- Email: [email protected]
New two-photon transitions in sodium vapor: Excitation spectrum and ellipsa detection of molecular-atomic hybrid resonances
Volume 38, number 2
OPTICS COMMUNICATIONS
15 July 1981
NEW TWO-PHOTON TRANSITIONS IN SODIUM VAPOR: EXCITATION SPECTRUM AND ELLIPSA DETECTION OF M O L E C U L A R - A T O M I C HYBRID RESONANCES * R. VASUDEV, T.M. STACHELEK and W.M. McCLAIN
Department of Chemistry, Wayne State University, Detroit, Michigan 48202, USA and J.P. WOERDMAN
Philips Research Laboratories, Eindhoven, The Netherlands Received 21 November 1980 Revised version received 9 March 1981
The nonlinear susceptibility of Na2 for a single frequency has been surveyed by the ELLIPSA method from $00 nm to 634 nm, with additional isolated portions down to 670 nm. Zero rank polarization behaviour is identified in the reddest portion of the excitation spectrum, indicating the existence of one or more hitherto unidentified t ~g+ electromc origins below 30 000 cm-1. Intense ELLIPSA resonances are observed near 568 nm which are explained in terms of an Na2-Na hybrid two-photon process which involves (a) excitation from the lowest repulsive state a 3 Zu to a repulsive, probably 3rig, state which dissociates into 3s + 3p Na atoms; followed by Co) excitation of 4d ~ 3p transition.
P2
1. Introduction Recent papers from this laboratory [1,2] described a new technique called elliptical polarization state a l t e r a t i o n (ELLIPSA) for the measurement o f nonlinear optical properties. The ELLIPSA apparatus, shown in fig. 1, is adjusted at low intensities to produce a null in the transmitted laser beam. As the laser intensity rises, optical nonlinearities in the sample permit transmission proportional to the cube o f the laser intensity. The optical property measured is Ixt~2112, the modulus o f a certain component o f the complex third order dectric susceptibility. The imaginary part o f X[3)21 is proportional to the linear-circular two-photon absorptivity difference. The test case used in the initial study o f ELLIPSA [ 1 - 3 ] was sodium vapor, containing b o t h Na atoms and Na 2 molecules. We observed strong S - S and weaker S - D atomic lines exactly as expected b y the ELLIPSA analysis. However, we deferred discussion o f the Na 2 ELLIPSA spectrum because o f its greater tom* Supported by a grant from the National Science Foundation.
D
R S ~ F IiS F Fig. 1. The ELLIPSA apparatus. Polarizer PI and retarder R1 produce ellipticallypolarized light in the sample SA. In the absence of nonlinear propagation effects, R2 and P2 produce a null at detector D. Nonlinear effects in the sample rotate the ellipse axis (Re X!3~)~,)and alter its ellipticity (Im X~32~i).The signal is proportiona~ to IX ~ l 12. plexity and because we did not have ELLIPSA and twophoton excitation (TPE) spectra taken under exactly comparable conditions. This paper presents such a study of Na 2. The theo149
Volume 38, number 2
OPTICS COMMUNICATIONS
retical background for understanding two-photon effects in symmetric tops has been given by McClain and Harris [4], and the specific case of homonuclear diatomics has been discussed by Bray and Hochstrasser [5]. Carlson et al. [6] have presented an optical-optical double resonance study using two photons of different frequency, while one of us (J.P.W.) has done several studies on a particular single frequency twophoton transition with accidentally resonant intermediate state [7]. The simple one-to-one correspondence between ELLIPSA and TPE lines which we found for atomic sodium does not hold for diatomic sodium. The major ELLIPSA resonance does not appear at all in TPE or in the linear spectrum, while the resonant line is not seen in ELLIPSA. Thus ELLIPSA is proving to be a complementary technique to the more usual TPE studies.
2. Experimental Sodium vapor was produced in a heat pipe oven (20 cm long) at 623 to 673 K. The fill gas was argon at 0.5 to 1.00 Torr. A survey ELLIPSA spectrum was taken over the range 634 nm to 500 nm using a Molectron DL-200 dye laser pumped by the Molectron UV-1000 nitrogen laser. Four dyes were needed to cover this range: Rhodamine B, Rhodamine 6G, Coumarin 540A, and Coumarin 500. This spectrum is reproduced in full in the dissertation of one of the authors (T. M. S.) [3]. More detailed spectra were obtained for certain regions using a Quanta-Ray PDL-1 dye laser pumped by a Quanta-Ray DCR oscillator/amplifier Nd: YAG laser. Saturation effects, which were not a problem with the Molectron laser system, were avoided by suitable attenuation. Output pulses were 5 ns, 0.3 cm -1 fwhm. The two-photon excited C - X ultraviolet fluorescence of Na 2 was monitored through a quartz side window in the heat pipe using an Amperex 56 DUVP photomultiplier and boxcar averager. Certain spectral regions were calibrated by tuning the laser to a TPE peak and then recording the laser wavelength on a 0.75 m spectrograph in the presence of Fe and Ne lines from a hollow cathode lamp. The power dependence was measured for both TPE and ELLIPSA. Plots of log (signal) versus log (laser 150
15 July 1981
power) yielded slopes of 1.94 + 0.02 for TPE and 2.96 +- 0.17 for ELLIPSA, nearly in accord with expectation (2.00 and 3.00, respectively). The dependence of ELLIPSA signal on sodium concentration was also studied over 2.8 orders of magnitude of signal change by varying the oven temperature. The appropriate log-log plot is slightly curved, but has a slope of 1.84 -+ 0.2 at the low pressure end, in rough agreement with the expectation 2.00 (see ref. [3] for details).
3. Results The longest wavelength we could usefully produce was about 690 nm. Already in this region the Na 2 ELLIPSA spectrum shows a dense forest of rotational lines. Our systematic survey ran from 630 nm to 500 nm, showing this impenetrable thicket nearly everywhere. A trivial exception is the region 595 to 585 rim, where the very intense atomic doublet 3P1/2, 3P3/2 prevents transmission. An interesting exception occurs from about 568 to 569 nm where several relatively broad and intense molecular features occur. Just to the blue of these at 567 nm we see an apparent antiresonance, followed by a region in which the rotational background seems less structured than usual. Another small exceptional molecular feature occurs at 515 nm. The expected atomic lines are, of course, superimposed on all of this. The survey ends at 500 nm. We now discuss in detail the regions where we believe molecular conclusions may be drawn.
3.1. Congested red region Fig. 2 shows a comparison of ELLIPSA and TPE in the red region near 635 nm. As is typical of the whole spectrum, TPE and ELLIPSA line widths are comparable, but ELLIPSA shows about twice the line density of TPE, with many features common to both spectra. But many ELLIPSA lines are not reflected in fluorescence, implying a strongly state-dependent quantum yield for TPE fluorescence in this region. Even without definite line assignments, it is possible to draw a firm conclusion about the ordering of electronic states in the red region. Fig. 3 shows the TPE as a function of laser polarization. If the only twophoton states in this region were of symmetry 1IIg or
Volume 38, number 2
OPTICS COMMUNICATIONS
15 July 1981
Na2
N~I 2
I!
TPE
i
ELLIPSA
't
I
355~
LASER
I
6357.5
WAVELENGTH/~
6609.0
i //'
6614.0
669.5.0
I 6700.0
L~t~-r Wavek-ngth].~
Fig. 2. A portion of the TPE and ELLIPSA spectra of Na2, recorded under identical conditions of cell and laser. Correspending lines are numbered.
Fig. 3. Polarization characteristics of TPE in the low energy regions. Peaks that axe lower in circular light must belong to • • the Q-branch of a 1~g+ _ 1 ~g+ transition.
1Ag, all of the TPE lines would show a circular/linear ratio of exactly 3/2, as they would all be governed by an absorption tensor of pure second irreducible rank [4]. On the other hand, i r a I y~ state is present, its Qbranch is governed by a tensor containing a contribution from zeroth irreducible rank, and the circular/tinear ratio may fall below 3/2, or even close to 0. No other allowed two-photon transition of a homonuclear diatomic can behave this way [5]. Several lines in fig. 3 show this characteristic near 6700 A, and we must conclude that at this energy a 1 ~ is being excited. Two 1 ~: origins have been identified in Na 2 [6], the lower lying at 32 725 cm - 1 . Our two-photon energy is only about 30 000 cm -1, and since temperature variation does not affect these lines particularly strongly, they cannot be hot bands with 2725 cm -1 (nearly 6 kT) of thermal energy. We therefore predict that careful observation will reveal new low-lying 1 ~ origins near or below 30 000 cm -1 .
3.2. The resonant TPE line o f Na 2
Woerdman [7] reported an intense TPE line of Na 2 at 602.17 nm, just beside the Na 5s-3s line at 602.23 run. We were surprised that we did not observe this feature in ELLIPSA, and made a careful TPE study of both lines. As may be seen in fig. 4, Woerdman's line is very easy to burn away by increasing the laser power. At very low laser powers it is stronger than the atomic Line, but disappears completely at the powers used for the ELLIPSA spectrum. This agrees with Woerdman's characterization of the line as one which passes through a real intermediate state. 3.3. Intense ELLIPSA resonances
We now turn to the exceptionally broad and in. tense ELLIPSA features in the region 568-569 nm, 151
Volume 38, number 2
OPTICS COMMUNICATIONS a)
TPE
Na
15 July 1981
Na 2
c) i
i
!
!
Fig. 4. TPE spectra of 6022 A region at various laser powers. Laser power decreases to the right; instrumental sensitivity increases. At very low power the accidently resonant Na2 line at 6021.75 A is much stronger than the neighboring Na line at 6022.31 A. At powers used for ELLIPSA, it vanishes completely. shown in fig. 5. Also shown, for comparison, are twophoton and one-photon excitation spectra. The excitation lines have about the same height, width, and density as in neighboring regions, while the ELLIPSA spectrum is dominated by two pairs of peaks, each of which has a central minimum. These resonances are several orders of magnitude more intense than typical lines, and 1 to 2 cm -1 wide (fwhm). Typical ELLIPSA widths elsewhere are laser limited at about 0.3 cm -1 . We recorded a portion of these peaks using an intracavity etalon which narrowed the linewidth to about 0.03 cm -1 , as judged by performance in other spectral regions. The intense bands, however, contained no additional structure at this resolution. We note that the positions of the central minima in fig. 5c correspond to atomic Na transitions 42D3/2 32P1/2 and 42D5/2,3/2 *-32P3/2 . In addition, the relative intensities of the pairs are approximately in the ratio 1:2 which is consistent with the statistical 152
I
5680.5
LASER WAV ELENGTH/,~
569r0.5
Fig. 5. (a) One-photon fluorescence excitation spectrum; (b) two-photon excitation spectrum; (c) ELLIPSA spectrum. weights of the lower levels 32P1/2 and 32P3/2 . We therefore conclude that these ELLIPSA resonances are associated with the 4 d - 3 p atomic transition. The only possible mechanism for the production of 3p Na atoms at the excitation wavelength (568-569 nm) is through a transition originating from the repulsive a 3 Zu+ state transiently formed during Na(3s) Na(3s) collisions. The transition terminates on another repulsive state which correlates with 3s + 3p separated Na atoms. Quite possibly, this first step of the overall two-photon excitation involves the recently observed 3 IIg +- 3 y+u + transition [8]. This hybrid Na 2 - N a twophoton process is summarized in fig. 6. Such hybrid two-photon resonances have previously been reported for the system Cs2-Cs by Tam and Happer [9], and by Koch et al. [10] for Na2-Na hybrid transition involving the atomic 4d ~ 3p transition. We note in passing that the relative intensities of
OPTICS COMMUNICATIONS
Volume 38, number 2 /a~3s
I
15 July 1981
computer simulation based on our analysis of the ELLIPSA optics. I f 8 is the angular misalignment of R2, the transmission coefficient T = 1/I 0 may be shown to be T = [/3' sin40 cos28 + cos(20 + 8 ) s i n 8] 2 (1) + [/3" sin 40 cos25 -- cos 8 sin 8 ] 2,
3s*3s
Fig. 6. Energy level diagram showing the sequential steps in Na2-Na hybrid resonances observed by ELLIPSA in the region 568-569 rim. The first step involves the a ng ,- a a I:u transition. The excited state, being repulsive, dissociates into Na(3p) and Na(3s). Na(3p) is then excited to Na(4d). The shapes of the potential energy curves are only qualitative.
the members of each pair of ELLIPSA peaks are very sensitive to minute changes in the orientation of rhomb R2 shown in fig. 1. Fig. 7 shows ELLIPSA spectrum at two such very slightly different orientations, and a o) I~----1S.0cm-t
d)
Fig. 7. (a) and Co): ELLWSA spectrum with two very slightly different orientations of the fresnel rhomb R2 shown in fig. 1. (c) and (d): Corresponding computer generated profiles.
where/3' + i/3" -- ~101 lco(41rla/nc)2(3×~3)221), 0 = the elliptieity angle of fig. 1, 1 = sample length, co = optical angular frequency,/a = magnetic permeability ~.1, n = index of refraction ~.1, c = speed of light, and 3 `'(3) is the nonlinear susceptibility component mea~1221 sured by this experiment. Clearly the effect is maximized when sin 40 = 1, which we used. Further assuming small 8, eq. (1) becomes T = [/3, + 2-1/28] 2 + [3,,_ 5] 2.
(2)
It remains then only to supply lineshapes for/3' and if'. A rough agreement between observation and the synthesized lineshape was obtained by starting with a sum of two lorentzians 2
(3 = ~ Ai/(co -- col + Jr'i) i=1 centered appropriately and with amplitude ratio A 2/.41 = 2 . We also assumed F 1 = F 2 = 1 cm -1 (on the laser wavenumber scale). This complex/3 was separated into /3' and/3", and if' was reduced by a factor of 4, cutting a dip into the ELLIPSA profiles. This imitates the apparent fact that the imaginary part saturates at lower laser powers than the real part. These functions were then used in eq. (2) with two values of 8 which approximately imitates the data. Similar lineshapes, also attributed to saturation of the absorptive susceptibility at lower laser powers than the dispersive susceptibility, have recently been seen in four-wave mixing experiments involving the Na D lines [11 ]. The hybrid resonances should also be detectable in the TPE spectrum through the second step of the cascade 4d ~ 4p --, 3s. Since, however, the 4p ~ 3s fluorescence is radiatively trapped and probably largely quenched [12] only weak signals are expected in this case. The two peaks in fig. 5b which appear at the same laser wavelength as the central minima in fig. 5c could possibly be attributed to the hybrid resonances. 153
Volume 38, number 2
OPTICS COMMUNICATIONS
Acknowledgements We would like to thank R.A. Harris for a valuable discussion of predissociation, and J.L. Gole for information on the Na 2 absorption spectrum.
References [1] R.J.M. Anderson, T.M. Stachelek and W.M. MeClain, Chem. Phys. Lett. 59 (1978) 100. [2] R.J.M. Anderson, T.M. Stachelek and W.M. McClain, in: Advances in laser chemistry, ed. A.H. Zewail (Springer, Berlin, 1978) pp. 336-42. [3] T.M. Stachelek, Ph.D. dissertation, Department of Chemistry, University of California, Berkeley (1979).
154
15 July 1981
[4] W.M. MeClainand R.E. Harris, in: Excited states, ed. E.C. Lim (Academic Press, New York, 1978) pp. 1-56. [5] R.G. Bray and R.M. Hochstrasser, Molec. Phys. 31 (1976) 1199. [6] N.W. Carlson, F.V. Kowalski, R.E. Teets and A.L. Schawlow, Optics Comm. 29 (1979) 302. [7] J.P. Woerdman, Optics Comm. 21 (1977) 243, and references therein. [8] J.P. Woerdman and J.J. de Groot, Chem. Phys. Letters 80 (1981) 220. [9] C.S. Tam and W. Happer, Optics Comm. 21 (1977) 403. [10] M.E. Koch, K.K. Verma and W.C. StwaUey, J. Opt. Soc. Am. 70 (1970) 627. [ 11] J.P. Woerdman and M.F.H. Schuurmans, J. Opt. Soc. Am. 70 (1980) 598; Optics Lett. 6 (1981) 239. [12] J.P. Woerdman, Optics Comm. 28 (1979) 69.
OPTICS COMMUNICATIONS
15 July 1981
NEW TWO-PHOTON TRANSITIONS IN SODIUM VAPOR: EXCITATION SPECTRUM AND ELLIPSA DETECTION OF M O L E C U L A R - A T O M I C HYBRID RESONANCES * R. VASUDEV, T.M. STACHELEK and W.M. McCLAIN
Department of Chemistry, Wayne State University, Detroit, Michigan 48202, USA and J.P. WOERDMAN
Philips Research Laboratories, Eindhoven, The Netherlands Received 21 November 1980 Revised version received 9 March 1981
The nonlinear susceptibility of Na2 for a single frequency has been surveyed by the ELLIPSA method from $00 nm to 634 nm, with additional isolated portions down to 670 nm. Zero rank polarization behaviour is identified in the reddest portion of the excitation spectrum, indicating the existence of one or more hitherto unidentified t ~g+ electromc origins below 30 000 cm-1. Intense ELLIPSA resonances are observed near 568 nm which are explained in terms of an Na2-Na hybrid two-photon process which involves (a) excitation from the lowest repulsive state a 3 Zu to a repulsive, probably 3rig, state which dissociates into 3s + 3p Na atoms; followed by Co) excitation of 4d ~ 3p transition.
P2
1. Introduction Recent papers from this laboratory [1,2] described a new technique called elliptical polarization state a l t e r a t i o n (ELLIPSA) for the measurement o f nonlinear optical properties. The ELLIPSA apparatus, shown in fig. 1, is adjusted at low intensities to produce a null in the transmitted laser beam. As the laser intensity rises, optical nonlinearities in the sample permit transmission proportional to the cube o f the laser intensity. The optical property measured is Ixt~2112, the modulus o f a certain component o f the complex third order dectric susceptibility. The imaginary part o f X[3)21 is proportional to the linear-circular two-photon absorptivity difference. The test case used in the initial study o f ELLIPSA [ 1 - 3 ] was sodium vapor, containing b o t h Na atoms and Na 2 molecules. We observed strong S - S and weaker S - D atomic lines exactly as expected b y the ELLIPSA analysis. However, we deferred discussion o f the Na 2 ELLIPSA spectrum because o f its greater tom* Supported by a grant from the National Science Foundation.
D
R S ~ F IiS F Fig. 1. The ELLIPSA apparatus. Polarizer PI and retarder R1 produce ellipticallypolarized light in the sample SA. In the absence of nonlinear propagation effects, R2 and P2 produce a null at detector D. Nonlinear effects in the sample rotate the ellipse axis (Re X!3~)~,)and alter its ellipticity (Im X~32~i).The signal is proportiona~ to IX ~ l 12. plexity and because we did not have ELLIPSA and twophoton excitation (TPE) spectra taken under exactly comparable conditions. This paper presents such a study of Na 2. The theo149
Volume 38, number 2
OPTICS COMMUNICATIONS
retical background for understanding two-photon effects in symmetric tops has been given by McClain and Harris [4], and the specific case of homonuclear diatomics has been discussed by Bray and Hochstrasser [5]. Carlson et al. [6] have presented an optical-optical double resonance study using two photons of different frequency, while one of us (J.P.W.) has done several studies on a particular single frequency twophoton transition with accidentally resonant intermediate state [7]. The simple one-to-one correspondence between ELLIPSA and TPE lines which we found for atomic sodium does not hold for diatomic sodium. The major ELLIPSA resonance does not appear at all in TPE or in the linear spectrum, while the resonant line is not seen in ELLIPSA. Thus ELLIPSA is proving to be a complementary technique to the more usual TPE studies.
2. Experimental Sodium vapor was produced in a heat pipe oven (20 cm long) at 623 to 673 K. The fill gas was argon at 0.5 to 1.00 Torr. A survey ELLIPSA spectrum was taken over the range 634 nm to 500 nm using a Molectron DL-200 dye laser pumped by the Molectron UV-1000 nitrogen laser. Four dyes were needed to cover this range: Rhodamine B, Rhodamine 6G, Coumarin 540A, and Coumarin 500. This spectrum is reproduced in full in the dissertation of one of the authors (T. M. S.) [3]. More detailed spectra were obtained for certain regions using a Quanta-Ray PDL-1 dye laser pumped by a Quanta-Ray DCR oscillator/amplifier Nd: YAG laser. Saturation effects, which were not a problem with the Molectron laser system, were avoided by suitable attenuation. Output pulses were 5 ns, 0.3 cm -1 fwhm. The two-photon excited C - X ultraviolet fluorescence of Na 2 was monitored through a quartz side window in the heat pipe using an Amperex 56 DUVP photomultiplier and boxcar averager. Certain spectral regions were calibrated by tuning the laser to a TPE peak and then recording the laser wavelength on a 0.75 m spectrograph in the presence of Fe and Ne lines from a hollow cathode lamp. The power dependence was measured for both TPE and ELLIPSA. Plots of log (signal) versus log (laser 150
15 July 1981
power) yielded slopes of 1.94 + 0.02 for TPE and 2.96 +- 0.17 for ELLIPSA, nearly in accord with expectation (2.00 and 3.00, respectively). The dependence of ELLIPSA signal on sodium concentration was also studied over 2.8 orders of magnitude of signal change by varying the oven temperature. The appropriate log-log plot is slightly curved, but has a slope of 1.84 -+ 0.2 at the low pressure end, in rough agreement with the expectation 2.00 (see ref. [3] for details).
3. Results The longest wavelength we could usefully produce was about 690 nm. Already in this region the Na 2 ELLIPSA spectrum shows a dense forest of rotational lines. Our systematic survey ran from 630 nm to 500 nm, showing this impenetrable thicket nearly everywhere. A trivial exception is the region 595 to 585 rim, where the very intense atomic doublet 3P1/2, 3P3/2 prevents transmission. An interesting exception occurs from about 568 to 569 nm where several relatively broad and intense molecular features occur. Just to the blue of these at 567 nm we see an apparent antiresonance, followed by a region in which the rotational background seems less structured than usual. Another small exceptional molecular feature occurs at 515 nm. The expected atomic lines are, of course, superimposed on all of this. The survey ends at 500 nm. We now discuss in detail the regions where we believe molecular conclusions may be drawn.
3.1. Congested red region Fig. 2 shows a comparison of ELLIPSA and TPE in the red region near 635 nm. As is typical of the whole spectrum, TPE and ELLIPSA line widths are comparable, but ELLIPSA shows about twice the line density of TPE, with many features common to both spectra. But many ELLIPSA lines are not reflected in fluorescence, implying a strongly state-dependent quantum yield for TPE fluorescence in this region. Even without definite line assignments, it is possible to draw a firm conclusion about the ordering of electronic states in the red region. Fig. 3 shows the TPE as a function of laser polarization. If the only twophoton states in this region were of symmetry 1IIg or
Volume 38, number 2
OPTICS COMMUNICATIONS
15 July 1981
Na2
N~I 2
I!
TPE
i
ELLIPSA
't
I
355~
LASER
I
6357.5
WAVELENGTH/~
6609.0
i //'
6614.0
669.5.0
I 6700.0
L~t~-r Wavek-ngth].~
Fig. 2. A portion of the TPE and ELLIPSA spectra of Na2, recorded under identical conditions of cell and laser. Correspending lines are numbered.
Fig. 3. Polarization characteristics of TPE in the low energy regions. Peaks that axe lower in circular light must belong to • • the Q-branch of a 1~g+ _ 1 ~g+ transition.
1Ag, all of the TPE lines would show a circular/linear ratio of exactly 3/2, as they would all be governed by an absorption tensor of pure second irreducible rank [4]. On the other hand, i r a I y~ state is present, its Qbranch is governed by a tensor containing a contribution from zeroth irreducible rank, and the circular/tinear ratio may fall below 3/2, or even close to 0. No other allowed two-photon transition of a homonuclear diatomic can behave this way [5]. Several lines in fig. 3 show this characteristic near 6700 A, and we must conclude that at this energy a 1 ~ is being excited. Two 1 ~: origins have been identified in Na 2 [6], the lower lying at 32 725 cm - 1 . Our two-photon energy is only about 30 000 cm -1, and since temperature variation does not affect these lines particularly strongly, they cannot be hot bands with 2725 cm -1 (nearly 6 kT) of thermal energy. We therefore predict that careful observation will reveal new low-lying 1 ~ origins near or below 30 000 cm -1 .
3.2. The resonant TPE line o f Na 2
Woerdman [7] reported an intense TPE line of Na 2 at 602.17 nm, just beside the Na 5s-3s line at 602.23 run. We were surprised that we did not observe this feature in ELLIPSA, and made a careful TPE study of both lines. As may be seen in fig. 4, Woerdman's line is very easy to burn away by increasing the laser power. At very low laser powers it is stronger than the atomic Line, but disappears completely at the powers used for the ELLIPSA spectrum. This agrees with Woerdman's characterization of the line as one which passes through a real intermediate state. 3.3. Intense ELLIPSA resonances
We now turn to the exceptionally broad and in. tense ELLIPSA features in the region 568-569 nm, 151
Volume 38, number 2
OPTICS COMMUNICATIONS a)
TPE
Na
15 July 1981
Na 2
c) i
i
!
!
Fig. 4. TPE spectra of 6022 A region at various laser powers. Laser power decreases to the right; instrumental sensitivity increases. At very low power the accidently resonant Na2 line at 6021.75 A is much stronger than the neighboring Na line at 6022.31 A. At powers used for ELLIPSA, it vanishes completely. shown in fig. 5. Also shown, for comparison, are twophoton and one-photon excitation spectra. The excitation lines have about the same height, width, and density as in neighboring regions, while the ELLIPSA spectrum is dominated by two pairs of peaks, each of which has a central minimum. These resonances are several orders of magnitude more intense than typical lines, and 1 to 2 cm -1 wide (fwhm). Typical ELLIPSA widths elsewhere are laser limited at about 0.3 cm -1 . We recorded a portion of these peaks using an intracavity etalon which narrowed the linewidth to about 0.03 cm -1 , as judged by performance in other spectral regions. The intense bands, however, contained no additional structure at this resolution. We note that the positions of the central minima in fig. 5c correspond to atomic Na transitions 42D3/2 32P1/2 and 42D5/2,3/2 *-32P3/2 . In addition, the relative intensities of the pairs are approximately in the ratio 1:2 which is consistent with the statistical 152
I
5680.5
LASER WAV ELENGTH/,~
569r0.5
Fig. 5. (a) One-photon fluorescence excitation spectrum; (b) two-photon excitation spectrum; (c) ELLIPSA spectrum. weights of the lower levels 32P1/2 and 32P3/2 . We therefore conclude that these ELLIPSA resonances are associated with the 4 d - 3 p atomic transition. The only possible mechanism for the production of 3p Na atoms at the excitation wavelength (568-569 nm) is through a transition originating from the repulsive a 3 Zu+ state transiently formed during Na(3s) Na(3s) collisions. The transition terminates on another repulsive state which correlates with 3s + 3p separated Na atoms. Quite possibly, this first step of the overall two-photon excitation involves the recently observed 3 IIg +- 3 y+u + transition [8]. This hybrid Na 2 - N a twophoton process is summarized in fig. 6. Such hybrid two-photon resonances have previously been reported for the system Cs2-Cs by Tam and Happer [9], and by Koch et al. [10] for Na2-Na hybrid transition involving the atomic 4d ~ 3p transition. We note in passing that the relative intensities of
OPTICS COMMUNICATIONS
Volume 38, number 2 /a~3s
I
15 July 1981
computer simulation based on our analysis of the ELLIPSA optics. I f 8 is the angular misalignment of R2, the transmission coefficient T = 1/I 0 may be shown to be T = [/3' sin40 cos28 + cos(20 + 8 ) s i n 8] 2 (1) + [/3" sin 40 cos25 -- cos 8 sin 8 ] 2,
3s*3s
Fig. 6. Energy level diagram showing the sequential steps in Na2-Na hybrid resonances observed by ELLIPSA in the region 568-569 rim. The first step involves the a ng ,- a a I:u transition. The excited state, being repulsive, dissociates into Na(3p) and Na(3s). Na(3p) is then excited to Na(4d). The shapes of the potential energy curves are only qualitative.
the members of each pair of ELLIPSA peaks are very sensitive to minute changes in the orientation of rhomb R2 shown in fig. 1. Fig. 7 shows ELLIPSA spectrum at two such very slightly different orientations, and a o) I~----1S.0cm-t
d)
Fig. 7. (a) and Co): ELLWSA spectrum with two very slightly different orientations of the fresnel rhomb R2 shown in fig. 1. (c) and (d): Corresponding computer generated profiles.
where/3' + i/3" -- ~101 lco(41rla/nc)2(3×~3)221), 0 = the elliptieity angle of fig. 1, 1 = sample length, co = optical angular frequency,/a = magnetic permeability ~.1, n = index of refraction ~.1, c = speed of light, and 3 `'(3) is the nonlinear susceptibility component mea~1221 sured by this experiment. Clearly the effect is maximized when sin 40 = 1, which we used. Further assuming small 8, eq. (1) becomes T = [/3, + 2-1/28] 2 + [3,,_ 5] 2.
(2)
It remains then only to supply lineshapes for/3' and if'. A rough agreement between observation and the synthesized lineshape was obtained by starting with a sum of two lorentzians 2
(3 = ~ Ai/(co -- col + Jr'i) i=1 centered appropriately and with amplitude ratio A 2/.41 = 2 . We also assumed F 1 = F 2 = 1 cm -1 (on the laser wavenumber scale). This complex/3 was separated into /3' and/3", and if' was reduced by a factor of 4, cutting a dip into the ELLIPSA profiles. This imitates the apparent fact that the imaginary part saturates at lower laser powers than the real part. These functions were then used in eq. (2) with two values of 8 which approximately imitates the data. Similar lineshapes, also attributed to saturation of the absorptive susceptibility at lower laser powers than the dispersive susceptibility, have recently been seen in four-wave mixing experiments involving the Na D lines [11 ]. The hybrid resonances should also be detectable in the TPE spectrum through the second step of the cascade 4d ~ 4p --, 3s. Since, however, the 4p ~ 3s fluorescence is radiatively trapped and probably largely quenched [12] only weak signals are expected in this case. The two peaks in fig. 5b which appear at the same laser wavelength as the central minima in fig. 5c could possibly be attributed to the hybrid resonances. 153
Volume 38, number 2
OPTICS COMMUNICATIONS
Acknowledgements We would like to thank R.A. Harris for a valuable discussion of predissociation, and J.L. Gole for information on the Na 2 absorption spectrum.
References [1] R.J.M. Anderson, T.M. Stachelek and W.M. MeClain, Chem. Phys. Lett. 59 (1978) 100. [2] R.J.M. Anderson, T.M. Stachelek and W.M. McClain, in: Advances in laser chemistry, ed. A.H. Zewail (Springer, Berlin, 1978) pp. 336-42. [3] T.M. Stachelek, Ph.D. dissertation, Department of Chemistry, University of California, Berkeley (1979).
154
15 July 1981
[4] W.M. MeClainand R.E. Harris, in: Excited states, ed. E.C. Lim (Academic Press, New York, 1978) pp. 1-56. [5] R.G. Bray and R.M. Hochstrasser, Molec. Phys. 31 (1976) 1199. [6] N.W. Carlson, F.V. Kowalski, R.E. Teets and A.L. Schawlow, Optics Comm. 29 (1979) 302. [7] J.P. Woerdman, Optics Comm. 21 (1977) 243, and references therein. [8] J.P. Woerdman and J.J. de Groot, Chem. Phys. Letters 80 (1981) 220. [9] C.S. Tam and W. Happer, Optics Comm. 21 (1977) 403. [10] M.E. Koch, K.K. Verma and W.C. StwaUey, J. Opt. Soc. Am. 70 (1970) 627. [ 11] J.P. Woerdman and M.F.H. Schuurmans, J. Opt. Soc. Am. 70 (1980) 598; Optics Lett. 6 (1981) 239. [12] J.P. Woerdman, Optics Comm. 28 (1979) 69.