Non-linear stark polarization spectroscopy

NON-LINEAR h1.E. COLES

19 August 1983

CHEMICAL PHYSICS LETTERS

Volume 99. number 5.6

STARK POLARIZATION

SPECTROSCOPY

and R.F. CURL Jr.

Chemistry Deportment

a31d

Kecei\ed 75 April 1983;in

Rice Qucintum Imtitute, Rice Uniwrsit~~,Houston. Texas 77251. USA fiial form 15 June 1983

The effects of electric and magnetic field? upon the polariition of a single mode cw dye laser propagating through a low pressure sample of NOa have been explored. It is found that with electric field modulation the various Stark sensitive features in drc complex NO2 visible spectrum affect the polarization, producing a spectrum with a much simpler appearance than the normal absorption spectrum. The signal magnitudes are proportional to the square of the laser power. These electric field modulation signals are dominated by the influence of a weak stray laboratory magnetic field. All the phenomena observed are thought to arise from non-linear level crossing.

l_ introduction

The success of the polarization saturation spectroscopy method of Weiman and Hansch [I] and the polrlrization labeling method of Teets et al. [2] has led us to espiore

the possibility

of developing

a sirni-

for Stark spectroscopy. As originally conceived. a Stark field at 45” to the electric field of the laser radiation would lead to a linear dichroism in the gas sample. This linear dichroism in turn would result in a slight rotation of the plane of polarization of the laser_ In order to induce such a linear dichroism. it is ordinarily necessary to cause Stark shifts comparable with the Doppler widths of the molecular transition_ However, at high laser PO\\ers, a linear dichroism based upon the level crossing phenomenon described by Feld and Javan [3] is possible which requires only that the Stark shifts be compxdble with the homogeneous widths of the levels. There are significant practical difficulties in achieving high Stark fields while maintaining high degree of polarization of a light beam traversing the high field region: in order to have a high electric field without electrical breakdown of the gas, the plates must have a small separation which puts them into the fringes of the laser beam. The smaller field required by the non-linear level crossing is of considerable advantage_ The highly complex visible absorption system of lar polarization

494

nitrogen dioxide was thought to be a suitable test system for this method with the view in mind that considerable simplification of the spectrum would result from the selection of Stark sensitive lines. The Stark modulation spectrum of this system has been studied by Uehara [ 141 and is available for comparison_

technique

2. Experimental The overall experimental arrangement is depicted in fig. 1_ The arrangement permits the observation of the effect of the Stark and Zeeman fields upon both the orientation and ellipticity of the laser polarization by allowing biasing of the ellipticity by means of the quarter-wave plate. In addition, provision has been

I

I

I

Fig. 1. Experimental

0 009-2614/S3/0000-0000/S

arrangement.

03.00 0 1983 North-Holland

Volume99, number5,6

CHEMICALPHYSICSLETTERS

made to rotate the Stark plates with respect to the laser polarization without moving the windows. Inasmuch as the observed signals depend significantly upon the laser beam ellipticity and the ellipticity of the laser is strongly dependent upon the accidental strains in the windows, it is necessary to keep the windows fured in order to explore the effect of relative orientation of the Stark and laser electric fields. In a typical scan, the cell is fiued with ~80 mTorr of NO2 with a path length modulated by the Stark field of =80 cm. The Stark modulation field is 5 kHz zerobased square wave with an amplitude of 500 V. The Stark plate spacing is 5 mm giving total field of 1000 V/cm. The single mode laser power of aSO0 mW is focused near the center of the modulated region by means of a 1 m focal length convex lens. The Halle quartz polarizer is placed immediately after the focusing lens followed by the Halle quartz quarter-wave plate. The cell windows are Schott lens quality flat glass. The detector, RCA lP28 with the dynode chain wired to increase dynamic range, is located bebind an iris which removes scattered light _With the optics adjusted for maximum extinction, the laser spot seen behind the analyzing polarizer is not visible on a white card in dim light _The laser is a Coherent CR 699-02 ring dye laser operating with Rh 6G pumped with 6.5 W of Ar+ (all lines) and is mode-hop scanned (mode spacing ~200 MHz) under computer control_ The computer control system is a simple modification of that used previously for control of another cw dye laser [5] and al20 for control of a color center laser [6] _More thar_ 40 cm-l can be easily scanned with automatic dats acquisition_ Simultaneous acquisition of the fluarescence spectrum of I, and NO, in separate cells provides frequency calibration and a comparison NO, spectrum_ As is described below, several different kinds of experiments involving various combinations of electric and magnetic fields were performed. The most elaborate experiment, which is the one depicted in fig_ 1, involved double modulation by both magnetic and electric fields. The magnetic field modulation frequency (10 KHz) was detected by the first phase-sensitive detector (PSD) and the output of that PSD was introduced into the input of the second PSD syncbronyzed to the Stark modulation frequency (100 Hz).

19 August 1983

3. Observations Most of the observations reported here involved scans over a small frequency region of =3 S cm-l SCaMiIIg to lower frequency from 16844.0 cm-l_ This region was chosen because it is in the 5933 A band analyzed by Stevens and Zare [i] and had been previously surveyed in Stark modulation by Uehara [4]. It is known to contain one of the most Stark sensitive lines. Fig. 2 shows a typical Stark polarization scan of this region together with the fluorescence excitation spectrum and simple Stark modulation spectrum taken at much higher field. In the Stark polarization spectrum depicted in fig_2, the angle between the Stark field and the electric field of the laser radiation is =45”, and the polarizers are crossed to minimum transmission_ When the polarizers are uncrossed clockwise by an amount sufficient to double the detected laser power, signals are not greatly affected, indicating that the Stark signal is primarily out of phase

-

16+3.2

.

16842.4

FREQ

16841.6

.

ISFAO.8

(cm-‘)

Fig. 2. Stark polarizationsignals(uppertrace) obtained when the angle between the Stark and laser electric fields is 49 with the polarizer crossed to maximum extinction. The next trace is the NOp photoexcitation spectrum acquired simults neously. The bottom trace is the simple Stark modulation spectrum with a plate spacing of ==l mm and a square wave modulation of 1200 volts obtained upon a different occasion_ The operating conditions for the Stark polarization spectra were as follows: Dye laser power 450 mW. NO1 pressure 80 mTorr, Stark voltage 500 V, pathlength 80 cm, time constant 100 ms.

495

Volume 99. number 5.6

CHEMICAL

with the main laser field, or, more specifically, that the Stark signal mainly changes the minor axis of the slightly elliptically polarized light rather than tilting the major axis of polarization_ This observation was verified by deliberately introducing additional ellipticity by slightly rotating the quarter-wave plate away from alignment of its optic axes from the direction of polarization and observing that these signals increased as expected. Measurements of the dependence of these signals upon laser power show that their magnitude is proportional to the square of the laser power, as is expected for non-linear level crossing_ Originally the signals were thought to be entirely due to Stark non-linear level crossing_ However, signals of about the same magnitude were still observed when the Stark field -and laser electric field were parallel or perpendicular. If only a Stark field is present_ these observations are inconsistent with symmetry_ Therefore an esplanation of these signals as arising from a Stark effect upon the non-linear Faraday effect due to the earth’s or a stray laboratory magnetic field was sought, and readily found. A solenoid was wound upon the Stark cell, and the effect of an additional small magnetic field was observed. It was found possible to reverse the phase of the Stark signals with a reverse magnetic field of less than 3 G in the conliguration with the Stark field and laser field parallel. The presence of a non-hnear (magnetic rotation) Faraday effect was verified -my observing the signals with an ac magnetic field ar d no Stark field. As expected. these signals are very small with the polarizers crossed the minimum transmitted power since the effect of the magnetic field upon the ellipticity of the laser should be independent of the sign of the field. The bi-asing of this effect by the stray magnetic field is essentially cancelled because the non-linear magnetic rotation was found to saturate at fields of -1 G and the amplitude of the modulating ac field was 4.S G. Fig. 3 displays the spectrum obtained with the nonlinear Faraday effect for the same spectral region as fig. 2. In this trace, the analyzing polarizer has been uncrossed clockwise looking along the direction of propagation to double the power at crossing_ The signals are due to tilting of the major axis of the polarization ellipse because of the difference between the index of refraction of right hand and left hand circular polarized light. The tilting reverses when the direction of the magnetic field reverses and thus gives rise to an

496

19 Auyrst 1983

PHYSICS LETTERS

FLUORESCEACE

166i40

168b32

’

FREQ

16642.4

’

166’41 6

.

166’40.6

(cm-‘)

Fi_e. 3. Non-linear magnetic rotation_ The sample was modulated with a sine wave magnetic field of peak amplitude 4.8 G and frequency 4 kHz- l-be polarizer is uncrossed to triple the minimum power clockwise looking down the laser beam.

ac signal at the magnetic field modulation frequency when the analyzing polarizer is biased off maximum extinction. As is expected, these non-linear magnetic rotation or Faraday effect signals are proportional to the square of the laser power. In order to see clearly the effect of Stark modulation upon the magnetic rotation signal, a double modulation experiment was performed in which the magnetic field was modulated at 10 kHz (since wave modulation) and the Stark field was modulated at 100 Hz (square wave modulation) using two phasesensitive detectors in series, the first tuned to 10 kHz and the second to 100 Hz. Fig. 4 compares the signals obtained in this experiment with the same region in simple Stark modulation in the presence of the stray magnetic field for the laser electric field parallel to the Stark field. As expected the Stark effect upon magnetic rotation is clearly the only source of signal when the laser field is parallel or perpendicular to the Stark field, but there appears to be a difference between the double modulation and Stark modulation only signals at intermediate orientations (e.g. an angle of 45” between the two fields). In the double modulation experiment, the signals are out of phase with the main laser field (change in ellipticity rather than tilt) especially in the configurations where the Stark and laser fields are parallel or perpendicular_

Vohxme 99, number 5.6

CHEMICAL PHYSICS LETTERS

f OOUBLE

fiOlXJLATJON

I

16843 2

16842.4

16841.6

16840.0

19 Au,wt 1983

cell, it was necessary to shorten the Stark electrodes to 432 cm length. Even after shielding the cell, signals were still observable with the Stark and laser electric fields parallel. These were eliilnated by also shielding the argon ion laser gain tube with the mu metal. (The gain tube is located ~30 cm from the Stark cell and parallel with it.) The pure Stark signal with the Stark field and laser electric fields at 45O is shown in fig_ 5 _Also shown is a scan under the same conditions except that the solenoid around the cell was energized to produce a dc magnetic field along the direction of laser propagation. Clearly the two field signals are substantially larger and qualitatively different from the Stark only signals.

FREQ ( cm-‘) Fig. 4. Double modulation signalscompared with Stark polarization signalswith laser electric field parallel to Stark field. Note the similarity of the two sign& except for the 180” phase difference resulting from PSD phase settings.

The Stark polarization effect in the absence of a magnetic field was investigated by shielding the cell with mu metal (0.03 cm thick). In order to shield effectively the Stark modulation region and support the

NO Z’IUGNETIC

FIELD

Y 16843

16842

16841

FREQ [ cm-‘1 Fig_ 5. Stark polarization only signalswith the sample shielded from stray magnetic fields for laser and Stark electric fields at 45” (upper trace) compared with the Stark magnetic rotation signal (lower trace). For the lower trace the solenoid around the sample was ener@izedwith a dc current of 13 A producing a magnetic field of less than 3 G along the direction of laser propagation.

4. Theory These signaIs must arise from the non-linear level crossing phenomenon treated theoretically by FeId and Javan 131 and Feld et al_ IS] _Their treatment has recently been extended to saturation magnetic rotation (the magnetic field only experiment of fig,. 3) by Thomas [9] _In this treatment, the axis of quantization is chosen to be along the magnetic field direction which is also the direction of laser propagation, and the laser electric field is broken into right- and left-handed circularly polarized components_ The third-order steady state (rotating wave) solutions are found for the density matrix with a given Doppler shift. These solutions are then velocity averaged and used to calculate the polarization of the sample and from that the complex susceptibility_ The non-linear magnetic rotation effect comes from the difference in the real parts of the susceptibility (refractive index) between right-handed and left-handed circularly polarization_ Pure Stark non-linear level crossing observed in polarization is closely analogous to electric field power enhancements seen in optically-pumped molecular lasers [IO]. Stark level crossing has been used to study saturation parameters [l l] of gases. In principle, the theory of Feld and co-workers f3,8] may be extended to polarization Stark level crossing in analogy with the non-linear magnetic rotation treatment of Thomas 191. However, the calculations rapidly become more complicated and we have not carried this through. Theoretical treatment of the combined magnetic 497

19 August 1983

CHEMICAL PHYSICS LETTERS

Volume 99. number 5,6

and electric field effect (non-parallel fields) on polarization is even more difficult. In this effect the upper

5_ Potential utility

level of the transition is Stark coupled to an unseen level (J”‘), which is probably a vibrationally excited level of the ground electronic state. This Stark coupling may be removed by a Van Vleck perturbation treatment (provided J’, J”‘, I~J~~-~. and aE,# Js,, are hnown) resulting in an effective hamiltonian matrix for J’. The eigenvalues and eigenvectors of this hamiltonian may be obtained numerically for given values of the electric and magnetic fields, and used in

Fig. 6 shows a longer scan of the 5933 a band in which many of the prominent features have been identified using the assignments of Stevens and Zare [7] _Clearly the Stark polarization spectrum is much simpler than the photoexcitation spectrum which is also shown in fig. 6. The lines selected by Stark polarization must have a nearby level (J”‘) which Stark interacts with the upper state level. It appears that lines with K’ = 0 and K’ = 1 are prominent in Stark polarization_ This suggests that a series of unseen J”’ levels are marching in near coincidence with the upper state levels K’ = 0 and K’ = 1 with the nearest coincidence betw;cn J’ and J”’ occurring at J’ = 7 for K’ = 0 and J’=6forK’= 1. Several small polyatomic XY2 molecules (e.g. SO,, CS,, NO& have highly perturbed, dense electronic absorption spectra with this system of NO, being the most studied example. The energy levels of the ground electronic state are unperturbed and well known; the

the density matrix treatment of the level crossing. Inasmuch as J”‘, pJl,Jree. and AEs,rl. are unknown and the calculations just indicated are quite complex. no effort to carry this through has been made. It is unfortunate that we can see no way to carry this calculation through analytically in order to explain the esperimental observation that the signals are dominated by changes in the ellipticity of the polarization rather than by changes in the tilt of the major axis of polarization.

STARK POLARIZATION

0

6543

2

2

4

5

16842.7+

697

j-42.445

Pig_ 6. A scan over most of the 5933 A band in Stark polarization. This scan was done with the electric fields at ==45”in the presence of the stray magnetic field. The assignments of Stevens and Zare are shown for some of the Stark polarization lines. Operating conditions: NO2 pressure 70 mTorr, laser power 500 mW, Starkfield 800 V. 49s

Volume 99, number 5,6

CHEMICAL PHYSICS LETTERS

complexity of the spectrum arises from the perturbation of the upper electronic levels by excited vibrational states of the ground electronic state and in some cases, other lower excited electronic states. Stark polarization picks out and labels a few upper state levels. This level labeling can be of assistance in making assignments. For example, without looking at the labels one might expect that the line marked with an asterisk in fig. 6 might involve the same upper level as one of the lines marked 1 and 2. Indeed this is the case, it involves the same upper level as line 1_ The difference in frequency between the asterisk line and line 1 is the well-known ground state energy separation between 8,, J = 7.5 and 6, J = 5.5. The common level is 7o7 J= 6.5 of the excited state.

us, and both he and Professor Michael Feld for extremely helpful discussions.

References [l]

[2] [3] [4] [S] [6] [ 71

Acknowledgement This work was supported by National Science Foundation Grant CHE825096 and The Robert A. Welch Foundation Grant C-071. The help of Professor Anthony J. Merer and Dr. J.V.V. Kasper in setting up the experiment is gratefully acknowledged. We wish to thank Dr. J.E. Thomas for making his calculations on non-linear magnetic rotation available to

19 August 1983

[S]

[9] [lo] [ll]

and T-W. Hans& Phys. Rev. Letters 36 (1976) 1170. R-E. Teets, R. Feinberg, T-W. Hansch and A-L. Schawlow, Phys. Rev. Letters 37 (1976) 683. MS. Feld and A. Javan, Phys. Rev. 177 (1969) 540. K. Uehara and K. Shimoda, Jap. J. Appl. Phys. 16 (1977) 633. J.V.V. Kasper, CR. PolIock, R.F. Curl and F-K. Tittel, Appl. Opt. 21 (1982) 236. CR_ Pollock, J.V.V. Kasper, G-K. Ernst, WE. Ernst, S. Blit and F_K_Tittel, Appl. Opt 18 (1979) 1907. C-G. Stevens and R.N. Zare, J. Mol. Spectry. 56 (1975) 167. hf.S. Feld, R. Sanchez, A. Javan and B.J. Feldman, Proceedings of Aussois Symposium. Methodes de Spectroscopic sans Largeur Doppler de Niveaux Excites de Systemes hloleculaires Simples, hfay 1973, Pub]. No. 217 du CNRS, Paris (1974) pp_ 87 ff. J-E. Thomas, to be published. hl. Inguscio, A. hloretti and F. Strumia, IEEE J. Quantum Electron. QE-16 (1980) 955 and references therein. F. Strumia, hl. lnguscio and A. Moretti, in: Laser spectroscopy, Vol. 5, eds. A.R.W_ McKellar, T_ Oka and BP. Stoicheff (Springer, Berlin, 1981) p_ 255. C. Weman

499