CZ309439B6 - Frequency comb tooth resolution Fourier spectroscopy - Google Patents

Abstract

Fourier spectroscopy uses radiation from a femtosecond optical frequency comb generator. The frequency comb radiation is coupled into the interferometer and the interferogram is detected as a series of samples of the interferometer output signal at an interval long enough to contain an interference signal corresponding to the distance or delay of at least two consecutive frequency comb pulses. The variable delay is provided either by varying the optical length of the interferometer arm(s) or by varying the repetition rate or spacing of the comb pulses. The resulting interferogram is processed by Fourier transformation.

Description

Frequency comb tooth resolution Fourier spectroscopy

Field of technology

The invention relates to the method of precise spectroscopy - measuring the optical properties of substances/environments depending on the wavelength/frequency. The properties measured in this way can then be further used, for example, for chemical or physical analysis.

Current state of the art

Fourier spectroscopy is used for accurate spectroscopic measurements in a wide spectral range and with high resolution, the dynamic range can be increased by combining different cuvette lengths or using different concentrations (gas pressures). Traditional spectrometers use a continuous broadband radiation source, for example a special light bulb, or more recently a "white" continuum generated by a frequency-unstabilized pulsed laser. In such a case, the maximum interference (the greatest contrast of the interference fringes) occurs when the lengths of the arms of the interferometer are balanced (the arms have the same or similar optical length). Shift range - the length of the recorded interferogram is chosen with regard to the required resolution - the longer the range, the greater the resolution. The spectrometer can be used to measure the radiation bound to it and then also to measure the changes in this spectrum caused by the optical environment (sample) inserted before, in or behind the interferometer.

Stabilized (optical) frequency comb generation [1] is widely used for precise frequency measurements [2] [3] and for the generation of ultrashort light/electromagnetic pulses [4]. The use of this frequency comb for direct spectroscopy has been demonstrated using diffraction spectrometers for high repetition rate lasers [5] or using a high resolution spectrometer for both low repetition rate (dense tooth) lasers [6] [7]. Other variants of spectroscopy using a frequency comb are "cavity ring down spectroscopy" (measurement of the "decay" time of light circulating in a resonator) [8] or a fiber interferometer with a fiber Bragg grating [9].

Fourier spectroscopy with two frequency combs is described in [10],

A frequency comb Fourier spectrometer (most similar to that described in this invention) was published in [11].

Coherence (interference) of different pulses of a train generated by a laser - frequency comb has been demonstrated several times in vacuum and in air [12],[13],[14], accurate and fast detection of fringes for different arm lengths of the interferometer in air has been proposed and to some extent implemented in [15], the introduction of ridge radiation using a (dispersive) optical fiber and Fourier transformation (including phase evaluation) for shorter displacement ranges (low spectral resolution) were also proposed and demonstrated there.

The essence of the invention

The aforementioned disadvantages are removed to a large extent by Fourier spectroscopy with resolution of the teeth of the frequency comb, the essence of which is that the radiation of the frequency comb is coupled into the interferometer and the interferogram is detected as a series of samples of the interferometer output signal for an interval long enough to contain an interference signal corresponding to the distance or delay of at least two consecutive pulses of the frequency comb, the variable delay being provided either by varying the optical length of the interferometer arm or arms or

- 1 CZ 309439 B6 repeaters varying the frequency or spacing of the ridge pulses and the resulting interferogram is processed by Fourier transformation.

The subject of the solution is the measurement method - a variant of interferometric spectroscopy, which consists in using the radiation of the generator of the optical frequency comb and detection when moving through an interval longer than the distance between the following pulses of the frequency comb. It makes it possible to distinguish the individual components (teeth) of the frequency comb after the Fourier transformation. Accurate knowledge of the frequency of the teeth makes it possible to increase the accuracy of determining the frequency and wavelength of the spectral properties measured by the interferometer. The use of a stabilized frequency comb allows measurements to be made with very different lengths of the interferometer arms, which brings about an amplification of the measured phase ratios (passed comb teeth) and an increase in the sensitivity of the measurement compared to measurements with approximately the same lengths of the interferometer arms, which are necessary in measurements with continuous radiation.

The main differences of the procedure according to the invention from the method described in [11] are:

- the resolution of the teeth of the comb thanks to the longer shift/recording and the evaluation method described below), - the possibility to place the sample in the interferometer to increase the sensitivity of the phase/dispersion measurement, - another method of detection (phase-sensitive/lock-in detectors are not needed),

- in [11], zero dispersion (vacuum) and perfect dispersion compensation are assumed (all wavelengths are in phase for a zero interferogram), but real values are processed in the spectrometer according to the invention

The procedure according to the invention combines the advantages of the above-mentioned existing techniques and brings a new quality of sensitive phase measurements.

The advantages over diffraction spectrometers, including those with frequency comb radiation, are mainly:

- simultaneous detection of a wide spectrum, for example millions of comb teeth - practically the entire spectral range, which is connected to the interferometer and falls within the sensitivity range of the detector/detectors,

- the possibility to measure the phase effect of the sample in addition to the amplitude effect - absorption or other interaction, - to accurately measure the wavelength of individual teeth (of a known frequency) and thus obtain information about the dispersion (dependency of the refractive index on the wavelength) or the absolute value of the refractive index, if they are compared the results of measurements in vacuum and in the tested environment.

The main advantages compared to a Fourier spectrometer with a continuous radiation source are mainly:

- the possibility to perform measurements with very different lengths of the interferometer arms, because the interferogram appears in the vicinity of each integer multiple of the distance between the pulses. This property is useful, for example, in detecting weak absorption lines or measuring low-pressure samples (less affected by pressure broadening),

- the resolution of individual teeth of the comb, leading to the exact assignment of frequency to the detected spectral characteristics.

Clarification of drawings

Giant. 1 is a diagram of one possible interferometer/spectrometer arrangement.

Giant. 2 is an example of the measurement result of the past amplitude spectrum (red curve) and spectral transmittance (black).

Giant. 3 is a detail of the spectral transmittance from Figure 2.

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Giant. 4 is an example of the measured phase spectrum.

Giant. 5 is an example of measured air dispersion.

Giant. 6 is a detail of Figure 5.

Giant. 7 is an example of the measured permeability of iodine vapors - rotationally vibrating spectral lines.

Examples of implementation of the invention

Fig. 1 shows a possible schematic of the interferometer/spectrometer arrangement. A regular train (sequence) of pulses of a laser 1 generating a frequency comb passes through a collimator 2, which can contain a standard (dispersive) optical fiber, since the extension (chirp) of the pulse is not important if it is stable in time [15], The collimator should be achromatic, advantageous is a combination of a polarization preserving optical fiber and a parabolic mirror. The collimated beam is divided by a divider 3 into two arms of the interferometer. Each part is reflected back by a mirror or corner reflector 4 and 5, and both are combined again into the output beam(s) which is detected by photodetector 6. It is possible to use two detectors in a differential connection as in [ll]. The longitudinal position of (one of) the mirrors or corner reflectors is changed using a slide 9 or 9\ The interferometer or part of it (a slide with a reflector) can be placed in a vacuum or a container filled with the medium being investigated. We denote the distance 7 between the following pulses of the frequency comb l _p . _p . The maximum interference signal (packet of fringes) is detected when the path difference in the arms of the interferometer is close to an integral multiple of l _p . _p .

If the shift is carried out in vacuum, the detected interferogram is perfectly periodic (except for the effect of any non-zero offset frequency of the ridge and the unwanted effect of diffraction and collimation error) the fringe packets are repeated when the position of the reflector is shifted ol _p . _p /2. The interferogram is recorded as the dependence of the detected signal on the displacement position. The Fourier transform of the interferogram gives the spectrum of the radiation coupled into the interferometer. The spectrum is continuous if only one packet is processed, padded with zeros to infinity. If an absorption medium (sample) is inserted before or behind the interferometer, or an absorption/dispersion medium is inserted into (one of the arms of) the interferometer, the interferogram will change. The spectral amplitudes or phases obtained by the Fourier transform of the interferogram differ from the original one by the absorbed part/obtained phase shift.

If a longer interferogram is recorded and processed - containing two or more pulses (corresponding to the displacement of the reflector by more than 1^2), then the spectrum obtained by Fourier transformation already shows the spectral components of the frequency crest. For N packages, the spectral shape I(x) of the detected tooth is ₍ sm(X - x) sm(x) (1) where A is the coefficient - constant for one tooth (given by the intensity of that tooth and the sensitivity of the detector for the frequency of this tooth), x is the wavelength/frequency deviation from the tooth center expressed relative to the tooth spacing (for frequencies x=2n(f-ft)/(2F _rep )') for 2 packs this leads to the form shiX) |cos(x)| (2)

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Sufficient sampling accuracy must be ensured. Particular attention should be paid to:

- the samples must be sufficiently dense in space - more than two for the shortest wavelength to be evaluated,

- the spatial position of each sample must be known with sufficient accuracy (better than half of the shortest wavelength to be evaluated),

- the dynamic range of the detector and the AD converter should be as large as possible, and the stability of the performance and spectrum of the frequency comb should be as good as possible.

During initial experiments, we used a commercial titanium: sapphire femtosecond frequency comb with a center wavelength of -800 nm, repeater frequency Frep = 197.28 MHz (4p~1.52m), offset frequency 20 MHz, feeding the radiation into a 10 m long polarization-preserving interferometer single-mode fiber (for 600 to 900) nm, non-polarizing beam splitter (-50:50 at 800 nm), beam diameter about 2 mm, gold-plated hollow corner reflectors. An auxiliary frequency-stabilized 633 nm He-Ne laser was coupled into the interferometer parallel to the comb beam (but spatially separated).

The output beams of both lasers (comb and continuous laser) were detected by silicon photodiodes (with a bandwidth of -1Hz to >200kHz) and the signals of these detectors were digitized and stored (AD conversion 2 x 24bit x ~60kS/s). Traversing over ~0.8m (>l _PP /2, l.5m=ll _pp would be more advantageous) was performed using a motorized optical bench with a stepper motor (with vibration suppression using a flywheel combination, suitable power and speed settings) at a speed of 2.5 mm/s, i.e. during a 5.5 minute sweep over 825 mm, approximately 20 million pairs of samples spaced -40 nm apart were recorded and stored synchronously for both channels/detectors (approximately 8 samples per 633nm strip).

The measured data was processed as follows:

- for both channels, wavelengths shorter than -300 nm and longer than -1600 nm were filtered out using a back-and-forth Fourier transformation,

- the comb channel data was linearized by resampling (so that the new samples are equidistant in space) with the help of the second channel signal (assisted by lasso),

- wave packets corresponding to possible unwanted reflections were attenuated by multiplying with a smooth function (going to the value of 1 further from the center of the unwanted fringe packet),

- the resampled data were processed by a fast Fourier transform (e.g. FFTW [16]) and the resulting amplitudes and phases were saved. The Fourier transformation can be performed in several variants - for different length "parts" of the detected interferogram, by an interval including one packet and a selected length up to l _pp /2. Intervals of the same length comprise the first and second packages and their amplitude and phase spectra can be compared, with the entire record padded with zeros to obtain a longer interferogram (longer than 3/2 l _pp ) allowing finer resolution of the Fourier transform results. This interferogram is then processed as mentioned above to distinguish individual comb teeth by fast Fourier transformation. If the displacement was not carried out in a vacuum, the dispersion will cause the spatial frequencies of the comb teeth to no longer be equidistant and thus do not "fit" into the frequencies calculated by the Fourier transform of the interferogram. The amplitude and wavelength of each tooth can then be determined by fitting the profile according to relation (1) or (2) to the results of the discrete Fourier transform.

The measurement and processing is repeated for different conditions, for example, changed interferometer arm length, different sample pressure/concentration, etc., and the results are compared to evaluate the effect of the change made.

The narrow spatially separated beams used in the initial experiments can be replaced by a wide beam in which the radiation of the comb and the auxiliary continuum laser propagates together.

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Both radiations can be combined in front of the interferometer/collimator by means of a dichroic mirror and divided into the respective detectors at the output of the interferometer in the same way.

Example 1 Measurement of air absorption and dispersion

The arrangement described above (Fig. 1) is used in air without a cuvette or other samples.

A non-polarizing splitter (-50% at 800 nm, on a 30' wedge pad) introduces dispersion (dispersion difference) between arms due to the finite thickness of the glass pad. This difference is approximately compensated for by inserting an uncoated pad of the same glass and with the same wedge into the respective arm of the interferometer (the wedges are oriented against each other to compensate for the angular deviations of the different wavelengths. Perfect compensation is not necessary because the residual phase difference for each wavelength is evaluated using the Fourier transformation of the reference (zero) interferogram and subtracted from the detected phase difference for other positions (interferograms). Similarly, the amplitude of the passed spectrum of the fringe package for a certain displacement is divided by the spectrum obtained from the fringe package of the reference (zero) interferogram to determine the air permeability corresponding to the given displacement (path length in air equal to twice this displacement).

Measurement - displacement by more than l _p . _p - was repeated several times for different distances: first in the range covering the zero and first packages, then in the range covering the fourth and fifth packages. The measured data were processed both for shorter displacements (not allowing teeth to be distinguished) and for entire data sets (completed with zeros, to distinguish teeth).

Fig. 2 shows an example of the passed spectrum (red curve, 10) and transmittance (dark blue, 11). Doppler and pressure broadened absorption lines of O2 (-760 to -765) nm with a peak absorption of about 10% are clearly detected. In the graphs, there are 370,000 points of comb teeth in the spectral range (725 to 885) nm, the average power is about a quarter of a microwatt per tooth.

The oxygen absorption (detail of Fig. 2; with 2500 comb tooth points) is shown in Fig. 3, the spectral phase (phase shift caused by the interaction with oxygen) in Fig. 4 (not yet corrected for the spectral phase of the zero interferogram). The amplitude noise of a single measurement (without any averaging) was below 0.5% during initial experiments in the optimum (spectral region where the laser power is large enough), comparable to the results described for lock-in detection in [11]. The spectral phase (Fig. 4) clearly shows the positions of the center of the lines. The frequency distance between absorption lines can be precisely determined by counting the number of teeth between the centers of these lines (integer and non-integer multiples of the repeater frequency). If the absolute frequency of one (reference) absorption line is taken as known, the absolute frequencies of the others can also be determined in this way. If such a reference is not available, radiation from an (absolutely measured) frequency-stabilized laser (wavelengths falling within the spectral region of the comb and detector) can be coupled into the interferometer and used as a reference to identify the tooth number of the comb.

The spectrometer actually measures wavelengths (in air or in another environment in which displacement is carried out) - as a ratio to the wavelength of a reference - in our case a stabilized 633 nm laser, a reference absorption line or another auxiliary laser. If the frequency of each tooth is identified (ie very well known - with the uncertainty of the comb generator) and its wavelength measured, the dispersion can be determined as the ratio of the refractive index η(λ) to the refractive index of the reference n _re f.

(3)

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An example of air dispersion evaluated in this way is shown in Fig. 5. The range of the vertical axis is about 5 χ 10 ^-7 rel. (in the graph of Fig. 5 n(Z)/n _re f -1 is plotted in [ppm]), the detection noise in the preliminary experiment was less than 1 χ 10 ^-9 rel.. The detail of the measured dispersion in the vicinity of the absorption lines of oxygen O2 is in Fig. 6 (horizontal axis wavelength in [nm], vertical refractive index - 1 in [ppm]). Raw data of 2848 teeth are shown, vertical axis division 0.5 ppb, approximately equal to the measurement sensitivity (corresponding to a delay of 0.5 nm/m or 1.7 attoseconds, or a relative accuracy of measuring the wavelength distance of adjacent comb teeth of 1/500. In vacuum this would correspond to the uncertainty of determining the tooth frequency with an interferometer of 390 kHz (position deviations/tooth spacing = 390 kHz /Frep 200 MHz).

The total uncertainty was limited by the chromatic aberration of the collimator in the initial experiments. With a properly adjusted achromatic collimator, the uncertainty will be given by a combination of diffraction contributions, wavefront shape distortion by optical elements, power stability of the coupled radiation, detection noise by homogeneity, and stability of the measured refractive index (along the travel path).

Example 2 spectrum of iodine

For the test measurement of the iodine vapor spectrum, we placed a 50 cm long iodine cuvette in the measuring arm of the interferometer/spectrometer. For this purpose, the fs radiation spectrum of the frequency comb was expanded by a photonic microstructure fiber so that it contained a band of green wavelengths. This radiation was introduced into the spectrometer by a standard polarization-preserving fiber and collimated as in experiment 1 (beams from both the comb and the auxiliary laser pass through the cuvette twice). The shift was carried out over the interval of the difference in the lengths of the paths of the interferometer arms (1 *l _pp , 2*l _PP ), the interferograms were recorded and processed as in example 1. The measurement was repeated for different iodine vapor pressures: ~1 Pa and ~20 Pa (set using the temperature of the iodine cuvette finger). Absorption/dispersion of iodine molecules can be detected by comparing the ratio of amplitude spectra/difference of phase spectra. An example of the results (with a still unoptimized layout and detector settings) is shown in Fig. 7.

Phase unwrapping is more complicated when the phase of adjacent teeth changes significantly near strong absorption or when several teeth are absorbed below the detection noise level. But the high sensitivity of the phase/wavelength measurement described above (1/500 of the distance between adjacent teeth) will allow the results to be established even if tens of teeth are below the detection threshold.

Literature

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[5] A. Bartels, D. Heinecke, and S.A. Diddams, Passively mode-locked 10 GHz femtosecond Ti:sapphire laser, Opt. Lett. 33, 1905-1907 (2008).

[6] Scott A. Diddams, Leo Hollberg & Vela Mbele Molecular fingerprinting with the resolved modes of a femtosecond laser frequency comb, Nature 445, 627-630 (8 February 2007) doi :10.103 8/nature05 524.

[7] A. Bartels, R. Gebs, M. S. Kirchnerm, and S. A. Diddams, “Spectrally resolved optical frequency comb from a self-referenced 5 GHz femtosecond laser,” Opt. Lett. 32, 2553-2555 (2006).

[8] Kamil Stelmaszczyk, Philipp Rohwetter, Martin Fechner, Manuel QueiBer, Adam Czyzewski, Tadeusz Stacewicz, and Ludger Wóste, Cavity Ring-Down Absorption Spectrography based on filament-generated supercontinuum light, Opt. Express 17, 3673-3678 (2009).

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[9] C. E. Towers, D. P. Towers, D. T. Reid, W. N. MacPherson, R. R. J. Maier, and J. D. C. Jones, “Fiber interferometer for simultaneous multiwavelength phase measurement with a broadband femtosecond laser,” Opt. Lett. 29, 2722-2724 (2004).

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Claims (2)

PATENT CLAIMS 1. Fourier spectroscopy with resolution of the teeth of a frequency comb as an interferometric spectroscopic measurement using the radiation of a femtosecond comb generator of optical 5 frequencies, characterized by the fact that the radiation of the frequency comb is connected to the interferometer and the interferogram is detected as a series of samples of the interferometer output signal for a sufficiently long interval, so as to contain an interference signal corresponding to the distance or delay of at least two consecutive pulses of the frequency comb, the variable delay being provided either by varying the optical length of the arm or arms of the interferometer or by varying the repeater frequency ίο or the spacing of the comb pulses, and the resulting interferogram is processed by Fourier transformation. 2. Fourier spectroscopy according to claim 1, characterized in that one or more simultaneous laser beams of a known wavelength are used for linearization of the detected interferogram, i.e. recalculation of the detected samples so that they become equidistant in space, which makes it possible to use fast Fourier transformation algorithms and /or to determine the order of the frequency comb component. 15 3. Fourier spectroscopy according to claim 1 or 2, characterized in that the displacement is carried out in a vacuum.