SELECTIVE REFLECTION - METHOD OF INTRADOPPLER SPECTROSCOPY OF OPTICALLY DENSE GASEOUS MEDIA V. A. Sautenkov, A. M. Akul'shin, and V. L. Velichanskii

UDC 621.373.826:535.338.334

To study optically dense gaseous media, where the absorption length at resonance frequencies is comparable to the wavelength of the radiation, it is virtually impossible to employ traditional methods for eliminating the Doppler broadening of atomic lines [I]. Intradoppler spectroscopy of optically dense gases must apparently be based not on the passage of radiation through a cell with gas, but rather on reflection. The resonant increase in the coefficient of reflection from the interface between a transparent dielectric and a gas near an absorption line of the gas is known as selective mirror reflection (SMR) [2]. Intradoppler resonances of saturated reflection have been recorded comparatively recently under glancing incidence of two oppositely propagating laser beams on a cell with sodium vapors [3]. However the form of the resonances was not analyzed. Intradoppler resonances of SMIR, observed on the resonance lines of mercury [4], sodium [5, 6], cesium [7-11], and potassium [II] accompanying the propagation of incident radiation along the normal to the interface between a transparent dielectric and a gas, have been studied in greater detail. It is significant that intradoppler resonances of reflection are formed with linear interaction of the resonance radiation with the atoms of the gas. The narrowing of the contour of selective reflection at low pressures, where the homogeneous width 7 is less than the Doppler broadening of the atomic line AgD, is explained in [12] by depolarizing collisions of gas atoms with the window of the cell. The nonlocal coupling between the polarization of atoms flying away from the window and the external field leads to the appearance of a narrow resonance of SMR at the frequency of the atomic transition ~0. In [12, 7] an approximate expression R ~ -in[(4Av 2 + 72)/Av~] was obtained for the peak of the intradoppler resonance of SMR (4&v 2 + 72 ) << A ~ , ~ - ~0 = A9. In [8] it was found that the derivative of the intradoppler resonance of SMR with respect to the frequency has the form of a Lorentzian dispersion curve

R'~

4hvu-[-Y

z 9

(1)

The frequency interval F between the extrema of the derivative R' is called the width of intradoppler resonance of SMR (F = 7). The impact self-broadening constant of the D 2 line" k = ~F/AN was first measured in [9, 11] based on the dependence of the width of the resonance of reflection F on the concentration of cesium atoms N. The constant obtained equals within the limits of the measurement error (=10%) the theoretical value k T = 1.2.10 -7 Hz'cm s [13]. Nonlinear SMR was analyzed theoretically for two limiting cases: a) high (~ >> 7) [14] and b) low (~ < 7) [15] intensities of the laser radiation. Here ~ = Ed/h; E is the amplitude of the light field; and, d is the dipole moment of the atomic transition. Power broadening accompanying high radiation intensity ~ >> 7 was recorded in [16]. The purpose of this work was to study experimentally the form of intradoppler resonances of SMR with different intensity of the resonance radiation incident on the cell with the gas I = cE2/8~. A diagram of the experimental setup is shown in Fig. i. The selective reflection in the vicinity fo the D 2 line of ISSCs (the wavelength equals 852 nm and the radiation linewidth 7r = 5.3 MHz, A~D = 21.8 TI/2) [ii] was studied. A semiconductor injection laser with

1989.

Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 50, No. 2, pp. 260-263, February, Original article submitted January 12, 1988.

0021-9037/89/5002-0189512.50

9 1989 Plenum Publishing Corporation

189

L

J

117

Fig. I. Diagram of experimental setup for studying selective reflection from alkali-metal vapor: i) injection laser; 2) microobjective; 3) rotating mirror based on a piezoelectric ceramic; 4) holographic selector; 5) output objective; 6) photodiode; 7) confocal scanning interferometer with a baseline of 22 cm and sharpness of 30; 8) electronic circuit for automatic control of the lasing frequency of the laser; 9) generator of a linearly varying voltage; I0) cell with cesium vapors; ii) automatic plotter; 12) synchronous detector. an external resonator (ILER) was employed as a source of frequency-tunable monochromatic radiation. The injection laser (laser diode) based on the compound GaAIAs operated in the continuous mode at room temperature. A holographic total internal reflection selector [Ii, 17] was employed to tune the wavelength of the radiation of the ILER within the gain line =10 nm. The output power equalled approximately 5 mW. The lasing frequency of ILER was stabilized based on the transmission resonance of a confocal scanning interferometer. The thermal drift of the resonances of the interferometer did not exceed 1 MHz over 1 min. A system for stabilizing and monitoring the spectrum is described in [17]. The width of the radiation spectrum of the stabilized ILER equalled 0.5 MHz with an averaging time of 0.1 sec. Part of the laser radiation (=3 mW) was directed into a glass cell with saturated cesium vapor, placed in a thermostat. T h e concentration of cesium atoms N at the temperature of the cell T was determined from the Langmuir-Taylor formula [ii]. The intensity I of the laser radiation incident on the cell was varied from 0.1 mW/cm 2 up to 5 W/cm 2 with the help of focusing optics and calibrated attenuators. The angle of incidence of the radiation 8 on the internal face of the window of the cell and the nonparallelism of the light beam ~ had an upper limit of 6.10 -2 rad. In the process of recording the spectral dependence of the reflection coefficient the signal from the FD-24K photodiode was fed directly into an automatic plotter. The derivative of the intradoppler resonances of SMR was recorded by means of synchronous detection of the signal after narrow-band amplificationat 20 kHz (the deviation of the lasing frequency was set to be quite small, 16vl << 7). The spectra were recorded over a time of 3 min. The error in measuring F did not exceed 5%. The collisional shift of the intradoppler resonances of SMR was measured for atom concentrations in the range 3.1012 cm -s ~ N ~ 3.1014 cm -2. It was found that AVe/AN < 10 -8 Hz.cm s. As the concentration of atoms N and the intensity of the radiation I were increased appreciable broadening of intradoppler resonances of SMR occurred. It should be noted that even with linear reflection (6 << 7) the width of the resonance F differed from the computed homogeneous linewidth X = Xr + kTN by 3-4 MHz. The difference 6 = F - 7 is due to the presence of residual Doppler broadening (8 + ~)A~ D [5, 9] and the finite spectral resolution of 0.5 MHz. The spectral contour of SMR with virtually linear interaction of laser radiation with cesium atoms (N = 2.1014 cm -s, I = 1 mW/cm 2, ~ < 0.i 7) is presented in Fig. 2a. The width of the intradoppler resonances of reflection F = 33 MHz. The power broadening of intradoppler resonances of SMR with the rate of excitation of cesium atoms comparable to the rate of relaxation (6 = 2X) is demonstrated in Fig. 2b. Figure 3 shows the experimental and computed spectral dependences of the frequency derivative of the linear coefficient of reflection ( N = 1.5.10 z4 cm -s, 8 < 0.i X) in the vicinity of the transition (F = 3 - F' = 3). In the calculation of R' = =Ag/[4Av 2 + F 2] the quantity F was set equal to the measured width of the reflection resonance 26 MHz. The other adjustable parameter ~ was determined so as to achieve the best agreement between 0~max/2F and C~min/2F (A9 = • and the experimental data. One can see that the experimental de-

190

R1

b

v3z v~3 vx~

F

v

Fig. 2

-I

Fig. 3

Fig. 2. Intradoppler resonances of SMR on transitions 6Sl/= (F = 3) - 6Pa/2 (F' = 2, 3, 4) of the cesium atom with linear (a) (I = 1 M W / c m 2) and nonlinear (b) (I = 1 W/cm 2) interaction of laser radiation with the vapors. Fig. 3. Spectral dependence of the frequency derivative of the linear contour of SMR near the resonance frequency Vsa with N = 1.5.1014 cm -3, I = 1 mW/cm 2. i) Experimental curve; 2) computed curve. pendence of the derivative of the contour SMR agrees qui~e well with the Lorentzian dispersion curve. The discrepancy for detunings Av > F/2 could be associated with the fact that in the calculation the effect of neighboring atomic transitions F - F' was neglected. In addition, it must not be forgotten that a simple asympotic approximation was employed to calculate R' Special attention was devoted to the change in the spectral dependence of the coefficient of SMR as the intensity of the laser radiation incident on the cell was increased. For N ~ 2.1014 cm -a and 0.i y ~ ~ ~ Av D, taking into account the instrumental width 6, the expression F 2 = ~ + 6 2 was obtained based on the experimental data. On the whole R' follows closely the Lorentzian dispersion curve:

R,

4Av2 q_ Vz + ~2

(2)

The analytical expression for the coefficient of SMR for ~ >> ~ in [14] agrees with our empirical formula

R~_ln[ 4Av~-~?~+i 3~] " aG

(3)

In [15] an error was apparently made in the calculations of the contour of SMR for ~ < 7, since the nonlinear dips predicted in this work at the frequencies of the atomic transitions were not observed in the experiment.' Only the power broadening of intradoppler resonances of SMR without any qualitative change in their shape was recorded. Thus the investigation of nonlinear selective reflection at low pressure of alkali-metal vapors yielded an empirical formula describing the form of the intradoppler resonance of SMR for different intensities of the incident resonance radiation. The experimental and theoretical data were compared. A real possibility for using the narrowing of the contour of SMR for ~ < AVD, owing to the nonlocal nature of the polarization of the gas atoms, for intradoppler spectroscopy of optically dense gaseous media has opened up. In addition to studying the hyperfine structure, impact self-broadening, and the collisional shift of resonance atomih lines, the new method appears to be promising for studying the effect of strong light fields on collisional processes in gases [18]. We thank T. A. Vartanyan, A. M. Dykhne, and I. I. Sobel'man for their interest in this work and G. T. Pak for providing the laser diodes. 191

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Ii. 12. 13. 14. 15. 16. 17. 18.

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