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Doppler-free fluorescence induced by strong quasi-resonant laser field
DOPPLER-FREE
March 1979
OPTICS COMMUNICATIONS
Volume 28. number 3
FLUORESCENCE
INDUCED BY STRONG QUASI-RESONANT
LASER FIELD
A.K. POPOV and L.N. TALASHKEVICH L. V. Kirensky Institute of Physics, USSR Academy of Sciences, Siberian Branch and Krasnoyarsk University, 660036, Krasnoyarsk, USSR
Received 17 November 1978
Alteration of the frequency-correlation properties and Doppler widths of the double-quantum and double-step processes with the increase of the field strength is considered. Possibilities to observe laser-induced Doppler-free fluorescence at the electronic-vibrational molecular transitions are shown. Various transitions can be involved into the Doppler-free regime when the pump field strength is varied.
The concept of multistep and multiphoton processes takes up an important place in contemporary laser physics. Under resonant conditions their distinctions decrease and separation criterions of these processes become of particular interest. The corresponding theory has been developed in ref. [ 11. It was shown that with the increase of the strength of the illuminating field the correlation between input and scattered frequencies is altered for both processes and their distinctions vanish. The possibilities of Doppler-free not only two-photon-absorption-type but Raman-type spectroscopy due to the mentioned alteration were emphasized. In this paper we show that the condition for laserinduced Doppler-free fluorescence can be satisfied in molecular spectra. We will consider fluorescence at the frequency w,, and wave-vector k, as a function of a2, = w,, - arnl detunings. A molecule is illuminated by the field E at the frequency o and wave-vector k. This field is quasiresonant with the adjacent transition arnn with detuning m = 0 - arnn. It is supposed that IGl 3 max{ku, ls21) and when E = 0, only the level n is populated. Here hG = -Ed,, is the interaction energy, and ku the Doppler half-width of the mn transition. Then, as it was shown in ref. [l], the fluorescence probability w,, at wcI, averaged over the distribution of molecule velocities v, for example for fluorescence (Raman-like) level scheme Em > El > En is equal to
-1
IGG,12
Yrn
Re
(w,) = Cl2 +
41G12
yl t CUTt i[s2, - (k,-M1k)v]
r,l
t y/to;
(1)
ti[fi2,-(k,-M1k)v]
Here yi are the corresponding o1,2=4(7m
level half-widths,
‘Yn+ia2)
f i{ ICI2 t $ [a - i(-y, - -rm)]2}1/2
,
(2)
Ml,, = dim cu,,,/dR if7,
=Yn>
M, 2 = ; [l f a(a2
+ 41G12)-‘/2]
(3) .
An expression for the double-quantum absorption case (Em > En > El) can be easily obtained from (1) by substitution a -+ &?;M,,, -+ -M1,2. One can see that fluorescence light consists of two components with the center positions R,, 2 = Im oyl 2 depending on the intensity of the strong field E. The’ “memory factors” M, 2 represent the degree of correlation between u,, and o for each component. When G -+ 0 then crl + y,., t iR, Ml -+ 1 (complete correlation); o2 + yrn, M2 + 0 (no correlation), and the corresponding components can be interpreted as due to two-photon and step-wise processes. For the simplest case yn = -rrn = r/2 in the strong (ICI 9 ku) field of al,2 + I * ilGI,M1,2-+ l/2 and the interpretation 315
Volume
28, number
3
OPTICS COMMUNICATIONS
such radiative processes as multistep and multiphoton appears to have no physical meaning. Moreover, as a consequence of this behaviour eq. (1) predicts the dependence of the Doppler width ]k,, -- Mi,2k]u of the spectral components not only on the angle between k, and k but on the intensity of E. When E is weak (C Q ku) the condition of Dopplerfree spectroscopy can be satisfied only for the twophoton absorption (k,, = -k) because in the Raman case k, f k. In a strong field E, the condition of Doppler-free spectroscopy becomes possible even for k, # k (c+[ # wmil). With the increase of E M, varies from 1 to l/2 and M, from 0 to I/?. Thus, quasi-double-quantum emission at the transition with = k) and quasi-two-step emission at %l = %2/Z (k/l the transitions with c+,,, < c+rn (kp
ku} .
(4)
The above formulated conditions of laser-induced Doppler-free quasi-resonant fluorescence can be easily satisfied for the molecular spectra even in the cw illuminating field. For the chosen transitions the emission at various adjacent electronic-vibrational ml transitions can be involved into the Doppler-free regime. For in-
316
March 1979
stance, a lot of electronic-vibrational transitions of the B III, * X 1”: system of Na, resonate with various lines of the argon-ion laser [2,3], and its radiation with X = 5 14.5 nm is resonant to a lot of transitions of I, [4]. Using the data from [2-61 and supposing a power of 50 W is focused with the confocal parameter b = 10 cm into the area A = bX/4 = 4 X lo5 W/cm2 one can estimate that the factor G lies within the interval of 1 to 4 cm-l for different transitions of Na, and within 0.03 to 0.04 cm-l for 12, Factor M, varies within the interval of 0.93 to 0.507 and M, from 0.067 to 0.493 cm-l for the above mentioned Na, transitions. For I2 the factor M, varies within the interval of 0.994 to 0.73, and M, from 0.006 to 0.27. Thus, for example, laser-induced fluorescence at the U’= 10 + u’l = 19 P(13) transition of Na, can be involved in the Doppler-free regime with the pumping power of about 0.1 W. For other transitions this power appears to be much less.
References [l]
T. Ya. Popova, A.K. Popov, S.G. Rautian and A.A. Feoktistov, ZETF 52 (1969) 444. [ 21 W. Demtroder, M. Clintock and R.N. Zare. J. Chem. Phys. 51 (1969) 5495. [3] W. Demtrodcr and M. Stock, J. Mol. Spectr. 55 (1975) 416. [4] G.D. Patterson, S.H. Dworetsky and R.S. Hozack, J. Mol. Spectr. 55 (1975) 175. [5] R.N. Zare and W.J. Tango, J. Chem. Phys. 53 (1970) 3094. [6] A. Gene, A. Capelle and H.P. Brodia, J. Chem. Phys. 58 (1973) 4212.
March 1979
OPTICS COMMUNICATIONS
Volume 28. number 3
FLUORESCENCE
INDUCED BY STRONG QUASI-RESONANT
LASER FIELD
A.K. POPOV and L.N. TALASHKEVICH L. V. Kirensky Institute of Physics, USSR Academy of Sciences, Siberian Branch and Krasnoyarsk University, 660036, Krasnoyarsk, USSR
Received 17 November 1978
Alteration of the frequency-correlation properties and Doppler widths of the double-quantum and double-step processes with the increase of the field strength is considered. Possibilities to observe laser-induced Doppler-free fluorescence at the electronic-vibrational molecular transitions are shown. Various transitions can be involved into the Doppler-free regime when the pump field strength is varied.
The concept of multistep and multiphoton processes takes up an important place in contemporary laser physics. Under resonant conditions their distinctions decrease and separation criterions of these processes become of particular interest. The corresponding theory has been developed in ref. [ 11. It was shown that with the increase of the strength of the illuminating field the correlation between input and scattered frequencies is altered for both processes and their distinctions vanish. The possibilities of Doppler-free not only two-photon-absorption-type but Raman-type spectroscopy due to the mentioned alteration were emphasized. In this paper we show that the condition for laserinduced Doppler-free fluorescence can be satisfied in molecular spectra. We will consider fluorescence at the frequency w,, and wave-vector k, as a function of a2, = w,, - arnl detunings. A molecule is illuminated by the field E at the frequency o and wave-vector k. This field is quasiresonant with the adjacent transition arnn with detuning m = 0 - arnn. It is supposed that IGl 3 max{ku, ls21) and when E = 0, only the level n is populated. Here hG = -Ed,, is the interaction energy, and ku the Doppler half-width of the mn transition. Then, as it was shown in ref. [l], the fluorescence probability w,, at wcI, averaged over the distribution of molecule velocities v, for example for fluorescence (Raman-like) level scheme Em > El > En is equal to
-1
IGG,12
Yrn
Re
(w,) = Cl2 +
41G12
yl t CUTt i[s2, - (k,-M1k)v]
r,l
t y/to;
(1)
ti[fi2,-(k,-M1k)v]
Here yi are the corresponding o1,2=4(7m
level half-widths,
‘Yn+ia2)
f i{ ICI2 t $ [a - i(-y, - -rm)]2}1/2
,
(2)
Ml,, = dim cu,,,/dR if7,
=Yn>
M, 2 = ; [l f a(a2
+ 41G12)-‘/2]
(3) .
An expression for the double-quantum absorption case (Em > En > El) can be easily obtained from (1) by substitution a -+ &?;M,,, -+ -M1,2. One can see that fluorescence light consists of two components with the center positions R,, 2 = Im oyl 2 depending on the intensity of the strong field E. The’ “memory factors” M, 2 represent the degree of correlation between u,, and o for each component. When G -+ 0 then crl + y,., t iR, Ml -+ 1 (complete correlation); o2 + yrn, M2 + 0 (no correlation), and the corresponding components can be interpreted as due to two-photon and step-wise processes. For the simplest case yn = -rrn = r/2 in the strong (ICI 9 ku) field of al,2 + I * ilGI,M1,2-+ l/2 and the interpretation 315
Volume
28, number
3
OPTICS COMMUNICATIONS
such radiative processes as multistep and multiphoton appears to have no physical meaning. Moreover, as a consequence of this behaviour eq. (1) predicts the dependence of the Doppler width ]k,, -- Mi,2k]u of the spectral components not only on the angle between k, and k but on the intensity of E. When E is weak (C Q ku) the condition of Dopplerfree spectroscopy can be satisfied only for the twophoton absorption (k,, = -k) because in the Raman case k, f k. In a strong field E, the condition of Doppler-free spectroscopy becomes possible even for k, # k (c+[ # wmil). With the increase of E M, varies from 1 to l/2 and M, from 0 to I/?. Thus, quasi-double-quantum emission at the transition with = k) and quasi-two-step emission at %l = %2/Z (k/l the transitions with c+,,, < c+rn (kp
ku} .
(4)
The above formulated conditions of laser-induced Doppler-free quasi-resonant fluorescence can be easily satisfied for the molecular spectra even in the cw illuminating field. For the chosen transitions the emission at various adjacent electronic-vibrational ml transitions can be involved into the Doppler-free regime. For in-
316
March 1979
stance, a lot of electronic-vibrational transitions of the B III, * X 1”: system of Na, resonate with various lines of the argon-ion laser [2,3], and its radiation with X = 5 14.5 nm is resonant to a lot of transitions of I, [4]. Using the data from [2-61 and supposing a power of 50 W is focused with the confocal parameter b = 10 cm into the area A = bX/4 = 4 X lo5 W/cm2 one can estimate that the factor G lies within the interval of 1 to 4 cm-l for different transitions of Na, and within 0.03 to 0.04 cm-l for 12, Factor M, varies within the interval of 0.93 to 0.507 and M, from 0.067 to 0.493 cm-l for the above mentioned Na, transitions. For I2 the factor M, varies within the interval of 0.994 to 0.73, and M, from 0.006 to 0.27. Thus, for example, laser-induced fluorescence at the U’= 10 + u’l = 19 P(13) transition of Na, can be involved in the Doppler-free regime with the pumping power of about 0.1 W. For other transitions this power appears to be much less.
References [l]
T. Ya. Popova, A.K. Popov, S.G. Rautian and A.A. Feoktistov, ZETF 52 (1969) 444. [ 21 W. Demtroder, M. Clintock and R.N. Zare. J. Chem. Phys. 51 (1969) 5495. [3] W. Demtrodcr and M. Stock, J. Mol. Spectr. 55 (1975) 416. [4] G.D. Patterson, S.H. Dworetsky and R.S. Hozack, J. Mol. Spectr. 55 (1975) 175. [5] R.N. Zare and W.J. Tango, J. Chem. Phys. 53 (1970) 3094. [6] A. Gene, A. Capelle and H.P. Brodia, J. Chem. Phys. 58 (1973) 4212.