U.S. patent application number 13/055909 was filed with the patent office on 2011-11-03 for interferometer with frequency combs and synchronisation scheme.
This patent application is currently assigned to Centre National de la Recherche Scientifique-CNRS. Invention is credited to Guy Guelachvili, Theodor W. Hansch, Nathalie Picque.
Application Number | 20110267625 13/055909 |
Document ID | / |
Family ID | 41119851 |
Filed Date | 2011-11-03 |
United States Patent
Application |
20110267625 |
Kind Code |
A1 |
Guelachvili; Guy ; et
al. |
November 3, 2011 |
INTERFEROMETER WITH FREQUENCY COMBS AND SYNCHRONISATION SCHEME
Abstract
An embodiment relates to an interferometer comprising: a first
frequency comb; a second frequency comb adapted to interact with
the first frequency comb in order to produce interferences; means
for isolating the beating signal between a subset of frequency
components among the frequency components of the two combs. This
subset of frequency components may be preferably, but not
necessarily, a single line of the first frequency comb and a single
line of the second frequency comb; means for monitoring this
beating signal and using it as a trigger or as a clock for the
acquisition unit device recording the beating interference signal
between the entire frequency components of the first and the second
frequency combs.
Inventors: |
Guelachvili; Guy; (Etampes,
FR) ; Hansch; Theodor W.; (Munchen, DE) ;
Picque; Nathalie; (Gif-Sur-Yvette, FR) |
Assignee: |
Centre National de la Recherche
Scientifique-CNRS
PARIS CEDEX 16
FR
|
Family ID: |
41119851 |
Appl. No.: |
13/055909 |
Filed: |
July 20, 2009 |
PCT Filed: |
July 20, 2009 |
PCT NO: |
PCT/IB2009/006288 |
371 Date: |
July 18, 2011 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
|
61083620 |
Jul 25, 2008 |
|
|
|
Current U.S.
Class: |
356/454 ;
356/450; 356/451 |
Current CPC
Class: |
G01J 3/453 20130101 |
Class at
Publication: |
356/454 ;
356/450; 356/451 |
International
Class: |
G01J 3/45 20060101
G01J003/45; G01B 9/02 20060101 G01B009/02 |
Claims
1. An interferometer comprising: a first frequency comb generator a
second frequency comb generator adapted to interact with the first
frequency comb generator in order to produce interferences; wherein
the interferometer comprises means for isolating a first single
line of the first frequency comb and a second single line of the
second frequency comb and beating means for generating at least one
beating signal from the first single line and the second single
line, measuring means adapted to trigger data acquisition of said
interferences on the beating signal.
2. An interferometer according to claim 1 further comprising a
first external optical reference generator and a second external
optical reference generator, wherein the beating means are adapted
to generate a first beating signal of the first single line and the
first external optical reference and a second beating signal of the
second single line and the second external optical reference.
3. An interferometer according to claim 1 wherein the beating means
are adapted to generate a beating signal of the first single line
and the second single line.
4. An interferometer according to claim 1 wherein the isolating
means comprise an optical filter and/or a Fiber Bragg grating
and/or a Fabry-Perot etalon and/or an electronic filtering.
5. An interferometer according to claim 1, wherein the isolating
means comprise a continuous wave laser adapted to beat with the
first frequency comb generator and the second frequency comb
generator.
6. (canceled)
7. An interferometer according to claim 1 wherein the measuring
means are adapted to use the beating signal as a clock for data
acquisition of said interferences.
8. An interferometer according to claim 1 having two outputs (A,
B), and means for differentially measuring the two outputs.
9. A spectroscopic device for measuring the spectrum of a sample,
the device comprising an interferometer comprising: a first
frequency comb generator a second frequency comb generator adapted
to interact with the first frequency comb generator in order to
produce interferences; wherein the interferometer comprises means
for isolating a first single line of the first frequency comb and a
second single line of the second frequency comb and beating means
for generating at least one beating signal from the first single
line and the second single line, measuring means adapted to trigger
data acquisition of said interferences on the beating signal,
wherein at least one of said first frequency comb generator and
said second frequency comb generator are adapted to interact with
the sample.
10. A spectroscopic device according to claim 8 wherein only one of
said first frequency comb generator and said second frequency comb
generator is adapted to interact with the sample.
11. A spectroscopic device according to claim 8 wherein said first
frequency comb generator and said second frequency comb generator
are adapted to interact with the sample.
Description
PRIORITY CLAIM
[0001] The present application is a national phase application
filed pursuant to 35 USC .sctn.371 of International Patent
Application Serial No. PCT/IB2009/006288, filed Jul. 20, 2009;
which further claims the benefit of U.S. Provisional Patent
Application Ser. No. 61/083,620 filed Jul. 25, 2008; all of the
foregoing applications are incorporated herein by reference in
their entireties.
RELATED APPLICATION DATA
[0002] This application is related to U.S. patent application Ser.
No. ______, entitled FOURIER TRANSFORM SPECTROMETER WITH A
FREQUENCY COMB LIGHT SOURCE (Attorney Docket No.: 2931-002-03)
filed ______, and which is incorporated herein by reference in its
entirety.
TECHNICAL FIELD
[0003] An embodiment relates to the field of interferometers. It is
directed to an interferometer and to a method for measuring
interferences in such an interferometer.
SUMMARY
[0004] An embodiment is more particularly directed to an
interferometer comprising:
1) a first frequency comb 2) a second frequency comb adapted to
interact with the first frequency comb in order to produce
interferences. 3) means for isolating the beating signal between a
subset of frequency components among the frequency components of
the two combs. This subset of frequency components is preferably
but not necessarily a single line of the first frequency comb and a
single line of the second frequency comb. 4) means for monitoring
this beating signal and using it as a trigger or as a clock for the
device recording the beating interference signal between the entire
frequency components of the first and the second frequency
combs.
[0005] An embodiment therefore provides an improved interferometer
with a triggering scheme based on the monitoring of the fringes
variation. The synchronization method described herein is based on
the determination of the beating frequency for a narrowband part of
the two combs and the use of its knowledge in a trigger or clock
scheme that allows to sample the interferometric signal with a new
grid, independently of the combs instabilities versus time.
[0006] According to an embodiment, there is provided an
interferometric method for analyzing a sample having spectroscopic
absorption and dispersion signatures. The interferometric method
comprises:
1) a first frequency comb which probes the sample under study 2) a
second frequency comb adapted to interact with the first frequency
comb in order to produce interferences. This second comb may or may
not be probing the sample. 3) means for isolating the beating
signal between a subset of frequency components among the frequency
components of the two combs. This subset of frequency components is
preferably but not necessarily a single line of the first frequency
comb and a single line of the second frequency comb. 4) means for
monitoring, as a function of time, this beating signal and using it
as a trigger or as a clock for the device recording the beating
interference signal between the entire frequency components of the
first and the second frequency combs. 5) means for recording the
beating interference signal between the entire frequency components
of the first and the second frequency combs using the signal
described in 4) as a clock or as a trigger.
[0007] An optical Frequency Comb (FC) is an optical spectrum, which
consists of phase-coherent equidistant laser lines. Frequency combs
are well known in the art, for example from the patents "Generation
of stabilized, ultra-short light pulses and the use thereof for
synthesizing optical frequencies" R. Holzwarth, J. Reichert, T.
Udem, T. W. Hansch, U.S. Pat. No. 6,785,303, 2004 or "Method and
device for producing radio frequency waves", R. Holzwarth, T. Udem,
T. W. Hansch, U.S. Pat. No. 7,026,594, 2006 or the publication
Optical frequency metrology" T. Udem, R. Holzwarth, T. W. Hansch
Nature 416, 233 (2002), which are incorporated by reference, and
are most often used in frequency metrology.
[0008] Interferometers based on two frequency combs are also well
known in the art, for example from the publications "Time-Domain
mid-infrared frequency comb spectrometer", Keilmann et al, Opt
Lett. 29, 1542-1544 (2004), or "Spectrometry with frequency combs",
Schiller, S. Opt. Lett. 27, 766-768 (2002), which are incorporated
by reference. In these systems, the time-domain interference
pattern between the two similar frequency combs with slightly
different repetition rates is recorded. The key is to make a down
conversion of the optical frequencies characterizing the spectrum
of interest so to allow practical measurements. A single detector
may be used to record, generally as a function of time, the data
called interferogram. This interferogram may be Fourier transformed
for spectroscopic purpose's. As this interferometer does not
involve moving parts, it may lead to very fast acquisition
times.
[0009] If the first comb is expressed as:
f.sub.01+nf.sub.rep1
and the second comb is expressed as:
f.sub.02+nf.sub.rep2
with f.sub.01 and f.sub.02 being the respective offsets of the
first and second frequency combs and f.sub.rep1 and f.sub.rep2 the
respective repetition rates of the first and second frequency combs
and n an integer typically ranging between 10.sup.5 and 10.sup.6,
their beating signal is as follows:
I ( t ) = n A n cos ( ( f 01 - f 02 + n ( f rep 1 - f rep 2 ) ) t )
##EQU00001##
and only depends on the differences between combs repetition rates
and offsets, which are required to be constant at the time scale of
a recording sequence.
[0010] The optical frequency down conversion is obtained from the
interference between two similar FC. The two combs are named
hereafter by FC1 and FC2. They have slightly different repetition
rate frequencies f.sub.rep1 and f.sub.rep2 related to each other
by
f.sub.rep1=f.sub.rep2(1+a);0<a<<1
The beating difference frequency b.sub.n between the respective
comb components f.sub.1,n and f.sub.2,n, is given by
b.sub.n=f.sub.1,n-f.sub.2,n=anf.sub.rep2+(f.sub.01-f.sub.02)
which shows that a is the down conversion factor. In other words,
the beat notes between pairs of lines from the two combs, which
occur typically in the radio-frequency domain, provide a
down-converted image of the optical spectrum. To avoid aliasing, a
must be chosen such as a<f.sub.rep2/2. This is however more than
three orders of magnitude higher than the down-conversion factors
induced by a moving mirror. Additionally, due to heterodyne
detection of coherent signals in the radio-frequency domain, very
weak signals may be detected with efficient technical noise
rejection and co-additions are not necessary, unlike with an
incoherent light source. This approach is multiplex and enables the
simultaneous analysis of an extended spectral domain with a single
detector. With the benefit of a much reduced measurement time when
compared to sequential or multichannel methods, the multiplex
approach has the unique advantage of extended spectral domains
observation.
[0011] However, these known systems do not take into account the
residual instabilities of the two combs. Even when the combs are
locked, the parameters f.sub.rep1, f.sub.rep2. f.sub.01, f.sub.02
encounter, on short time scales (few .mu.s or longer), slight
fluctuations, which may be lower than one part in 10.sup.6. Because
of these residual instabilities, the difference between the
repetition, rates of the two combs may vary, thus leading to errors
in the interference pattern sampling. Such interferometers indeed
require to keep a f.sub.rep2 and (f.sub.01-f.sub.02) constant
during the time of a measurement with a very high level of
constraint on the stability of the repetition rates of both
frequency combs and on the stability of the carrier-envelope offset
frequencies, when applicable. In other words, the relative
coherence between the two independent comb sources must be forced
within the time of a measurement, which may be very short. This
constraint is stringent and prevents the practical implementation
of the method with simple means. Using state-of-the-art reference
cavities to lock the combs, as shown in I. Coddington, W. C. Swann
and N. R. Newbury, "Coherent multiheterodyne spectroscopy using
stabilized optical frequency combs", Physical Review Letters 100,
013902 (2008), which is incorporated by reference, excellent
results may be obtained, but such systems require an extensive
knowledge of the most modern and expensive tools of frequency
metrology and cannot be used in a standard spectroscopy laboratory,
in the industry or in field measurements. This stability constraint
on the difference in repetition rates and carrier-envelop offsets
of the two combs is different from those of Fourier Transform
Spectroscopy (FTS) with a Michelson interferometer, where the
Doppler-shifted replica of a comb source is produced by appropriate
control of the moving mirror of the interferometer, independently
of the comb stability. It also differs from the use that is made of
frequency combs in metrology, where the phase-coherence of the comb
with a radio-frequency or optical clock is needed on long time
scales (several seconds).
[0012] An embodiment is an improved interferometer, based on two
frequency combs, accounting for the instabilities of the combs. In
other words, an embodiment of a proposed device and method enable
measurement of the interferences between two frequency combs where
at least one comb has its line positions which are varying as a
function of time. An embodiment allows monitoring the variations in
the mapping between the two frequency combs in order to overcome
the accuracy and measurement time limitations of the prior art.
Constraints on frequency comb stability are consequently
reduced.
[0013] According to an embodiment, the interferometer
comprises:
[0014] a first frequency comb generator;
[0015] a second frequency comb generator adapted to interact with
the first frequency comb signal in order to produce interferences;
and
[0016] a system serving as a clock synchronized on the combs
instabilities or enabling to trigger the sampling of the
interference process.
[0017] An embodiment also relates to Frequency Comb Fourier
Transform Spectroscopy (FC-FTS) and is directed to a spectroscopic
device for measuring the spectrum of a sample, at least one of said
first frequency comb generator and said second frequency comb
generator being adapted to interact with the sample.
BRIEF DESCRIPTION OF THE DRAWINGS
[0018] One or more embodiments will be set forth in detail with
reference to the drawings in which:
[0019] FIG. 1 shows a schematic view of a frequency comb
interferometer adapted in an absorption spectrometer for Fourier
transform spectroscopy;
[0020] FIG. 2 comprises FIG. 2A and FIG. 2B which are plots
respectively showing an example of two optical frequency comb
spectra and the corresponding beating spectrum of an example
frequency comb sources;
[0021] FIG. 3 shows a conceptual view of a system enabling to
trigger the data acquisition according to an embodiment;
[0022] FIG. 4 shows a conceptual view of a system serving as a
clock for the data acquisition according to an embodiment;
[0023] FIG. 5 shows a detailed embodiment of an interferometer,
where the spectral filtering of the combs synchronization beating
signal is performed with the aid of a cw laser;
[0024] FIG. 6 shows a distorted spectrum that is typically obtained
without applying an embodiment;
[0025] FIG. 7 shows a block diagram illustrating an interferometric
system using the synchronization method according to an embodiment,
particularly according to an embodiment of the principle of FIG.
4;
[0026] FIG. 8 shows a distortion-free spectrum recorded using the
interferometric system of FIG. 7;
[0027] FIG. 9 shows a detailed embodiment of an interferometer,
where the spectral filtering of the combs synchronization beating
signal is performed with passive filters;
[0028] FIG. 10 comprises FIG. 10A, FIG. 10B and FIG. 10C which are
plots respectively showing an example of the optical layout for
using the interferometer of an embodiment as a spectrometer probing
absorption and/or dispersion of a sample.
[0029] FIG. 11 shows an interferogram obtained with an
interferometer.
[0030] FIG. 12 illustrates an embodiment of a interferometer with
differential measurements;
[0031] FIG. 13 comprises FIG. 13A, FIG. 13B, FIG. 13C and FIG. 13D
and illustrates an embodiment for velocity modulation;
[0032] FIG. 14 illustrates an embodiment for Zeeman
spectroscopy;
[0033] FIG. 15 illustrates an embodiment with polarization
modulation.
DETAILED DESCRIPTION
[0034] One or more embodiments will be set forth in detail with
reference to the drawings, in which like reference numeral refers
to like elements throughout. The herein presented interferometer
with synchronization technique is best understood considering the
illustrative example of frequency comb Fourier Transform
Spectroscopy and all related instrumental methodologies
(hyperspectral imaging, microscopy, vibrational circular dichroism,
attenuated total reflection, Zeeman modulation, velocity
modulation, selective detection techniques, time-resolved
spectroscopy . . . ), but it is noted that the interferometer with
synchronization technique may also be used beyond the herein
described applications. For example, the herein described
interferometer with synchronization technique may be adapted to be
used in Optical Coherence Tomography (OCT), interferometric length
measurements, Light Detection And Ranging (LIDAR), reflectometry,
linear optical sampling, cross-correlation measurements between
electrical fields. Other interferometric applications, based on
wavefront or amplitude recombination, not specifically described
herein may also benefit from the synchronization technique.
[0035] As known in the art, a frequency comb is a spectral source
made of laser monochromatic emission lines regularly spaced over a
spectral range. Most often, femtosecond lasers are used, leading to
a femtosecond frequency comb (FFC). Alternatively, the combs may be
produced by four-wave mixing in appropriate material, including
toroidal microresonators or optical fibers. The combs may be also
produced by a phase-modulated electro-optic device.
[0036] Summarizing, when using a mode-locked laser, ultra short
pulses are periodically emitted by the mode-locked laser with a
time period T=l/v.sub.g where l is the length of the laser cavity
and v.sub.g is the net group velocity. Due to dispersion in the
cavity, the group and phase velocities differ, resulting in a phase
shift of the carrier with respect to the peak of the envelope of
each pulse. In the frequency domain the spectrum, Fourier transform
of the train of periodic pulses, is made of a comb of laser modes,
which are separated by the pulse repetition frequency f.sub.rep.
The modes frequencies obey the relation:
f.sub.n=nf.sub.rep+f.sub.0, with n integer and f.sub.0 due to
carrier-envelop pulse-to-pulse phase-shift. Presently the output
spectrum of the comb may span more than one octave and the best
level of stabilization of f.sub.rep and f.sub.0 is such that there
is no deviation from a perfect grid larger than one part in
10.sup.19.
[0037] In other words, a frequency comb is an optical spectrum
which consists of equidistant lines. The generation of a frequency
comb from a mode-locked laser requires that the periodicity applies
not only to the pulse envelopes, but to the whole electric field of
the pulses, including their optical phase, apart from a constant
phase. Coherence between the pulses is therefore required.
[0038] As shown in FIG. 1 and known per se, a specific layout of an
interferometer 1 comprises a frequency comb "Frequency Comb 1" and
a frequency comb "Frequency Comb 2". "Frequency Comb 1" probes a
sample contained in a cell 100. The interferences that are
generated from the recombination on a beam-splitter 101 of the
frequency combs "Frequency Comb 1" and "Frequency Comb 1" are
measured by a detector 102 and an interferogram is measured at a
computer 103. The beat notes between pairs of lines from two combs
having slightly different repetition rates, which occur in the
radio-frequency domain, provide a down-converted image of the
optical spectrum.
[0039] Note that the interferometer does not necessarily probe a
sample 100, and that the sample 100, if present, may interact with
both combs. Wavefront recombination instead of amplitude
recombination may also be used. In such case, the beam-splitter 101
is not needed.
[0040] According to an embodiment, the frequency combs FC1 and FC2
have slightly different repetition rate frequencies f.sub.rep1 and
f.sub.rep2 related to each other by
f.sub.rep1=f.sub.rep2(1+a);0<a>>1
[0041] According to an embodiment, frequency combs FC1 and FC2 may
be generated by femtosecond mode-locked lasers with repetition
rates and carrier-envelop offset stabilized or free-running. The
mode-locked laser may be broadened by a non-linear optical fiber
and it may be coupled to a frequency conversion system such as
difference/sum frequency generation, harmonic generation and/or
parametric interaction. Frequency combs FC1 and FC2 may also be
generated by four-wave mixing effect or by an electro-optic
modulator seeded by a continuous wave laser.
[0042] The spectrometer according to an embodiment comprises an
interferometer 1 on FIG. 1 as described above. The spectrum of each
laser (as shown in FIG. 2A), numbered 1 or 2, is a comb of laser
modes f.sub.n,i separated by the pulse repetition frequency
f.sub.rep,i:
f.sub.n,i=f.sub.0,i+nf.sub.rep,i
where i=1 or 2, integer n typically in the range of 10.sup.5 to
10.sup.6, and f.sub.0,i is the carrier-envelope offset frequency,
induced by the difference between the group and phase velocities of
the pulses in the laser cavities, in the case of a frequency comb
based on a mode-locked laser. Repetition frequencies are generally
in the radio-frequency domain (in the present example they are
close to 100 MHz with f.sub.rep,1-f.sub.rep,2 ranging from 10 Hz to
20 kHz, depending on the free spectral range). One laser probes
(FIG. 1) the absorbing sample and both beams are combined on a
beam-mixer. Their beating signal I, recorded on a fast
photodetector, is amplified and sampled using a high-resolution
digitizer on a personal computer.
[0043] The beating difference frequency b.sub.n between the
respective comb components f.sub.1,n and f.sub.2,n, as shown in
FIG. 2B, is given by
b.sub.n=f.sub.1,n-f.sub.2,n=naf.sub.rep2+(f.sub.01-f.sub.02)
which shows that a is the down conversion factor.
[0044] The interferogram which is recorded on the photodetector may
therefore be written as:
I ( t ) = n A n cos ( ( f 0 , 1 - f 0 , 2 + n ( f rep , 1 - f rep ,
2 ) ) t ) ##EQU00002##
where A.sub.n is the product of the amplitude of the electric
fields of the two lasers, attenuated by sample absorption.
Similarly to what happens with a Michelson interferometer, the
frequencies of the optical spectrum
f.sub.n,i=f.sub.0,i+nf.sub.rep,i are down-converted to
f.sub.0,1,-f.sub.0,2+n(f.sub.rep,1,-f.sub.rep,2) However, thanks to
the absence of moving parts, the down-conversion, limited by
aliasing, may lead to the radio-frequency domain between 0 and
f.sub.rep,i/2, and not to the audio-range like in Michelson-based
FTS. This may result in a drastic reduction of the recording time.
The signal I(t) is then Fourier-transformed to reveal the spectrum;
the longer the measurement time, the better the optical resolution.
The interferometric signal exhibits a periodic succession of huge
bursts occurring every 1/.delta.=1/(f.sub.rep,1-f.sub.rep,2) when
femtosecond pulses from the two lasers coincide.
Fourier-transforming a temporal sequence including more than two
such bursts resolves the comb lines. As the combs parameters
(f.sub.rep1, f.sub.rep2, f.sub.01, f.sub.02) may be
straightforwardly measured with radio-frequency counters, the
optical absolute frequency scale may be easily retrieved
afterwards. It may also be possible to use known molecular or
atomic lines present in the spectrum to rescale the optical
frequency axis.
[0045] During the time of the measurement of the beating signals
(which may be as short as a few microseconds), at least one
parameter of one of the combs (f.sub.rep1, f.sub.rep2, f.sub.01,
f.sub.02) may be slightly fluctuating as a function of time. In
other words, b.sub.n is a function of time. FIG. 2B therefore only
provides therefore an instantaneous image of the down-converted
spectrum. In practice, the fluctuations of the repetition rates
(f.sub.rep1, f.sub.rep2) of the combs may be much more troublesome
than the fluctuations of the carrier-envelop offset frequencies
(f.sub.01, f.sub.02) because the fluctuations on the repetition
rates are amplified by the harmonic index n. Therefore, sampling
the interferogram at constant time intervals may lead to distorted
information.
[0046] An embodiment provides a simple way of sampling the
interferogram in a manner that is synchronous to the most
troublesome comb fluctuations. An embodiment of a new sampling grid
is provided. The idea consists in isolating the beating signal
between two individual lines from the interfering combs and to use
the resulting signal, which is a sine wave if the line positions of
the combs are fluctuating in a negligible manner, as a trigger
(FIG. 3 in the special example embodiment where the zero crossings
of the synchronization beating signals are used as a trigger) or as
a clock (FIG. 4) for the sampling process of the interferometric
signal between the two entire combs. If the comb lines are not
isolated well enough, i.e. if the synchronization beating signal
consists in the beat note of more than one couple of lines, the
synchronization process still works but maybe within a more limited
time sequence, i.e. with a more limited resolution for Fourier
transform spectroscopy.
[0047] According to an embodiment shown in FIG. 5, the
synchronization device consists first in isolating a single line
from each comb. A part of the optical signal delivered by
"frequency comb 1" is sent to a fast photo-detector 501 with the
aid of a beam-splitter, while most of the signal is used for the
interferometric measurements (some examples are described
hereafter). The beam of a continuous-wave laser 503 falls also on
the same detector 501. The continuous wave laser 503 emits at the
frequency f.sub.cw in the same spectral region as the combs. It may
be locked to a reference or free-running and its spectral purity,
as well as its frequency stability, mainly determines the maximum
sampling duration of the interferometric measurement. The beating
signal between the frequency comb 1 and the cw laser is a comb of
down-converted modes lying partly in the radio-frequency and
microwave domains. With proper choice of the photodetector 501
bandwidth and further electronic filtering 502, the beating signal
between a single comb line and the cw laser, which may be written
(n f.sub.rep1+f.sub.01-f.sub.cw), may be isolated. The same
procedure is applied to the frequency comb 2, with photodetector
504 and electronic filter 505, in order to isolate the electric
beating signal of a single line of the frequency comb 2 with the
same cw laser 503, (m f.sub.rep2+f.sub.02-f.sub.cw). The two
beating signals, obtained as described herein, are mixed with an
electronic mixer 506 in order to suppress the contribution of the
cw laser and to provide the clock beating signal between the two
comb lines (n f.sub.rep1+f.sub.01-f.sub.rep2-f.sub.02). n and m may
be chosen so that (n f.sub.rep,1+f.sub.01-m f.sub.rep2-f.sub.02) is
greater than the sampling frequency imposed by the Nyquist
criterion which is Max(f.sub.rep1,f.sub.rep2). Special markers (for
instance but not mandatorily the zero-crossings) of this sine wave
which has a period varying with time are used to trigger the data
acquisition of the interferometric signal on an acquisition unit
508. The interfero metric signal comes from the beating signal
between the entire (or filtered parts) spectra of frequency combs 1
and 2. It is measured on a fast photodetector 507 and monitored on
the acquisition unit 508. Electronic filters and amplifiers may be
inserted between 507 and 508 to improve the signal to noise ratio.
Alternatively, as shown also in FIG. 5, this (n
f.sub.rep,1+f.sub.01-f.sub.rep2-f.sub.02) frequency signal may
serve as a clock to the acquisition unit 508. The acquisition unit
508 may be for instance a high speed digitizer onboard a personal
computer. The data points are then for instance stored on the hard
drive of the computer or are coded on a field-programmable gate
array or are directly Fourier-transformed before storage.
[0048] According to a specific example of an embodiment aimed at
Fourier spectroscopy of an absorbing sample, two Er-doped fiber
lasers emit pulses at a repetition rate around 100 MHz and 20 mW
output power. The difference between the repetition rate of the two
combs is set to a value equal to 150 Hz. The repetition rate of
each comb is stabilized to a quartz oscillator and the
carrier-envelop offset of each comb is not stabilized. The two
combs are recombined with a 50-50 beam-mixer and the two outputs of
the interferometer are measured to improved measurement dynamics,
as explained below. The signal is amplified and digitized with
home-made electronics and acquisition systems. FIG. 6 shows the
spectrum which is obtained without using an embodiment. The lines
are strongly distorted by a phase error. A free-running continuous
wave Er-doped fiber laser emitting at 1557.4 nm beats with each of
the frequency combs, following to the principle displayed in FIG.
5, according to the detailed scheme shown in FIG. 7. In FIG. 7, the
cw Er-doped fiber laser is optically isolated and its beam is split
into two parts with the aid of a 50/50 fiber coupler. A part of the
beam at the output of frequency comb 1 probes a sample consisting
of acetylene in gas phase. It beats on a detector with a part of
the beam at the output of frequency comb 2 and the beating signal
is monitored using an acquisition unit, which may consist of a
digitizer and proper electronics for filtering and amplifying the
interferometric signal. Another part of the beam of frequency comb
1 is directed into a beat detection unit where its lines beat with
the beam from the cw laser. A beat detection unit is a means to
measure the radio-frequency or microwave beating signal between two
optical beams. It consists in a fast photodetector and for instance
optics to balance, polarize, filter one or both optical beams and
electronics to filter the produced electrical signal. At the output
of this beat detection unit, an electrical signal at a frequency of
42 MHz corresponding to the beat note between a single line of
frequency comb 1 and the cw laser is produced, filtered and
amplified and directed towards a mixer. In a similar manner, the
beating signal between one line of frequency comb 2 and the cw
laser is produced at a frequency of 118 MHz and is directed towards
the second input of the mixer. A beating signal between two
individual lines from each comb is consequently delivered at the
output of the mixer at a frequency of 76 MHz. It is filtered and
amplified and used as a clock for the sampling of the
interferometric signal using the acquisition unit. FIG. 8 shows the
spectrum which was measured when using this 76 MHz signal as a
clock for the 16-bit 180 MSamples/s digitizer used as an
acquisition unit. Little or no distortion is noticeable on the
spectrum of FIG. 8.
[0049] Alternative configurations may be utilized to produce the
clock beating signal between the two combs. For instance, an
embodiment may be relying on optical filtering, instead of using a
cw laser in the synchronization scheme. As shown in FIG. 9, each
comb may be frequency filtered with optical filters or fiber Bragg
gratings or Fabry-Perot cavities or any combination of these items.
The two filtered combs beat on a fast photodiode. After proper
electronic filtering, the clock beating signal (n
f.sub.rep1+f.sub.01-m f.sub.rep2-f.sub.02) is used as a clock or a
trigger for the acquisition unit.
[0050] Further embodiments are described below. These embodiments
may be used in combination with the aforementioned embodiments of
the interferometer or may be used as such.
[0051] The aforementioned embodiments may be used according to a
specific example embodiment aimed at Frequency Comb Fourier
transform spectroscopy of an absorbing sample. Several optical
configurations may be implemented, as illustrated in FIG. 10. In
FIG. 10A, only frequency comb FC1 interacts with the sample 1000.
The sample 1000 may be directly probed or it may be inserted inside
a single pass cell, or inside a multipass cell, or inside a high
finesse cavity that is resonant to the comb FC1. The two beams from
combs FC1 and FC2 are recombined on a beam combiner. One or both
outputs of the beam combiner may be used to measure the
interferometric signal on fast photodetectors. The detectors may
consist of simple photodetectors (photodiode, bolometer, antenna)
or non-linear frequency converters, e.g. frequency doubling
devices, coupled to photodetectors. The detectors may be
microphones. In FIG. 10B, both frequency combs FC1 and FC2 interact
with the sample 1000. For simultaneous absorption and dispersion
measurements, the optical layout of the interferometer may be
implemented as displayed in FIG. 10C. Two frequency combs, FC1 and
FC2, have slightly different line spacing. One of these combs, FC1,
is transmitted through the cell and heterodyned against the second
comb, yielding a down-converted radio-frequency comb containing
information on the absorption and dispersion experienced by each
line of the comb FC1. Appropriate optics transmits the combs beams
to two interferometers. The interferometer probing the sample
contains the cell and leads to the sample interferogram I.sub.1(t)
while the interferometer serving as a reference without the sample
provides the normalization interferogram (I.sub.2(t)). The two
interferograms (with and without sample) are measured
simultaneously and computed with a complex Fourier transform. The
phase and module of the complex ratio of these two spectra give
respectively the phase-shift and attenuation imposed on the
detected radiation by the sample, providing access to the full
characterization of the optical constants of the medium, its
refractive index and absorption coefficient. Alternatively, the
difference between the two interferograms I.sub.1(t) and I.sub.2(t)
may be measured directly with an appropriate differential amplifier
before digitization. In such case, only the interferogram of the
spectral signatures of the sample are measured, with an improved
signal to noise ratio.
[0052] The frequency combs interact with a sample and experience
attenuation and phase-shift due to absorption and dispersion. This
interaction may be written as
exp(-.delta.{.omega.)-i.phi.(.omega.)) where .delta. is the
amplitude attenuation and .phi. is the phase shift. The following
convention is adopted: .delta..sub.i,n and .phi..sub.i,n denotes
the respective components experienced by the comb i(i=1 or 2) at
the frequency f.sub.0,i+n f.sub.rep,i. As illustrated in FIG. 10A,
only comb FC1 interacts with the sample 1000. The expression of the
interferogram I contains the following interesting terms:
I ( t ) n ( - .delta. 1 , n [ cos ( 2 .pi. ( ( f 0 , 1 - f 0 , 2 )
+ anf rep 2 ) t ) cos .PHI. 1 , n + sin ( 2 .pi. ( ( f 0 , 1 - f 0
, 2 ) + anf rep 2 ) t ) sin .PHI. 1 , n ] + 2 - .delta. 1 , n cos (
2 .pi. f rep 2 t ) [ cos ( 2 .pi. ( ( f 0 , 1 - f 0 , 2 ) + anf rep
2 ) t ) cos ( .PHI. 1 , n ) + sin ( 2 .pi. ( ( f 0 , 1 - f 0 , 2 )
+ anf rep 2 ) t ) sin ( .PHI. 1 , n ) ] ) ( 1 ) ##EQU00003##
[0053] The first term of Eq. (1) tells that the spectral
information at frequency f.sub.0,1+n f.sub.rep,1 is down-converted
at frequency ((f.sub.0,1-f.sub.0,2)+anf.sub.rep2). The
interferogram is similar to an interferogram from classical FTS.
Making a synchronous detection of the signal at frequency
f.sub.rep,2 is not interesting, as it does not bring additional
information.
[0054] Both combs FC1 and FC2 may also interact with the sample
1000 as shown in FIG. 10B. The expression of the interferogram
contains the following interesting terms:
I ( t ) n ? ( cos ( 2 .pi. ( ( f c 1 - f c 2 ) + ? ) t ) cos (
.PHI. 1 , n - .PHI. 2 , n ) + sin ( 2 .pi. ( ( f c 1 - f c 2 ) + ?
) ? ) sin ( .PHI. 1 , n - .PHI. 2 , n ) ) + ? { cos ( 2 .pi. f rep
2 t ) { cos ( 2 .pi. ( ( f c 1 - f c 2 ) + a ( n - 1 ) f rep 2 ) t
) cos ( ? - ? ) + sin ( 2 .pi. ( ( f c 1 - f c 2 ) + a ( n - 1 ) f
rep 2 ) t ) sin ( ? - ? ) } + sin ( 2 .pi. f rep 2 t ) { sin ( 2
.pi. ( ( f c 1 - f c 2 ) + a ( n - 1 ) f rep 2 ) t ) cos ( ? - ? )
- cos ( 2 .pi. ( ( f c 1 - f c 2 ) + a ( n - 1 ) f rep 2 ) t ) sin
( ? - ? ) } } + ? { cos ( 2 .pi. f rep 2 t ) { cos ( 2 .pi. ( ( f c
1 - f c 2 ) - an f rep 2 ) t ) cos ( ? - ? ) - sin ( 2 .pi. ( ( f c
1 - f c 2 ) - an f rep 2 ) t ) sin ( ? - ? ) } - sin ( 2 .pi. f rep
2 t ) { sin ( 2 .pi. ( ( f c 1 - f c 2 ) - an f rep 2 ) t ) cos ( ?
- ? ) + cos ( 2 .pi. ( ( f c 1 - f c 2 ) - an f rep 2 ) t ) sin ( ?
- ? ) } } + ? { cos ( 2 .pi. f rep 2 t ) { cos ( 2 .pi. ( ( f c 1 -
f c 2 ) + an f rep 2 ) t ) cos ( ? - ? ) + sin ( 2 .pi. ( ( f c 1 -
f c 2 ) + an f rep 2 ) t ) sin ( ? - ? ) } + sin ( 2 .pi. f rep 2 t
) { sin ( 2 .pi. ( ( f c 1 - f c 2 ) + an f rep 2 ) t ) cos ( ? - ?
) - cos ( 2 .pi. ( ( f c 1 - f c 2 ) + an f rep 2 ) t ) sin ( ? - ?
) } } + ? { cos ( 2 .pi. f rep 2 t ) { cos ( 2 .pi. ( ( f c 1 - f c
2 ) - a ( n + 1 ) f rep 2 ) t ) cos ( ? - ? ) - sin ( 2 .pi. ( ( f
c 1 - f c 2 ) - a ( n + 1 ) f rep 2 ) t ) sin ( ? - ? ) } - sin ( 2
.pi. f rep t ) { sin ( 2 .pi. ( ( f c 1 - f c 2 ) - a ( n + 1 ) f
rep 2 ) t ) cos ( ? - ? ) + cos ( 2 .pi. ( ( f c 1 - f c 2 ) - a (
n + 1 ) f rep 2 ) t ) sin ( ? - ? ) } } ? indicates text missing or
illegible when filed ##EQU00004##
[0055] The first line of the expression (2) is the quantity
measured by direct detection of the interferogram; without
synchronous detection. Compared with what is obtained from the
interferogram of Eq. (1), the detection is more sensitive, because
both combs FC1 and FC2 experience interaction with the sample, but
the instrumental line shape is a bit more complicated as it is
frequency dependent: as frequency grows, the difference between the
frequencies of the two combs increases. Also, synchronous detection
at f.sub.rep,2 frequency is interesting since the absorption and
dispersion may be retrieved thanks to in-phase and in-quadrature
detections.
[0056] Any interferogram may present a ratio of about 10.sup.6
between its highest and smallest samples. An important decrease of
the interferometric signal as a function of time is illustrated
with the interferogram shown in FIG. 11. As a consequence, one of
the main difficulties associated with Fourier transform
spectroscopy, in particular--but not only--at high spectral
resolution, is due to the limited dynamic range of the
measurements. In Frequency comb Fourier Transform Spectroscopy, the
dc component I.sub.0 is no more a constant but becomes a function
I.sub.0(t) of time t, linked to the Fourier components of the pulse
repetition rates. Therefore it is difficult to satisfactorily
eliminate it by electronic filtering, since this could seriously
degrade the sampling. A technical consideration of importance is
that, nowadays, the most performing fast acquisition board offers a
limited dynamic range of 16 bits, i.e. of 65538 different levels of
measurement, which essentially characterize the ADC converters. As
a consequence, the recording procedure may be unable to make direct
use of a commercial product.
[0057] A specific example embodiment provides a dynamic range
solution that is a combination of several points. Fast Detector
signals I.sub.A and I.sub.B delivered, as shown on FIG. 12, at two
outputs A and B of the interferometer are balanced and subtracted
so to remove the unmodulated background, and to obtain only the
modulated part of the interferogram. In practice, two electronic
gains G.sub.A and G.sub.B, respectively applied to I.sub.A and
I.sub.B, are determined before the experiment, by minimizing the
difference signal (G.sub.AI.sub.A-G.sub.BI.sub.B). These gains are
fixed within an experiment. Different electronic gains G.sub.T are
applied to the difference signal, depending on time to adapt at
best the interferometric signal to the maximum input value of the
acquisition unit.
[0058] The gain may be switched in real time or several recording
channels may be used for a posteriori selection. Alternatively the
gain change is made in a predetermined manner by computer program.
In this latter case, the best measured sample is chosen a
posteriori, by computer program, and the final value
G.sub.T(G.sub.AI.sub.A-G.sub.BI.sub.B) is normalized to give back
the whole interferogram, well measured. Synchronous detection may
be performed before digitalization as discussed below.
[0059] According to a specific embodiment, the signal measured by
the two receivers, A and B, is synchronously detected at the
frequency repetition rate f.sub.rep. Since f.sub.rep lies typically
in the radio-frequency range 0.1-5 GHz, the time-domain method
reduces considerably the technical noise when compared to the
presently best commercial interferometers detecting interferograms
at audio frequencies around 20 kHz. Additionally, absorption and
dispersion parameters are given at once from the Fourier Transform
of the in-phase and in-quadrature radio-frequency signals, as it
may be seen from Eq (2). An embodiment is similar to
frequency-modulation spectroscopy with tunable lasers. It has the
additional benefits of broadband coverage, optimal modulation index
and no need of external modulation.
[0060] An embodiment may also be adapted to selective-spectroscopy
methodologies as described below.
[0061] Firstly, velocity modulation is intended to selectively
detect the transitions of atomic or molecular ions. With FC-FTS,
different schemes may be implemented as illustrated in FIG. 13.
FIG. 13A and FIG. 13B make use of a dc discharge 1300. Neutral
species are insensitive to the electric field, while due to the
electric field, ions acquire a net drift velocity. The effect of
this velocity is that the frequencies of the transitions of the
ions are Doppler-shifted. Each comb, as in FIG. 13A, or only one of
them, as in FIG. 13B, may be split into two counter propagating
beams in order to form two interferometers. Difference between the
two resulting interferograms or spectra, which may be made by
differential detection as shown in FIG. 13A and FIG. 13B (where the
two output of the two interferometers, respectively S1 and S2, and
S3 and S4, are used according to an embodiment) or a posteriori,
brings the selective information, as in one spectrum all the ion
frequencies are blue shifted and in the other red shifted. All
neutral signals and systematic errors are suppressed from the
spectra, leaving only the two Doppler-shifted components of the ion
transitions.
[0062] The FIG. 13C and FIG. 13D exploit an ac modulated discharge
1301 to acquire two interferograms with opposite Doppler shifts at
a frequency rate depending on the discharge modulation or the
recording time of the interferogram. Synchronous detection at the
ac modulation cancels the neutral signatures. It is noted that the
double differential detection scheme shown in FIG. 13A, FIG. 13B,
FIG. 13C, FIG. 13D, may be preferable for signal to noise ratio
improvement but not mandatory. For selective detection in the
scheme of FIG. 13A or FIG. 13B, it may be for instance enough to
consider the difference between the interferograms measured at
detectors S1 and S3 (or S2 and S4) or the difference between the
resulting spectra. For selective detection in the scheme of FIG.
13C or FIG. 13 D, it may be for instance enough to consider only
the signal at detector S1 (or S2).
[0063] Secondly, Zeeman spectroscopy may be performed. In a first
scheme as illustrated in FIG. 14A, a magnetic field 1400
interacting with the source 1401 is periodically varied. After
synchronous or differential detection, only the frequency shifted
transitions by the magnetic field may be detected. However, one may
consider the symmetry of the Zeeman splitting: one may have to
modulate the field between B.sub.C+B.sub.M and B.sub.C-B.sub.M,
where B.sub.C and B.sub.M are two constants values of the magnetic
field. B.sub.C may be equal to B.sub.M but typically cannot be
zero, otherwise no signal variation will be detected.
Alternatively, as shown in FIG. 14B, the combs beams may be split
into two beams, one probing a cell 1402 with a constant magnetic
field B.sub.C+B.sub.M while the other probes a cell 1403 with a
constant magnetic field B.sub.C-B.sub.M for differential detection.
As it is the case for velocity modulation, it may be preferable but
not mandatory to use the two outputs of the interferometers to
achieve selective detection. In FIG. 14A, only the signal at
detector S1 (or S2) may be measured. In FIG. 14B, it may be for
instance enough to consider the difference between the
interferograms measured at detectors S1 and S3 (or S2 and S4) or
the difference between the resulting spectra.
[0064] Similarly to Zeeman spectroscopy, an electric field may be
applied and modulated to selectively detect transitions that are
sensitive to the Stark effect.
[0065] Thirdly, different schemes for polarization modulation FCFTS
may be implemented as illustrated in FIG. 15. As schematized in
FIG. 15A, it may be possible to use a polarization modulator 1500
on one (as illustrated in FIG. 15A with comb FC1 probing the sample
1501) or both combs FC1 and FC2 and to measure in a quick
succession one interferogram with a given polarization and one
second with the other polarization and to subtract them. As shown
in FIG. 15B, it may also be possible to split one (FC1 in FIG. 15B)
or both combs beams into two beams, with complementary polarization
provided by the polarizers 1502 and 1503. The two beams from FC1 in
FIG. 15B probe the sample 1504 and a direct differential detection
is performed, as illustrated in FIG. 15B. Alternatively two
interferograms may be acquired and subtracted a posteriori.
Polarization modulation may be useful to selectively detect
polarization-sensitive transitions. It may also be called linear
(comparison between s and p polarization) or vibrational circular
dichroism (comparison left and right circularly polarized
radiation). Some examples of the subject of studies are chiral
molecules or the orientation of molecules in thin solid films,
liquid crystals, or Zeeman transitions from paramagnetic species.
The difference between the absorption of radiation by two
polarization states is often extremely small. The idea is to
compare, in a quick succession, spectra resulting from the
interaction of the sample with light polarized in two different
states. In FIG. 15, the use of the two output of the interferometer
is a specific example embodiment. As already noted for velocity and
Zeeman modulations, a single detector S1 or S2 in the configuration
of FIG. 15A may be used. In FIG. 15B, it may be for instance enough
to consider the difference between the interferograms measured at
detectors S1 and S3 (or S2 and S4) or the difference between the
resulting spectra.
[0066] An embodiment may also be adapted to time-resolved
applications as described below. In conventional spectroscopy,
time-resolved FTS has been a powerful tool to investigate dynamic
phenomena, with all the well-known advantages of FTS, especially
the wide-spectral range of observation. It consists in performing a
time sampling of the evolution of the observed sample, which is
excited at every optical path-difference positions. At the end of
the experiment, as many interferograms as time samples of the
evolution of the source are obtained and transformed to give
spectra, each characterizing the light source at a given time.
However a major limitation is that the observed sample has to
behave in a well repetitive and reproducible manner.
[0067] Time-resolved FC-FTS for dynamic studies may overcome this
limitation. Various schemes may be implemented depending of the
time-resolution which is looked at. Furthermore, as acquisition
time for a high resolution spectrum is only of the order of 1
millisecond or even 1 microsecond for low resolution information, a
way to real-time broadband spectroscopy or single-event
spectroscopy is opened with an embodiment.
[0068] For time-resolutions that are worse than the time required
for measuring a full interferogram, the measurement principle is
straightforward. It consists of measuring the interferograms in
sequence. It may be possible to improve the time resolution up to a
few .mu.s by varying the repetition rate of one of the combs in
order to provoke the burst which occur when laser pulses from the
two combs overlap. This variation in the repetition rate of one of
the combs may for instance be achieved by modulating the length of
one of the laser cavity with a piezo-electric transducer. If the
source behaves in a repetitive manner, it may be possible to repeat
several times this method to improve signal-to-noise ratio.
[0069] When the time-resolution or repetition rate of the source
cannot fit the optimal sampling requirements, then specific
sampling and synchronization schemes may have to be developed. The
idea is to lower the interferogram sampling rate by adjusting the
frequency difference between the two combs so to meet the source
operating conditions.
[0070] If the desired time-resolution is higher than the sampling
step of each individual interferogram resulting from the optimal
frequency difference between the two combs and if the source of
interest has a high repetition rate, it may be possible to perform
a high frequency sampling of the time-domain interferogram and to
rearrange a posteriori the samples so to generate several
interferograms each of them characteristic of the absorption of the
source at a given time. The source may then be synchronized to the
sampling step of the first time-sample interferogram.
[0071] An embodiment may also be adapted to reflection measurements
as described below. With FC-FTS, instead of looking at the light
which is transmitted by the sample, it may be possible to look at
the light which is reflected by the sample. The sample may be a
bulk material, a layer of material (thinner or thicker than the
wavelength of the comb radiation) present on a flat reflective
surface.
[0072] Furthermore, attenuated total reflection may enable one to
probe samples in liquid or solid phase with very easy sample
preparation. A probing light beam is passed through a well chosen
crystal in such a way that it reflects at least once on the
internal surface in direct contact with the sample. This reflection
forms an evanescent wave which extends into the sample, typically
by a few micrometers. The attenuated energy from each evanescent
wave is passed back to the light beam and the beam transmitted by
the crystal is then collected by the second comb of the FT
spectrometer as it exits the crystal. Attenuated total reflection
FC-FTS may also be implemented with the two combs probing the
crystal/sample assembly.
[0073] An embodiment may also be adapted to spatially resolved
measurements as described below.
[0074] Firstly, as the section of a laser beam may be small, it may
be possible to selectively probe tiny spatial regions of a
macroscopic sample.
[0075] Secondly, an efficient way with FCFTS to map the composition
of a sample may be to measure all the FT spectra simultaneously
with an array detector. The object is imaged on the array detector
with appropriate optics. Simultaneous measurement of spectra from
each point of an image brings hyperspectral imaging.
[0076] Thirdly, microscopy with FC-FTS may bring together the
advantages of microscopy with Fourier transform spectroscopy and
microscopy with laser sources. Increase of spatial resolution may
be obtained together with accurate spectral diagnostics and
extremely short measurement times.
[0077] Fourthly, due to the low divergence and high intensity of
laser beams, FC-FTS may probe long columns of sample.
Alternatively, a laser beam may propagate into a long distance
before reaching the sample of interest. LIDAR-type FC-FTS
experiment may also be implemented: the sample-scattered light from
an intense frequency comb may be collected and analyzed with the
second comb.
[0078] From the foregoing it will be appreciated that, although
specific embodiments have been described herein for purposes of
illustration, various modifications may be made without deviating
from the spirit and scope of the disclosure. Furthermore, where an
alternative is disclosed for a particular embodiment, this
alternative may also apply to other embodiments even if not
specifically stated.
* * * * *