques for processing high
time-bandwidth signals using a material with inhomogeneously
broadened absorption spectrum, Inventors: K. D. Merkel, Z. Cole, K.
M. Rupavatharam, W. R. Babbitt, T. Chang and K. H. Wagner, 27 Nov.
2003 (hereinafter Merkel), the entire contents of which are hereby
incorporated by reference as if fully set forth herein.
[0008] In some circumstances, including those described by Merkel,
the medium is an optically absorptive medium when most of the
population is in the ground state of the two electron quantum level
states. This reduces the signal level of a readout beam transmitted
through the medium. However, when the population is evenly divided
between the two states, and all coherent superposition states have
decayed away, the medium is transparent, e.g., signal levels
transmitted are essentially equal to the signal levels impinging.
Furthermore, when most of the population is in the excited state,
the medium is amplifying, e.g., signal levels transmitted are
greater than the signal levels impinging.
[0009] Once the medium has been endowed with spectral content in
the form of frequency dependent or spatially dependent populations,
or both, the same portion of the medium can not be reused
immediately without contamination by the previously stored spectral
content. It is therefore necessary to return the populations of the
two states to a uniform level over a range of frequencies,
independent of the previously stored spectral content, before
processing independent signals in the medium. The process of making
population uniform over a frequency range is called erasure.
[0010] One approach used to erase spectral content in a frequency
range is to wait for the atoms in the excited state to decay to the
ground state, so that essentially the entire population of atoms of
interest is in the ground state. A disadvantage of this approach is
that decay is typically exponential and requires waiting very long
times, compared to desirable processing rates, to effectively
return the population to the ground state.
[0011] Another approach is to add energy to the system so that the
entire population is in the excited state, making a uniform
spectrum, and wait for the system to decay to a level desired for
processing, such as all in the ground state or equal populations in
both states. A disadvantage of this approach is that it takes
substantial energy. Another disadvantage is that it takes a long
time to decay to a desired population distribution, even to equal
populations in both states.
[0012] Another approach is to write on top of the previously
written spectrum with approximately the opposite spectral content,
such that the process cancels the previous spectral grating. A
disadvantage of this approach is that the spectral content already
stored in the medium must be known well. Another disadvantage is
that perfect cancellation is not possible due to non-linearities
and population decay. Furthermore, the population decay time must
be very long compared to the time to perform the erasure, so that
the over-write does not impose a lower strength inversion of the
original spectrum.
[0013] It is sometimes advantageous to invert the population
levels, without removing the spectral content. For example, when
the spectral content in an absorbing medium is such that most of
the atoms are in the ground state, it is advantageous to invert the
population levels so that the readout beam signal level is higher.
The process of inverting the population of the two states is called
inversion. However, no publication known to applicants has
addressed inversion of frequency-dependent populations;
publications have only addressed uniform populations.
[0014] In one approach to inverting a uniform population over a
frequency band, a chirped optical field has been used. The
frequency and amplitude of the chirped field are as given for a
hyperbolic secant in Table 1, described next.
[0015] Other two-state atomic systems have been used. For example,
in nuclear magnetic resonance (NMR) applications, the populations
of atoms in two quantum spin states are measured. These spin states
affect the signals emitted at electromagnetic frequencies outside
the optical frequency range.
[0016] Inversion of a uniform spin population in a two spin system
has been proposed, using a variety of functional forms for time
dependence of amplitude and frequency, in a series of papers
including U.S. Pat. No. 6,064,207, by E. Kupce, entitled "Adiabatic
pulses for wideband inversion and broadband decoupling", May 16,
2000 (hereinafter Kupce), the entire contents of which are herby
incorporated by reference as if fully set forth herein. Table 1
summarizes the functional forms described in these series of
publications. TABLE-US-00001 TABLE 1 Amplitude and frequency of
electromagnetic field for used for uniform population inversion in
NMR. Name Amplitude, A(t) = Frequency, .omega.(t) = Hyperbolic Amax
sech (.beta.t) .lamda. tanh (.beta.t) Secant Gaussian Amax
e.sup.-.beta.t .lamda. erf (.beta.t) Lorenzian Amax/(1 +
(.beta.t).sup.2) .lamda. (arctan (.beta.t) + .beta.t/(1 +
(.beta.t).sup.2))/2 Cosine Amax cos (.beta.t) .lamda. (.beta.t +
sin(.beta.t) cos(.beta.t))/2 Cosine Square Amax cos.sup.2 (.beta.t)
.lamda. (12.beta.t + 8sin(.beta.t) + sin(4.beta.t))/32 WURST-n Amax
(1 - |sin (.beta.t)|.sup.n) .kappa..sub.c t
In Table 1, the angle .beta.t runs from -.pi./2 to +.pi./2; Amax is
the maximum amplitude of the electromagnetic field (the magnetic
field in Kupce); .kappa..sub.c is a constant chirp rate equal to a
constant frequency change per unit time; and n is a large integer.
The constant .lamda. is given by Expression 1
.lamda.=Amax.sup.2/.beta.Q (1) where Q is an adiabatic factor
greater than one. Thus the frequency range scale .lamda., the
temporal duration scale .beta., the amplitude scale Amax are
related. Kupce also proposes a stretched pulse in which a central
part is a constant-amplitude (Amax) linear sweep with constant
chirp rate .kappa..sub.c, and the rising and falling edges are
adiabatic pulses of the form given in Table 1 for .beta.t<0, and
.beta.t>0, respectively.
[0017] Based on the foregoing, there is a clear need for techniques
to configure a medium to eliminate the influence of prior stored
spectral features, such as gratings, that do not suffer all the
deficiencies of prior approaches.
[0018] Based on the foregoing, there is also a need for techniques
to configure a medium to invert prior stored, non-uniform spectral
features, such as gratings, that do not suffer all the deficiencies
of prior approaches.
SUMMARY OF THE INVENTION
[0019] Techniques are provided for reconfiguring spectral features
in a medium using a chirped electromagnetic field. These techniques
allow for erasure or inversion or both and enable faster OCT and
NMR processing as well as adjustable integrated absorption of a
material in selectable frequency bands and selectable spatial
portions of the medium.
[0020] In a first set of embodiments, a method for erasing spectral
features stored in a medium includes causing a chirped
electromagnetic field to pass into the medium. The spectral
features are based on a two-state atomic system having a transition
dipole moment of .mu., in which an atom transitions between a first
state and a second state. The chirped electromagnetic field has a
monochromatic frequency that varies in time by a chirp rate .kappa.
over an erasure frequency band of bandwidth B.sub.E during an
erasure time interval T.sub.E. A maximum amplitude A.sub.E of the
electromagnetic field oscillations in the chirped electromagnetic
field over the erasure frequency band is substantively constant and
substantively specified by an equation of form
A.sub.E=(hbar/.mu..pi.) {square root over ((.kappa. ln 2))} in
which hbar is reduced Plank's constant and ln is a natural
logarithm function. As a result, substantively fifty percent of the
two-state atomic system responsive in the erasure frequency band
exposed to the chirped electromagnetic field is in the first state
after erasure regardless of a percentage in the first state before
erasure.
[0021] In some embodiments of the first set, the chirped
electromagnetic field further includes a start edge in a start time
interval T.sub.S adjacent before the erasure time interval T.sub.E.
An amplitude A.sub.S of the electromagnetic field oscillations
during the start time interval T.sub.S increases with a
substantively continuous first derivative from substantively zero
at a start of the start time interval T.sub.S to A.sub.E and a
substantively zero rate of change at an end of the start time
interval T.sub.S.
[0022] In some embodiments of the first set, a frequency .omega.(t)
of the electromagnetic field oscillations at a time t during the
start time interval T.sub.S changes with a substantively continuous
first derivative to match a start frequency .omega..sub.0 and start
frequency rate of change .kappa.s at a start of the erasure time
interval T.sub.E.
[0023] In some embodiments of the first set, a phase of the
electromagnetic field oscillations during the start time interval
T.sub.S changes with a substantively continuous first derivative to
match a start phase and start phase rate of change at a start of
the erasure time interval T.sub.E.
[0024] In some embodiments of the first set, the chirped
electromagnetic field further includes a finish edge in a finish
time interval T.sub.F adjacent after the erasure time interval
T.sub.E. An amplitude A.sub.F of the electromagnetic field
oscillations during the finish time interval T.sub.F decreases with
a substantively continuous first derivative from a value
substantively equal to A.sub.E with a substantively zero rate of
change at a start of the finish time interval T.sub.F to zero at an
end of the finish time interval T.sub.F.
[0025] In some embodiments of the first set, a frequency .omega.(t)
of the electromagnetic field oscillations at a time t during the
finish time interval T.sub.F changes with a substantively
continuous first derivative to match an end-erase frequency
.omega.e and an end-erase frequency rate of change .kappa.e at an
end of the erasure time interval T.sub.E.
[0026] In some embodiments of the first set, a phase of the
electromagnetic field oscillations during the finish time interval
T.sub.F changes with a substantively continuous first derivative to
match an end-erase phase and an end-erase phase rate of change at
an end of the erasure time interval T.sub.E.
[0027] In some embodiments of the first set, the chirp rate .kappa.
is substantively constant over the erasure frequency band and
substantively equal to B.sub.E/T.sub.E.
[0028] In some embodiments of the first set, interactions of the
chirped electromagnetic field and the medium are coherent over a
time scale up to time T.sub.2. The chirp rate .kappa. within the
erasure frequency band satisfies an inequality given by
.kappa.>>ln 2/(.pi.T.sub.2).sup.2, whereby erasure is
effective even at small values for T.sub.2.
[0029] In a second set of embodiments, a method for inverting
non-uniform spectral features stored in a medium includes causing a
chirped electromagnetic field to pass into the medium. The
non-uniform spectral features are based on a two-state atomic
system having a transition dipole moment of .mu., in which an atom
transitions between a first state and a second state. The chirped
electromagnetic field has a monochromatic frequency that varies in
time by a chirp rate .kappa. over an inversion frequency band of
bandwidth B.sub.1 during an inversion time interval T.sub.1. A
maximum amplitude A.sub.1 of the electromagnetic field oscillations
in the chirped electromagnetic field over the inversion frequency
band is substantively constant and substantively specified by an
equation of form A.sub.1=(hbar/.mu..pi.) {square root over
((.kappa. ln [2/.epsilon.]))}, in which hbar is Plank's constant,
ln is a natural logarithm, and .epsilon. is a non-zero fractional
difference from complete inversion. As a result, a particular
relative population (r) of the excited state of the two-state
atomic system, responsive at a particular frequency in the
inversion frequency band exposed to the chirped electromagnetic
field, is substantively equal to X*(1-.epsilon.) after inversion
when the relative population of the excited state is -X before
inversion, wherein r is +1 for all atoms in the excited state and
-1 for all atoms in the ground state.
[0030] In other sets of embodiments, an apparatus is configured to
perform one or more steps of the above methods.
[0031] In various embodiments, these population reconfiguration
techniques enable a medium to be erased and reused in a shorter
time than population decay, even when the stored spectrum is
unknown.
[0032] Furthermore, in various embodiments, these population
reconfiguration techniques enable a net absorptive path through a
stored spectrum to switch to a net gain (amplification) path
through the same spectrum.
[0033] Furthermore, in various embodiments, these techniques allow
a portion of an absorptive medium to be set to any desired level of
absorption, such as any between absorption associated with fully
populated ground state and gain associated with fully populated
excited state.
BRIEF DESCRIPTION OF THE DRAWINGS
[0034] The present invention is illustrated by way of example, and
not by way of limitation, in the figures of the accompanying
drawings and in which like reference numerals refer to similar
elements and in which:
[0035] FIG. 1 is a block diagram that illustrates components of an
optical system for storing spectral features and reconfiguring an
optical medium, according to an embodiment;
[0036] FIG. 2A is a graph that illustrates spectral content in
relative population of excited state in a two state atomic
medium;
[0037] FIG. 2B is a graph that illustrates erasure of a selected
portion of the spectral content in the medium, according to an
embodiment;
[0038] FIG. 2C is a graph that illustrates inversion of a selected
portion of the spectral content in the medium, according to an
embodiment;
[0039] FIG. 3A and FIG. 3B are graphs that illustrate the effects
of driving electromagnetic force on the populations of two states
in a two-state atomic system;
[0040] FIG. 4 is a graph that illustrates the temporal shape of
amplitude and frequency of a chirped electromagnetic field to
selectively reconfigure populations of two atomic states in a
medium, according to an embodiment;
[0041] FIG. 5 is a flow diagram that illustrates at a high level a
method for selectively reconfiguring populations of two atomic
states in the medium, according to an embodiment;
[0042] FIG. 6 is a graph that illustrates measured transmission
signal through a medium with a spectral grating before and after
erasure in a selected frequency band;
[0043] FIG. 7 is a graph that illustrates measured transmission
signal through a medium with a spectral grating before and after
inversion in a selected frequency band;
[0044] FIG. 8 is a graph that illustrates multiple simultaneous
chirps used to reconfigure multiple frequency bands in a medium,
according to an embodiment;
[0045] FIG. 9A and FIG. 9B are block diagrams that illustrates
multiple chirps in different spatial modes used to reconfigure a
medium, according to an embodiment;
[0046] FIG. 10 is a graph that illustrates the effect of coherence
time on the selection of a chirp rate for erasure, according to an
embodiment;
[0047] FIG. 11 is a graph that illustrates the effect of coherence
time on the selection of a chirp rate for inversion, according to
an embodiment;
[0048] FIG. 12 is a graph that illustrates the effect of absorption
length on amplitude expressed as a Rabi frequency;
[0049] FIG. 13 is a graph that illustrates the relative population
of the excited state versus frequency for a given Rabi frequency;
and
[0050] FIG. 14 is a block diagram that illustrates a computer
system upon which an embodiment of the invention may be implemented
as controller.
DETAILED DESCRIPTION
[0051] Techniques are described for reconfiguring atomic state
populations using a chirped laser field. In the following
description, for the purposes of explanation, numerous specific
details are set forth in order to provide a thorough understanding
of the present invention. It will be apparent, however, to one
skilled in the art that the present invention may be practiced
without these specific details. In other instances, well-known
structures and devices are shown in block diagram form in order to
avoid unnecessarily obscuring the present invention.
[0052] Several embodiments of the invention are descried below in
the context of spectral-spatial gratings formed by optical
absorption variations in an IBT material. However, the invention is
not limited to this context. In other embodiments of the invention,
the techniques are applied to other two-state atomic systems in
which population in each state determines other optical or
non-optical electromagnetic properties, including such properties
as absorption, refraction, reflection, polarization, fluorescence.
In some embodiments, the atomic systems include one or more
additional states that are relatively rarely populated compared to
the two primary transition states or that can be substantially
populated, such as one or more bottleneck states in the decay from
the excited state, to inhibit transitions to those additional
states.
[0053] Swept frequency modulated electromagnetic signals are called
herein "chirped electromagnetic fields," and "chirped laser fields"
when the frequencies are confined to the optical range. The
frequency sweep can be linear in time with a constant chirp rate
(called linear chirp or linear frequency modulation, LFM) or
non-linear with a time varying chirp rate. Optical LFM signals have
been used as waveforms in pulse sequences to write spatial-spectral
gratings for applications of storage, signal processing, true time
delay generation, and arbitrary waveform generation, and also as
probe waveforms for readout of spectral gratings. Such LFM probe
waveforms generate a temporal output signal that represents a
collective readout of all the absorbers, as with brief pulse
excitation, but under the condition of swept excitation. By
properly choosing the rate of frequency change with time, called
herein the chirp rate .kappa., a temporal readout is produced that
is slow enough to be digitized by low cost, high performance
digitizers in the frequency bands of interest, as described by
Merkel. The frequency sweep rate or chirp rate over the band,
.kappa., is defined as the frequency scan range, or bandwidth of
the chirp, Bc, divided by the duration of the sweep time, Tc, as
given by Expression 2a .kappa.=Bc/Tc, (2a) 1. Structural
Overview
[0054] FIG. 1 is a block diagram that illustrates components of an
optical system for storing spectral content and reconfiguring
atomic state populations in an optical medium, according to an
embodiment. Although a certain number of components are shown in
FIG. 1 for the purposes of illustration, in other embodiments more
or fewer components are included in system 100. Furthermore, the
components described here refer to operation for optical
frequencies. In other embodiments, other equivalent or
corresponding components for other electromagnetic phenomena, such
as nuclear magnetic resonance (NMR) replace or add to the
components described with reference to FIG. 1.
[0055] Electromagnetic spectral processing system 100 includes a
controller 102, one or more electromagnetic (EM) source 110,
electromagnetic couplers 120a, 120b, 120c (collectively referenced
hereinafter as couplers 120), electromagnetic modulators 130,
two-atomic-state material (such as IBT material 150),
electromagnetic detectors 160, and post-detection electronics, such
as electromagnetic signal analyzer 170.
[0056] In the illustrated embodiment 100, EM source 110 includes an
input laser 112 and a laser stabilization block 114. This laser 112
provides stabilized optical carrier frequency beams 113a in the
TeraHertz range (THz, 1 THz=10.sup.12 cycles per second) used to
carry a target optical spectrum and a chirped laser field used as a
probe waveform and a population reconfiguration waveform. In some
embodiments, a single laser provides the carrier frequency beam
113a for both the target optical spectrum and probe signals. In
some embodiments, additional laser sources are included in EM
source 110. In some various embodiments, electric signals from
laser stabilization block 114 controls frequency, amplitude or
phase, or some combination, for laser 112. Propagation of EM
waveforms is indicated in FIG. 1 by straight arrows. Electronic
connections for signal processing and control are represented by
segmented lines without arrowheads.
[0057] The EM couplers 120 direct EM waveforms, such as optical
beam 113a, between the various components and include such optical
couplers as mirrors, phase plates, optical fibers, among others
well known in the art of optics and electromagnetic propagation. In
the illustrated embodiment, EM coupler 120a splits carrier beam
113a into two carrier beams 113b, 113c at the same optical
frequency.
[0058] The EM modulators 130 modulate the carrier frequency beams
to produce signal beams with rich frequency content. In the
illustrated embodiment, EM modulators 130 include input signal
source 136, acousto-optic modulators (AOMs) 134a, 134b
(collectively referenced hereinafter as AOMs 134) and arbitrary
waveform generator (AWG) 132. In some embodiments, one or more AOMs
134 are replaced with or added to other optical modulators such as
one or more electro-optic phase modulators (EOPMs), electro-optic
amplitude modulators, and electro-absorption modulators. In some
embodiments, AWG 132 is replaced by or added to other wave
generators, such as one or more pulse pattern generators.
[0059] The input signal source 136 is any combination of components
that generate a target optical spectrum to be placed on an optical
carrier for use in system 100. For example, input signal source 136
is a radio frequency signal to be analyzed, such as a radar pulse
or its reflected return, or both, as described in Merkel. The input
signal source 136 is an electronic signal, such as a voltage. AOMs
134 are used to modulate the optical carrier 113b from input laser
112 in proportion to the sign and magnitude of an applied RF
voltage. This produces an encoded optical field 115 with a target
optical spectrum. In other embodiments, other modulators are used
in place of or in addition to AOMs 134 to produce optical field 115
encoded in frequency or amplitude or both with the target optical
spectrum. In other embodiments, multiple modulated laser beams 115
in one or more directions interact to form the optical target
optical spectrum. The single direction of the depicted optical
field 115 is called a collinear geometry, which records only the
spectral content of the signal. In some embodiments, various angled
beam geometries are used, in which the signal 115 consists of
multiple beams impinging on the two-state material (e.g., IBT
material 150) in different directions.
[0060] The AWG 132 generates a chirped radio frequency waveform
(such as a linear radio-frequency chirp) of bandwidth B around a
carrier radio frequency. The AOM 134a imposes this same chirp
bandwidth B on the laser carrier beam 113c to produce one or more
chirped laser fields 125 starting at an optical frequency
(.omega.s). In other embodiments, the laser 112 can create an
optical chirp, and no external modulator scheme, such as the
combination of components 134a and 132, is needed or used
[0061] The EM two-atomic-state material (e.g., IBT material 150)
records one or more EM fields 115 that impinge on the material with
sufficient intensity and duration. When multiple beams interact in
the material at different angles, spatial-spectral structures are
formed in the material. When all beams impinge in the same
direction only spectral content is recorded. For example, in some
embodiments the two-atomic-state material is an IBT material 150
that stores a complex spatial-spectral grating as absorption
variations within a doped, low temperature crystal. In some
embodiments, the one or more optical fields 115 produce target
optical spectra as spectral or spatial-spectral gratings. In some
embodiments, one or more chirped laser fields 125, are recorded as
spectral or spatial-spectral gratings in IBT material 150. At a
later time, another optical beam is directed with relatively lower
intensity to the optical material IBT to produce one or more
response fields 127a, 127b (collectively referenced hereinafter as
response fields 127). The chirped laser field 125 and the optical
field 115 may impinge on the material at the same location and
angle or at different locations and angles.
[0062] In some embodiments, for laser stabilization, field 113a is
also passed by coupler 120a into IBT material 150 and a feedback
field 129a is emitted by the IBT material 150. The feedback field
129a is passed by EM coupler 120b as field 129b to laser
stabilization block 114. Based on the properties of feedback field
129b, the laser stabilization block 114 controls laser 112.
[0063] For heterodyne readout processes, a reference optical field
(e.g., field 127b) is also produced in addition to a primary
response field (e.g., 127a). Any method of generating a reference
field may be used. In the illustrated embodiment, the reference
optical field 127b emerges from the optical material, usually in a
spatial mode that has not recorded the target optical spectrum from
optical field 115, such as experienced by chirped laser field 125.
In some embodiments, the reference signal 127b is a chirped laser
field (not shown) that has not passed through the IBT material 150.
In some embodiments, the reference signal 127b is the transmitted
probe signal that is naturally in the same direction as the
response signal 127a that itself is often delayed. Thus, in such
embodiments, the signal detected at the optical detectors 160 is
naturally heterodyne. In some embodiments, the reference signal
127b is a response signal from the chirped optical field
interacting with one or more spatial-spectral gratings recorded in
the IBT material 150 for the purpose of generating a reference
field.
[0064] The EM detectors 160 include one or more detectors such as
optical detector that detect the time-varying optical intensity in
a certain optical bandwidth. In some embodiments, a one- or
two-dimensional array of optical detectors is used to
simultaneously detect a response field 127 on multiple spatial
modes. Scanned or instant images can be generated by the array of
detectors. In some embodiments, the EM detector 160 detects only
the response field 127a. In some embodiments, the EM detector 160
detects the heterodyne combination of the response field 127a and
reference field 127b. For example, the heterodyne combination
generates beat frequency variations that are much lower in
frequency and larger in amplitude than response signal 127
intensity variations; therefore the beat frequency variations are
more accurately measured with current detectors.
[0065] The post-detection electronics in EM analyzer 170 use
electrical signals output by detectors 160. In the illustrated
embodiment, EM analyzer 170 includes a scope, digitizer and
processor. In various embodiments, EM analyzer 170 includes
different hardware and software components.
[0066] The controller 102 uses electronic signals to control EM
modulators and EM source 110. In some embodiments the controller
uses electronic signals from EM analyzer 170 to determine how to
control EM source 110 and EM modulators 130. In various
embodiments, controller 102 includes different hardware and
software components that perform the methods described in the next
section.
[0067] In various embodiments, spectral content is imposed in the
IBT material or read or both based on the interaction of one or
more optical fields 115 or 125 or both. The spectral content is
then erased or inverted or both based on one or more subsequent
chirped electromagnetic fields 125 designed for reconfiguration of
atomic state populations in IBT material 150.
[0068] For example, FIG. 2A is a graph 201 that illustrates
spectral content in at least a portion of a medium in terms of
relative population of excited state in a two state atomic medium,
such as IBT material 150. The horizontal axis 212 represents
frequency of electromagnetic oscillations, .omega., that interact
with the medium in the portion of interest. The vertical axis 214
represents the relative population of atoms in the excited state
(r) in the portion of the medium of interest. In some publications,
the quantity r represented by the vertical axis is called
population inversion, because it increases as the percentage of
atoms in the excited state. However, to avoid confusion with the
use of the term "inversion" for the inverting action described
herein, the term "relative population of excited state" is used
herein. A value of -1 indicates that substantively 100% of the
atoms are in the ground state. A value of +1 indicates that
substantively 100% of the atoms are in the excited state. A value
of 0 indicates that substantively 50% of the atoms are in the
ground state and substantively 50% of the atoms are in the excited
state. The same atom type with the same dipole moment absorbs and
emits at different frequencies based on inhomogeneities of the
surrounding material.
[0069] It is assumed for purposes of illustration that in the
ground state an atom absorbs an incident photon of the associated
EM frequency, and in the excited state an atom emits a photon of
the associated EM frequency when stimulated by an incident photon
of that frequency. As a result, the medium is a maximum absorbing
medium when the relative population is -1, is a transparent medium
when the relative population is about 0, and is a maximum
amplifying (gain) medium when the relative population is +1.
Between -1 and 0, the medium is an absorbing medium to various
degrees. Between 0 and +1, the medium is a gain medium to various
degrees.
[0070] The graph 201 includes trace 220 that depicts the relative
populations of the excited state for atoms that respond to
different incident photon frequencies. The population shows
frequency-dependent variations called herein spectral features or
spectral content. The spectral features may be imposed in any
manner known in the art, including illuminating the medium with one
or more signals made up of photon beams of various frequency
components with sufficient intensity for sufficient duration, such
as described in Merkel.
[0071] For purposes of illustration, it is assumed that, in a
frequency band of interest from .omega..sub.0 222 to
.omega..sub.0+B.sub.R 226 on axis 212, in this spatial portion of
interest in the medium, it is desirable to reconfigure the
population. The bandwidth B.sub.R 224 of the frequency band of
interest to be reconfigured is depicted in FIG. 2A. The
reconfiguration involves erasure or inversion or both, as described
in more detail below. It is noted that the medium is mostly
absorbing in the frequency band to be reconfigured.
[0072] FIG. 2B is a graph 202 that illustrates erasure of a
selected portion of the spectral content in the medium, according
to an embodiment. The axes 212, 214 and values .omega..sub.0 222,
.omega..sub.0+B.sub.R 226, and bandwidth B.sub.R 224 are as
described in graph 201. In the reconfiguration band .omega..sub.0
222 to .omega..sub.0+B.sub.R 226 for erasure, the relative
population of the excited state is zero. No residue of the former
spectral content in this erasure frequency band is evident. In the
illustrated embodiment, the medium is transparent for the entire
frequency band. The medium can be reused for storing new spectral
features after some of the population has decayed to the ground
state.
[0073] FIG. 2C is a graph 203 that illustrates inversion of a
selected portion of the spectral content in the medium, according
to an embodiment. The axes 212, 214 and values .omega..sub.0 222,
.omega..sub.0+B.sub.R 226, and bandwidth B.sub.R 224 are as
described in graph 201. In the reconfiguration band .omega..sub.0
222 to .omega..sub.0+B.sub.R 226 for inversion, the relative
population of the excited state at each frequency .omega. is
complementary to the relative population formerly at that
frequency. The same spectral information is evident, but the medium
is mostly amplifying in the inverted frequency band. This inversion
may be useful in providing a stronger signal when the medium is
subsequently read with a probing beam.
[0074] It is noted that uniform absorbing/amplifying properties of
the medium can be set with a combination of erasure, waiting for
decay and inversion. For example, in some embodiments, absorption
associated with a relative population value of -0.5 is achieved for
any frequency band of interest by erasing that band and waiting for
a particular time until population decay has produced a relative
population value of -0.5. In general, to achieve a desired relative
population value, rd, after the erasure process has been completed,
the waiting time, T.sub.W, is given by Expression 2b.
T.sub.W=T1*ln(1/(rd+1)) (2b) where T1 is the excited state
population lifetime. As a result, absorption associated with an rd
value of -0.5 is achieved in these embodiments by 1) erasing that
band, 2) waiting for a time T.sub.W given by Expression 2b with
rd=-0.5. As a further example, in some embodiments, a gain
associated with a relative population value of +0.5 is achieved for
any frequency band of interest by adding the following step after
the above two steps: 3) inverting the same frequency band.
[0075] The following sections show how erasure or inversion of an
arbitrary frequency band in a portion of interest in a material can
be achieved.
2. Theoretical Overview
[0076] The following theoretical considerations are presented so
that the working of embodiments of the invention may be more
readily described and understood. However, the invention is not
limited by the assumptions or statements or accuracy of these
theoretical descriptions.
[0077] It has been observed that, when an atom (or some other
two-state system) is illuminated by a coherent beam of photons, it
will cyclically absorb photons and re-emit them by stimulated
emission. One such cycle is called a Rabi cycle and the inverse of
its duration is called the Rabi frequency of the photon beam,
designated herein as .OMEGA.. The Rabi frequency .OMEGA. depends on
a dipole moment .mu. of a transition between the two states and the
maximum amplitude Amax of the electromagnetic field oscillations of
the coherent beam. Amax is proportional to the square root of the
intensity of the beam. A Rabi frequency may be defined for electric
charge states interacting with an electric field E or for magnetic
states interacting with a magnetic field H of the propagating
electromagnetic wave. The Rabi frequency is defined by Expression
3. .OMEGA.=.mu.Amax/hbar (3) where hbar is reduced Plank's constant
and, as suggested above, .mu. is the transition dipole moment of a
two-level atom on which the field acts.
[0078] For population reconfiguration over a frequency band of
interest, it is ideal that the amplitude Amax be constant for all
frequencies in the band. A constant amplitude linear chirp with a
high time bandwidth product (Tc Bc) over a band much larger than
the band of interest has such a constant amplitude in the band of
interest. The changes in relative population r driven by such an
ideal chirp with Rabi Frequency .OMEGA..sub.C have been
investigated and can be expressed by the following Expressions 4a
and 4b. r(.omega.,tf)=(1-2.THETA.)r(.omega.,ti) (4a)
.THETA.=1-exp(-.pi..sup.2.OMEGA..sub.C.sup.2/.kappa.) (4b) where ti
is time before application of the chirp, tf is time after
application of the chirp, and exp(x) is the function representing
e, the base of the natural logarithm (ln e=1), raised to the power
x. In the following, the symbol ri denotes r(.omega., ti) and the
symbol rf denotes r(.omega., tf). The quantity .THETA. is called
the driving strength of the field with chirp rate .kappa. and Rabi
Frequency .OMEGA..sub.C. .THETA. varies between 0 and 1. It is
expected that Expressions 4a and 4b also apply for slowly changing
chirp rate .kappa. over the frequency band of interest and for
magnetic states responding to magnetic oscillations at non-optical
frequencies.
[0079] FIG. 3A and FIG. 3B are graphs 301 and graph 302,
respectively, that illustrate the effects of driving
electromagnetic force on the populations of two states in a
two-state atomic system. FIG. 3A is a graph 301 that illustrates
the value of .THETA. as a function of a dimensionless quantity
.OMEGA..sub.C/ .kappa., a square root of a factor in the argument
of the function exp in Expression 4b. The horizontal axis 312 gives
the value of .OMEGA..sub.C/ .kappa.. The vertical axis 314 gives
the value of .THETA. on a logarithmic axis to show detail at small
values .THETA.. FIG. 3B is a graph 302 that illustrates the value
of 2.THETA.-1 (the negative of the factor for r(w,ti) in Expression
4a) as a function of the same dimensionless quantity .OMEGA..sub.C/
.kappa.. The horizontal axis 312 is as described above. The
vertical axis 314 gives the value of 2.THETA.-1.
3. Functional Overview
[0080] According to various embodiments of the invention, amplitude
Amax of electromagnetic oscillations is chosen so that over a
finite frequency band of a chirp, Amax leads to a value of .THETA.
associated with either erasure or relative population
inversion.
[0081] It is noted that, when .THETA. equals 1/2, rf equals zero.
Because .THETA. does not depend on .omega., rf equals zero for all
frequencies, thus effectively erasing all frequencies in the linear
chirp, regardless of the initial populations at those frequencies.
This can be seen in FIG. 3B. When 2.THETA.-1 equals 0 (i.e.,
.THETA.=1/2) at value 332 on axis 312, the relative population at
all frequencies goes to zero and the spectral content is erased.
Using the definition of the Rabi Frequency in Expression 2a and the
definition of .THETA. in Expression 4b, Amax can be determined that
is associated with erasure, as derived in Expressions 5a through
5g. 2.THETA.-1=0 (5a)
1-exp(-.pi..sup.2.OMEGA..sub.C.sup.2/.kappa.)=1/2 (5b)
exp(-.pi..sup.2.OMEGA..sub.C.sup.2/.kappa.)=1/2 (5c)
-.pi..sup.2.OMEGA..sub.C.sup.2/.kappa.=ln(1/2) (5d)
.OMEGA..sub.C.sup.2=(1/.pi..sup.2).kappa. ln 2 (5e)
.OMEGA..sub.C=Amax/hbar=(1/.pi.) (.kappa. ln 2) (5f)
Amax=(hbar/.mu..pi.) (.kappa. ln 2) (5g)
[0082] It is further noted that, as .THETA. approaches a value of
1, the relative population inverts from ri at time ti to -ri at
time t. When 2.THETA.-1 equals 1, the populations are inverted. As
can be seen in FIG. 3A and FIG. 3B, neither .THETA. nor 2.THETA.-1
ever equal 1, but both asymptotically approach 1. It is noted
however, that for any difference .epsilon. 334,
2.THETA.-1=1-.epsilon., at point 336 on axis 312. Therefore it is
possible to select a desired value .epsilon. 334 that is
arbitrarily small. The associated value of .OMEGA..sub.C/ .kappa.
results in a relative population that is arbitrarily close to
complete inversion. Amax can be determined that is associated with
near complete inversion, as derived in Expressions 6a through 6g.
2.THETA.-1=1-.epsilon. (6a)
1-exp(-.pi..sup.2.OMEGA..sub.C.sup.2/.kappa.)=1-.epsilon./2 (6b)
exp(-.pi..sup.2.OMEGA..sub.C.sup.2/.kappa.)=.epsilon./2 (6c)
-.pi..sup.2.OMEGA..sub.C.sup.2/.kappa.=ln [.epsilon./2] (6d)
.OMEGA..sub.C.sup.2=(1/.pi..sup.2).kappa. ln [2/.epsilon.] (6e)
.OMEGA..sub.C=.mu.Amax/hbar=(1/.pi.) (.kappa. ln [2/.epsilon.])
(6f) Amax=(hbar/.mu..pi.) (.kappa. ln [2/.epsilon.]) (6g)
[0083] It is noted that Expression 5g is equivalent to Expression
6g with .epsilon.=1. However, inversion is nearly achieved using
Expression 6g only when .epsilon.<<1.
[0084] Theoretically, Expression 4a (and consequently Expression 5g
and Expression 6g) applies for a large time-bandwidth product,
i.e., Tc Bc>>1, which ensures a uniform spectral amplitude
for the chirped electromagnetic pulse over the frequency band. A
linear chirp truncated in time to the band of interest typically
has spectral amplitude fluctuations within the frequency band of
interest. The spectral amplitude fluctuations can be minimized by
adding edges before and after the frequency band of interest in
which the amplitude rises and falls, respectively, sufficiently
slowly to achieve this effect. Several functional forms for slowly
rising and falling amplitudes are listed in Table 1. Others may
also be used.
[0085] According to some embodiments of the invention, functional
forms for rising and falling edges (also called start edge and
finish edge, respectively) are selected so that the values and
first derivatives of amplitude, frequency and phase are all
continuous at the boundaries with the frequency band of interest.
In some embodiments, the frequency functional forms are selected to
use as little of the frequency bandwidth available in the equipment
as possible during the start and finish edges, so that most of the
available bandwidth is left for the band of interest to be
reconfigured. In various embodiments, both linear and non-linear
chirps are used in the frequency band to be reconfigured.
[0086] FIG. 4 is a graph that illustrates the temporal shape of
amplitude and frequency of a chirped electromagnetic field to
selectively reconfigure populations of two atomic states in a
medium, according to an embodiment. The horizontal axis 412 is time
in microseconds (.mu.s, 1 .mu.s=10.sup.-6 seconds). The left side
vertical axis 414 is field amplitude maximum of the coherent beam
in arbitrary units, in which the value 1 corresponds to Amax. The
right side vertical axis 416 is frequency of the coherent beam in
arbitrary units.
[0087] Trace 430 plots the maximum amplitude for a coherent beam
with a square maximum amplitude envelope. Trace 440 plots the
maximum amplitude for a coherent beam with a slowly varying start
edge and a slowly varying finish edge sandwiching a constant
amplitude reconfiguration chirp. The constant amplitude
reconfiguration chirp has duration T.sub.R 424 beginning at time
t.sub.0 421. The start edge has duration T.sub.S 422 ending at to
421. The finish edge has duration TF 426 beginning at time t.sub.0
421 plus T.sub.R 424. Trace 460 plots a non-linear frequency
variation of the electromagnetic oscillations for both trace 430
and trace 440. In some embodiments, a linear frequency chirp (not
shown) is used instead of trace 460 for one or more beams, in the
reconfiguration interval or one or both edges or in all three
bands. During the time interval T.sub.R for the constant amplitude
reconfiguration chirp, the frequency changes from .omega..sub.0 462
to .omega..sub.0462 plus reconfiguration bandwidth B.sub.R 464. The
trace 430 for the square envelope begins at a lower frequency
.omega..sub.S 463 and extends to a higher frequency .omega..sub.F
465.
[0088] The sharp edges of the square envelope trace 430 cause
spectral amplitude variations in frequencies throughout the
reconfiguration band B.sub.R 464. The slowly rising and falling
amplitude envelopes of trace 440 smooth the amplitude in the
reconfiguration band B.sub.R 464 at the cost of losing available
bandwidth outside B.sub.R 464, e.g., between .omega..sub.S 463 and
.omega..sub.0462, and between .omega..sub.F 465 and
.omega..sub.0462 plus B.sub.R 464.
4. Coherence Time Restrictions
[0089] The coherence time of the medium restricts the coherent
response to the coherent beam of photons propagating through the
medium. Here is described how the coherence time puts a lower limit
on the chirp rate that can be effective in reconfiguring the atomic
state populations.
[0090] When the coherent electromagnetic field has frequency
.omega..sub.1, the atoms in the frequency range
.omega..sub.1+/-.DELTA..omega. are also driven by the field, due to
the coherence limit of the atomic transitions or laser carrier
frequency or other effects, where .DELTA..omega. is the effective
coherent bandwidth for the various participants in the interaction.
The coherence time T.sub.2 is the reciprocal of .DELTA..omega.. The
more coherent the process, the longer is T.sub.2, and the narrower
is .DELTA..omega.. The condition to ignore incoherent driving is
given by Expressions 7a through 7f.
.omega..sub.C<<.epsilon.T.sub.2 (7a) Substituting for
.OMEGA..sub.C using Expression 6f, for inversion, yields
.kappa.>>(1/.pi.T.sub.2).sup.2 ln [2/] (7b)
[0091] Similarly using Expression 5e (or substituting 1 for
.epsilon. in 7b), for erasure, yields
.kappa.>>(1/.pi.T.sub.2).sup.2 ln 2 (7c)
[0092] The material coherence time T.sub.2 can be increased by
various well-known methods, such as lowering doping concentrations,
applying an external electromagnetic field, or lowering
temperature. Such activities increase T.sub.2 and allow lower chirp
rates K to be used effectively.
5. Method for Reconfiguring Atomic State Populations in a Frequency
Band of Interest
[0093] FIG. 5 is a flow diagram that illustrates at a high level a
method 500 for selectively reconfiguring populations of two atomic
states in at least a portion of a medium, according to an
embodiment. Although steps are shown in FIG. 5 in a particular
order for purposes of illustration, in other embodiments some steps
may be performed in a different order, or overlapping in time, or
one or more steps may be omitted, or additional steps added, or
changes can be made in some combination of ways.
[0094] In step 510, the start frequency .omega..sub.0 and bandwidth
B.sub.R of the frequency band to reconfigure for each of one or
more frequency bands are determined.
[0095] In step 520, it is determined whether the frequency band is
to be erased or inverted. If it is determined that the frequency
band is to be erased, then control passes to step 522. In step 522
a value for .epsilon. is set to one (1), and control passes to step
530.
[0096] If it is determined in step 520 that the frequency band is
to be inverted, then control passes to step 524. In step 524 a
value for .epsilon. is set to an arbitrarily small value, and
control passes to step 530. There is a tradeoff during step 524.
The smaller the value of .epsilon. selected, in the case of
infinite material coherent time T.sub.2, the stronger the Amax of
the chirp must be for a given chirp rate. The larger the value of
.epsilon., the less accurately is the original spectral content
represented in the inverted populations. In some circumstances due
to incoherence, a particularly small value of .epsilon. cannot be
achieved, as described in more detail later with reference to FIG.
11
[0097] In step 530, a minimum chirp rate is determined in the
reconfiguration band based on the coherence time T.sub.2, using
Expression 7b or 7c, as appropriate for erasure and inversion,
respectively. Once the minimum chirp rate is determined, a
functional form for the chirp in the reconfiguration band is also
selected using a linear or non-linear chirp rate. Based on the
functional form for the chirp and the start frequency .omega..sub.0
and bandwidth B.sub.R selected in step 510 for the reconfiguration
band, the duration T.sub.R of the chirp in the reconfiguration band
is determined.
[0098] In step 540, the constant maximum electromagnetic field
amplitude A.sub.R for the reconfiguration band is determined based
on Expression 5g or 6g, as appropriate for erasure and inversion,
respectively.
[0099] In step 550, start and finish edges are determined to
bracket the reconfiguration band. The maximum amplitude A.sub.S of
the electromagnetic field oscillations during the start time
interval T.sub.S increases with a substantively continuous first
derivative from substantively zero at a start of the start time
interval T.sub.S to A.sub.R and a substantively zero rate of change
at an end of the start time interval T.sub.S. Similarly, the
maximum amplitude A.sub.F of the electromagnetic field oscillations
during the finish time interval T.sub.F decreases with a
substantively continuous first derivative from a value
substantively equal to A.sub.R with a substantively zero rate of
change at a start of the finish time interval T.sub.F to zero at an
end of the finish time interval T.sub.F.
[0100] The frequency .omega.(t) of the electromagnetic field
oscillations at a time t during the start time interval T.sub.S
changes with a substantively continuous first derivative to match a
start frequency .omega..sub.0 and start frequency rate of change
.kappa.s at a start of the reconfiguration time interval T.sub.R.
Similarly, a frequency .omega.(t) of the electromagnetic field
oscillations at a time t during the finish time interval T.sub.F
changes with a substantively continuous first derivative to match
an end-reconfigure frequency .omega.e and an end-reconfiguration
frequency rate of change .kappa.e at an end of the reconfiguration
time interval T.sub.R. In some embodiments, the functional forms of
the frequency variations in the start and finish time intervals are
selected to minimize the total bandwidth in the start and finish
time intervals. In some embodiments, the frequency variation in the
start edge is constant and equal to .kappa.s. In some embodiments,
the frequency variation in the finish edge is constant and equal to
.kappa.e. In some of these embodiments, when .kappa.c is constant
in the reconfiguration interval, .kappa.s=.kappa.e=.kappa.c.
[0101] A phase of the electromagnetic field oscillations during the
start time interval T.sub.S changes with a substantively continuous
first derivative to match a start phase and start phase rate of
change at a start of the reconfiguration time interval T.sub.R.
Similarly, a phase of the electromagnetic field oscillations during
the finish time interval T.sub.F changes with a substantively
continuous first derivative to match an end-reconfiguration phase
and an end-reconfiguration phase rate of change at an end of the
reconfiguration time interval T.sub.E.
[0102] In step 560 it is determined whether there is another
frequency band to be probed or reconfigured during the same
reconfiguration time interval. If so, control passes back to step
520 to determine whether the next band is to be erased or inverted.
If not, control passes to step 570. In some embodiments that
reconfigure only one band at one time, step 560 is omitted.
[0103] In step 570, the one or more electromagnetic chirped fields
that combine the reconfiguration signal with start and finish edges
are caused to pass into the medium so that the reconfigured
frequency bands have the associated amplitude A.sub.R at the target
site. When the medium is thin or non-attenuating, the beam can be
incident with the value of A.sub.R in the reconfiguration band.
However, when the medium is thick or heavily attenuating, the
incident beam must be amplified so that after any attenuation
during passage to a target site in the medium, the amplitude in the
reconfiguration band (and matching amplitudes in the start and
finish bands) have the value computed in steps 540 and 550.
[0104] As a result of step 570, the selected one or more frequency
bands are reconfigured. In some embodiments, control passes to step
580 to receive a readout signal and determine pre-erasure spectral
features based on the readout signal. In such embodiments, the
chirp that erases the spectral features also causes a readout
signal. The generation and processing of the readout signal is
described in Merkel; and in U.S. patent Ser. No. 11/179,765 filed
Jul. 12, 2005 entitled "Techniques for Recovering Optical Spectral
Features Using a Chirped Optical Field," by T. Chang, M. Tian, W.
R. Babbitt and K. Merkel (hereinafter Chang), the entire contents
of which are herby incorporated by reference as if fully set forth
herein. In some embodiments, step 580 is omitted.
[0105] In the illustrated embodiment, method 500 includes step 590.
In step 590, the process waits for the population to decay to a
desired (target) absorption level. For example to get to a desired
relative population rd after erasure, the process waits a time
T.sub.W given by Expression 2b.
[0106] In some embodiments control passes back to step 510 after
step 590 to reprocess the same band at a different time. For
example, in some embodiments to achieve a relative population of
about -rd, after waiting a time T.sub.W given by Expression 2b
during step 590, control passes back to step 510 to invert the same
frequency band.
6. EXAMPLE EMBODIMENTS
[0107] FIG. 6 is a graph 600 that illustrates measured transmitted
signal strength through a medium with a spectral grating before and
after erasure in a selected frequency band. The horizontal axis 612
is frequency deviations from an optical carrier frequency in
MegaHertz (MHz, 1 MHz=10.sup.6 cycles per second). The vertical
axis 614 is detected transmitted signal strength in volts. In such
a graph, transmitted signal strength is low for r near -1, high
(about 0.04 volts) for transparent conditions with r near 0, and
very high (about 0.10 volts) for gain conditions with r near +1.
Trace 620 shows the effect of a spectral grating in the medium at
frequency deviations between 125 and 130 MHz. It was determined to
erase the features in a reconfiguration band with bandwidth B.sub.E
632 from about 122 MHz to about 128 MHz. Trace 630 shows the effect
of erasure. The spectral grating is not in evidence in the erasure
band marked by bandwidth B.sub.E, and is still evident above about
128 MHz.
[0108] In this example, the spectral grating was burned into the
IBT material using interacting fields, such as fields 115. The
electromagnetic chirped field 125 includes a constant amplitude
reconfiguration signal that is a linear chirp and includes
hyperbolic secant start and finish edges. The linear chirp in the
reconfiguration band has a constant chirp rate of .kappa.=1
MHz/.mu.s and has a Rabi frequency .OMEGA..sub.C=.mu.Amax/hbar
given by Expression 5f of 265 kiloHertz (kHz, 1 kHz=10.sup.3 cycles
per second) suitable for erasure (.epsilon.=1).
[0109] In practice at optical frequencies, the quantity Amax is not
measured directly but is derived from measurements of the power (P)
and radius (s) of the optical beam, as given in Expression 8a.
Amax=Z* /(P/(.pi.s.sup.2)) (8a) where Z is a proportionality factor
that depends on material. The Rabi frequency is observable. For a
given material, the factor of proportionality between the Rabi
frequency and Amax is proportional to Z*.mu./hbar converted to the
units of choice and can be determined by experiment. For Tm:YAG,
the material used in the measurements depicted in FIG. 6 (and in
FIG. 7, described below), the proportionality factor at .omega.
corresponding to a wavelength of 793 nm is 570
(Hz/sqrt(Watts/m.sup.2)). Thus, for this material .OMEGA..sub.C=570
(Hz/sqrt(Watts/m.sup.2))* (P/(.pi.s.sup.2)) (8b) where the Rabi
frequency is in Hz. Other materials and transitions may have
different values, which scale with the dipole moment of the
transition of interest. As an example, a 100 micron (1
micron=10.sup.-6 m) diameter optical beam of power 7 milliWatts
(mW, 1 mW=10.sup.-3 Watts) that is resonant with 793 nm transition
in Tm:YAG results in a Rabi frequency of 270 kHz.
[0110] Including hyperbolic secant start and finish edges, the
amplitude of the coherent electromagnetic chirped field as a
function of time is given by Expression 9a, where
T.sub.S=T.sub.F=2T.sub.H, where T.sub.H is the half width of the
edge intervals. A .function. ( t ) = { A .times. .times. max
.times. .times. sech .times. { ( t - t 0 ) / T H } t 0 - 2 .times.
T H < t < t 0 A .times. .times. max t 0 .ltoreq. t .ltoreq. t
0 + T R A .times. .times. max .times. .times. sech .times. { ( t -
t 0 - T R ) / T H } t 0 + T R < t < t 0 .times. T R + 2
.times. T H ( 9 .times. a ) ##EQU1## Including non-linear frequency
functions in the start and finish edges, the frequency .omega.(t)
is given by Expression 9b. .omega. .function. ( t ) = { .omega. 0 -
.kappa. .times. .times. T R / 2 + .kappa. .times. .times. T H
.times. .times. tanh .times. { ( t - t .times. 0 ) / T .times. H }
t 0 - 2 .times. T H < t < t 0 .omega. 0 + .kappa. .times. { t
- t 0 - T R / 2 } t 0 .ltoreq. t .ltoreq. t 0 + T R .omega. 0 +
.kappa. .times. .times. T R / 2 + .kappa. .times. .times. T H
.times. tanh .times. { ( T .times. 0 - t .times. 0 - T .times. R )
/ T .times. H } t 0 + T 1 < t < t 0 + T R + 2 .times. T H ( 9
.times. b ) ##EQU2## With these functional forms, the amplitude,
frequency, rate of change of frequency (chirp rate) and phase are
continuous in time; and thus leave the amplitude flat in the
reconfiguration frequency band, as can be determined by the Fourier
transform of the above functions. Since the use of a hyperbolic
chirp minimizes the bandwidth devoted to the edges, the excitation
spectrum is both uniform in the reconfiguration band and sharp
edged.
[0111] For the erasure shown in FIG. 6, T.sub.R was 5 .mu.s and
T.sub.H was 0.5 .mu.s.
[0112] Before and after erasure, a linear chirp with chirp rate of
0.05 MHz/.mu.s, duration of 400 .mu.s, and Rabi Frequency of 32 kHz
was used for readout of spectral features. This Rabi frequency
corresponds to a low amplitude chirp (about one eighth the
amplitude Amax of the erasure chirp) that does not reconfigure the
atomic state populations.
[0113] FIG. 7 is a graph 700 that illustrates measured transmitted
signal strength through a medium with a spectral grating before and
after inversion in a selected frequency band. The horizontal axis
612, vertical axis 614 and trace 620 are as described above for
graph 600. It was determined to invert the spectral features in
reconfiguration band with bandwidth B.sub.1 732 from about 122 MHz
to about 128 MHz. Trace 730 shows the effect of inversion. The
medium is a pure gain medium, inverted from a pure absorbing medium
from 122 MHz to the start of the grating at 125 MHz. From 125 MHz
to about 128 MHz, the spectral grating is in evidence but inverted
with amplified transmitted signal strength levels indicative of
gain. At frequencies above the inverted band marked by bandwidth
BI, above about 128 MHz, the original spectral grating is still
evident.
[0114] As in FIG. 6, the spectral grating is burned into the IBT
material using interacting fields, such as fields 115. The
electromagnetic chirped field includes a constant amplitude
reconfiguration signal that is a linear chirp and includes
hyperbolic secant start and finish edges. The linear chirp in the
reconfiguration band has a constant chirp rate of .kappa.=1
MHz/.mu.s and has a Rabi frequency .OMEGA..sub.C=.mu.Amax/hbar
given by Expression 6f of 730 kHz suitable for inversion with
.epsilon..apprxeq.0.01.
[0115] Including hyperbolic secant start and finish edges, the
amplitude of the coherent electromagnetic chirped field as a
function of time is given by Expression 9a, where
T.sub.S=T.sub.F2T.sub.H. With the start and finish edges, the
frequency .omega.(t) is given by Expression 9b. As in FIG. 6, for
the inversion shown in FIG. 7, T.sub.R was 5 .mu.s and T.sub.H was
0.5 .mu.s.
[0116] Also as described above for FIG. 6, before and after
inversion, a linear chirp with chirp rate of 0.05 MHz/.mu.s,
duration of 400 .mu.s, and Rabi Frequency of 32 kHz was used for
readout of spectral features. This Rabi frequency corresponds to a
low amplitude chirp (about one twentieth the amplitude Amax of the
inversion chirp with .epsilon.=0.01) that does not reconfigure the
atomic state populations.
[0117] Other experiments were carried out to selectively erase and
invert single and multiple spectral holes in the IBT material 150.
Similar results were obtained and are not reported here as being
cumulative.
[0118] Simulations were also carried out to experiment with the
effects of different edge functional forms. Among the functional
forms demonstrated to perform adequately was a cosine edge function
of the form, given by Expression 10. A.sub.S(t)={cosine
[.pi.(t-t.sub.0)/T.sub.S]+1}A.sub.E/2 for
t.sub.0-T.sub.S<t<t.sub.0 (10a) A.sub.F(t)={cosine
[.pi.(t-t.sub.0-T.sub.R)/T.sub.F]+1}A.sub.E/2 for
t.sub.0+T.sub.R<t<t.sub.0+T.sub.R+T.sub.F (10b) In some of
these simulations, a constant chirp rate .kappa. is used throughout
the electromagnetic chirped field, including both start and finish
edges.
[0119] FIG. 8 is a graph 800 that illustrates multiple simultaneous
chirps used to reconfigure multiple frequency bands in a medium,
according to an embodiment. The horizontal axis 812 is time in
.mu.s. The left side vertical axis 814 is normalized intensity in
which 1 corresponds to Amax for a population reconfiguration of
interest. The right side vertical axis 816 is frequency deviations
in MHz from an optical carrier frequency 866. The atomic state
populations in two frequency bands are reconfigured with this field
plotted in FIG. 8. A first band centered at -15 MHz 862 is
reconfigured by the chirp 840a, and a second band centered at +15
MHz 864 is reconfigured by chirp 840b. Both chirps are modulated in
amplitude by the intensity curve 830 between 5 .mu.s 822 and 25
.mu.s 824. The reconfiguration chirp duration is 10 .mu.s from 10
.mu.s to 20 .mu.s, with 5 .mu.s duration start and finish edges.
Both frequency bands are reconfigured at the same time.
[0120] In the illustrated embodiment, both frequency bands are
reconfigured with chirps of the same linear chirp rate .kappa..
Therefore, if both are erasures, the value of Amax represented by
normalized intensify value of 1 is the same for both chirps. If one
is erasure and the other is inversion, then the value of Amax
represented by normalized intensify value of 1 is different for the
two chirps. The value corresponding to a normalized intensity value
of 1 is greater for the frequency band to be inverted. Similarly,
if the chirp rates were different for the two bands, since Amax
depends on .kappa., the values of Amax corresponding to a
normalized intensity value of 1 would be different for the two
frequency bands.
[0121] Chirped fields used to erase spectral features may
themselves interact with subsequent signals intended for
reprogramming the medium because of the atomic memory over
coherence times. To reduce this effect, it may be desirable to use
different spatial modes for reprogramming signals. FIG. 9A and FIG.
9B are block diagrams that illustrates multiple chirps in different
spatial modes used to reconfigure a medium 910 according to
embodiments 901 and 902.
[0122] In embodiment 901 depicted in FIG. 9A, two sets of angled
beams are used. One set programs the material by imposing spectral
content while the other set erases spectral content in different
spatial modes. Then the two sets switch, with the first set erasing
in those spatial modes while the second set programs the different
spatial modes. For example, at an initial time the first set of
beams 920a and 920b interact to program the medium 910 with
spectral contents in a first spatial mode. At a later time, when
processing of that spectral content is completed, one or both of
the first set of beams 920a and 920b send an erasure chirp into the
medium 910 along the first spatial mode. Instead of waiting for the
coherence time to reprogram the medium 910, the second set of beams
930a and 930b interact to program the medium 910 with new spectral
content in a different second spatial mode. At successively later
times, the first set 920a, 920b and the second set 930a, 930b,
alternate in programming and erasing the medium. In this way, a
user need not wait for the coherence time before reusing the medium
910.
[0123] In embodiment 902 depicted in FIG. 9B, multiple single
spatial modes 940 and 950 are use for programming. A single channel
960 is used for erasure. As one spatial mode, e.g., 940 is erased
by mode 960, the other spatial mode 950 is being programmed with
new spectral content.
[0124] FIG. 10 is a graph 1000 that illustrates the effect of
coherence time on the selection of a chirp rate for erasure,
according to an embodiment. The horizontal axis 1012 is coherence
time T.sub.2, described above, in .mu.s. The vertical axis 1014 is
relative population of excited state r, also defined above. The
different traces 1020a, 1030a, 1040a, 1050a correspond to different
chirp rates of 0.5, 1, 2 and 3 MHz/.mu.s, respectively. For a given
coherence time T.sub.2, the higher chirp rates more closely attain
an r value of zero that provides erasure. Perfect erasure
corresponds to infinite coherence time or infinite chirp rate.
Practical erasure is achieved with moderately high values of
T.sub.2>15 .mu.s and chirp rate .kappa.>3 MHz/.mu.s. The
dashed traces 1020b, 1030b, 1040b, 1050b are analytical fits to
different chirp rates of 0.5, 1, 2 and 3 MHz/.mu.s, respectively,
using an equation of the form of Expression 11.
r(.omega.,tf)=-.xi..OMEGA..sub.C(erasure)/.kappa.T.sub.2 (11) The
plotted fits are achieved with a value of .xi.=0.75. Expression 11
and FIG. 10 are consistent with the inequality given in Expression
7c.
[0125] FIG. 11 is a graph 1100 that illustrates the effect of
coherence time on the selection of a chirp rate for inversion,
according to an embodiment. The horizontal axis 1112 is normalized
Rabi frequency .omega..sub.C/ .kappa., described above, which is
dimensionless. The vertical axis 1114 is relative population of
excited state r, also defined above. The different traces 1120a,
1130a, 1140a, 1150a, 1160a, 1170 correspond to different chirp
rates of 0.5, 1, 2, 3, 4 and infinite MHz/.mu.s, respectively, for
a coherence time T.sub.2 of 16 .mu.s. The dashed traces 1120b,
1130b, 1140b, 1150b, 1160b are analytical fits to different chirp
rates of 0.5, 1, 2, 3 and 4 MHz/.mu.s, respectively, using an
equation of the form of Expression 12.
r(.omega.,tf)=(1-2.THETA.)r(.omega.,ti)-.xi..OMEGA..sub.C(inversion)/.kap-
pa.T.sub.2 (12) The plotted fits are achieved with a value of
.xi.=2.4. For several chirp rates, best inversion is achieved at
normalized Rabi frequencies between about 0.7 and 0.8.
[0126] FIG. 11 indicates that some chirp rates may not be practical
if the difference from perfect inversion, .epsilon., is set too
small or the coherence time is too short. The maximum chirp rate
may be limited by the laser power and the other hardware
components. Thus the maximum inversion for normalized Rabi
frequencies between about 0.7 and 0.8 has important practical
application.
[0127] FIG. 12 is a graph 1200 that illustrates the effect of
absorption length on amplitude expressed as a Rabi frequency. The
vertical axis 1214 is Rabi frequency, which is proportional to
Amax. The horizontal axis 1212 is absorption length, equal to the
thickness of the medium times the coefficient of absorption
.alpha.. For weak field, the coefficient of absorption .alpha. is
defined by equations of the form of Expression 13a for intensity
I(x) at distance x into the medium I(x)=I(0)exp(-.alpha.x) (13a)
and for amplitude A(x) at distance x by Expression 13b
A(x)=A(0)exp(-.alpha.x/2) (13b) The absorption length L of a
distance x is given by Expression 13c L(x)=x*.alpha. (13c) Thus
when L=1, the field intensity is 1/e of the incident intensity, and
when L=2 field amplitude becomes 1/e of the incident amplitude.
[0128] For weak field, an exponential decay trace is expected.
However, for strong field, due to the field induced transparency
effect, the attenuation of the incident field though the
propagation is much less than that of weak field. The trace 1230
indicates how Amax is attenuated with depth in an absorbing medium
for a strong field. FIG. 12 is based on measurements made for an
inversion chirped electromagnetic field with an incident Rabi
frequency of 1 MHz and a chirp rate of 1 MHz/is.
[0129] For a given Amax to be effective for erasure or inversion,
it must have that value at the depth in the medium to be erased or
inverted. To account for attenuation, the incident beam may have to
have an Amax (and Rabi frequency) greater than the Amax desired at
the target site.
[0130] In this respect inversion of a thick medium is easier.
Erasure involves a narrow range of Amax values. For inversion,
however, any amplitude above Amax for inversion is also effective
at inversion. Thus, to invert all of a thick medium, it is only
required to select an incident beam Amax that will not be
attenuated below the minimum Amax for a selected degree of
inversion .epsilon.. As graph 1200 shows, a 3% increase in Amax is
sufficient to invert the entire thickness of a medium with
absorption length of 2.
[0131] FIG. 13 is a graph 1300 that illustrates the relative
population of the excited state r versus frequency for a given
incident Rabi frequency over a 10 MHz reconfiguration band. The
horizontal axis 1312 is frequency .omega. in MHz; and the vertical
axis is relative population of excited state r. Trace 1330 shows
the population inversion achieved in the first layer of the medium
of absorption length L=2, before attenuation. Trace 1340 shows the
population inversion achieved in the last layer of the medium,
after 3% attenuation. It is noted that inversion is still very
close to 100% and very flat over almost the full 10 MHz bandwidth
of the reconfiguration band.
[0132] To erase completely such a medium requires an Amax given by
Expression 5g over the full thickness of the medium. This can be
achieved with a series of erasure chirps. Each erasure chirp is
incident at a different amplification over the target Amax for
erasure so that each reaches the target Amax for erasure at
different depths in the medium. In some embodiments, different
erasure chirps are incident on the medium in different directions;
so that erasure can be accomplished from both sides. Simulations
have shown the viability of this approach, but are not presented
here.
[0133] The descriptions presented above are for systems with two
atomic states. Many atomic systems include additional states that
are also occupied. It is expected that erasure and inversion can be
accomplished in such systems provided that the time of occupancy in
the additional states is limited or controllable.
7. Medium Absorption Control
[0134] In some of the IBT material based applications, the
performances of the material depends on the optical thickness, also
called total absorption length, which is the integration of the
absorption coefficient, .alpha., over the physical length of the
material, Lmat. For a constant absorption coefficient .alpha. the
optical thickness is simply .alpha.Lmat.
[0135] The absorption coefficient of the medium is proportion to
absorbers concentration and the population inversion of the
absorbers, .alpha.(.omega.)=-.alpha..sub.0r(.omega.), where
.alpha..sub.0 is defined as the absorption coefficient for the
population at ground state (i.e., r=-1) in a particular frequency
band of interest. For a given medium, the absorption coefficient
can be adjusted by varying the population inversion level as a
function of frequency. The present population reconfiguration
techniques can be used for effective absorption control and
adjustment. By combining reconfiguration of atomic state
populations with population decay, the effective absorption can be
adjusted in selected spectral bands and locations within the medium
within a short time.
[0136] These procedures can be used to form transparent windows for
spectral filtering and for inversion of an absorbing medium to a
gain medium. If the relative population r is initially uniform over
the bandwidth of interest, either inversion or erasure can be used
as the first operation. If there are any spectral features
initially, then erasure is preferably used as the first
operation.
[0137] If the frequency bandwidth of interest is comparable with
inhomogeneous broadening, the inhomogeneous broadening profile
affects the overall absorption. For example, if the initial
absorption profile has a Gaussian shape, the adjusted profile also
has the Gaussian shape.
8. Combination Chirps
[0138] In some applications, one or more chirped pulses are used
for processing or readout of spectral features. For example, a
chirp that is used for readout can also be used for erasure so that
the readout and erasure can be implemented simultaneously. This
combined operation has the advantages of reducing the number of
operations and shortening the operation time.
[0139] The chirped field used in the erasure may also be used for
reprogramming the next spatial-spectral features. The erasure and
reprogramming chirps can be temporally separated or temporal
overlapped.
[0140] In some applications, the chirp bandwidths for inversion,
readout, and erasure are the same, and constitute the bandwidth of
interest. It is convenient to use a series of chirps with varied
amplitude for inversion, readout, and erasure. For example, in most
applications, the spectral features stored in the material are in
the absorptive range, and the inversion of these absorptive
spectral features results in amplified readout signals. After
readout, the spectral features in gain regime can then be erased.
In some embodiments, the series of chirps are repeated to implement
the inversion/readout/erasure operations. In some embodiments, the
chirps are combined. For example, the readout and erasure are
combined and implemented using one chirp. As another example, the
inversion and the readout chirps are combined.
[0141] In the erasure of strong spectral features, especially
spectral gratings with high strength, the erasure field will be
diffracted by the spectral features. In some applications where
high dynamic range is desired, this diffraction should be
considered. In some embodiments, two or more chirps are used each
with effective erasure amplitudes. After the first erasure pulse,
some small spectral features remain due to the secondary effect of
diffraction. The second chirp is used for erasing the small
spectral features. In most embodiments, two erasure steps are
enough. In some embodiments more erasures are used. The chirps in
this technique are different than the multiple chirps used in thick
medium, where two or more chirps with different amplitudes are used
to account for different attenuations to different spots in the
material.
9. Example Applications
[0142] A spatial-spectral holographic (SSH) medium is usually
absorptive, which reduces the performance of SSH based
applications. Using inversion, absorptive SSH material can be
converted into a gain medium without degradation of the information
carried by the existing SSH features. In some SSH based
applications, a gain medium is preferred over an absorptive one.
One such application is to process extremely weak and noisy
signals, such as the return signals captured by a laser RADAR
receiver. A gain medium has several advantages including, 1)
processing gain (instead of loss accompanied by absorptive media);
2) compactness by incorporating signal processing and amplification
in one element; 3) better noise figure compared to systems with
separate processing and amplification elements; and 4) flexible
temporal, spectral, and spatial configurations for various signal
processing requirements, such as impulsive and/or continuous
signals, integrated processing through accumulation, multiple
spectral and/or spatial channel operations, and collinear and/or
angled spatial arrangements.
[0143] These operations are applicable to both optically thin and
thick media. It is more important to achieve high gain for various
signal processing applications in thick media. On the other hand,
quantum computing systems most likely use thin media. The technique
can be used to operate on multiple spatial and/or spectral
channels. Temporal overlapped multiple chirped pulses can be
configured to reduce the time to prepare inversion for multiple
channel operation.
[0144] Light controlled population inversion and transfer between
the energy levels of atoms is also a highly demanded technique in
the areas of quantum computing and quantum control.
[0145] The erasure technique is critical to high speed, high
density, continuous optical storage/processing applications
based-on Optical Coherent Transients (OCT) and Spectral Hole
Burning (SHB). The technique erases spatial-spectral features by
setting the relative population r to zero on the order of the
coherence time of the medium, which is much faster than population
decay time. This erasure technique can be applied to many OCT/SHB
processing applications, such as spectral-spectral coherent
integrated processor, spectral analyzer, spectral filtering,
optical memory, and networking using one or more OCT processing
routers. In these applications, the spatial-spectral channels are
repetitively swept to achieve high capacity and high speed. Due to
the lifetime of the absorptive features in the medium (usually the
excited state population lifetime) the same channel can be reused
only after the affects from the previously processed signals
vanish. Any residual of the previous processing leads to crosstalk
with the following processing.
[0146] These techniques can also be applied to selectively erase a
strong jammer and preserve the desired signal in RADAR signal
processing in other bands.
[0147] This technique can be used to switch the processing medium
to be temporarily transparent in selected spatial-spectral
channels. After erasure, the medium becomes transparent.
[0148] In most applications, one crystal is used. This crystal may
be used for different purposes or for different processing
operations. For example, the crystal is used both for laser
stabilization and for processing using the stabilized laser, as
shown in FIG. 1. These two processes may require different
absorption coefficients in the crystal. In some applications of
signal processing, the processing requires different absorption
coefficient for different signal strengths or different settings.
In some embodiments, the effective absorption coefficient is
adjusted to satisfy different requirement within one crystal.
[0149] Furthermore, an adjustable spectral filter has applications
such as but not limited to pulse shaping and optical spectral
filtering.
[0150] The techniques of the present invention can be applied to
nuclear magnetic resonance (NMR) related applications and devices.
The chirp in NMR is a chirped magnetic field. In these embodiments,
the inversion method is used to invert the spectral features of the
spin population. The erasure method is used to erase the spectral
features of the spin population. The effective spin population
inversion is controlled and adjusted using inversion and erasure
combined with the decay process. In various embodiments, the linear
and non-linear chirps described above, such as the chirp with
hyperbolic secant edges, are used in NMR related applications and
devices.
10. Controller Hardware Overview
[0151] FIG. 14 is a block diagram that illustrates a computer
system 1400 upon which an embodiment of the invention may be
implemented as controller 102. Computer system 1400 includes a
communication mechanism such as a bus 1410 for passing information
between other internal and external components of the computer
system 1400. Information is represented as physical signals of a
measurable phenomenon, typically electric voltages, but including,
in other embodiments, such phenomena as magnetic, electromagnetic,
pressure, chemical, molecular atomic and quantum interactions. For
example, north and south magnetic fields, or a zero and non-zero
electric voltage, represent two states (0, 1) of a binary digit
(bit). A sequence of binary digits constitutes digital data that is
used to represent a number or code for a character. A bus 1410
includes many parallel conductors of information so that
information is transferred quickly among devices coupled to the bus
1410. One or more processors 1402 for processing information are
coupled with the bus 1410. A processor 1402 performs a set of
operations on information. The set of operations include bringing
information in from the bus 1410 and placing information on the bus
1410. The set of operations also typically include comparing two or
more units of information, shifting positions of units of
information, and combining two or more units of information, such
as by addition or multiplication. A sequence of operations to be
executed by the processor 1402 constitute computer
instructions.
[0152] Computer system 1400 also includes a memory 1404 coupled to
bus 1410. The memory 1404, such as a random access memory (RAM) or
other dynamic storage device, stores information including computer
instructions. Dynamic memory allows information stored therein to
be changed by the computer system 1400. RAM allows a unit of
information stored at a location called a memory address to be
stored and retrieved independently of information at neighboring
addresses. The memory 1404 is also used by the processor 1402 to
store temporary values during execution of computer instructions.
The computer system 1400 also includes a read only memory (ROM)
1406 or other static storage device coupled to the bus 1410 for
storing static information, including instructions, that is not
changed by the computer system 1400. Also coupled to bus 1410 is a
non-volatile (persistent) storage device 1408, such as a magnetic
disk or optical disk, for storing information, including
instructions, that persists even when the computer system 1400 is
turned off or otherwise loses power.
[0153] Information, including instructions, is provided to the bus
1410 for use by the processor from an external input device 1412,
such as a keyboard containing alphanumeric keys operated by a human
user, or a sensor. A sensor detects conditions in its vicinity and
transforms those detections into signals compatible with the
signals used to represent information in computer system 1400.
Other external devices coupled to bus 1410, used primarily for
interacting with humans, include a display device 1414, such as a
cathode ray tube (CRT) or a liquid crystal display (LCD), for
presenting images, and a pointing device 1416, such as a mouse or a
trackball or cursor direction keys, for controlling a position of a
small cursor image presented on the display 1414 and issuing
commands associated with graphical elements presented on the
display 1414.
[0154] In the illustrated embodiment, special purpose hardware,
such as an application specific integrated circuit (IC) 1420, is
coupled to bus 1410. The special purpose hardware is configured to
perform operations not performed by processor 1402 quickly enough
for special purposes. Examples of application specific ICs include
graphics accelerator cards for generating images for display 1414,
cryptographic boards for encrypting and decrypting messages sent
over a network, speech recognition, and interfaces to special
external devices, such as robotic arms and medical scanning
equipment that repeatedly perform some complex sequence of
operations that are more efficiently implemented in hardware.
[0155] Computer system 1400 also includes one or more instances of
a communications interface 1470 coupled to bus 1410. Communication
interface 1470 provides a two-way communication coupling to a
variety of external devices that operate with their own processors,
such as printers, scanners and external disks. In general the
coupling is with a network link 1478 that is connected to a local
network 1480 to which a variety of external devices with their own
processors are connected. For example, communication interface 1470
may be a parallel port or a serial port or a universal serial bus
(USB) port on a personal computer. In some embodiments,
communications interface 1470 is an integrated services digital
network (ISDN) card or a digital subscriber line (DSL) card or a
telephone modem that provides an information communication
connection to a corresponding type of telephone line. In some
embodiments, a communication interface 1470 is a cable modem that
converts signals on bus 1410 into signals for a communication
connection over a coaxial cable or into optical signals for a
communication connection over a fiber optic cable. As another
example, communications interface 1470 may be a local area network
(LAN) card to provide a data communication connection to a
compatible LAN, such as Ethernet. Wireless links may also be
implemented. For wireless links, the communications interface 1470
sends and receives electrical, acoustic or electromagnetic signals,
including infrared and optical signals, that carry information
streams, such as digital data. Such signals are examples of carrier
waves.
[0156] The term computer-readable medium is used herein to refer to
any medium that participates in providing information to processor
1402, including instructions for execution. Such a medium may take
many forms, including, but not limited to, non-volatile media,
volatile media and transmission media. Non-volatile media include,
for example, optical or magnetic disks, such as storage device
1408. Volatile media include, for example, dynamic memory 1404.
Transmission media include, for example, coaxial cables, copper
wire, fiber optic cables, and waves that travel through space
without wires or cables, such as acoustic waves and electromagnetic
waves, including radio, optical and infrared waves. Signals that
are transmitted over transmission media are herein called carrier
waves.
[0157] Common forms of computer-readable media include, for
example, a floppy disk, a flexible disk, a hard disk, a magnetic
tape, or any other magnetic medium, a compact disk ROM (CD-ROM), a
digital video disk (DVD) or any other optical medium, punch cards,
paper tape, or any other physical medium with patterns of holes, a
RAM, a programmable ROM (PROM), an erasable PROM (EPROM), a
FLASH-EPROM, or any other memory chip or cartridge, a carrier wave,
or any other medium from which a computer can read.
[0158] Network link 1478 typically provides information
communication through one or more networks to other devices that
use or process the information. For example, network link 1478 may
provide a connection through local network 1480 to a host computer
1482 or to equipment 1484 operated by an Internet Service Provider
(ISP). ISP equipment 1484 in turn provides data communication
services through the public, world-wide packet-switching
communication network of networks now commonly referred to as the
Internet 1490. A computer called a server 1492 connected to the
Internet provides a service in response to information received
over the Internet. For example, server 1492 provides information
representing video data for presentation at display 1414.
[0159] The invention is related to the use of computer system 1400
for implementing the techniques described herein. According to one
embodiment of the invention, those techniques are performed by
computer system 1400 in response to processor 1402 executing one or
more sequences of one or more instructions contained in memory
1404. Such instructions, also called software and program code, may
be read into memory 1404 from another computer-readable medium such
as storage device 1408. Execution of the sequences of instructions
contained in memory 1404 causes processor 1402 to perform the
method steps described herein. In alternative embodiments,
hardware, such as application specific integrated circuit 1420, may
be used in place of or in combination with software to implement
the invention. Thus, embodiments of the invention are not limited
to any specific combination of hardware and software.
[0160] The signals transmitted over network link 1478 and other
networks through communications interface 1470, which carry
information to and from computer system 1400, are exemplary forms
of carrier waves. Computer system 1400 can send and receive
information, including program code, through the networks 1480,
1490 among others, through network link 1478 and communications
interface 1470. In an example using the Internet 1490, a server
1492 transmits program code for a particular application, requested
by a message sent from computer 1400, through Internet 1490, ISP
equipment 1484, local network 1480 and communications interface
1470. The received code may be executed by processor 1402 as it is
received, or may be stored in storage device 1408 or other
non-volatile storage for later execution, or both. In this manner,
computer system 1400 may obtain application program code in the
form of a carrier wave.
[0161] Various forms of computer readable media may be involved in
carrying one or more sequence of instructions or data or both to
processor 1402 for execution. For example, instructions and data
may initially be carried on a magnetic disk of a remote computer
such as host 1482. The remote computer loads the instructions and
data into its dynamic memory and sends the instructions and data
over a telephone line using a modem. A modem local to the computer
system 1400 receives the instructions and data on a telephone line
and uses an infra-red transmitter to convert the instructions and
data to an infra-red signal, a carrier wave serving as the network
link 1478. An infrared detector serving as communications interface
1470 receives the instructions and data carried in the infrared
signal and places information representing the instructions and
data onto bus 1410. Bus 1410 carries the information to memory 1404
from which processor 1402 retrieves and executes the instructions
using some of the data sent with the instructions. The instructions
and data received in memory 1404 may optionally be stored on
storage device 1408, either before or after execution by the
processor 1402.
11. Extensions and Modifications
[0162] In the foregoing specification, the invention has been
described with reference to specific embodiments thereof. It will,
however, be evident that various modifications and changes may be
made thereto without departing from the broader spirit and scope of
the invention. The specification and drawings are, accordingly, to
be regarded in an illustrative rather than a restrictive sense.
* * * * *