Department of Physics, Middlebury College 1992-93
Modern Physics Laboratory


XVIII. Doppler-Free Saturated Absorption Spectroscopy of Iodine and Sodium Using a Tunable Ring Dye Laser


Discussion

Narrow line width, tunable lasers have revolutionized optical spectroscopy because of their unique ability to resolve closely spaced lines in optical spectra and thereby reveal some of the most subtle details of the underlying atomic and molecular structure. An example of the precision achieved with modern tunable lasers is the recent laser measurement of the Balmer lines of atomic hydrogen that were used to determine the Rydberg constant R, defined by

R   1/2 me2
_________
  

to be R = 10973731.573(3) m-1.1 With eleven significant figures, the Rydberg is the the most precisely measured fundamental constant. A distinguishing feature of many high resolution laser measurements made on hydrogen and other atoms is the use of spectroscopic techniques that eliminate the Doppler broadening of spectral lines caused by the random, thermal motion of the absorbing or emitting atoms at ordinary temperatures.

In this experiment you will use a modern, narrow linewidth, tunable ring dye laser to resolve spectral absorption features separated by less than a few thousandths of an Å in the spectra of molecular iodine (I2) and sodium (Na). To do this you will obtain spectra that are free of Doppler broadening using a technique known as Doppler-free, saturated absorption spectroscopy. The widths of the absorption peaks you measure will approach the natural linewidths of the respective transitions. For free atoms, these linewidths cannot be reduced further, because the Heisenberg uncertainty principle requires an uncertainty E in the energy of a quantum state occupied for a finite length of time . For a transition between an atomic ground state and an excited state of lifetime , absorption occurs for a range of photon energies given by E  / , or equivalently, over a range of photon frequencies given by 1/(2 ). The linewidths in this experiment are therefore determined largely by the finite lifetimes of the states of the absorbing molecules and atoms, and are not due to inadequacies of the laser, such as a lack of stability or a large spectral width of the output beam. In fact, the stability and spectral purity of the dye laser beam used in this experiment is of such a high quality that you could resolve features as small as 1/100,000 of an Å, which by way of comparison, is nearly a factor of a thousand better resolution than can be obtained with the SPEX 1704 1 m spectrometer.

(1) Argon Ion - Ring Dye Laser System.

No attempt will be made here to describe in detail the physical principles of operation of the argon ion and ring dye lasers; this discussion will only describe the operation of these lasers and characterize the beams emitted by them. The major emphasis in this experiment will be the Doppler-free saturated absorption technique and how the highly stable, narrow linewidth laser beam of a cw ring dye laser system can be exploited for high resolution spectroscopy. Complete discussions of the cw ring dye laser can be found in Refs. 2 and 3.

The Coherent 90-6 argon ion laser shown in Fig. 1 produces 8-9 W of blue-green light (seen in the photograph of Fig. 2) when operated on all Ar+ lines (predominantly 488 and 514 nm). The sole purpose of the argon ion laser is to serve as a bright, highly collimated, blue-green light source to pump the Coherent 699-21 Ring Dye Laser, whose optical layout is shown schematically in Fig. 3(a). Molecules flowing in the dye jet of the ring dye laser readily absorb the blue-green argon ion laser light and reemit fluorescence light of longer wavelength into the cavity formed by the impressive array of optical components that make up the ring laser resonator. For the common dye Rhodamine 6G (R6G), fluorescence emission occurs for wavelengths in the range from 560 to 620 nm, as shown in Fig. 3(b). The main purpose of the frequency selective components of the ring cavity, such as the birefringent filter, and the thin and thick etalons, is to "convince" excited dye molecules to emit light into a single longitudinal mode of the laser cavity so as to produce a single frequency laser output beam. The frequency of the single oscillating mode is tuned by rotating the Brewster plate synchronously with the thin and thick etalons. The frequency of the laser is actively stabilized by an external, temperature-controlled Fabry-Perot reference cavity. An error signal from the reference cavity drives a piezoelectric transducer that translates mirror M1 of Fig. 3(a) so that the optical length of the ring cavity is maintained despite the unavoidable presence of temperature fluctuations and vibrations. An optical diode acts to insure that light travels in only one direction around the "figure 8" light path of the ring resonator. Unidirectional operation of the laser is essential to avoid standing waves in the dye jet and a subsequent loss of dye laser output.

With the R6G dye, our ring dye laser can tune anywhere in the range 560 to 620 nm and can produce more than 1 W of single frequency laser power at the 580 nm peak of the R6G fluorescence curve. The ring dye laser output is a single line stabilized to a width of less than 1/2 MHz, which corresponds to only 1 part in 109 of the laser frequency of approximately 520,000,000 MHz at 580 nm. The largest continuous frequency scan that the Coherent 699-21 dye laser can make is 30 GHz, which corresponds to approximately 0.3 Å at 580 nm. The ring dye laser frequency can be set by observing the laser output with a spectrometer, a wavemeter, or in the case of Na, by observing the bright yellow fluorescence of Na atoms in a cell when the laser is tuned to the D1 and D2 lines. Once the desired absorption or fluorescence signal for an experiment is located, the frequency range of the laser scan is narrowed to 1 or 2 GHz and the computer is used for laser scanning and data acquisition.

(2) Doppler-Free Saturated Absorption Spectroscopy.

The experimental arrangement for Doppler-free saturated absorption spectroscopy of I2 and Na is shown in Fig. 1. The output beam from the dye laser is split into two beams at beamsplitter BS. The more intense beam, called the pump beam, is chopped by a mechanical chopper, and, after passing through the window of the 300 MHz Fabry-Perot interferometer, traverses the I2 or Na cell from right to left in Fig. 1. The less intense beam, called the probe beam, passes through the I2 or Na cell from left to right, and through the slightly transmitting mirror M3, to a photodiode detector PD1.

In the arrangement of Fig. 1, imagine that all of the atoms in the Na cell are at rest and consider what happens when the laser frequency L is tuned to an atomic absorption line of the Na atoms. When the pump beam is blocked by the chopper, the probe beam is absorbed by ground state atoms, as shown in Fig. 4(a). When the pump beam is passed by the chopper, the pump intensity can be so great that a large fraction of the atoms are pumped to the excited state of the transition, producing what is called saturation of the transition, as depicted schematically in Fig. 4(b). A probe beam passing through the saturated medium will experience increased transparency, or equivalently, reduced absorption, due to the reduction in the number of ground state atoms available to absorb the probe beam. As the pump beam is blocked and unblocked by the chopper, the photodiode PD1 measures a modulated intensity at the chopping frequency that can be detected by a lock-in amplifier. The modulated intensity of the probe beam reflects the situation that the pump and probe beam can interact with the same atoms, here assumed to be at rest.

The random thermal motion of atoms at room temperature complicates the simple picture of Fig. 4, because atoms moving with different speeds along the pump-probe axis absorb laser light of different frequencies because of the Doppler effect. Specifically, an atom that absorbs light at frequency o, when at rest, will absorb laser light of frequency L given by

L = o ( 1 v/c )         (1)

when the atom moves with speed v toward (- sign) or away from (+ sign) a laser light source. Therefore, an ensemble of atoms moving at different thermal speeds will absorb light over a range of laser frequencies determined by the atomic velocity distribution. This Doppler broadening of spectral absorption lines was seen clearly for the 6678 Å He absorption line of Expt. XVII. The analogous Doppler broadening of emission lines is evident in the hydrogen Balmer line spectra of Expt.XII.

The effects of Doppler broadening can be overcome in a pump-probe saturated absorption measurement scheme such as the one shown in Fig. 1. Consider the familiar Maxwell distribution of atomic velocities shown in Fig. 5(a), where the number of ground state atoms is plotted against the component of atom velocity along the pump-probe axis. It is useful to distinguish the three cases of Fig. 5. separately.

(a) L < o. In Fig. 5(a), atoms moving toward  either the pump or probe beams see the pump or probe beam as blue-shifted in the atom's rest frame, and the number of ground state atoms at a speed v given by

v = c ( L/o - 1 )        (2)

is reduced because the laser frequency is no in the rest frame of these atoms. It is important to recognize in this case that because a Doppler shift of a particular sign is required for absorption, an atom that absorbs light from one beam, cannot absorb light from the other beam. The pump and probe beams therefore interact with entirely different groups of atoms within the cell. The transparency of the cell as seen by the probe beam is therefore unaffected by the presence of the pump beam.

(b) L > o. Atoms moving away from  either the pump or probe beams with a speed given by Eq. (2) will see the pump or probe beams as red-shifted to frequency o in the atom's rest frame and the number of ground state atoms at these speeds will be reduced, as shown in Fig. 5(c). (Skip Fig. 5(b) for the moment.) Again, because a Doppler shift of a specific sign is required for absorption, the pump and probe beams interact with entirely different atoms in the cell. Probe beam absorption in the cell is entirely unaffected by the pump beam.

(c) L = o. Atoms with speed v = 0, that is, those atoms that do not move along the pump-probe axis, can absorb light from both  beams, as depicted in Fig. 5(b), because for these atoms there is no Doppler shift of the laser light in the atom's rest frame. Therefore, the group of atoms with v = 0 interact with both laser beams and the probe beam will experience an alternating transparency produced by the chopped pump beam, that can be detected at PD1 by a lock-in amplifier that is referenced to the chopper.

The modulation of the transmitted probe beam by the chopped pump beam occurs only when the pump and probe beams interact with the same  atoms. Because of the Doppler effect this condition only occurs for atoms near v = 0. The lineshape of the probe signal detected by the lock-in detector is therefore determined by the natural linewidth of the atomic transition and not by the effects of Doppler broadening.

The effectiveness of the Doppler-free saturated absorption technique can be seen in Figs. 6(a) and 6(b). Fig. 6(a) shows a typical absorption spectrum for the 5682 Å, P(117), 21-1, X --> B transition of 127I2 without the use of Doppler free techniques; only a single broad line of approximately 1 GHz width is observed. The Doppler-free saturated absorption spectrum of Fig. 6(b) reveals fully the complicated hyperfine structure underlying this transition.4,5,6 A total of 21 lines are seen in this Doppler-free spectrum, with the hyperfine line splittings providing valuable information on the magnitudes of the hyperfine interaction strengths for the upper and lower molecular states of this transition. Although no detailed account of the line splittings expected for this I2 transition will be given here (consult Refs. 4-6 for a complete discussion) the value of Doppler-free techniques for molecular and atomic structure determinations should be evident.

Procedure

It is important that you pay close attention to laser safety during this experiment. The light beam present at the exit of the argon ion laser is more than 1000 times as intense as the HeNe and diode laser beams you worked with in previous experiments. Even though there should be no need for you to put anything in the path between the argon ion laser and the ring dye laser, you should be aware that the laser beam intensities there are very dangerous. The beam from the ring dye laser may have a power as high as several hundred mW during this experiment and direct eye exposure to such a beam will surely cause permanent eye damage.

To limit potentially damaging exposure of the eyes, attenuate the laser beam intensity to the lowest possible level necessary to perform a given part of the experiment. If you are simply positioning mirrors or beamsplitters, or aligning the pump and probe beams through the I2 cell, insert an attenuator into the primary dye laser beam to reduce its intensity to a power level near 1 mW. Use white index cards to determine the location of laser beams. Do not bring your head down to the horizontal plane of the laser beams for any reason. Before you sit down at the IBM PC/XT computer to acquire data, check to see if any stray beams from the optical bench will be at your eye level when you sit down.

(1) Doppler-Free I2 Spectra. Set up the arrangement of Fig. 1 using the I2 cell. Adjust the dye laser frequency using the birefringent filter and the Laser Scan Controls of the 699-21 Dye Laser Control unit to obtain fluorescence along the pump and probe beams in the I2 cell. Use the I2 fluorescence to bring the pump and probe beams to perfect collinearity throughout the I2 cell. Align the 300 MHz interferometer so that high quality transmission peaks are obtained using the Coherent 251 Spectrum Analyzer Controller. Adjust the PAR 121 lock-in amplifier reference and signal settings so that a proper lock-in output signal is sent to the X1 A/D input on the rear panel of the SR530 Lock-In Amplifier.

At the IBM PC/XT computer, start the SR577 data acquisition program for the SR530 Lock-In Amplifier. Set the X5 Analog Output to provide a -5 to +5 V voltage ramp to the External Scan input on the rear panel of the Dye Laser Control unit. When the Dye Laser Control unit is set to EXTERNAL, the voltage ramp provided by the SR530 will scan the dye laser frequency over the frequency range set on the SCAN WIDTH thumbwheel switches of Dye Laser Control unit. The SCAN OFFSET thumbwheel switches are used to center the laser scan at a particular I2 line. The laser is scanned manually when the mode switch of the Dye Laser Control unit is set to the MANUAL position and the Manual knob is turned. Manual tuning of the dye laser frequency will be necessary, especially during alignment, so it is good to familiarize yourself with the process of changing between computer and manual control.

Adjust the dye laser to the center of an isolated, bright, I2 fluorescence line somewhere near 580 nm. Take a scan with the SR577 program to see if you obtain a Doppler-free saturated absorption spectrum of I2 and high quality interferometer peaks. A short period of further adjustment and alignment should allow you to obtain an I2 spectrum comparable to the one shown in Fig. 6(b). You may have to set the dye laser to several I2 fluorescence lines before obtaining a 21 line spectrum, like that in Fig. 6(b), but there are at least 100 such transitions available within the R6G tuning range of the dye laser. When you obtain satisfactory Doppler-free spectra and interferometer peaks, write your data to disk and plot it.

(2) Doppler-Free Na Spectra. With all optical components aligned for the I2 saturated absorption measurement, it is a simple matter to remove the I2 cell and install the Na cell. The Na cell must be heated to obtain sufficient Na vapor pressure for the Doppler-free measurement. A heating tape, powered by a variable transformer, is wrapped around the Na tube to provide adjustable temperatures in the range from 50 to 150 oC.

The dye laser frequency may be tuned to the vicinity of the Na D1 and D2 lines using the 1/4 m Minuteman 302VM monochromator set to 5890 and 5896 Å. Fine tuning of the laser frequency near the D lines is accomplished using the Thin Etalon Adjust control on the 699-21 Dye Laser Control unit. When the dye laser is tuned to either D line, a bright yellow fluorescence will be seen in the Na cell.

Take Doppler-free spectra of both the D1 and D2 lines of Na, with simultaneous recordings of the 300 MHz interferometer transmission peaks. Write these spectra to disk. Sample Doppler-free spectra for the D1 and D2 lines are given in Figs. 7(a) and 7(b), respectively.

Analysis

(1) Doppler-Free I2 Spectrum. No attempt will be made to use the detailed information available in your I2 spectra to derive information about the hyperfine splittings of the upper and lower states involved in the transitions you observed. Instead, you are asked to make two rather qualitative calculations.

(a) First, use your knowledge of the Doppler-free I2 spectrum and Doppler broadening to explain the Doppler broadened profile of Fig. 6(a). Your argument should be quantitative and make use of a formula for Doppler broadening such as the one given in Eq. (2) of Lab XVII.

(b) Second, determine the width in MHz of the narrowest line in your Doppler-free spectrum. The width of that peak will be much greater than the 1/2 MHz linewidth of the dye laser so that you can assume that the measured width is due largely to the finite lifetimes of the states involved in the transition. Use your knowledge of the uncertainty principle to estimate a lower bound for the lifetimes of the molecular states involved in the observed transitions.

(2) Doppler-Free Na Spectra. An energy level diagram of Na indicating the fine and hyperfine splitting of the 3S and 3P terms is given in Fig. 8.7

(a) Interpret your Doppler-free Na D line spectra in terms of the hyperfine levels shown in Fig. 8. Label all of the peaks observed in your Na D line spectra according to the allowed transitions between the various 3S and 3P hyperfine levels indicated in Fig. 8.

(b) With suggestions from the instructor or from Refs. 8 and 9, interpret the large, central negative signal known as a "crossover" resonance at the center of your sodium D line spectra. Use a series of energy level and velocity distribution diagrams to explain the physical origin of the crossover peak.

(c) Measure the width, in MHz, of the narrowest line in your Doppler-free spectra of the Na D1 and D2 transitions. Use your knowledge of the uncertainty principle to estimate a lower bound for the lifetime of the atomic states involved in this transition.

(d) Your Na D1 and D2 spectra were obtained in separate scans, but imagine that they could be taken in a single scan. Approximately how far apart would the D1 and D2 peaks be on your plot if they were part of a single, continuous scan printed at the scale of your plot? Consult Ref. 10 for a cartoon depicting this situation and for a personal history of some of the first saturated absorption experiments performed with tunable dye lasers.

References
1. P. Zhao, W. Lichten, H.P. Layer, and J.C. Bergquist, in Laser Spectroscopy VII, edited by W. Persson and S. Svanberg (Springer-Verlag, New York, 1987) p. 12.
2. T.F. Johnston, in Encyclopedia of Physical Science and Technology, Vol. 14, edited by Robert A. Meyers (Academic Press, New York, 1987) p. 96.
3. L. Hollberg, in Dye Laser Principles with Applications, edited by F.J. Duarte and L.W. Hillman (Academic Press, New York, 1990) p. 185.
4. M.D. Levenson, Hyperfine Interactions in Molecular Iodine, Ph.D. thesis, Stanford University, 1971.
5. M.S. Sorem, Spectroscopy by Saturated Fluorescence and Absorption in Molecular Iodine, Ph.D. thesis, Stanford University, 1972.
6. K.B. Davis, The Hyperfine Structure of Molecular Iodine, B.A. thesis, Middlebury College, 1990.
7. H. Jänsch, Messung der Relativen Besetzungszahlen am 23Na Atomstrahl durch Selektives Optisches Anregen im Magnetfeld, Diplomarbeit, Marburg University, 1982.
8. T.W. Hänsch, I.S. Shahin, and A.L. Schawlow, Phys. Rev. Lett. 27, 707 (1971).
9. W. Demtröder, Laser Spectroscopy  (Springer-Verlag, New York, 1982).
10. T.W. Hänsch, in Lasers, Spectroscopy and New Ideas, edited by W.M. Yen and M.D. Levenson (Springer-Verlag, New York, 1987) p. 3.

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