Frequency modulation Fourier transform spectroscopy

Transcription

1 Frequeny modulation Fourier transform spetrosopy Julien Mandon, Guy Guelahvili, Nathalie Piqué To ite this version: Julien Mandon, Guy Guelahvili, Nathalie Piqué. Frequeny modulation Fourier transform spetrosopy. Optis Letters, Optial Soiety of Ameria, 007, 3 (5), pp <hal > HAL Id: hal Submitted on 4 Apr 007 HAL is a multi-disiplinary open aess arhive for the deposit and dissemination of sientifi researh douments, whether they are published or not. The douments may ome from teahing and researh institutions in Frane or abroad, or from publi or private researh enters. L arhive ouverte pluridisiplinaire HAL, est destinée au dépôt et à la diffusion de douments sientifiques de niveau reherhe, publiés ou non, émanant des établissements d enseignement et de reherhe français ou étrangers, des laboratoires publis ou privés.

2 Frequeny modulation Fourier transform spetrosopy Julien Mandon, Guy Guelahvili, Nathalie Piqué Laboratoire de Photophysique Moléulaire, CNRS; Univ. Paris-Sud, Bâtiment 350, 9405 Orsay, Frane Corresponding author: Dr. Nathalie Piqué, Laboratoire de Photophysique Moléulaire Unité Propre du CNRS, Université Paris Sud, Bâtiment Orsay Cedex, Frane Phone number: Fax number: Web: Abstrat: A new method, FM-FTS, ombining Frequeny Modulation heterodyne laser spetrosopy and Fourier Transform Spetrosopy is presented. It provides simultaneous sensitive measurement of absorption and dispersion profiles with broadband spetral overage apabilities. Experimental demonstration is made on the overtone spetrum of C H in the.5 µm region. OCIS odes: 0.600, , , , , , Spetrometers and spetrosopi instrumentation, Spetrosopy, Fourier transforms, Spetrosopy, modulation, Spetrosopy, laser, Spetrosopy, heterodyne, Spetrosopy, moleular, Phase modulation

3 Improving sensitivity is presently one of the major onern of spetrosopists. This may be obtained both from the enhanement of the intrinsi signal, and from the redution of the bakground noise. In this latter ase, modulation has been one of the most effetive approah. In partiular, Frequeny Modulation (FM) absorption spetrosopy [] has reahed detetion sensitivity near to the fundamental quantum noise limit, by shifting the frequeny modulation of the measurements to a frequeny range where the /f noise beomes negligible. Moreover, FM spetrosopy benefits from high-speed detetion and simultaneous measurement of absorption and dispersion signals. Sine Bjorklund s first demonstrations [,] of the effiieny of FM spetrosopy with a single-mode ontinuous-wave dye laser, the tehnique has been widely used as a tunable laser spetrosopi method in fields suh as laser stabilization [3], two-photon spetrosopy [4], optial heterodyne saturation spetrosopy [5], trae gas detetion [6]. In most shemes, the laser wavelength is sanned aross the atomi/moleular resonane to retrieve the line shape. More rarely, the modulation frequeny is tuned. However in both ases, the measurements are limited to narrow spetral ranges. This letter reports the first results in FM broadband spetrosopy. This work is motivated by our ongoing effort of implementing a new spetrosopi approah simultaneously delivering sensitivity, resolution, auray, broad spetral overage and rapid aquisition. The basi idea, named FM-FTS, is to assoiate the advantages of FM spetrosopy and high-resolution Fourier transform spetrosopy (FTS). FTS is able to reord at one extended ranges, with no spetral restrition. In partiular it gives easy aess to the infrared domain. In this letter, a new way of modulating the interferogram is implemented. The key onept is that a radio frequeny (RF) modulation is performed. The beat signal at the output port of the Fourier transform spetrometer is modulated at onstant RF, whih is about 0 4 times greater than the audio frequeny generally delivered by the interferometer optial onversion. Together with the advantage, over lassial FTS, of measurements performed at muh higher frequeny, our approah benefits from the synhronous detetion ability and from the simultaneous aquisition of both the absorption and the dispersion of the reorded profiles. The experimental priniple is presented in Fig.. The light emitted by the broadband soure is first passing through the interferometer. The output beam is then phase-modulated by an eletro-opti modulator (EOM) before entering the absorption ell and falling on the fast detetor. The synhronous detetion of the detetor signal is realized by the lok-in amplifier at the EOM driver referene frequeny f m. Reorded data are finally stored on the omputer disk with their orresponding path differene position. Their Fourier transform is the spetrum. In more details, the eletri field E at the output of the interferometer may be written as: ( ) 0 ω E (, t) = E + exp iω exp( iωt)dω +.. () where E 0 is the eletri field amplitude of the soure at ω optial pulsation, is the veloity of light and. the onjugate omplex of the preeding expression in Eq.. The EOM effet on the beam is assumed to have a low modulation index M. As a onsequene, eah arrier wave of pulsation ω, has two weak sidebands loated at ± ω m = ± π f m. Equation () beomes: ( 0 ω ) E(, t) = E + exp iω { exp( iωt) ( ) ( ) } + M exp i ω + ωm t M exp i ω ωm t dω +.. () When interating with the gas, the arrier and the sidebands experiene attenuation and phaseshift due to absorption and dispersion. Following the notations introdued in [], this interation may be written as exp(-δ(ω)- i φ(ω)) where δ is the amplitude attenuation and φ is

4 the phase shift. The following onvention is adopted: δ n and φ n denotes for n = 0, ± the respetive omponents at ω and ω ± ω m. Then Eq. may be written: 0( ω ) E(, t) = E + exp iω { exp( δ0 iφ0) exp( iωt) ( + i + ) i( ) t ( i ) i( ) t } + M exp δ φ exp ω + ωm M exp δ φ exp ω ωm dω +.. (3) The intensity I deteted by the fast photodetetor is proportional to : * I(,) t E(,) t E (,). t (4) I(, t) exp( δ0) + exp( δ+ ) + exp( δ ) + os ω ( t) ( ) ( ) ( ) ( ) + M os ωm exp δ0 δ+ os φ0 φ+ exp δ0 δ os φ0 φ + os ω ω δ δ φ φ δ δ φ φ ω ( t) ( ) ( ) ( ) ( ) + M sin m exp 0 sin 0 exp 0 + sin os ( t) ( ) ( ) + M os ωm exp δ+ δ sin φ φ+ + os ω + ( t) ( ) ( ) + M sin ωm exp δ+ δ os φ φ+ os ω d ω. (5) After synhronous detetion at f m frequeny and with the assumption that δ 0 -δ j << and φ 0 - φ j << (with j = ±), the in-phase I os ( ) and the in-quadrature I sin ( ) parts of the eletri signal are given by I os( ) M + os ω exp( δ0 )( δ δ+ ) d ω. (6) I sin ( ) M + os ω exp( δ0 )( φ+ + φ φ0 ) d ω. (7) Summarizing, two interferograms are simultaneously measured, allowing to obtain broadband FM spetra. The in-phase interferogram provides spetrally resolved information on the differene of absorption experiened by eah group of two sidebands. The inquadrature interferogram gives the differene between the average of the dispersions experiened by the sidebands and the dispersion undergone by eah arrier. For this first experimental demonstration, a narrow-band emission soure overing 0.5 m - (7.5 GHz) has been implemented as a test soure. It is made of a fiber-oupled distributed feedbak laser diode emitting around 530 nm with an output power of a few mw. The urrent of the laser diode is modulated at about 0 Hz by a ramp generator. At eah path differene step, while the interferometer is reording one interferogram sample, the laser frequeny exursion is equal to 7.5 GHz, orresponding to one period of the triangular ramp. Consequently, for the interferometer, the laser diode behaves as a ontinuous emission soure emitting over 0.5 m -. The interferometer output light is phase-modulated at f m = 50 MHz by the EOM and passes through an 80-m ell filled at 0 hpa with aetylene in natural abundane. The light is next foused on an InGaAs nanoseond infrared photodetetor, whih aording to Eq.5 delivers a signal proportional to the intensity of the beam ontaining a beat signal at the RF modulation frequeny. The amplified detetor signal is mixed with the referene signal at f m, down to d.., using a ommerial high frequeny dual-phase lok-in amplifier. The referene may be phase-shifted with respet the signal used to drive the EOM. The two hannels deteted in-phase and in-quadrature are measured simultaneously. 3

5 Figure shows a typial in-phase interferogram of C H. Its shape is harateristi of an interferogram of first-derivative type line-shapes. The 3 m period amplitude modulation is due to the beat between the two strongest aetylene lines in the explored spetral domain. Figure 3 shows the two narrow-band spetra, Fourier transform of the in-phase (absorption) and in-quadrature (dispersion) interferograms. The spetral domain extension is limited by the tuning apabilities of the diode laser, whih was used as a test soure. This does not restrit the generality of the present demonstration. The lines belong to the ν +ν 3 and ν +ν 3 +ν 5 -ν 5 overtone bands of C H. The unapodised spetral instrumental resolution: m - (0.375 GHz) is narrower than the Doppler width of the lines. Signal to noise ratio is of the order of 00. The total reording time of the order of 5 minutes is due to the need of adapting the interferometer reording mode proedure to the rather low laser diode frequeny exursion period. The present validation of FM-FTS with a narrow band light soure made the experiene muh simpler. Indeed, in wideband FTS, proessing the signal of the interferogram needs speial dynami range solutions. Thanks to the only 0.5 m - -wide spetrum analysed in this experiment, a sophistiate RF detetion hain, presently under development, was not neessary. The design of our Connes-type interferometer allows a balaned detetion of the signals reorded at the two output ports. This will be helpful to remove the part of the interferogram whih is not modulated by path differene and to onsequently improve the dynami range of the measurements. Similar solutions have already been suessfully pratied for time-resolved FTS [7]. In FM-FTS, they are formally even easier to implement sine the signal may be band-pass filtered around the modulation radio-frequeny. In the present experimental set-up, the light should sequentially reah the equipment parts as shown in Fig.. Briefly, to have a broadband equivalent of FM tunable laser spetrosopy, the sidebands generated by the EOM must not be resolved by the spetrometer. Also, sine eah arrier and its sidebands have to experiene different attenuation and phaseshift, the EOM must be plaed before the ell ontaining the gas of interest. This matter will be disussed in more detail elsewhere. This first FM-FTS experiment demonstrates the feasibility of oupling broadband laser soures, Fourier spetrometers and RF detetion. This opens new perspetives in high sensitivity multiplex spetrosopy. FM-FTS may be oupled to a large variety of high brightness soures. This inludes broadband w lasers, superontinua soures, mode-loked lasers as demonstrated reently [8], and Amplified Spontaneous Emission soures. Frequeny nonlinear onversion may also be used when no laser soure is available in the spetral range of interest. FM-FTS may be pratied with any kind of Fourier transform spetrometers, inluding ommerially available instruments, at the expense of reasonable modifiations in the signal detetion sheme. The approah is also suitable at low spetral resolution. In suh ase, modulation frequenies lying in the GHz domain may be used. Moreover, FM-FTS indues new praties in Fourier transform spetrosopy. The modulation frequeny is very high. The optial fringes generated by the interferometer an then be sanned at a muh higher frequeny than what is usually pratied nowadays. Path differene variation of the order of m/s, is easily affordable. It orresponds to aquisition times expressed in seond when presently the most effiient existing high resolution interferometers need to 0 hours to reord interferograms. Additionally, due to the low étendue of the analysed laser beams in our method, miniaturized instruments may be implemented. In addition to the radio-frequeny detetion sheme, sensitivity may be further enhaned by using an external optial resonator, thus inreasing the effetive absorption length. With FM-FTS, both the absorption and the dispersion assoiated with eah spetral features are measured simultaneously. Despite its reognized interest for lineshape parameters retrieval, traditional dispersion spetrosopy has been poorly developed, only at low spetral 4

6 resolution, mostly due to its experimental omplexity. FM-FTS should represent an easy manner of getting this information over extended spetral domains, whih may indue new interest to the experimental investigation of dispersion profiles. Referenes [] G.C. Bjorklund, Frequeny-modulation spetrosopy: a new method for measuring weak absorptions and dispersions, Optis Letters 5, 5-7 (980). [] G.C. Bjorklund, M.D. Levenson, W. Lenth, C. Ortiz, Frequeny-modulation (FM) spetrosopy. Theory of lineshapes and signal-to-noise analysis, Applied Physis B 3, 45-5 (983). [3] R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley and H. Ward, Laser phase and frequeny stabilization using an optial resonator, Applied Physis B 3, (983). [4] W. Zapka, M. D. Levenson, F. M. Shellenberg, A. C. Tam, G. C. Bjorklund, Continuouswave Doppler-free two-photon frequeny-modulation spetrosopy in Rb vapor Optis Letters 8, 7-9 (983) [5] J.L. Hall, L. Hollberg, T. Baer, H.G. Robinson, Optial heterodyne saturation spetrosopy, Applied Physis Letters 39, (98). [6] P. Maddaloni, P. Malara, G. Gagliardi, P. De Natale, Two-tone frequeny modulation spetrosopy for ambient-air trae gas detetion using a portable differene-frequeny soure around 3 µm, Applied-Physis-B-Lasers-and-Optis B85, 9- (006). [7] N. Piqué, G. Guelahvili, High-information time-resolved Fourier transform spetrosopy at work, Applied Optis 39, (000). [8] J. Mandon, G. Guelahvili, N. Piqué, Frequeny Comb Spetrometry with Frequeny Modulation, in preparation,

7 Figure aptions Fig.. Shemati of the experimental setup. Fig.. Absorption interferogram using in-phase RF detetion with FM-FTS. Maximum path differene is 40 m orresponding to m - unapodized resolution. Fig. 3. FM-FTS dispersion and absorption spetra of the aetylene moleule at 58.6 nm. The middle plot represents the line relative intensities taken from the HITRAN database. 6

8 Broadband soure FTS EOM Sample Cell PC Detetor EOM Driver Lok-In Fig.. Shemati of the experimental setup. FM-FTS Interferogram (absorption hannel) Path differene (m) Fig.. Absorption interferogram using in-phase RF detetion with FM-FTS. Maximum path differene is 40 m orresponding to m - unapodized resolution. Dispersion C H R e () R f () P e (6) ν +ν 3 +ν 5 -ν 5 ν +ν 3 Absorption (m - ) Fig. 3. FM-FTS dispersion and absorption spetra of the aetylene moleule at 58.6 nm. The middle plot represents the line relative intensities taken from the HITRAN database. 7