U.S. patent application number 12/819806 was filed with the patent office on 2010-10-07 for carrier-envelope phase shift using linear media.
This patent application is currently assigned to MASSACHUSETTS INSTITUTE OF TECHNOLOGY. Invention is credited to Richard Ell, Franz X. Kaertner.
Application Number | 20100253950 12/819806 |
Document ID | / |
Family ID | 37852337 |
Filed Date | 2010-10-07 |
United States Patent
Application |
20100253950 |
Kind Code |
A1 |
Kaertner; Franz X. ; et
al. |
October 7, 2010 |
Carrier-Envelope Phase Shift Using Linear Media
Abstract
The carrier-envelope phase in a train of optical pulses is
varied utilizing the dispersive properties of lossless plates while
the total dispersion in transmission is maintained practically
constant. The plates include sloped surfaces and are mounted for
displacement such that the ratio of the thicknesses of the two
plates through which the optical pulses will pass can be varied by
displacing the plates so as to shift the carrier-envelope phase in
the optical pulses. In one embodiment, the plates include a barium
fluoride wedge and a fumed silica wedge, wherein the wedges are
bond together to form a composite structure with thicker and
thinner portions of the wedges inversely matched.
Inventors: |
Kaertner; Franz X.; (Newton,
MA) ; Ell; Richard; (OberKirch, DE) |
Correspondence
Address: |
MODERN TIMES LEGAL
ONE BROADWAY , 14TH FLOOR
CAMBRIDGE
MA
02142
US
|
Assignee: |
MASSACHUSETTS INSTITUTE OF
TECHNOLOGY
Cambridge
MA
|
Family ID: |
37852337 |
Appl. No.: |
12/819806 |
Filed: |
June 21, 2010 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
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11608666 |
Dec 8, 2006 |
|
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12819806 |
|
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60748858 |
Dec 9, 2005 |
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Current U.S.
Class: |
356/484 ;
359/615 |
Current CPC
Class: |
G02F 1/0102 20130101;
H01S 3/0057 20130101; G02B 5/04 20130101; G02F 2203/26 20130101;
H01S 3/0014 20130101; G02B 26/06 20130101; G02F 2203/54 20130101;
G01J 11/00 20130101; H01S 3/1022 20130101; G02F 2203/50 20130101;
H01S 3/10053 20130101 |
Class at
Publication: |
356/484 ;
359/615 |
International
Class: |
G01B 9/02 20060101
G01B009/02; G02B 5/04 20060101 G02B005/04 |
Goverment Interests
GOVERNMENT SUPPORT
[0002] The invention was supported, in whole or in part, by a
grant, N00014-02-1-0717, from the Office of Naval Research. The
Government has certain rights in the invention.
Claims
1. An optical system for controlling a carrier-envelope phase
comprising: a light source configured to generate a train of
optical pulses along an optical path; a first plate positioned in
the optical path, wherein the first plate has a thicker portion and
a thinner portion with a range of thicknesses there between, and
wherein the first plate has a refractive index, second order
dispersion, and ratio of group and phase velocities for the optical
pulses; and a second plate positioned in the optical path, wherein
the second plate has a thicker portion and a thinner portion with a
range of thicknesses there between, wherein the thicker portion of
the second plate is aligned with the thinner portion of the first
plate, measured parallel to the optical path, and wherein the
thinner portion of the second plate is aligned with the thicker
portion of the first plate, measured parallel to the optical path,
and wherein the second plate has a refractive index, second order
dispersion, and ratio of group and phase velocities for the optical
pulses, wherein the refractive indices of the two plates and the
second order dispersions of the optical pulses in the two plates
both are substantially the same, and wherein the ratios of group
and phase velocities for the optical pulses in the two plates are
substantially different.
2. The optical system of claim 1, further comprising a displacement
mechanism coupled with the first and second plates to displace the
plates in a plane orthogonal to the light path.
3. The optical system of claim 1, wherein the plates are bond
together.
4. The optical system of claim 1, wherein the system is an
interferometric autocorrelator with two arms, and wherein the
plates are in one arm of the interferometric autocorrelator.
5. The optical system of claim 1, wherein the combined thickness of
the plates is between 1 and 2 mm.
6. The optical system of claim 1, wherein the light source is a
laser.
7. The optical system of claim 1, wherein the light source is
configured to generate a train of optical pulses with a pulse
length of 2.5 to 7.5 femtoseconds along an optical path.
8. The optical system of claim 1, wherein the second plate
comprises silica glass.
9. The optical system of claim 8, wherein the silica is fused
silica.
10. The optical system of claim 8, wherein the first plate
comprises barium fluoride.
11. The optical system of claim 1, wherein the first and second
plates are both wedge shaped, though inversely oriented with
respect to one another.
12. A method for controlling carrier-envelope phase in an optical
system that comprises: a light source configured to generate a
train of optical pulses along an optical path; a first plate
positioned in the optical path, wherein the first plate has a
thicker portion and a thinner portion with a range of thicknesses
there between, and wherein the first plate has a refractive index,
second order dispersion, and ratio of group and phase velocities
for the optical pulses; and a second plate positioned in the
optical path, wherein the second plate has a thicker portion and a
thinner portion with a range of thicknesses there between, wherein
the thicker portion of the second plate is aligned with the thinner
portion of the first plate, measured parallel to the optical path,
and wherein the thinner portion of the second plate is aligned with
the thicker portion of the first plate, measured parallel to the
optical path, and wherein the second plate has a refractive index,
second order dispersion, and ratio of group and phase velocities
for the optical pulses, wherein the refractive indices of the two
plates and the second order dispersions of the optical pulses in
the two plates both are substantially the same, and wherein the
ratios of group and phase velocities for the optical pulses in the
two plates are substantially different; the method comprising
transmitting a train of optical pulses along the optical path, the
optical pulses including a lower-frequency envelope and a
higher-frequency carrier within the envelope.
Description
RELATED APPLICATION
[0001] This application claims the benefit of U.S. Provisional
Application No. 60/748,858 filed Dec. 9, 2005 and is a Divisional
of U.S. Ser. No. 11/608,666, filed 8 Dec. 2006.
BACKGROUND
[0003] Optical pulses have an electric field associated therewith.
As shown in FIG. 1, the electrical field can be described as a
high-frequency oscillation, known as the "carrier" (or
"carrier-wave") 12. The carrier 12 is contained within a
lower-frequency "envelope" 14. As shown, the carrier peak magnitude
16 and the envelope peak magnitude 18 are not always aligned, and
the difference in relative position between the carrier and the
envelope is known as the offset phase. The offset phase can shift
as the optical pulses pass through a medium in which the carrier
and envelope propagate at different speeds.
[0004] Only recently, it became possible to completely control the
temporal evolution of the electric light field of a train of
mode-locked laser pulses. Mastering the manipulation of phase and
magnitude of the electric field has been made possible by
technological advances in femtosecond laser technology and
nonlinear optics together with ground-breaking ideas and insights
in the field of precision spectroscopy with pulsed laser sources.
This unprecedented high level of control enables a wide range of
new applications in science and technology. Time domain
applications focus on studies of physical phenomena directly
depending on the electric field rather than on the pulse envelope
only. Examples of such applications include carrier-wave
Rabi-flopping, quantum interference of photocurrents, photoemission
from metal surfaces, or electron emission from ionized atoms.
Furthermore, attosecond physics has been made accessible by using
carrier-envelope-offset-frequency-controlled femtosecond pulses to
generate coherent light in the deep UV and X-ray spectral regions
in a well-controlled manner. Analogously, the high degree of
control of the electric field is also very beneficial for
applications in the frequency domain where the laser spectrum,
composed of discrete longitudinal modes, is being used for
pioneering experiments in optical frequency metrology.
SUMMARY
[0005] As described, herein, a pair of plates, either joined as a
composite structure or separate, have surfaces that are sloped to
produce thinner and thicker portions. The plates have similar
refractive indices and exhibit similar second order dispersions of
an optical pulse; the ratios of the group and phase velocities for
the optical pulse in the two plates, however, substantially differ.
The plates can be aligned such that the thinner portion of one
plate is aligned with the thicker portion of the other plate, and
vice versa. As the plates are displaced (e.g., within a plane or
rotationally) in the path of a train of optical pulses, the optical
pulses will travel through a shifting ratio of the respective
thicknesses of the two plates. By changing this ratio, the offset
of the carrier with respect to the envelope can be changed (and set
to any frequency between zero and the frequency of the repetition
rate, f.sub.rep) while keeping dispersion substantially constant
and, therefore, without producing a substantial change in the
energy, spectrum, shape or duration of the optical pulse.
[0006] This capacity for governing the offset is very important
since, on one hand, many experiments require particular values for
the carrier-envelope-offset frequency, f.sub.CEO, due to frequency
selective detection schemes or pulse-picking constraints for
successive amplification. In addition, very often, technical
constraints of detection and/or control electronics make a free
choice of f.sub.CEO very attractive.
[0007] In many applications utilizing
carrier-envelope-phase-controlled oscillators with or without
successive amplification, it is technically very attractive to
fully control the carrier-envelope phase or its temporal evolution
f.sub.CEO without alteration of pulse energy, pulse spectrum or
pulse duration which is not possible by pure material insertion of
removal. By implementation of a novel composite plate we establish
a method to arbitrarily shift the carrier-envelope offset phase
while keeping dispersion in transmission practically constant. We
first prove the principle by varying the carrier-envelope phase in
an interferometric autocorrelator measuring a series of ultrashort
(.about.6 fs) autocorrelations. To be able to set the
carrier-envelope offset frequency f.sub.CEO to any desired value
between zero and the repetition frequency, we use the novel plate
inside a 200 MHz, octave-spanning Ti:sapphire laser and demonstrate
a variation of f.sub.CEO by half the repetition frequency. Over the
whole demonstrated tuning range, pulse energy and spectrum stay
nearly unaltered.
[0008] Besides the demonstrated applications, the composite plate
is helpful in many applications where a precise and "neutral"
control of the carrier-envelope phase is desirable, such as in
high-harmonic generation or ionization experiments. The composite
plate also is beneficial for compensation of (temporal) long term
drifts in the carrier-envelope phase.
BRIEF DESCRIPTION OF THE DRAWINGS
[0009] FIG. 1 is an illustration of a carrier and envelope.
[0010] FIG. 2 is a graph that charts the change of the group delay
over the relevant spectral range when varying the carrier-envelope
phase by 2.pi..
[0011] FIG. 3 is an exaggerated illustration of a "phase-plate"
composite structure including a thick barium fluoride wedge and a
thinner fused silica wedge.
[0012] FIG. 4 is a graph that measures the average second order
dispersion in the composite wedge structure and fit.
[0013] FIG. 5 is a schematic illustration of the layout for an
interferometric autocorrelator used to demonstrate the
functionality of the plates.
[0014] FIG. 6 is a graph showing a measured and retrieved
autocorrelation revealing a pulse duration of 6 fs; the inset shows
the laser spectrum on a linear scale.
[0015] FIG. 7(a) shows the interferometric autocorrelation before
insertion of the plates for comparison, while FIG. 7(b)-(f) show a
series of interferometric autocorrelation measurements with
monotonically varying plate position corresponding to a
carrier-envelope phase shift in steps of .pi./2.
[0016] FIG. 8 is a graph providing a sequence of measurements
illustrating the arbitrary choice of the carrier-envelope-offset
frequency, f.sub.CEO, by varying the position of the plates inside
the laser cavity of an octave-spanning 200 MHz laser.
[0017] FIG. 9 is a plot illustrating variation of the
carrier-envelope-offset frequency, f.sub.CEO, as a function of the
plate position.
[0018] FIG. 10 is a graph illustrating the optical laser spectrum
of the usable laser output after transmission of the spectral wings
for carrier-envelope-offset frequency control.
[0019] The foregoing and other features and advantages of the
invention will be apparent from the following, more-particular
description. In the accompanying drawings, like reference
characters refer to the same or similar parts throughout the
different views. The drawings are not necessarily to scale,
emphasis instead being placed upon illustrating particular
principles, discussed below.
DETAILED DESCRIPTION
A) The Carrier-Envelope Offset Frequency
[0020] The real electric field, E(z,t), of a laser pulse may be
decomposed into
E(z,t)=Re{A(z,t)e.sup.i(.omega..sup.0.sup.t+k(.omega..sup.0.sup.)ze.sup.-
t.phi.(t)e.sup.I.phi..sup.CEO} (1)
with A(z,t) representing the real envelope and the following
exponential describing the oscillation with the carrier frequency,
.omega..sub.0, where the time-dependent phase term, .phi.(t),
describes the chirp of the pulse and .phi..sub.CEO describes the
phase between the maximum 16 of the carrier-wave 12 and the maximum
18 of the envelope 14 (as shown in FIG. 1)--the so-called
carrier-envelope phase. During propagation of the wave-packet, the
carrier-wave propagates with the phase velocity, .nu..sub.p, and
the envelope 14 propagates with the group velocity, .nu..sub.g.
Since all media, and even air, exhibit a wavelength-dependent index
of refraction, phase and group velocity through a medium are
generally different. As a consequence, .phi..sub.CEO changes
continuously over time. The carrier-envelope phase shift,
.DELTA..phi., caused by passing through a dispersive medium of
length, z, can be expressed as
.DELTA..phi. = 2 .pi. c .lamda. ( 1 v p - 1 v g ) z = 2 .pi. n
.lamda. z ( 2 ) ##EQU00001##
with n representing the index of refraction of the medium described
by the corresponding Sellmeier equations. The above phase shift,
.DELTA..phi., is solely due to linear propagation of the
wave-packet in media such as glass, the laser crystal or air.
Besides this linear effect, also nonlinear effects give rise to a
relative phase shift between the carrier 12 and the envelope 14.
The most prominent effect in femtosecond lasers is the third-order
Kerr nonlinearity responsible for self-phase modulation (SPM)
leading to spectral broadening, whereas the spatial Kerr effect is
exploited in Kerr-lens mode-locking (KLM). It can be shown that the
Kerr effect leads to a self-phase shift of the carrier 12 similar
to the soliton self-phase shift in fiber optics. Furthermore, the
Kerr effect induces a distortion of the envelope 14, called
self-steepening, causing a shift of the envelope 14 with respect to
the underlying carrier-wave 12.
[0021] During the periodic propagation of the laser pulses inside a
laser cavity, the carrier-envelope phase is different for each
emitted laser pulse since the total phase shift, .DELTA..phi.,
accumulated per round trip is generally not an integer multiple of
2.pi.. In other words, this means that the envelope 14 repeats
itself after each roundtrip, while the carrier-wave 12 is different
for successive pulses and repeats itself with the frequency,
f.sub.CEO--the carrier-envelope offset (CEO) frequency,
f CEO = .DELTA..phi. 2 .pi. f rep ( 3 ) ##EQU00002##
where f.sub.rep is the fundamental pulse repetition frequency.
Changing the linear or nonlinear contributions to the phase shift,
.DELTA..phi., inside the laser cavity changes the CEO
frequency.
B) The Combined Plates for Arbitrary Carrier-Envelope
Phase-Control
[0022] There are two well-established ways to influence the value
of the carrier-envelope offset frequency, f.sub.CEO. First, the
pump power of the laser can be changed to change the pulse energy
and, hence, the nonlinear contribution to the phase shift,
.DELTA..phi..sub.nonl. Typical values of the conversion factor
measured in 200-MHz octave-spanning lasers are on the order of
15-20 MHz per Watt of pump power variation. Varying f.sub.CEO over
the whole repetition rate of 200 MHz is, therefore, impracticable
absent a capacity to vary the pump power by 10 W. For lower and
higher repetition rates, the conversion factor scales accordingly
and never allows a variation of f.sub.CEO over the full repetition
frequency. This scheme is extremely useful in locking f.sub.CEO to
a reference frequency by modulating the pump power via an
acousto-optic modulator. Since the operation within a closed
control loop only necessitates pump power modulation on the order
of a few percent, the nonlinear phase shift, .DELTA..phi..sub.nonl,
can be exploited in a very efficient manner.
[0023] A second method of changing f.sub.CEO is via material
dispersion according to Eq. (2). The carrier-envelope offset
frequency, f.sub.CEO, is changed, for example, by moving a wedged
BaF.sub.2 plate and thereby changing the material insertion.
Varying the carrier-envelope phase by 2.pi. (and, hence, varying
f.sub.CEO between 0 and f.sub.rep) is achieved by introducing (or
removing) roughly 80 .mu.m of BaF.sub.2. An alternative is to
rotate a glass plate (formed, e.g., of fused silica) that is
operated close to Brewster's angle--in which case, a material
thickness variation of approximately 60 .mu.m is utilized.
[0024] As shown in FIG. 2, the group delay over the relevant
spectral range changes when varying the carrier-envelope phase by
2.pi.. The top curve 20 shows the effect of inserting 80 .mu.m of
BaF.sub.2 into the optical path to vary the carrier-envelope phase
by simply changing material insertion, whereas the bottom curve 22
displays the effective group delay variation when using a composite
wedge made of fused silica and BaF.sub.2. Meanwhile, the middle
curve 24 shows the group delay as a function of wavelength when 60
.mu.m of fused silica is inserted into the optical path.
[0025] The main problem associated with the previous approach using
single-material insertion or removal is that, unavoidably, one
simultaneously also changes the dispersion properties of the
corresponding plate experienced by the transmitted femtosecond
laser beam. FIG. 2 shows theoretical calculations as to how the
group delay changes when the carrier-envelope phase is varied by
2.pi.. Shown is the relevant spectral range supporting a short,
few-cycle pulse inside the cavity on the order of about 5
femtoseconds (fs). Due to pure material insertion (or removal) of
80 .mu.m of BaF.sub.2 or 60 .mu.m of fused silica, the pulse
experiences a group delay variation of around 3.5 fs and 2.5 fs,
respectively, which is not negligible considering the pulse
duration of only about 5 fs. In terms of second order dispersion,
this corresponds to a change of 3 fs.sup.2 and 2.2 fs.sup.2,
respectively in the group delay dispersion (GDD) at 800 nm. The
kind of dispersion-managed femtosecond lasers that are relevant for
this discussion operate with close to zero second order dispersion
a few fs.sup.2 above or below zero GDD. Accordingly, a change of
2-3 fs.sup.2, as introduced by the few tens of microns of solitary
BaF.sub.2 or fused silica has a serious impact on the laser
dynamics and, hence, on pulse spectrum and energy. Employing the
mentioned BaF.sub.2 wedges, alone, in the lasers, precludes the
ability to tune f.sub.CEO over the full repetition rate. Due to the
varying dispersion, the pulse spectrum and energy are strongly
modified; and the laser finally becomes unstable, or the
signal-to-noise ratio of the f.sub.CEO beat decreases
dramatically.
[0026] The approach here is not to remove or insert a single glass
material but, rather, to replace one kind of material with a
different kind of material. By doing so, second order dispersion is
kept nearly constant; consequently, alteration of pulse energy,
spectrum and f.sub.CEO beat signal strength is substantially
reduced.
[0027] A (not-to-scale) top view of a composite "phase-plate"
comprising a thick BaF.sub.2 wedge 26 and a thinner fused silica
wedge 28 is illustrated in FIG. 3. In other embodiments, different
material combinations with refractive indices and second order
dispersions that are very close for the two materials but with
greater differences in their ratios of group and phase velocities
are used. For example, in one embodiment, calcium fluoride
(CaF.sub.2) is used as one of the wedges. In the illustrated
embodiment, the inversely oriented wedges 26 and 28 are glued
together to form a composite plate 30. Alternatively, the wedges 26
and 28 can be spaced apart (not joined). The composite plate 30 was
used in the experiments, described herein. The thickness of the
composite plate 30 (measured horizontally, as shown) is exaggerated
relative to the length (measured vertically, as shown) of roughly
one inch (25 mm). The composite plate 30 is 10 mm in height
(measured orthogonally to the illustrated view); and the laser beam
passes through both materials in the plane of the drawing along an
optical path 29, and a displacement mechanism 31 (e.g., a
linear-displacement motor) for displacing the composite plate 30 in
a direction orthogonal to the optical path 29 to change the ratio
of thicknesses of the two wedges 26 and 28 through which the
optical pulses pass.
[0028] Using a white light interferometer, the dispersion of the
composite plate 30 was measured. An average of four measurements of
group delay dispersion (or second order dispersion) is shown in
FIG. 4 as line 32 and represents the dispersion in the center of
the composite plate 30. A fit 34 gives information about the
composition of the composite plate 30. BaF.sub.2 is a preferred
material for intracavity dispersion management since it has the
highest ratio of second- to third order dispersion at 800 nm; and,
additionally, the dispersion of 0.5 mm of BaF.sub.2 is similar to
that of 1 in of air, allowing for an easy scaling of the laser to
higher repetition rates. The chart reveals a total thickness for
the composite plate 30 of 1.58 mm.
[0029] Moving the composite plate, along its length, continuously
replaces BaF.sub.2 30 with fused silica 28 or vice versa. Eq. (2)
is used to calculate that the replacement of 200 .mu.m of fused
silica with the same amount of BaF.sub.2 allows a shift of 2.pi. in
the carrier-envelope phase, whereas the impact on second order
dispersion is negligible (+/-0.4 fs.sup.2 at 800 nm). The bottom
curve 22 in FIG. 2 confirms that the alteration in group delay is
significantly smaller in comparison to the direct use of pure
material insertion/removal.
C) Adjusting the Carrier-Envelope Phase in an Interferometric
Autocorrelator
[0030] To first prove the functionality of the wedges 26 and 28
independent of any sensitive laser dynamics, the composite plate 30
was incorporated into an interferometric autocorrelator suitable
for sub-10-fs pulse characterization. Femtosecond autocorrelators
(AC) are usually built such that dispersion is balanced in both
arms to avoid distortion of the measurement result. In
interferometric autocorrelators, in particular, identical optical
paths in both aims of the Michelson interferometer are also
required for a symmetrical interferometric autocorrelation (IAC)
trace, as predicted by theory. By introducing the composite plate
into one arm of the autocorrelator allows us to vary the
carrier-envelope phase with respect to the second arm, thereby
leading to asymmetric and/or double-peaked interferometric
autocorrelations.
[0031] The layout of the autocorrelator 36 used for these
experiments is sketched in FIG. 5--i.e., a standard balanced
autocorrelator with an additional input port for a calibration
laser 37 that enables calibration of the time axis. A thin type-I
potassium-dihydrogen-phosphate (KDP) crystal was used as the
nonlinear medium 38 to generate a second harmonic detected by a
photomultiplier tube 40. The composite plate 30 was introduced in a
first arm 42, whereas a sole BaF.sub.2 plate 44 of the same
dispersion was placed into the second arm 46. The autocorrelator
also includes a photodiode 48 for the calibration (reference) laser
37, which is used to calibrate the delay (i.e., the time axis) and
a filter 50 to block fundamental light. This configuration afforded
pre-compensation for the additional chirp introduced by the
composite plate 30 (and by the BaF.sub.2 plate 44) by a bounce on
dispersion-compensating mirrors 51. For these experiments, a
mirror-only ultrabroadband titanium-sapphire (Ti:sapphire) laser 54
with a full-width-at-half-maximum (FWHM) optical bandwidth of more
than 300 nm (available from VENTEON UB, NanoLayers Optical Coatings
GmbH, Germany, http://www.nanolayers.de/) was used.
[0032] A pair of 50/50 broadband beamsplitters 55 and 56 split the
incoming pulses from lasers 37 and 54 (reflecting half and
transmitting half), respectively, along two orthogonal pathways
toward respective mirrors 52 and 53, each of which laterally
shifted the incoming optical pulses (from mirror 55/56) over to a
second pathway and then back along the second pathway (which
intersects the other mirror 56/55). Though the pulse trains from
the respective lasers 37 and 54 traveled common pathways, the
system is configured such that the pulse trains travel in opposite
directions over the common pathways in the two arms 42 and 46.
Consequently, only the optical pulse train originating from the
laser 54 was directed through the nonlinear medium 38 en route to
its detection in the photomultiplier tube 40, while the optical
pulse train originating from the calibration laser 37 was
independently directed to the photodiode 48 for a separate
measurement.
[0033] The graph in FIG. 6 includes measured (represented by
background circles 54) and retrieved (represented by the overlaid
line 60) interferometric autocorrelation without the plates. The
inset in FIG. 6 shows the laser spectrum on a linear scale. A phase
retrieval leads to an estimated pulse duration of 6 fs. After
placing the plates 30 into the autocorrelator 36, the
carrier-envelope phase is tuned to an integer multiple of the
carrier-envelope phase in the second arm 46, producing a symmetric
single-peak trace as expected from the theory. It is interesting to
notice how this interferometric autocorrelation trace [shown in
FIG. 7(c)] resembles the measurement without the plates [shown in
FIG. 7(a)], which means the composite plate 30 does not cause any
cognizable harm in terms of dispersion management.
[0034] A series of measurements was taken, where the position of
the composite plate 30 was varied in steps of 4 mm, corresponding
to shifts of the carrier-envelope phase of .pi./2. FIG. 7(a) charts
the interferometric autocorrelation before insertion of the plates
30 for comparison, while FIG. 7(b)-(f) present a series of
interferometric autocorrelation measurements with monotonically
varying plate position corresponding to a carrier-envelope phase
shift in steps of .pi./2. During this measurement, we noticed that
the composite plate 30 exhibited structural inhomogeneities that
changed the alignment of the autocorrelator 36. After moving the
composite plate 30 a few millimeters, the autocorrelator 36 was
realigned by adjusting one of the silver mirrors 52 in the arm 42
with the composite plate 30. After doing so, the original power
level was always obtained within 10%. The observed structural
inhomogeneities were due to difficulties in the manufacturing
process reported by the manufacturer--specifically, difficulties in
fabricating the relatively thin fused silica part 28 of the plate
30 and gluing it to the soft BaF.sub.2 26 while keeping the
specifications and high optical quality in terms of polishing and
wave front distortion. The total loss of the composite plate 30,
however, is the same as for a regular BaF.sub.2 plate 44, as
observed when tested inside the laser cavity. Since, in this
experiment, the composite plate 30 was moved 16 mm to obtain a
phase shift of 2.pi. and since we know from Eq. (2) that this must
correspond to removal of 200 .mu.m of BaF.sub.2 26 (and addition of
200 .mu.m of fused silica 28), we deduce a wedge angle of
0.72.degree..
D) Varying f.sub.CEO in a 200-MHz Octave-Spanning Femtosecond
Laser
[0035] After the successful test of the composite plate 30 in the
autocorrelator 36, the composite plate was implemented into a
200-MHz octave-spanning Ti:sapphire laser [as described in O. D.
Mucke, et al., "Self-Referenced 200 MHz Octave-Spanning Ti:Sapphire
Laser with 50 Attosecond Carrier-Envelope Phase Jitter," 13 Opt.
Express 51623 (2005)]. The composite plate was part of the
dispersion management of the laser cavity and was placed into the
short arm of the z-folded asymmetric, standing wave resonator. In
the other arm two wedged BaF.sub.2 plates are located for
optimization of intracavity dispersion.
[0036] Use of the composite plate assumes optimization of the
dispersion of the cavity to maximize the signal-to-noise ratio of
the f.sub.CEO beat signal. After doing so, dispersion should stay
unaltered, though the composite plate affords one the advantageous
ability to freely choose the exact value of f.sub.CEO. FIG. 8
illustrates how f.sub.CEO was varied over half the repetition rate
(f.sub.rep/2). Initially, f.sub.CEO and its mixing product with the
repetition frequency (f.sub.rep-f.sub.CEO) were close to half the
repetition rate. By moving the composite plate stepwise by 0.2 mm,
a series of measurements were registered until f.sub.CEO was close
to the repetition frequency, f.sub.rep. The initial signal-to-noise
ratio was about 35 dB and stayed practically unaltered until
closing in on f.sub.CEO=f.sub.rep. During the measurement sequence,
the laser stayed in mode-locked operation and did not need any kind
of realignment.
[0037] In FIG. 9, the carrier-envelope-offset frequency, f.sub.CEO,
is plotted against the position of the composite plate, where the
right vertical axis is normalized to the carrier-envelope phase
shift per roundtrip. A linear fit to the data results in an inverse
slope of 4.93 mm/2.pi.. Taking into account a factor of two for the
double pass inside the laser and another factor of 1.2 due to
Brewster's angle, we end up with a value of 11.83 mm per 2.pi.
phase shift. In comparison to the result of 16 mm/2.pi. in the
interferometric autocorrelation investigation, we obtain a stronger
gradient. There are several explanations for this observation.
First, the two plates used for the two experiments were not the
same and deviations may be due to fabrication tolerances. Second,
the deviations may be due to the above-mentioned
inhomogeneities.
[0038] Ti:sapphire pulse energy and laser beam properties also vary
when moving the plate and, hence, influence the value of f.sub.CEO.
This influence manifests itself in a strong variation in the local
slope of the data set in the graph of FIG. 9. FIG. 10 displays the
corresponding optical laser spectrum for each of the data points
shown in FIG. 8. All spectra of the twelve data points taken are
shown; though for the last three data points close to f.sub.CEO=0,
the spectra exhibit slight modifications visible around the
prominent peak around 680 nm due to inhomogeneities of the
"phase-plate". Only the last two data points are close to
f.sub.CEO=f.sub.rep, corresponding to the deviation form the
original spectrum at the beginning of the tuning range in FIG. 10.
Average power and, equivalently, the pulse energy only varied
within 10% over the whole tuning range, except again for the last
two data points which we attribute to the imperfectness of the
plate due to structural inhomogeneities.
[0039] In describing embodiments of the invention, specific
terminology is used for the sake of clarity. For purposes of
description, each specific term is intended to at least include all
technical and functional equivalents that operate in a similar
manner to accomplish a similar purpose. Additionally, in some
instances where a particular embodiment of the invention includes a
plurality of system elements or method steps, those elements or
steps may be replaced with a single element or step; likewise, a
single element or step may be replaced with a plurality of elements
or steps that serve the same purpose. Further, where parameters for
various properties are specified herein for embodiments of the
invention, those parameters can be adjusted up or down by
1/20.sup.th, 1/10.sup.th, 1/5.sup.th, 1/3.sup.rd, 1/2, etc, or by
rounded-off approximations thereof, within the scope of the
invention unless otherwise specified. Moreover, while this
invention has been shown and described with references to
particular embodiments thereof, those skilled in the art will
understand that various substitutions and alterations in form and
details may be made therein without departing from the scope of the
invention; further still, other aspects, functions and advantages
are also within the scope of the invention. The contents of all
references, including patents and patent applications, cited
throughout this application are hereby incorporated by reference in
their entirety. The appropriate components and methods of those
references may be selected for the invention and embodiments
thereof. Still further, the components and methods identified in
the Background section are integral to this disclosure and can be
used in conjunction with or substituted for components and methods
described elsewhere in the disclosure within the scope of the
invention.
* * * * *
References