2242 J. Opt. Soc. Am. B/ Vol. 22, No. 10/ October 2005 Gagné et al.

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1 2242 J. Opt. Soc. Am. B/ Vol. 22, No. 10/ October 2005 Gagné et al. Measurement o the atomic Cs 6 2 P 3/2 F e =5 hyperine level eective decay rate near a metallic ilm with diode laser retroluorescence spectroscopy Jean-Marie Gagné and Claude Kondo Assi Laboratorie d Optique et de Spectroscopie, Département de Génie Physique, École Polytechnique de Montréal, C.P. 6079, Succ. Centre-Ville, Montréal, Québec H3C 3A7, Canada Karine Le Bris Département de Chimie, Université de Montréal, Montréal, Québec H3T 1J4, Canada Received December 16, 2004; revised manuscript received April 21, 2005; accepted April 23, 2005 Sub-Doppler signals o the hyperine Cs 6 2 P 3/2 F e 6 2 S 1/2 F g transition lines in a diode laser-induced retroluorescence spectrum at the interace between glass and Cs vapor are, or the irst time to our knowledge, experimentally identiied and phenomenologically investigated. We propose a qualitative explanation o the origin o the sub-doppler hyperine line, based on kinematic eects o the population o the excited 6 2 P 3/2 F e atoms o the laser-pumped velocity classes conined in the near-ield region o the interace. The role played by dierent relaxation processes contributing to the retroluorescent atomic linewidth has been characterized. The eective decay rate o the atomic hyperine level 6 2 P 3/2 F e =5 near a metallic thin ilm has been measured by using both sub-doppler retroluorescence and requency-modulated selective relection spectroscopies. For a saturated Cs vapor in a glass cell at a temperature o 130 C, the eective nonradiative relaxation rate o the 6 2 n P 3/2 F e =5 energy hyperine level due to the coupling with a metallic ilm is estimated to be A Fe =5 F g = s Optical Society o America OCIS codes: , , , INTRODUCTION The study o the integrated retroluorescent spectral signals generated with a diode laser at the interace between a metallic vapor optically thick at resonance and a surace composed o adsorbed atoms, metallic clusters, and atoms chemically bonded to the surace is a promising new way o experimental spectroscopic research or the in situ determination o the physical properties o interaces. The retroluorescence spectroscopy method is complementary to the methods o selective relection spectroscopy and evanescent wave spectroscopy. 1,2 In Res. 3,4 the authors have used a nonradiative and noncollisional mechanism o relaxation o the excited atomic level in the vicinity o a metallic ilm to interpret the inhibition eect o the spectral retroluorescent signal observed at the interace between glass and saturated Cs vapor optically thick at resonance. Moreover, these authors mentioned the existence o a sub-doppler spectral structure located in the spectral region o inhibition o the retroluorescent signal associated with the nm resonant line. The phenomenological model developed 3,4 does not allow, in its present orm, the identiication and explanation o the origin o this sub-doppler spectral structure. In this paper our objective is to present experimental results that corroborate the existence o a spectral substructure in the retroluorescence signal associated with the resonant nm 6 2 P 3/2 6 2 S 1/2 line at the interace between glass and Cs vapor at a temperature around 130 C. Using requency-modulated (FM) selective relection spectroscopy, we show by comparison that this substructure really corresponds to the sub-doppler hyperine structure o the atomic 6 2 P 3/2 6 2 S 1/2 absorption line. We have measured and analyzed the proiles o the cycling F e =5 F g =4 hyperine spectral line o the retroluorescence and FM selective relection spectra. Starting with the spectral properties o this sub-doppler hyperine line, we propose and carry out an experimental method allowing the in situ measurement o the eective decay rate o the population o atoms, excited in the atomic 6 2 P 3/2 F e =5 hyperine level, which is located near a metallic ilm. By using these measurements, and the physical concepts o the methods o selective relection spectroscopy 5,6 and o retroluorescence spectroscopy, 3 we estimate the eective decay rate due only to the nonradiative relaxation process o the excited atomic level in the vicinity o a metallic ilm. The value o the eective nonradiative decay rate due to the coupling o the excited atom with the metallic surace, A Fe =5 F g =4, obtained by using this n new /05/ /$ Optical Society o America

2 Gagné et al. Vol. 22, No. 10/October 2005/J. Opt. Soc. Am. B 2243 method and based on the retroluoresecence sub-doppler eect, is compared with the values measured by Le Bris et al. 3 and Gagné et al EXPERIMENTAL SETUP The diode laser-induced retroluorescence spectroscopy technique reported here is the same as the one described in Re. 3. The experimental setup is illustrated in Fig. 1. The Cs cell is embedded in an aluminum block and heated to a programmed temperature (between 90 and 180 C), controlled by a Mirak thermometer (Model HP72935). A diode laser rom Environmental Optical Sensors, Inc. (Model LCU 2001), with a bandwidth below 10 MHz, is used to excite the Cs atomic vapor around the 852 nm resonance line. We limited ourselves to weak laser powers (between 20 and 570 W or a beam area o cm 2 ) to avoid nonlinear eects. The calibration was carried out with a Fabry Perot intererometer by directing a raction o the exciting laser beam to it. The main laser beam is directed to the cylindrical Cs cell along the cell axis at an angle o incidence o 2 with respect to the normal o the entrance window surace. The luorescence emitted backward at an angle o 16 with respect to the normal o the surace was captured by a 0.5 m ocal-length Jarell Ash spectrometer (Model 5) equipped with a photomultiplier. The luorescence signals were ampliied by a picoammeter (Keithley Instruments) and were then digitized and recorded by a computer. FM selective relection spectroscopy signals were simultaneously collected by a Si photodiode. For studies at high resolution related to the hyperine structures o the Cs ground state covering a bandwidth o 20 GHz, we used a piezoelectric device having a resolution o a ew megahertz to ensure the spectral stepping o the laser sweep. Fig. 2. (a) Integrated retroluorescence spectrum at a nm wavelength as a unction o the laser detuning or a cell temperature 130 C and laser power 50 W. (b) Simultaneous recording o the FM selective relection spectrum. 3. RESULTS Figure 2(a) shows the integrated retroluorescence spectrum and Fig. 2(b) shows the FM selective relection spectrum generated at the glass Cs vapor interace at a temperature 130 C and a laser power 50 W when the Fig. 1. Schematic o the experimental setup. P, polarization rotator; L, lens; M, mirror; P.P., polarizing prism; P.M., photomultiplier; D, spatial ilter. Fig. 3. (a) Enlarged plot o the integrated nm resonant retroluorescence and (b) the FM selective relection spectra as a unction o laser detuning rom the resonance center or the 6 2 S 1/2 F g =4 6 2 P 3/2 F e =3,4,5 transition obtained at a temperature 130 C and laser power 50 W. diode laser is tuned over the nm 6 2 S 1/2 6 2 P 3/2 atomic transition line or a bandwidth laser sweeping o 20 GHz. As mentioned in Re. 3 and as speciied in Fig. 2, the simultaneous measurement o the FM selective relection and retroluorescence spectra shows that the deep dips in the retroluorescence spectrum correspond, as a irst approximation, to the centers o the two transitions lines 6 2 S 1/2 F g =3 6 2 P 3/2 and 6 2 S 1/2 F g =4 6 2 P 3/2 associated with the hyperine structure o the ground state 6 2 S 1/2, energetically separated rom each other by a gap o 9.2 GHz. For dierent cell temperatures 150 C, we observe a weak spectral substructure signal in the deep dips o the retroluorescence spectrum as previously mentioned. 3 For the identiication and a detailed analysis o the substructure, we choose as an example the spectral band corresponding to the deep dip o the spectral line associated with the 6 2 S 1/2 F g =4 6 2 P 3/2 transition. The analysis perormed on this spectral line can easily be extended

3 2244 J. Opt. Soc. Am. B/ Vol. 22, No. 10/ October 2005 Gagné et al. to the 6 2 S 1/2 F g =3 6 2 P 3/2 line. To this end, Fig. 3(a) displays an enlarged plot o the integrated retroluorescence and Fig. 3(b) shows the FM selective relection spectra in the inhibition spectral region or the optical 6 2 S 1/2 F g =4 6 2 P 3/2 pumping transition, obtained at a temperature 130 C. Since the FM selective relection spectra o Cs vapor are well known, 5 we use them [Fig. 3(b)] as reerence requency scaling spectra and or comparison to identiy the substructure observed in the retroluorescence signal. The high-resolution analysis (with a data recording requency stepping o the order o megahertz) reveals, as a irst approximation, that the peaks o the substructure coincide in requency position with the three reerence lines o the sub-doppler signal obtained in selective relection spectroscopy. Accordingly, this retroluorescent substructure relects the signature o the hyperine structure o the excited 6 2 P 3/2 F e =3,4,5 level when the pumping laser is tuned over the resonant 6 2 S 1/2 F g =4 6 2 P 3/2 transition. As in selective relection spectroscopy, no Doppler cross resonances were observed in the retroluorescence spectra. Similar results were obtained when we analyzed the 6 2 S 1/2 F g =3 6 2 P 3/2 line, i.e., the substructure is attributed to the hyperine structure o the excited 6 2 P 3/2 F e =2,3,4 levels. at laser requency L o the so-called stop-band ilter 3 or the atomic hyperine transition between the ground hyperine level F g =4 and the overall excited levels F e =3,4,5; and T is the eective spectral optical thickness o the stop-band ilter at requency. We can extract the experimental hyperine signal s n exp L by subtracting S T L, given by Eq. (1a), rom the total experiment signal S ob L. However, as a irst approximation, to evaluate the essential spectral characteristics o the hyperine F e =5 F g =4 line, we use a direct and simple method. To this end, we approximate S T L by using an aine unction a L 0 +b in the 100 MHz spectral band centered on the F e =5 F g =4 line, where a and b are constants determined experimentally. This linear approximation is illustrated in Fig. 4(a) where the dashed curve represents the approached unction o S T L. We have s n exp L = S ob L S T L S ob L a L 0 + b. 1b We scaled the requency axis by using the well-known gap between the two reerence hyperine lines F e =5 F g =4 and F e =4 F g =4 (value o 253 MHz), whose positions 4. HYPERFINE SPECTRAL DATA ANALYSIS AND DISCUSSION Using the spectral properties o the sub-doppler cycling hyperine 6 2 S 1/2 F g =4 6 2 P 3/2 F e =5 line, which is the strongest o the structure, we propose and carry out an experimental method allowing the measurement o the eective decay rate o the atomic 6 2 P 3/2 F e =5 hyperine level in the presence o a near-metallic thin ilm. To this end, one must extract and analyze this hyperine spectral line. In Subsections 4.A 4.C we present an extraction o the sub-doppler hyperine line proile rom the integrated retroluorescence signal, a phenomenological description o the origin o the sub-doppler signal, and an experimental characterization o the 6 2 P 3/2 F e =5 6 2 S 1/2 F g =4 transition linewidth. A. Experimental Sub-Doppler Hyperine Line Shape In this subsection we propose to extract the experimental hyperine line proile, which is added to the integrated retroluorescence spectral signal S T L that has been previously analyzed. 3 S T L has been associated with the 6 2 P 3/2 excited atoms population, completely redistributed. S T L has the ollowing orm 3 : S T L T L exp T L T T L + T exp T d, 1a where T L is the normalized proile o the eective atomic absorption coeicient o the F e =3,4,5 hyperine lines at the laser requency L ; T is the normalized proile o the eective atomic emission at requency in the vapor region ar away rom the cell entrance window where surace eects on the excited atoms are practically negligible; T L is the eective spectral optical thickness Fig. 4. (a) Extraction o the hyperine 6 2 P 3/2 F e =5 6 2 S 1/2 F g =4 transition signal proile. The dashed curve represents the approached unction o S T L ; the vertical line F e =5 indicates the center o the hyperine line. (b) Distribution o the points in the 100 MHz width spectral band around the F e =5 F g =4 transition line center, obtained ater subtraction o S T L rom the experimental data. The solid curve is a Lorentzian it o experimental points.

4 Gagné et al. Vol. 22, No. 10/October 2005/J. Opt. Soc. Am. B 2245 were determined by FM selective relection spectroscopy. The requency sweep is linear in the spectral band o interest. Each point o the hyperine signal proile is obtained by subtracting the value o S T L rom the measured signal S ob L or requency interval samples 5 10 MHz. The spectral distribution o points obtained by this method in the central area ( 100 MHz spectral band centered on the line) and normalized to unity at the maximum is shown in Fig. 4(b). It is well known that the resonance collisional broadening at the center o the line and in the wings diers in magnitude and mechanism. 5 The x axis is the laser requency detuning L rom the hyperine F e =5 F g =4 line center 0. A it o the normalized proile o the data [Fig. 4(b)] corresponding to the spectral band 100 MHz centered on the cycling F e =5 F g =4 hyperine transition line is obtained by using a Lorentzian distribution unction with a 90 MHz ull width at hal-maximum. We note an agreement o the Lorentzian it with the experimental data o the line proile. The ull width at hal-maximum o the spectral proile obtained is estimated to be RF 90 MHz. Note that RF is greater than the natural linewidth n 5.3 MHz, but is smaller than the Doppler width D 0.4 GHz. B. Origin o the Sub-Doppler Signal In this subsection we propose a phenomenological qualitative explanation o the origin o the sub-doppler hyperine line and we justiy the Lorentzian-type proile o the experimental spectral line. For that, we consider the thermalization processes and the kinematic properties o a velocity class o excited atoms in a thin vapor layer near the cell entrance window. The sub-doppler signal is associated with the kinematic properties o the population o a velocity class, which is conined in a thin vapor layer in contact with a metallic ilm. In Subsections 4.B.1 4.B.3, respectively, we briely recall the geometric and physical modeling o the glass Cs vapor interace, the thermalization processes in a pure Cs vapor and the kinematic properties o the laser-pumped velocity classes o the excited 6 2 P 3/2 F e atoms, and then we explain the origin o the sub-doppler signal. 1. Geometric and Physical Modeling o the Glass Cs Vapor Interace Figure 5 shows a schematic representation o the geometric and physical properties o the interace between the glass cell window and the Cs vapor. Because o its exposure to the saturated Cs vapor, the internal surace o the glass cell is covered by a thin metallic Cs ilm, probably composed o clusters, adsorbed atoms, atoms chemically bonded to the surace, and atoms diused into the glass (region a). The thin vapor layer (region b) in the vicinity o the cell surace is designated as the optical near-ield region o the interace, which has a thickness o x.region c, ar away rom the surace, designated as the arield region, is a semi-ininite vapor next to the near-ield region. In the present work we complement the simple model 3 by taking account o the signal generated in the near-ield region. This sub-doppler signal, having its origin in the near-ield region, is designated by s n L in Fig. 5. Fig. 5. Physical and geometric description o the characteristic regions o the glass cell window and Cs vapor interace: a, thin Cs metallic layer on the glass surace; b, proximity region o the surace x called the near-ield region o the interace; c, the ar-ield region o the interace. S T L designates the integrated retroluorescence signal rom the ar-ield region o the interace. s n L designates the integrated retroluorescence sub-doppler hyperine signal originating rom the near-ield region. The objects labeled (i) (iv) represent a Cs atom in the ground level, an atom adsorbed on the surace or on a Cs cluster, excited Cs atom undergoing a nonradiative relaxation, radiating (or luorescent) atom, respectively. 2. Thermalization Processes in a Pure Cs Vapor According to Huennekens et al., 7 in a pure Cs vapor, photon trapping processes and resonance exchange collisions can lead to substantial thermalization o the excited atom velocity distribution. In our case, in the vapor region ar rom the cell entrance window, the thermalization process by radiation trapping is more important than that o resonance exchange collisions. The authors o Re. 7 have noted that, in the case o a vapor layer conined in a thin cell, one can expect that the thermalization due to radiation trapping will be reduced to the point where the resonance collisions can be directly studied. On the basis o their work, it is reasonable to consider that a thin vapor layer o thickness x ( is the wavelength o the transition) at the interace, that we call the near-ield region, can be studied by using the hypothesis o partial thermalization o the population o the excited atoms o a velocity class in the vicinity o the cell entrance window. We take the escape actor o the retroluorescent photon 6 2 P 3/2 F e =5 6 2 S 1/2 F g =4 emitted rom the near-ield region close to one. Considering the results o Huennekens et al. 7 and considering the act that trapping eects are negligible in the near-ield region, we can assume that a raction o the population o a velocity class is not completely thermalized in the near-ield region o the glass Cs vapor interace, contrary to the case o the arield region where trapping eects are important and where the redistribution o the population o the excited 6 2 P 3/2 atoms is complete. As the spectral line considered here has a sub-doppler spectral width and a Lorentzian-type proile, it is reasonable to associate the origin o the sub-doppler signal with

5 2246 J. Opt. Soc. Am. B/ Vol. 22, No. 10/ October 2005 Gagné et al. the population o a velocity class o atoms o the ground 6 2 S 1/2 F g =4 level, located in the optical near-ield region, which is pumped to the excited 6 2 P 3/2 F e =5 level by the diode laser. On the velocity axis V x in the laser beam direction, a certain velocity interval V x is associated with the spectral width o the 6 2 S 1/2 F g =4 6 2 P 3/2 F e =5 absorption line. 8 We can write V x =, where is the spectral broadening o the transition or a homogeneous broadening related to the dierent competing relaxation processes o the nonthermalized atoms in the exited state. The atoms in the ground 6 2 S 1/2 F g =4 level, lying in this velocity interval, that are pumped to the excited 6 2 P 3/2 F e =5 level constitute the population o the velocity class interacting eectively with the laser. V x is the width o the velocity class population distribution. The mean velocity V x (along the laser propagation direction) o this velocity class at laser requency L is V x = L 0. Because o the Maxwell Boltzmann (MB) velocity distribution o the population in the ground state, the distribution o the population o the laser-pumped velocity class is modulated by this MB distribution. Thus the eective distribution o population D V x, V x, V x o 6 2 P 3/2 F e =5 atoms o a velocity class, along with the velocity component in the laser propagation direction, normalized to one at the maximum is given by 9 1 D V x, V x, V x 2 V x V x / V x 2 +1 exp V x/v 0 2, where V 0 is the most probable speed o the MB distribution [V 0 = 2kT/m Cs 1/2, here k is the Boltzmann constant, T is the vapor temperature, and m Cs is the Cs atom mass]. Considering relation (2), we can outline three kinematic properties o the excited population o a velocity class when V x 0. Note that or V x =0, the velocity class is composed o two groups o atoms moving in opposite directions ±V x. When V x 0, all the atoms o the velocity class move in the same direction as the mean velocity V x o the velocity class. In the intermediate case, we have two groups o atoms, with dierent population numbers, moving in opposite directions. 3. Origin o the Signal and Proile o the Spectral Line It is reasonable to assume that the atoms o a velocity class, moving away in ree light rom their origin in the near-ield region beore photon emission, do not contribute signiicantly to the sub-doppler hyperine signal generated at the interace. Indeed, the excited atoms colliding with the cell wall do not contribute to the retroluorescent signal. 10 We also consider that the excited atoms that enter the ar-ield region do not participate signiicantly with the sub-doppler signal because they are either thermalized or the photons emitted in this region are trapped and thermalized. 7 Only the excited 6 2 P 3/2 F e atoms o the laser-pumped velocity class having a larger residence time in the thin vapor layer close to the cell entrance window compared to the radiative lietime (spontaneous emission) may contribute signiicantly to the sub-doppler hyperine signal. It would be interesting to address the possible analogy with the physics o sub- 2 Doppler spectroscopy in a thin ilm o resonant vapor. 11 There is only a raction o the initial population o a velocity class that satisies this residence time constraint in the near-ield region. In the velocity space, this raction o atomic population contributing to the sub-doppler hyperine signal is conined in a velocity interval V x, centered at the one-dimensional MB velocity distribution o the atoms in the ground 6 2 S 1/2 F g =4 level, i.e., with a velocity V x 0. In other words, we consider that a raction o the population o the excited atoms o the velocity class in the near-ield region behave practically like a twodimensional gas normal to the laser beam. The sub- Doppler eect observed is attributed to the act that the velocity interval V x, centered on V x =0, is independent o the mean velocity V x, as we will explain in the ollowing. As the near-ield region (o thickness x ) is optically thin at resonance, the atomic population o the velocity class in the interval V x is uniorm along the x spatial coordinate in the near-ield region. The velocity interval V x is related to the geometric thickness x o the vapor layer and the radiative lietime Fe =5 F g =4 o the transition. We consider that V x satisies the ollowing constraint: where V x V x max, V x max = x / Fe =5 F g =4 = x g Fe =5,F g =4A Je J g, 3a 3b where g Fe =5,F g =4=1/2.908 is the statistical weight o the hyperine 6 2 P 3/2 F e =5 6 2 S 1/2 F g =4 transition and A Je J g = s 1 is the spontaneous emission rate o the 6 2 P 3/2 level. Considering that the escape actor o the photon emitted backward rom the near-ield region is close to one, then we can write that the optical thickness o this region at resonance L = 0 is smaller than one: x n Fg =4 Fg =4 F e =5 L 0 1, where n Fg =4 is the eective density o hyperine ground level F g and Fg =4 F e =5 L 0 is the eective cross section or atoms in the near-ield region at resonance L 0. The analytic orm o Fg F e in the presence o a metallic ilm has been studied by Le Bris et al. 3 By using Eqs. (3a), (3b), and (4), we have V x max = g Fe =5,F g =4A Je J g /n Fg =4 Fg =4 F e =5 L 0. Considering that RF D, we derive the ollowing relation 12 : Fg =4 F e =5 L 0 2 2J e J g +1 g F e =5,F g =4A Je J g 1+ Fe =5,F g =4 4ln2 1/2 1, D 6a where 4 5

6 Gagné et al. Vol. 22, No. 10/October 2005/J. Opt. Soc. Am. B 2247 Fe =5,F g =4 = A Fe =5,F g =4 g Fe =5,F g =4A Je =3/2,J g =1/2, 6b and A Fe =5,F g =4 is the total eective nonradiative decay rate o the excited atom in the near-ield region. Putting together Eqs. (5), (6a), and (6b), we have V x max 8 2J g +1 D J e Fe =5,F g =4 1 n Fg =4. 7 In this case we are concerned with J g =1/2, J e =3/2, and n Fg =4=9n/16 where n is the vapor density atoms/m 3 at a temperature o 130 C. Using these values and approximation (7), we have V x max ms Fe =5,F g =4 1. From approximation (8), note that the velocity domain V x max is related to the parameter characterizing the eective nonradiative decay rate o the excited atoms in the near-ield region. To illustrate the origin o the sub-doppler retroluorescence signal in the velocity space, we use a schematic representation. Figure 6 represents the normalized distribution along the velocity component in the laser beam direction at a spatial coordinate x in the near-ield region o the atomic population distribution brought up to the 6 2 P 3/2 F e =5 excited level by the laser at requency L. The curve G corresponds to the one-dimensional MB velocity distribution o the population o thermalized atoms at the ground 6 2 S 1/2 F g =4 level. The curves c 1, c 2, and c 3 represent the eective stationary distributions along the velocity component V x or dierent velocity classes o the 8 population o excited atoms nonthermalized at the 6 2 P 3/2 F e =5 level. For a velocity class c i, corresponding to the laser requency L i, we have V x i = L i 0. At laser requency zero detuning rom the resonance line center 0, we have V x =0. The V x width striped slice, centered on V x =0, is proportional to the eective population o radiating atoms in the near-ield region that contribute to generate the sub-doppler hyperine radiation. Thus we introduce a probability density per unit velocity, V x, V x, in which an excited atom o velocity V x in a velocity class contributes eectively to the sub-doppler retroluorescent signal. It is reasonable to take V x, V x = 1, or V x /2 V x + V x /2 = 0, elsewhere. 9 V x is the width o the V x, V x unction centered on V x =0. On the basis o the preceding paragraph, or a given value o v L (or V x ), the theoretical integrated retroluorescence sub-doppler hyperine signal s n V x originating rom the near-ield region o the interace is given by + s n V x V x, V x D V x, V x, V x dv x = V x, V x D V x, V x, V x, 10 where the symbol * denotes the convolution operation. It will be shown in Subsection 4.C that we have V x max V x, or Fe =5,F g =4 1 V x ; 11 and knowing that the intervals V x and V x max remain practically unchanged or all velocity classes c i,itisimportant to emphasize that the normalized theoretical integrated retroluorescent spectral signal s n V x, corresponding to the population conined in the velocity interval V x max in the near-ield region, is proportional to s n V x 1 2 V x / V x The theoretical signal reproduces a Lorentzian proile with a width V x corresponding to the velocity class and where V x is the experimental variable. The theoretical sub-doppler signal is maximum when the mean velocity V x coincides with the center o the one-dimensional velocity distribution o the ground level. The signal gradually decreases with the laser requency detuning v L rom the Bohr requency v 0 o the transition. By writing V x =, V x = v L v 0, and substituting them into relation (12), in the requency domain one arrives at s n v L 1 2 v L v 0 / Fig. 6. Illustration o the velocity population distribution o the thermalized 6 2 S 1/2 F g =4 ground level (G) and the nonthermalized 6 2 P 3/2 F e =5 excited level population c 1,c 2,c 3 pumped by a quasi-monochromatic diode laser at requency L in the near-ield region o the cell window and Cs vapor interace. For more details, see the text. As a conclusion to the theoretical model, let us note that the sub-doppler signal is a homogeneous proile (Lorentzian) and that is related to the lietime o the excited state (or to the total eective decay rate o the excited atoms in the near-ield region). We can link this theoretical result to the experimental data o the sub-doppler hyperine shape.

7 2248 J. Opt. Soc. Am. B/ Vol. 22, No. 10/ October 2005 Gagné et al. The experimental hyperine sub-doppler signal proile given in Fig. 4 is reasonably itted by relation (13) when is identiied with the experimental linewidth RF estimated to be 90 MHz. Thus RF is a spectral width, which is characteristic o the atomic excited level 6 2 P 3/2 F e =5 in the near-ield region. Now we need to characterize the spectral width RF to evaluate the value o the eective nonradiative decay rate relecting the coupling o the excited atom with the metallic ilm, as shown in Fig. 5. C. Characterization o the Linewidth o the Hyperine 6 2 P 3/2 F e =5 \6 2 S 1/2 F g =4 Signal To characterize contributions o dierent relaxation processes contributing to the experimental retroluorescent atomic line width RF, it is necessary to model the evolution o the population o the excited 6 2 P 3/2 F e =5 level conined in the thin vapor layer near the cell window. Because the atomic transition o interest can be treated as cycling, we consider the near-ield region as a vapor composed o two-level atoms. When the near-ield region is irradiated by a quasi-monochromatic laser beam, the vapor behaves like a mixture o Cs atoms in the ground 6 2 S 1/2 F g =4 level, nonthermalized excited 6 2 P 3/2 F e =5 atoms and atoms in a coherent state or pure state in the presence o a metallic ilm. The sub-doppler retroluorescence spectroscopic method permits an in situ characterization o the nonthermalized excited atoms o a velocity class in the 6 2 P 3/2 F e =5 level between the cell wall covered by a metallic ilm and a semi-ininite ar-ield region. We consider that the cycling transition line undergoes a homogeneous broadening related to the dierent competing relaxation processes o the nonthermalized atoms in the 6 2 P 3/2 F e =5 level. In our elementary analysis we retain three dominant causes generating the relaxation o the excited level: the spontaneous emission process, the process o nonradiative transition o the atomic dipole (atom in the energy hyperine level) due to the presence o the metallic ilm, and the resonant elastic collisions processes. Assuming that the relaxation probability is the same or all the excited atoms conined in the near-ield region, and taking into account the competing relaxation processes o the 6 2 P 3/2 F e =5 level, we sum up the corresponding spectral broadening and obtain the ollowing relation: RF n + coll + nr, 14 where coll is the resonance collisional broadening o the hyperine line, and nr is an additional broadening induced by the nonradiative energy-transer phenomena o the excited atoms near the cell window surace. 13,14 To evaluate nr, we use the FM selective relection spectroscopy technique. According to Akul shin et al. 5 and Vuletic et al., 6 or the FM selective relection or the hyperine line, the ollowing relation holds: RS = n + coll, 15 where RS is the width o a hyperine structure spectral line in selective relection ( RS is equal to the interval between the extrema on the experimental curve). By using Eqs. (14) and (15), we have nr RF RS. 16 Considering the (F g =4-F e =5) line o the selective relection spectra [Fig. 3(b)], we measure the linewidth RS 41 MHz. This value is in agreement with that measured by Akul shin et al. 5 Using the preceding experimental values, we deduce the spectral width associated with the nonradiative relaxation produced by the coupling o the excited atoms in the near-ield region with the metallic ilm: nr RF measured RS measured = 49 MHz. 17 n Note that nr RS. We have A Fe =5,F g =4=2 nr s 1. Using Eq. (15) and the value n 5.3 MHz, we obtain coll =35.7 MHz. The value o the nonradiative decay rate coll associated with the collisions is A Fe =5,F g =4=2 coll s 1. Using both preceding nonradiative decay rate n coll values, we get A Fe =5,F g =4=A Fe =5,F g =4+A Fe =5,F g =4= s 1. From the values o A Fe =5,F g =4, g Fe =5,F g =4, and Eq. (6b), we obtain Fe =5,F g =4 46. With this experimental value o the parameter Fe =5,F g =4, using approximation (8) we estimate that V max x 3.5 m s 1, which is much smaller than V x =76 m s 1 [which conirms inequality (11)]. Thus the experimental values are compatible with Eqs. (4), (9), (12), and (13) o the simple theoretical model used to explain the origin o the sub-doppler hyperine line. The parametric analysis, 4 based on the model developed by Le Bris et al., 3 o the integrated retroluorescence spectra at the temperature o 130 C gives the ollowing value or Fg =4: Fg =4x e 1 =49, 18 where x e is a parameter characterizing the eective geometric depth o the iltering region and is the transition wavelength. The parameter Fg =4 used by the authors in Re. 4 is an eective coeicient, i.e., it is the same or all the hyperine levels: Fe =3,F g =4 = Fe =4,F g =4 = Fe =5,F g =4 = Fg =4. 19 The value o Fg =4 evaluated by the parametric method is compatible with our value o Fe =5,F g =4 or the cycling F e =5 F g =4 transition line. The qualitative agreement between these two values, taking into account the dierence o the two models and the approximations used, conirm the validity o our phenomenological model and experimental method or measuring the atomic Cs 6 2 P 3/2 F e =5 hyperine level eective nonradiative n decay rate A Fe =5,F g =4 associated with the interaction between excited atoms and metallic ilm. The eect o modiication o the lietime o the excited atoms in the vicinity o the metallic ilm 13,14 is relected in the spectral properties o the integrated sub-doppler signal. The value o the eective nonradiative transer rate n A Fe =5,F g = s 1 seems relatively large compared to the spontaneous emission rate g Fe =5,F g =4A Je =3/2,J g =1/ s 1. The morphology o the metallic ilm on the cell window at a temperature o 130 C is not known. It can be complex, made o randomly distributed Cs me-

8 Gagné et al. Vol. 22, No. 10/October 2005/J. Opt. Soc. Am. B 2249 tallic clusters, atoms adsorbed on the clusters, and atoms chemically bonded to the surace. We do not have the necessary inormation to compare our experimental value o Fe =5,F g =4 with a theoretical value that takes into account the real structure o the metallic ilm. There is no theoretical work, to our knowledge, that has thoroughly analyzed such a case. It is well known that the lietime o an excited atom in the vicinity o a metallic ilm is inluenced by its nature, thickness, rugosity, complex dielectric constant, and other actors related to the surace eects (surace plasmons) modiying the nonradiative relaxation rate. 5. CONCLUSION We have conirmed the existence o a sub-doppler structure in the inhibition spectral band o the retroluorescence signal, corresponding to the atomic 6 2 S 1/2 6 2 P 3/2 transition at the interace between glass and saturated Cs vapor at 130 C temperature. Thanks to a comparative analysis with the help o the selective relection spectroscopy method, we have shown that the sub- Doppler hyperine structure o this atomic transition coincides with the sub-doppler structure observed in retroluorescence. A particular analysis o the hyperine 6 2 P 3/2 F e =5 6 2 S 1/2 F g =4 transition has been conducted to evaluate the inluence o the presence o a metallic ilm at the interace or this atomic transition. The origin o the sub-doppler line is mainly governed by the kinematic properties o the populations o the excited velocity classes conined in the vapor layer in the near-ield region o the cell. In act, in this region a raction o the nonthermalized population o a velocity class behaves like a two-dimensional vapor normal to the laser beam direction, playing the dominant role on the nature o the sub- Doppler proile. The population o a velocity class conined between the metallic ilm and the ar-ield region constitutes the eective population o radiating atoms generating the sub-doppler retroluorescent signal. The eect o the metallic ilm on the eective excited atom in the hyperine 6 2 P 3/2 F e =5 level in the near-ield region has been measured when the cell temperature is 130 C by using simultaneously both the retroluorescence and FM selective relection spectroscopic methods. We believe that the utilization o a requency modulation technique to suppress the retroluorescent signal originating rom the ar-ield region will improve the observation and the resolution o the sub-doppler hyperine signal. Because the cell is slightly tilted, there is an additional broadening mechanism involved. It will be interesting to evaluate the relative value o this eect. Measurements as a unction o laser intensity and measurements with the atomic 894 and 455 nm transitions would be interesting to complement the analysis. It is desirable to carry out a more elaborate theoretical development to justiy the phenomenological approach used or the estimation o the eective nonradiative relaxation rate o a hyperine excited level due to the coupling between an excited atomic state and a metallic ilm. We would also like to point out the physical analogy between the hyperine spectral properties o our vapor cell and the spectral properties o a vapor conined in an extremely thin cell studied by Sarkisyan et al. 15 and Briaudeau et al. 11 where the ar-ield region, in our case, plays the role o a photonic and atomic trap where the population o a velocity class and the resonant photons are thermalized. ACKNOWLEDGMENTS We acknowledge inancial support or this work rom the Natural Sciences and Engineering Research Council o Canada. REFERENCES 1. K. Zhao, Z. Wu, and H. M. Lai, Optical determination o alkali metal vapor number density in the vicinity 10 5 cm o cell suraces, J. Opt. Soc. Am. B 18, (2001). 2. V. G. Bordo, J. 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