U.S. patent number 3,619,796 [Application Number 05/032,190] was granted by the patent office on 1971-11-09 for phase-matching arrangements in parametric traveling-wave devices.
This patent grant is currently assigned to Bell Telephone Laboratories, Incorporated. Invention is credited to Harold Seidel.
United States Patent |
3,619,796 |
Seidel |
November 9, 1971 |
PHASE-MATCHING ARRANGEMENTS IN PARAMETRIC TRAVELING-WAVE
DEVICES
Abstract
The phase deficiency in a parametric traveling-wave device, due
to dispersion in the wavepath, is compensated by means of a grating
distributed along a surface of an otherwise uniform nonlinear
material. In one embodiment of the invention the grating is fixed.
In a second, tunable embodiment of the invention, an acoustic
surface wave serves as a moving grating.
Inventors: |
Seidel; Harold (Warren,
NJ) |
Assignee: |
Bell Telephone Laboratories,
Incorporated (Murray Hill, Berkeley Heights, NJ)
|
Family
ID: |
21863589 |
Appl.
No.: |
05/032,190 |
Filed: |
April 27, 1970 |
Current U.S.
Class: |
330/4.6; 307/424;
330/53; 359/331; 330/5; 359/328 |
Current CPC
Class: |
H03F
13/00 (20130101); G02F 1/395 (20130101); G02F
1/377 (20130101); G02F 1/125 (20130101) |
Current International
Class: |
G02F
1/125 (20060101); G02F 1/01 (20060101); G02F
1/35 (20060101); G02F 1/39 (20060101); G02F
1/377 (20060101); H03F 13/00 (20060101); H03f
007/04 () |
Field of
Search: |
;307/88.3 ;321/69
;330/4.5,4.6,5 |
Other References
Harris et al., "IEEE Journal of Quantum Electronics," May 1968, p.
354-355. 307-88.3.
|
Primary Examiner: Lake; Roy
Assistant Examiner: Hostetter; Darwin R.
Claims
I claim:
1. A traveling electromagnetic wave parametric device
comprising:
a dispersive waveguide supportive of electromagnetic wave energy
having angular frequencies .omega..sub.1, .omega..sub.2 and
.omega..sub.3, where .omega..sub.1 +.omega..sub.2 =.omega..sub.3
;
a uniform, nonlinear material extending longitudinally along a
portion of said guide in the direction of wave propagation;
said material having distributed along a surface thereof a
plurality of discontinuities longitudinally spaced apart a distance
d=2.pi.m/.DELTA..beta., where m is an integer, .DELTA..beta. is the
phase differential required to satisfy the phase relationship
.beta..sub.1 +.beta..sub.2 =.beta..sub.3 +.DELTA..beta., and
.beta..sub.1, .beta..sub.2, and .beta..sub.3 are, to a first-order
approximation, the phase constants, respectively, of said wave
energy.
2. The device according to claim 1 wherein .omega..sub.1
=.omega..sub.2 and .beta..sub.1 =.beta..sub.2.
3. The device according to claim 1 wherein said discontinuities
form a fixed grating.
4. The device according to claim 1 wherein said discontinuities
form a moving grating.
5. The device according to claim 1 including a first
electroacoustic transducer for launching an acoustic surface wave
along said material, and a second longitudinally spaced transducer
for receiving said acoustic wave;
and wherein the distance d is equal to the wavelength
.lambda..sub.a of said acoustic wave.
6. A frequency doubler comprising:
a parametric device according to claim 2;
a source of wave energy having an angular frequency .omega..sub.1
coupled to one end of said device;
and output apparatus for receiving wave energy having an angular
frequency .omega..sub.3 =2.omega..sub.1 coupled to the other end of
said device.
7. An amplifier comprising:
a parametric device according to claim 1;
a signal source having an angular frequency .omega..sub.1, and a
pump source having an angular frequency 107 .sub.3 coupled to one
end of said device;
and output apparatus for receiving amplified wave energy at angular
frequency .omega..sub.1 coupled to the other end of said
device.
8. A traveling electromagnetic wave parametric device
comprising:
a dispersive waveguide including a uniform, nonlinear material
extending longitudinally therealong in the direction of wave
propagation;
said guide being supportive of electromagnetic wave energy having
angular frequencies .omega..sub.1, .omega..sub.2....omega..sub.n
with phase constants .beta..sub.1, .beta..sub.2....beta..sub.n,
respectively, where
p.omega..sub.1 +m.omega..sub.2...+n.omega..sub.n =0
and
p.beta..sub.1 +m+.sub.2...+n.beta..sub.n =q.DELTA..beta.,
where p, m, n and q are integers;
characterized in that said material has distributed along a surface
thereof a plurality of discontinuities longitudinally spaced apart
a distance d=2.pi./.DELTA..beta..
Description
This invention relates to parametric optical devices.
BACKGROUND OF THE INVENTION
It is known that in traveling-wave parametric devices, such as
parametric amplifiers and harmonic generators, efficient
interaction requires that the so-called "Tien conditions" be
satisfied. As set forth in a paper by P. K. Tien, entitled
"Parametric Amplification and Frequency Mixing in Propagating
Circuits," published in the Sept. 1968 issue of the Journal of
Applied Physics, pp. 1,347-1,357, optimum parametric interaction
occurs when
f.sub.1 +f.sub.2 =f.sub.3 (1)
And
.beta..sub.1 +.beta..sub.2 =.beta..sub.3 (2)
Where
f.sub.1, f.sub.2 and f.sub.3 are the frequencies of the propagating
waves; and
.beta..sub.1, .beta..sub.2, and .beta..sub.3 are their phase
constants.
Because nonlinear materials are also dispersive, the preferred
phase conditions are not readily realized in the absence of special
arrangements such as, for example, the use of birefringent
materials, as described in U.S. Pat. No. 3,234,475, or the use of a
fourth, variable frequency, electromagnetic signal, such as is
described in the copending application by S. E. Miller, Ser. No.
813,425, filed Apr. 4, 1969, and assigned to applicant's assignee.
Such devices and arrangements, however, limit the type of nonlinear
materials that can be used, or require unduly complicated
circuitry.
SUMMARY OF THE INVENTION
The present invention is based upon the recognition that the phase
deficiency .DELTA..beta. of a parametric system can be directly and
efficiently met by means of a spatial mixing process produced by
introducing a periodicity in the waveguiding structure. This can be
done by means of a fixed grating or, if the parametric device is to
be tunable, by means of an acoustic surface wave. This, in the
first embodiment of the invention to be described hereinbelow, a
fixed grating having a periodicity .DELTA..beta., such that the
Tien phase condition is satisfied, is placed along one surface of
the wave path.
In a second embodiment of the invention, an acoustic wave, launched
so as to propagate along the optical wave path, serves as a moving
surface grating having the required periodicity. In this
arrangement, the parametric device is tunable by varying the
acoustic wave frequency.
It is an advantage of the present invention that the spatial mixing
is produced by means of a relatively strong interaction with either
a fixed or moving grating. As such, optimum phase conditions are
readily established and the resulting energy transfer is
efficiently accomplished over relatively short interaction
distances.
These and other objects and advantages, the nature of the present
invention, and its various features, will appear more fully upon
consideration of the various illustrative embodiments now to be
described in detail in connection with the accompanying
drawings.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 shows a first embodiment of the invention using a fixed
grating;
FIG. 2, included for purposes of explanation, shows the manner in
which the phase constant varies as a function of frequency; and
FIG. 3 shows a second embodiment of the invention using a moving
grating.
DETAILED DESCRIPTION
Referring to the drawings, FIG. 1 shows a first embodiment of an
optical, traveling-wave parametric device, in accordance with the
present invention, comprising a source 14 of electromagnetic wave
energy; a waveguide 10 for guiding and operating up said wave
energy; and output utilization apparatus 15 for receiving and
utilizing the transmitted wave energy.
Waveguide 10 is basically the same structure as is described in an
article by E. A. J. Maracatili entitled "Dielectric Rectangular
Waveguide and Directional Coupler for Integrated Optics," published
in the Sept., 1969 issue of the Bell System Technical Journal. As
described therein, the waveguide comprises a transparent (low-loss)
uniform dielectric guiding strip 12 of refractive index n.sub.1,
embedded in a second, transparent dielectric substrate 11 of
slightly lower refractive index n.sub.2 < n.sub.1. In the
illustrative embodiment shown in FIG. 1, strip 12 is embedded in
substrate 11 with its upper surface exposed. Alternatively, the
guiding strip can be totally surrounded by the substrate or can be
placed on top of the substrate. For a full discussion of the design
and operation of this type of waveguiding structure, see the
above-identified article by Marcatili.
In addition to being transparent at the frequencies of interest,
strip 12 is also nonlinear. That is, strip 12 is made of a
material, such as potassium dihydrogen phosphate (KDP), lithium
niobate, or gallium arsenide, whose index of refraction varies as a
function of the intensity of the signal. As is known, when a signal
of angular frequency .omega. is applied to such a material, a
modulation process occurs, resulting in the generation of sum and
difference frequencies. Thus, for example, harmonics of the applied
signal frequency are produced. The efficiency with which this
occurs depends, among other factors, upon how closely the Tien
phase condition is satisfied. In a second harmonic generator,
optimum interaction occurs where
.beta..sub.2 = 2.beta. (3)
where .beta. and .beta..sub.2 are the phase constants of the
fundamental and second harmonic waves, respectively.
Typically, however, most media are dispersive. Thus, the second
harmonic phase constant .beta..sub.2 is not equal to 2.beta. as
required by equation (3). This is illustrated in FIG. 2 which shows
a typical .beta.-.omega. curve 20 and an idealized, linear
.beta.-.omega. curve 21. The phase constant .beta. at frequency
.omega. is defined by point 1, which is common to curves 20 and 21.
At frequency 2.omega., the phase constant .beta.'.sub.2 defined by
point 2 on curve 20 is not equal to 2.beta. because of the
curvature of the actual .beta.-.omega. curve. The deficiency in the
phase constant of the harmonic wave is equal to the difference
.DELTA..beta. between the actual phase constant .beta.'.sub.2 ,
defined by point 2 on curve 20, and the idealized phase constant
.beta..sub.2 , defined by point 3 on curve 21.
In accordance with the present invention, the deficiency in the
magnitude of the phase constant of the harmonic wave is made up by
means of a spatial mixing process. Just as .omega. defines the
temporal variations of a signal, .beta. defines its spatial
variations. And just as a mixing process creates new temporal
variations, a spatial mixing process creates new spatial
variations. Referring to FIG. 2, it is apparent that in order to
satisfy the preferred phase condition for efficient harmonic
generation, a new space-time relationship, which differs from curve
20 by an amount .DELTA..beta. is needed. In accordance with one
embodiment of the invention, spatial sidebands are produced by
means of a fixed grating 13 placed upon a surface of guiding strip
12. The grating, most generally, can be any arrangement which
introduces a series of uniformly spaced discontinuities along the
direction of wave propagation, where the spacing d between
discontinuities is related to the phase constant difference
.DELTA..beta. by
d=2.pi.m/.DELTA..beta. (4)
where m is an integer.
The interaction of the optical waves with the grating gives rise to
a family of new space-time relationships, defined by curves 22, 23,
and 24, for difference values of m. As can be seen, by choosing d
for the grating in accordance with equation (4), there now exists a
realizable solution of the Tien phase condition since, for m = 1,
there is a .beta.-.omega. relationship defined by curve 23 for
which the second harmonic phase constant, .beta..sub.2 =
.beta.'.sub.2 + .DELTA..beta., is equal to 2.beta. .
It should be noted that the phase constants of the several waves
will be slightly perturbed by the presence of a grating. Hence, the
phase relationship using the unperturbed phase constants, is
correct to only a first order approximation.
Grating 13 can be formed along the upper surface of strip 12 by
means of any one of the many well-known techniques. For example,
the grating can be ruled onto the guiding strip, or formed by means
of a deposition process. The optimum length of the grating, to
produce maximum or any other degree of interaction, can be
determined experimentally. In the visible region of the spectrum,
this is easily done by visually noting the intensity of the signal
of interest, i.e., the harmonic wave in a harmonic generator, along
the direction of wave propagation. This intensity will vary along
this direction, reaching a maximum at regularly spaced intervals.
The optimum length for maximum interaction is defined by one of the
maxima.
It will also be noted that the guiding strip 12 need be made of a
nonlinear material only over a region coextensive with grating
13.
FIG. 3 shows an alternative embodiment of the invention including,
as in FIG. 1, a waveguide 30 comprising a nonlinear, transparent
guiding strip 31 embedded in a transparent substrate 32. For
purposes of illustration, the embodiment of FIG. 3 is a parametric
amplifier and, as such an input signal E.sub.s, derived from signal
source 33, is directed into one end of guide 30 along with a pump
signal E.sub.p derived from a pump source 34. Advantageously, both
sources are highly coherent signal sources such as lasers.
Output utilization apparatus 35 is located at the other end of
guide 30 to receive the amplified signal E.sub.s, along with pump
signal E.sub.p, and an induced idler signal E.sub.i. The latter two
signal components can be selectively attenuated by means of
filters.
The conditions for parameter amplifications are given by
f.sub.p =f.sub.s +f.sub.i (5)
and
.beta..sub.p =.beta..sub.s +.beta..sub.i (6)
where
f.sub.p, f.sub.s, and f.sub.i are the frequencies of the pump, the
signal and the idler waves, respectively; and
.beta..sub.p, .beta..sub.s, and .beta..sub.i are the phase
constants of the pump, the signal and the idler waves,
respectively.
The frequency condition is automatically satisfied by virtue of the
modulation process produced by the nonlinear guiding strip 31
wherein the pump and signal waves interact to generate the
difference frequency idler wave. For this interaction to grow,
however, and the signal to be amplified, the phase condition given
by equation (6) must also be satisfied. However, because of the
dispersion discussed in connection with FIG. 2, .beta..sub.p is, in
general, different than .beta..sub.2 + .beta..sub.i by an amount
.DELTA..beta.. This difference is made up in the embodiment of FIG.
3 by means of a moving acoustic grating induced along the strip by
longitudinally spaced electroacoustic surface wave transducers 40
and 41. The latter can be any one of the many known electroacoustic
transducers. Those illustrated in FIG. 3 are the type described by
J. H. Rowen in U.S. Pat. No. 3,289,114, and comprise wedge-shaped
members 42 and 43 to which are bonded bulk transducers 44 and 45,
respectively. An electrical signal source 46 is coupled to one of
the transducers 40, and an output absorptive load 47 is coupled to
the other transducer 45.
In operation, transducer 40 launches an acoustic surface wave along
guiding strip 31 in response to the signal derived from source 46.
The frequency of this signal is such that the acoustic wavelength
.lambda..sub.a of the induced acoustic wave is related to
.DELTA..beta. by
.lambda..sub.a =2.pi.m/.DELTA..beta. (7)
where m is an integer.
The acoustic wave thus induced along the optical wave path,
produces spatial sidebands in the same manner as the fixed grating
in the embodiment of FIG. 1. By selecting the frequency of the
acoustic wave in accordance with equation (7), the optimum phase
condition for parametric interaction is realized.
The second transducer couples the acoustic wave energy to
terminating load 47, thus defining the overall length of the
amplifier.
It will be noted that there will be a slight Doppler frequency
shift produced by the moving grating. However, the acoustic wave
frequency is typically much less than the frequencies of the
optical waves and, hence, the resulting frequency shift can
generally be neglected. It will also be noted that this second
embodiment of the invention is tunable. That is, if the optical
signal frequency is changed, a new optimum phase condition can be
readily established by merely adjusting the frequency of the
acoustic wave.
While the invention has been described with reference to optical
waves and with reference to a particular waveguiding structure, it
will be readily recognized that the same techniques can just as
readily be utilized at the lower millimeter and microwave
frequencies. In addition, the invention is not limited to the
specific parametric interaction described hereinabove but, more
generally, is applicable to any parametric system of the form
p.omega..sub.1 +m.omega..sub.2...+n.omega..sub.n =0 (8)
and
p.beta..sub.1 +m.beta..sub.2...+n.beta..sub.n =q.DELTA..beta.
(9)
where
p, m, n and q are integers, and
.DELTA..beta. is the phase deficiency of the system.
Thus, in all cases it is understood that the above-described
arrangements are illustrative of but a small number of the many
possible specific embodiments which can represent applications of
the principles of the invention. Numerous and varied other
arrangements can readily be devised in accordance with these
principles by those skilled in the art without departing from the
spirit and scope of the invention.
* * * * *