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Polarization intermodulated excitation (POLINEX) spectroscopy of the CuI 578.2 nm transition
Volume 38, number 5,6
OPTICS COMMUNICATIONS
1 September 1981
POLARIZATION INTERMODULATED EXCITATION (POLINEX) SPECTROSCOPY OF THE Cul 578.2 nm TRANSITION ¢~ Ph. DABKIEWICZ *, and T.W. HANSCH Department of Physics, Stanford University, Stanford, CA 94305, USA
Received 19 May 1981
Doppler-free spectra of the 578.2 nm transition of CuI atoms in a hollow cathode discharge have been recorded using Polarization Intermodulated Excitation (POLINEX). The POLINEX spectra, which are free of Doppler-broadened background despite velocity changing elastic collisions, are discussed and related to spectra recorded under the same experimental conditions with the older intermodulated fluorescence method.
1. Introduction
We have studied the 578.2 nm (3d 10 4p 2P1/23d 9 4s 2 2D3/2) transition of CuI atoms in a hollow cathode discharge by high resolution laser spectroscopy, using polarization intermodulated excitation (POL1NEX) [ 1]. Spectra free of Doppler-broadened pedestals could be observed despite velocity changing elastic collisions suffered by the absorbing metastable Cu atoms. We have also recorded spectra by the older intermodulated fluorescence method [2] under otherwise identical experimental conditions. The relatively complicated hyperfine spectrum reveals the differences in line strengths for co- and counter-rotating polarizations of the two laser beams, and it elucidates the close relationship between POLINEX spectroscopy and the older technique. The observed relative line strengths can be qualitatively reproduced by anisotropy factors which have been calculated in a rate equation approach. Long used in atomic spectroscopy, hollow cathode discharges have recently attracted interest for high resolution Doppler-free laser spectroscopy of excited atoms [3,4], because they can give convenient access ¢~Work supported by the National Science Foundation under Grant PHY-80-10689 and by the U.S. Office of Naval Research under Contract ONR N00014-78-C-0403. * Fellow of the Deutsche Forschungsgemeinschaft.
to many different elements, including refractory metals which would be difficult to vaporize by other means. In exploratory experiments, Doppler-free spectra of the 578.2 nm transition of copper have been successfully recorded in such discharges both by saturated absorption spectroscopy [3] and by intermodulated fluorescence spectroscopy [5]. However, even with a discharge tube especially designed for high resolution spectroscopy [5], the gas pressure remained so high that the spectra were complicated by large Doppler broadened pedestals underneath the Doppler-free signals. These pedestals have been ascribed to velocity changing elastic collisions which redistribute the atoms over the Maxwellian velocity distribution [6]. Similar pedestals had been observed previously for neon transitions [6,7,1] in positive column discharges. Neon spectra free of such pedestals could be recorded by polarization spectroscopy [7] and by the new POLINEX method [1 ], which can be applied even to weakly absorbing samples. In both these techniques the signals are due to light-induced atomic alignment or orientation, and atoms which have suffered velocity changing collisions will no longer contribute to the signal, if their polarization is destroyed in the collisions. Our present experiments suggest that the POLINEX method may provide a rather general technique for obtaining clean Doppler-free spectra even under the nonideal conditions inside a hollow cathode discharge tube. 351
Volume 38, number 5,6
OPTICS COMMUNICATIONS
1 September 198
2. Theory ++ In Doppler-free saturation spectroscopy the nonlinear interaction of two counterpropagating beams in an absorbing gas is observed. The POLINEX method is such a Doppler-free technique in which the polarization of one or two beams is modulated, while their intensity remains constant. A modulation in the total rate of absorption occurs when the absorption depends on the relative polarization. If we assume that the two counterpropagating beams are circularly polarized and that the quantization axis is chosen along the direction of light propagation, then the appropriate equation for the total rate of absorption is formula (2) of ref. [ 1 ]. In this formula only the last cross-saturation term
~+1~,
e~ @
if= (n - n')(7 -1 + 3"-1)(h6o)-2 X 2Ili 2 ~,
Omm,(ql)Omm,(q2)
mm
depends on the relative polarization of the two beams and gives rise to the POLINEX signal. Here n = iV/ (2./+ 1) and n' =N'/(2I' + 1) are the unsaturated equilibrium populations of the lower and upper states, 3' and 3" are the respective level decay rates, 11 and 12 the intensities of the two beams with the circular polarization q i and q2, and Ornm,(q) is the absorption cross-section for a dipole transition from an angular m o m e n t u m sublevel IJ, m) to an upper level IJ', m'), where m' = m + q, q = +-1, dependent on the circular polarization. The same cross-saturation term (1) can be used to describe the signal in the older (intensity) intermodulated fluorescence method. Here the intensities I 1 and 12 of the two beams are modulated with the frequencies f l and f2 respectively, and the signal is detected with a phase sensitive detector at the sum frequency 0el + f2)" Although all terms of formula (2) in ref. [ 1 ] are intensity dependent, only the cross-saturation term (1) is intermodulated at the sum (and difference) frequency. In the intermodulated fluorescence method the polarization of the two counterpropagating beams is constant. The signal is proportional to the change in absorption rate of one beam induced by the other and vice versa. For co-rotating polarizations both beams interact preferentially with atoms of the same orienta352
71-. ~!7Z
o e~
(1)
+
~,~
0)
I
,S c-
o e~ +a
e~
+ e~
II
H
I
"5
~'~ II
II
Volume 38, number 5,6
OPTICS COMMUNICATIONS
tion and the mutual saturation should be stronger in this case than for counter-rotating polarization. Thus one expects stronger Doppler-free intermodulated fluorescence signals for co- than for counter-rotating light fields. The corresponding POLINEX signals will be proportional to this difference in absorption ra.te if the polarization is modulated between co- and counter-rotation. This close relationship between both methods can be expressed in a common formula for the amplitude of the saturation signal:
~LS+,-, a oc IlI2O2~1,-, ~.
(2)
Here o is the averaged absorption cross section for unpolarized atoms, ~'~j, and ~-~, are the anisotropy factors for the intermodulated signals with the two circularly polarized light fields rotating in the same (+) and in the opposite ( - ) sense respectively, and ~~j, = ~'~j, - ~'jj, is the anisotropy factor for the POLINEX signal when the polar!zation of one beam is modulated between left- and right-hand circular polarization. The factors ~'~j, and ~'jj, are calculated by evaluating the sum of Clebsch-Gordan coefficients in formula (1) similar to the calculations for polarization spectroscopy [8]. The results are listed in table 1, together with the factor * ~j,, from ref. [1] which is also included for completeness.
1 September 1981
The anisotropy factors for linear polarization are also listed in table 1. Here ~'~./, and ~')j, denote the anisotropy factors for the intermodulated fluorescence signals with linearly polarized beams of parallel (11) and perpendicular (±) relative polarization, and ~'~j,= ~'~j,- ~'~j,is the anisotropy factor * for the corresponding POLINEX signals. The treatment of the cross-over signals is similar. These results are listed in table 2, together with the factor ~ ~j,j, from ref. [8] for completeness. H e r e J denotes the angular momentum of the common level, J' and J" those of the two other levels involved in the transition. From the anisotropy factors of table 1 one expects intermodulated signals larger or equal for co- than for counter-rotating polarization in all level configurations. Thus the corresponding POLINEX signals should have all the same sign. For cross-over signals, however, there exist two level configurations J -+ J, J + 1 and J-+ J - 1, J - 1 for which one expects, from table 2, smaller intermodulated signals for co- than for counter. rotating fields and POLINEX signals with the opposite sign. #: The anisotropy factors ~'~xarand ~j,j,, from this paper are identical with the factors ~jj, from ref. [1] and ~jdlj 2 from ref. [8] respectively.
Table 2 The anisotropy factor ~jj,j,, for cross-over signals av
J"
J-1
J
J-1
J+l
Circular polarization
3(33"+2) 10/
9(./-1) 10J
Linear polarization
__3 2./
3
9
3
1--0
}-
-2-
,:b,:
6::
3(J- 1) 5J
3(4/+1) 10J
4:: 3(2/+3) 10J
6
9
3
5
10
10
3(J+2) 5(J+l)
3(4J+3) 10(J+l)
J
J+l
3(3,/+1) 10(J+l)
9(./+2) 10(J+l)
J+l
J+l
3(62j+12J+5) 5(J+l)(2J+ 3)
3(J+2)(2J+5) 10(J+ 1)(2J+3)
3,/ 2(./+1)
3(4./2+8./+5) 5(./+1)(2./+3)
3(J+2)(6J+5) 10(J+ 1)(2J+3)
3./(2/- 1) 10(J+l)(2J+3)
J
ar
3(2/2+2/+1) 5J(J+ 1)
3(2/-1)(2/+3) 10J(J+ I )
3 2J(J+l)
3(3./2+3./- 1) 5J(J+l)
3(2/2+2/+1) 10J(J+l)
3(2/+3)(2./-1) 10J(J+l)
J-I
J-1
3(6./2-1) 5J(2J-1)
3(./-1)(2./-3) lOJ(2/-1)
3(./+1) 2./
3(447+1) 5J(2/-1)
3(J- 1)(6J+l) 10J(2/-1)
3(2da+SJ+3) 10./(2./-1)
3 2(J+l)
3(2J-1) 10(J+l)
353
Volume 38, number 5,6
OPTICS COMMUNICATIONS
These results from a rate equation approach hold only for low intensities and a Doppler-width which is large compared to the natural linewidth. Also spontaneous reemission from the upper into the lower state and multiple optical pumping cycles have been ignored. For the Cu transition under investigation this is a good approximation since the upper level decays predominantly via an additional radiative decay channel towards the ultraviolet.
3. Experiment The experimental set-up is similar to that described in ref. [I]. The output of a cw ring laser (Coherent Radiation, Model CR 699-21) is passed through a linear polarizer and a ),/4 plate wave to produce circularly polarized light. Then the laser beam is split into two parts of approximately the same intensity (0.18 W/ cm2). One of the beams is sent through an electrooptic modulator (Lasermetrics Model LM- 1FW without linear polarizer) which has a clear aperture of 2.3 mm diameter. A lens before the beam splitter focuses the beam at the site of the modulator, and produces a diameter of about 5mm for both beams at the interaction region. For POLINEX spectroscopy an ac-voltage is applied to the modulator to generate approximately a modulation between right- and left-hand circular polarization. The same set-up is used for intermodulated fluorescence spectroscopy, but in addition an intensity chopper for both laser beams is introduced. Now a dcvoltage is applied to the modulator to produce righthand and left-hand polarization, respectively. The atomic copper density is generated in a hollow cathode discharge which is described in detail in ref. [5]. It is operated at a discharge current of 110 mA and a pressure of 0.35 Torr of Ar. The saturation signal is monitored via fluorescence. Since the upper level of the transition under examination has an additional stronger radiative decay channel towards the ultraviolet, this transition at 327.4 nm is used to record the signal.
4. Discussion Natural copper consists of the two odd isotopes 354
1 September 1981
63Cu and 65 Cu with a relative abundance of 69.09% and 30.91% respectively [9]. Since the nuclear spin of both isotopes is I = 3/2, the hyperfine structure of the 587.2 nm (3d 10 4p 2P1/2-3d94s2 2D3/2) transition consists of six hyperfine components for each iso tope. Fig. 1 displays three scans from this transition. Scan (a) and (b) are intermodulated fluorescence spectra recorded with the two light fields co- (a) and counter-rotating (b) respectively. Spectrum (c) is recorded with the POLINEX method under otherwise the same experimental conditions. Both of the intermodulated fluorescence spectra (a) and (b) clearly reveal a large Doppler-broadened background resulting
/
(a)
A, (b)
(c) F' F
I
0
'
2
2
I 2
I
I
I
I
3
3
2
2
I
• I
I11
'
'
I 21 I II 221 ..
'
I
'
'
'
.
.
I 2 I I t I I I0 .
'
I0
DETUNING
(d)
.
I1111 I I I:,1
5
LASER
.
2 I I I I0
,
[_1 15
[GHz]
Fig. 1. Hyperfine spectrum of the 578.2 n m transition of CuI, a) Intermodulated fluorescence spectrum with co-rotating polarization of the mutual laser beams, b) Intermodulated fluorescence spectrum with counter-rotating polarization, c) POLINEX spectrum, d) Position of the hyperfine components. Those of 65Cu are marked with "*". The position of the cross-over signals is indicated by dashed lines.
Volume 38, number 5,6
OPTICS COMMUNICATIONS
from velocity changing elastic collisions while in the POLINEX spectrum (c) this background is completely eliminated. Comparing the Doppler-free signals of the two intermodulated spectra (a) and (b) the signal strengths recorded with co-rotating fields (a) are larger than or equal to those recorded with counter-rotating polarization (b), in agreement with the considerations presented above. Figure 2 shows a detail spectrum of the F = 2 ~ F ' = 1 and F = 2 ~ F ' = 2 transitions of 63Cu and their cross-over signal. From table 1 the anisotropy factors ~ j , and ~'jj,, for the F = 2 ~ F' = 1 transition are calculated to 2.3 and 0.05 respectively. The corresponding factors for the F = 2 ~ F ' = 2 transition are 1.3 and 1.05. Since both transitions have the same dipole transition strength [10] one expects the smallest intermodulated signal for the F = 2 ~ F ' = 1 transition
(o)
(b)
(e)
F'
I
F I
I
I
I
2
I
I
2
2
I
I
o
I
I
'
I
I
t
I
LASER
!
(d) I
I
I
i
2
DETUNING
[GHz]
Fig. 2. Detail spectrum of the F = 2 --, F' = 1 and F = 2 ~ / 7 = 2 hyperfine components of the 578.2 nm transition of 63Cu. Label (a), (b), (c), and (d) as in fig. 1.
1 September 1981
and counter-rotating polarization. The POLINEX method, however, is sensitive to the difference ~'~j, = ]}j, - ~ j j , , so one expects a larger POLINEX signal for this transition than for the transition F = 2 -+ F ' = 2, in qualitative agreement with the spectra in fig. 2. For the transition F = 0 -~ F' = 1 the Doppler-free signals from the intermodulated fluorescence spectra in fig. la and lb have about the same strength, while there is no indication for a signal in the POLINEX spectrum from fig. lc. These experimental observations are in agreement with the anisotropy factors calculated from table 1, which give the same value for ~'~j, and ~']j, and zero for ~ , . Physically this means that a J = 0 state cannot be oriented. Since for the transition under investigation the saturation effect results predominantly from this lower J = 0 metastable state (r ~ - 1 ) the saturation cross-section for the J = 0 -+ J ' = 1 transition is independent of the relative polarization of the mutual beams and therefore no POLINEX signal should occur. For the cross-over signals the anisotropy factor ~'~,j,, from table 2 correctly reproduces the positive sign for the F = 2 ~ F ' = 1, F " = 2 and the negative sign for the F = 1 -+ F ' = 1, F " = 2 level configuration in the POLINEX spectrum. From table 2 one further expects for the latter configuration a larger intermodulated signal for counter- than for co-rotating polarized beams. Despite the insufficient signal to noise ratio, indications for this trend can be observed in the spectra from fig. 1. + Although the anisotropy factors ~jj,, ~'jj, and ~ j , reproduce the trend in the relative line strength for all transitions correctly the numerical agreement is not good in all cases. These discrepancies may be partly explained by two facts; (i) the polarization of the beam going through the modulator is not homogeneous over the beam profile because the beam is focused into the modulator, (ii) the polarization is not exactly modulated between right and left hand circular polarization. We have also tried to reproduce the relative line strengths of the POLINEX signals numerically. Since we have operated the experiment in a weakly saturated regime, the relative line strength was calculated by weighting the anisotropy factor with the square of the relative transition strength [ 10]. The agreement with the experimentally observed line strength is poor. The reason for this discrepancy is not yet understood. 355
Volume 38, number 5,6
OPTICS COMMUNICATIONS
1 September 1981
5. Conclusions
References
Previously, it has been demonstrated [3,4,5] that the hollow cathode discharge is a useful device for high resolution Doppler-free laser spectroscopy on refractory elements. But if the transition under investigation involves a metastable state, velocity changing elastic collisions in the discharge produce Dopplerbroadened pedestals underneath the Doppler-free signals. In this paper we have demonstrated on the 578.2 nm transition o f CuI that this background can be completely eliminated with the new POLINEX method. Furthermore, we have examined the polarization dependence o f the intermodulated fluorescence technique and have shown its close relationship to the POLINEX method.
[ 1] T.W. Hansch, D.R. Lyons, A.L. Schawlow, A. Siegel, Z-Y. Wang and G-Y. Wang, Optics Comm. 38 (1981) 47. [2] M.S. Sorem and A.L. Schawlow, Optics Comm. 5 (1972) 148. [3] D.C. Gerstenberger, E.L. Latush and G.J. Collins, Optics Comm. 31 (1979) 28. [4] A. Siegel, J.E. Lawler, B. Couillaud and T.W. Hansch, Phys. Rev. A, accepted for publication (1981). [5 ] J.E. Lawler, A. Siegel, B. Couillaud and T.W. Hansch, J. Appl. Phys., accepted for publication (1981). [6] P.W. Smith and T.W. Hansch, Phys. Rev. Lett. 26 (1971) 740. [7] C. Delsart and J.C. KeUer, in: Laser Spectroscopy III, eds. J.L. Hall and J.L. Carsten (Springer Verlag, Berlin, Heidelberg, New York, 1977) pp. 154. [8] R.E. Teets, F.V. Kowalski, W.T. Hill, N. Carlson and T.W. Hansch, Proc. SPIE 113 (1977) 80. [9] R.L. Heath, Table of the Isotopes, in: Handbook of Chemistry and Physics (CRD Press, Boca Raton, Fla., 1980) B-268. [10] H. Kopfermann, Nuclear moments (Academic Press Inc., New York, 1958).
356
OPTICS COMMUNICATIONS
1 September 1981
POLARIZATION INTERMODULATED EXCITATION (POLINEX) SPECTROSCOPY OF THE Cul 578.2 nm TRANSITION ¢~ Ph. DABKIEWICZ *, and T.W. HANSCH Department of Physics, Stanford University, Stanford, CA 94305, USA
Received 19 May 1981
Doppler-free spectra of the 578.2 nm transition of CuI atoms in a hollow cathode discharge have been recorded using Polarization Intermodulated Excitation (POLINEX). The POLINEX spectra, which are free of Doppler-broadened background despite velocity changing elastic collisions, are discussed and related to spectra recorded under the same experimental conditions with the older intermodulated fluorescence method.
1. Introduction
We have studied the 578.2 nm (3d 10 4p 2P1/23d 9 4s 2 2D3/2) transition of CuI atoms in a hollow cathode discharge by high resolution laser spectroscopy, using polarization intermodulated excitation (POL1NEX) [ 1]. Spectra free of Doppler-broadened pedestals could be observed despite velocity changing elastic collisions suffered by the absorbing metastable Cu atoms. We have also recorded spectra by the older intermodulated fluorescence method [2] under otherwise identical experimental conditions. The relatively complicated hyperfine spectrum reveals the differences in line strengths for co- and counter-rotating polarizations of the two laser beams, and it elucidates the close relationship between POLINEX spectroscopy and the older technique. The observed relative line strengths can be qualitatively reproduced by anisotropy factors which have been calculated in a rate equation approach. Long used in atomic spectroscopy, hollow cathode discharges have recently attracted interest for high resolution Doppler-free laser spectroscopy of excited atoms [3,4], because they can give convenient access ¢~Work supported by the National Science Foundation under Grant PHY-80-10689 and by the U.S. Office of Naval Research under Contract ONR N00014-78-C-0403. * Fellow of the Deutsche Forschungsgemeinschaft.
to many different elements, including refractory metals which would be difficult to vaporize by other means. In exploratory experiments, Doppler-free spectra of the 578.2 nm transition of copper have been successfully recorded in such discharges both by saturated absorption spectroscopy [3] and by intermodulated fluorescence spectroscopy [5]. However, even with a discharge tube especially designed for high resolution spectroscopy [5], the gas pressure remained so high that the spectra were complicated by large Doppler broadened pedestals underneath the Doppler-free signals. These pedestals have been ascribed to velocity changing elastic collisions which redistribute the atoms over the Maxwellian velocity distribution [6]. Similar pedestals had been observed previously for neon transitions [6,7,1] in positive column discharges. Neon spectra free of such pedestals could be recorded by polarization spectroscopy [7] and by the new POLINEX method [1 ], which can be applied even to weakly absorbing samples. In both these techniques the signals are due to light-induced atomic alignment or orientation, and atoms which have suffered velocity changing collisions will no longer contribute to the signal, if their polarization is destroyed in the collisions. Our present experiments suggest that the POLINEX method may provide a rather general technique for obtaining clean Doppler-free spectra even under the nonideal conditions inside a hollow cathode discharge tube. 351
Volume 38, number 5,6
OPTICS COMMUNICATIONS
1 September 198
2. Theory ++ In Doppler-free saturation spectroscopy the nonlinear interaction of two counterpropagating beams in an absorbing gas is observed. The POLINEX method is such a Doppler-free technique in which the polarization of one or two beams is modulated, while their intensity remains constant. A modulation in the total rate of absorption occurs when the absorption depends on the relative polarization. If we assume that the two counterpropagating beams are circularly polarized and that the quantization axis is chosen along the direction of light propagation, then the appropriate equation for the total rate of absorption is formula (2) of ref. [ 1 ]. In this formula only the last cross-saturation term
~+1~,
e~ @
if= (n - n')(7 -1 + 3"-1)(h6o)-2 X 2Ili 2 ~,
Omm,(ql)Omm,(q2)
mm
depends on the relative polarization of the two beams and gives rise to the POLINEX signal. Here n = iV/ (2./+ 1) and n' =N'/(2I' + 1) are the unsaturated equilibrium populations of the lower and upper states, 3' and 3" are the respective level decay rates, 11 and 12 the intensities of the two beams with the circular polarization q i and q2, and Ornm,(q) is the absorption cross-section for a dipole transition from an angular m o m e n t u m sublevel IJ, m) to an upper level IJ', m'), where m' = m + q, q = +-1, dependent on the circular polarization. The same cross-saturation term (1) can be used to describe the signal in the older (intensity) intermodulated fluorescence method. Here the intensities I 1 and 12 of the two beams are modulated with the frequencies f l and f2 respectively, and the signal is detected with a phase sensitive detector at the sum frequency 0el + f2)" Although all terms of formula (2) in ref. [ 1 ] are intensity dependent, only the cross-saturation term (1) is intermodulated at the sum (and difference) frequency. In the intermodulated fluorescence method the polarization of the two counterpropagating beams is constant. The signal is proportional to the change in absorption rate of one beam induced by the other and vice versa. For co-rotating polarizations both beams interact preferentially with atoms of the same orienta352
71-. ~!7Z
o e~
(1)
+
~,~
0)
I
,S c-
o e~ +a
e~
+ e~
II
H
I
"5
~'~ II
II
Volume 38, number 5,6
OPTICS COMMUNICATIONS
tion and the mutual saturation should be stronger in this case than for counter-rotating polarization. Thus one expects stronger Doppler-free intermodulated fluorescence signals for co- than for counter-rotating light fields. The corresponding POLINEX signals will be proportional to this difference in absorption ra.te if the polarization is modulated between co- and counter-rotation. This close relationship between both methods can be expressed in a common formula for the amplitude of the saturation signal:
~LS+,-, a oc IlI2O2~1,-, ~.
(2)
Here o is the averaged absorption cross section for unpolarized atoms, ~'~j, and ~-~, are the anisotropy factors for the intermodulated signals with the two circularly polarized light fields rotating in the same (+) and in the opposite ( - ) sense respectively, and ~~j, = ~'~j, - ~'jj, is the anisotropy factor for the POLINEX signal when the polar!zation of one beam is modulated between left- and right-hand circular polarization. The factors ~'~j, and ~'jj, are calculated by evaluating the sum of Clebsch-Gordan coefficients in formula (1) similar to the calculations for polarization spectroscopy [8]. The results are listed in table 1, together with the factor * ~j,, from ref. [1] which is also included for completeness.
1 September 1981
The anisotropy factors for linear polarization are also listed in table 1. Here ~'~./, and ~')j, denote the anisotropy factors for the intermodulated fluorescence signals with linearly polarized beams of parallel (11) and perpendicular (±) relative polarization, and ~'~j,= ~'~j,- ~'~j,is the anisotropy factor * for the corresponding POLINEX signals. The treatment of the cross-over signals is similar. These results are listed in table 2, together with the factor ~ ~j,j, from ref. [8] for completeness. H e r e J denotes the angular momentum of the common level, J' and J" those of the two other levels involved in the transition. From the anisotropy factors of table 1 one expects intermodulated signals larger or equal for co- than for counter-rotating polarization in all level configurations. Thus the corresponding POLINEX signals should have all the same sign. For cross-over signals, however, there exist two level configurations J -+ J, J + 1 and J-+ J - 1, J - 1 for which one expects, from table 2, smaller intermodulated signals for co- than for counter. rotating fields and POLINEX signals with the opposite sign. #: The anisotropy factors ~'~xarand ~j,j,, from this paper are identical with the factors ~jj, from ref. [1] and ~jdlj 2 from ref. [8] respectively.
Table 2 The anisotropy factor ~jj,j,, for cross-over signals av
J"
J-1
J
J-1
J+l
Circular polarization
3(33"+2) 10/
9(./-1) 10J
Linear polarization
__3 2./
3
9
3
1--0
}-
-2-
,:b,:
6::
3(J- 1) 5J
3(4/+1) 10J
4:: 3(2/+3) 10J
6
9
3
5
10
10
3(J+2) 5(J+l)
3(4J+3) 10(J+l)
J
J+l
3(3,/+1) 10(J+l)
9(./+2) 10(J+l)
J+l
J+l
3(62j+12J+5) 5(J+l)(2J+ 3)
3(J+2)(2J+5) 10(J+ 1)(2J+3)
3,/ 2(./+1)
3(4./2+8./+5) 5(./+1)(2./+3)
3(J+2)(6J+5) 10(J+ 1)(2J+3)
3./(2/- 1) 10(J+l)(2J+3)
J
ar
3(2/2+2/+1) 5J(J+ 1)
3(2/-1)(2/+3) 10J(J+ I )
3 2J(J+l)
3(3./2+3./- 1) 5J(J+l)
3(2/2+2/+1) 10J(J+l)
3(2/+3)(2./-1) 10J(J+l)
J-I
J-1
3(6./2-1) 5J(2J-1)
3(./-1)(2./-3) lOJ(2/-1)
3(./+1) 2./
3(447+1) 5J(2/-1)
3(J- 1)(6J+l) 10J(2/-1)
3(2da+SJ+3) 10./(2./-1)
3 2(J+l)
3(2J-1) 10(J+l)
353
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OPTICS COMMUNICATIONS
These results from a rate equation approach hold only for low intensities and a Doppler-width which is large compared to the natural linewidth. Also spontaneous reemission from the upper into the lower state and multiple optical pumping cycles have been ignored. For the Cu transition under investigation this is a good approximation since the upper level decays predominantly via an additional radiative decay channel towards the ultraviolet.
3. Experiment The experimental set-up is similar to that described in ref. [I]. The output of a cw ring laser (Coherent Radiation, Model CR 699-21) is passed through a linear polarizer and a ),/4 plate wave to produce circularly polarized light. Then the laser beam is split into two parts of approximately the same intensity (0.18 W/ cm2). One of the beams is sent through an electrooptic modulator (Lasermetrics Model LM- 1FW without linear polarizer) which has a clear aperture of 2.3 mm diameter. A lens before the beam splitter focuses the beam at the site of the modulator, and produces a diameter of about 5mm for both beams at the interaction region. For POLINEX spectroscopy an ac-voltage is applied to the modulator to generate approximately a modulation between right- and left-hand circular polarization. The same set-up is used for intermodulated fluorescence spectroscopy, but in addition an intensity chopper for both laser beams is introduced. Now a dcvoltage is applied to the modulator to produce righthand and left-hand polarization, respectively. The atomic copper density is generated in a hollow cathode discharge which is described in detail in ref. [5]. It is operated at a discharge current of 110 mA and a pressure of 0.35 Torr of Ar. The saturation signal is monitored via fluorescence. Since the upper level of the transition under examination has an additional stronger radiative decay channel towards the ultraviolet, this transition at 327.4 nm is used to record the signal.
4. Discussion Natural copper consists of the two odd isotopes 354
1 September 1981
63Cu and 65 Cu with a relative abundance of 69.09% and 30.91% respectively [9]. Since the nuclear spin of both isotopes is I = 3/2, the hyperfine structure of the 587.2 nm (3d 10 4p 2P1/2-3d94s2 2D3/2) transition consists of six hyperfine components for each iso tope. Fig. 1 displays three scans from this transition. Scan (a) and (b) are intermodulated fluorescence spectra recorded with the two light fields co- (a) and counter-rotating (b) respectively. Spectrum (c) is recorded with the POLINEX method under otherwise the same experimental conditions. Both of the intermodulated fluorescence spectra (a) and (b) clearly reveal a large Doppler-broadened background resulting
/
(a)
A, (b)
(c) F' F
I
0
'
2
2
I 2
I
I
I
I
3
3
2
2
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'
'
'
.
.
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(d)
.
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5
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.
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,
[_1 15
[GHz]
Fig. 1. Hyperfine spectrum of the 578.2 n m transition of CuI, a) Intermodulated fluorescence spectrum with co-rotating polarization of the mutual laser beams, b) Intermodulated fluorescence spectrum with counter-rotating polarization, c) POLINEX spectrum, d) Position of the hyperfine components. Those of 65Cu are marked with "*". The position of the cross-over signals is indicated by dashed lines.
Volume 38, number 5,6
OPTICS COMMUNICATIONS
from velocity changing elastic collisions while in the POLINEX spectrum (c) this background is completely eliminated. Comparing the Doppler-free signals of the two intermodulated spectra (a) and (b) the signal strengths recorded with co-rotating fields (a) are larger than or equal to those recorded with counter-rotating polarization (b), in agreement with the considerations presented above. Figure 2 shows a detail spectrum of the F = 2 ~ F ' = 1 and F = 2 ~ F ' = 2 transitions of 63Cu and their cross-over signal. From table 1 the anisotropy factors ~ j , and ~'jj,, for the F = 2 ~ F' = 1 transition are calculated to 2.3 and 0.05 respectively. The corresponding factors for the F = 2 ~ F ' = 2 transition are 1.3 and 1.05. Since both transitions have the same dipole transition strength [10] one expects the smallest intermodulated signal for the F = 2 ~ F ' = 1 transition
(o)
(b)
(e)
F'
I
F I
I
I
I
2
I
I
2
2
I
I
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I
I
'
I
I
t
I
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!
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I
I
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DETUNING
[GHz]
Fig. 2. Detail spectrum of the F = 2 --, F' = 1 and F = 2 ~ / 7 = 2 hyperfine components of the 578.2 nm transition of 63Cu. Label (a), (b), (c), and (d) as in fig. 1.
1 September 1981
and counter-rotating polarization. The POLINEX method, however, is sensitive to the difference ~'~j, = ]}j, - ~ j j , , so one expects a larger POLINEX signal for this transition than for the transition F = 2 -+ F ' = 2, in qualitative agreement with the spectra in fig. 2. For the transition F = 0 -~ F' = 1 the Doppler-free signals from the intermodulated fluorescence spectra in fig. la and lb have about the same strength, while there is no indication for a signal in the POLINEX spectrum from fig. lc. These experimental observations are in agreement with the anisotropy factors calculated from table 1, which give the same value for ~'~j, and ~']j, and zero for ~ , . Physically this means that a J = 0 state cannot be oriented. Since for the transition under investigation the saturation effect results predominantly from this lower J = 0 metastable state (r ~ - 1 ) the saturation cross-section for the J = 0 -+ J ' = 1 transition is independent of the relative polarization of the mutual beams and therefore no POLINEX signal should occur. For the cross-over signals the anisotropy factor ~'~,j,, from table 2 correctly reproduces the positive sign for the F = 2 ~ F ' = 1, F " = 2 and the negative sign for the F = 1 -+ F ' = 1, F " = 2 level configuration in the POLINEX spectrum. From table 2 one further expects for the latter configuration a larger intermodulated signal for counter- than for co-rotating polarized beams. Despite the insufficient signal to noise ratio, indications for this trend can be observed in the spectra from fig. 1. + Although the anisotropy factors ~jj,, ~'jj, and ~ j , reproduce the trend in the relative line strength for all transitions correctly the numerical agreement is not good in all cases. These discrepancies may be partly explained by two facts; (i) the polarization of the beam going through the modulator is not homogeneous over the beam profile because the beam is focused into the modulator, (ii) the polarization is not exactly modulated between right and left hand circular polarization. We have also tried to reproduce the relative line strengths of the POLINEX signals numerically. Since we have operated the experiment in a weakly saturated regime, the relative line strength was calculated by weighting the anisotropy factor with the square of the relative transition strength [ 10]. The agreement with the experimentally observed line strength is poor. The reason for this discrepancy is not yet understood. 355
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1 September 1981
5. Conclusions
References
Previously, it has been demonstrated [3,4,5] that the hollow cathode discharge is a useful device for high resolution Doppler-free laser spectroscopy on refractory elements. But if the transition under investigation involves a metastable state, velocity changing elastic collisions in the discharge produce Dopplerbroadened pedestals underneath the Doppler-free signals. In this paper we have demonstrated on the 578.2 nm transition o f CuI that this background can be completely eliminated with the new POLINEX method. Furthermore, we have examined the polarization dependence o f the intermodulated fluorescence technique and have shown its close relationship to the POLINEX method.
[ 1] T.W. Hansch, D.R. Lyons, A.L. Schawlow, A. Siegel, Z-Y. Wang and G-Y. Wang, Optics Comm. 38 (1981) 47. [2] M.S. Sorem and A.L. Schawlow, Optics Comm. 5 (1972) 148. [3] D.C. Gerstenberger, E.L. Latush and G.J. Collins, Optics Comm. 31 (1979) 28. [4] A. Siegel, J.E. Lawler, B. Couillaud and T.W. Hansch, Phys. Rev. A, accepted for publication (1981). [5 ] J.E. Lawler, A. Siegel, B. Couillaud and T.W. Hansch, J. Appl. Phys., accepted for publication (1981). [6] P.W. Smith and T.W. Hansch, Phys. Rev. Lett. 26 (1971) 740. [7] C. Delsart and J.C. KeUer, in: Laser Spectroscopy III, eds. J.L. Hall and J.L. Carsten (Springer Verlag, Berlin, Heidelberg, New York, 1977) pp. 154. [8] R.E. Teets, F.V. Kowalski, W.T. Hill, N. Carlson and T.W. Hansch, Proc. SPIE 113 (1977) 80. [9] R.L. Heath, Table of the Isotopes, in: Handbook of Chemistry and Physics (CRD Press, Boca Raton, Fla., 1980) B-268. [10] H. Kopfermann, Nuclear moments (Academic Press Inc., New York, 1958).
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