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Frequency-locking of a CW dye laser to some absorption lines of a neon discharge by a Faraday filter
FREQUENCY-LOCKING
OF A CW DYE LASER TO SOME ABSORPTION
OF A NEON DISCHARGE BY A FARADAY T. YABUZAKI, Ionosphere
August 1977
OPTICS COMMUNICATIONS
Volume 22, number 2
LINES
FILTER
T. ENDO, M. KITANO and T. OGAWA
Research Laboratory,
Kyoto University, Kyoto, Japan
Received 18 May 1977
Single-mode oscillations of a CW dye laser at the center of five absorption lines from the 1s states to the 2p states of neon were obtained by means of a neon discharge Faraday filter, without any other frequency-selective elements. The most striking thing observed is that saturated absorption takes place at the center of several absorption lines in a Faraday filter, in addition to optical rotation.
Saturated
absorption
is now a powerful
tool for
It has also been used to lock single-mode frequencies of gaseous lasers and dye lasers to the centers of Doppler-broadened resonance lines of atoms and molecules with extremely high stability. However, in this method the laser system becomes relatively complicated, because one has to prepare a single-mode oscillation by means of a cavity system such as a Fox-Smith type cavity [e.g. l] or frequency-selective elements such as Fabry-Perot etalons [e.g. 21, before applying saturated absorption techniques. One of the more conventional methods to lock the frequency of a laser to an atomic line is to utilize a Faraday filter, by which means spectral narrowing and frequency locking can be made simultaneously. This method was first developed by Sorokin et al. [3] for frequency locking a pulsed dye laser to the sodium D lines, but they obtained oscillations only on the wings of the lines. Recently, we performed a similar experiment with a CW dye laser and obtained single-mode oscillations in the center regions of the D, and D2 lines of sodium. Details of this experiment will be reported elsewhere [4]. In this paper, we report experimental results on frequency locking of a CW dye laser to some absorption lines from the 1s states to the 2p states of neon in a discharge by means of a Faraday filter. It should be noted that, simply by inserting the Faraday filter inside the dye laser cavity without any other frequencyDoppler-free
laser spectroscopy.
selective elements, we could obtain single-mode oscillations at the center regions of absorption lines. Furthermore, the single-mode oscillations at the absorption lines originating from the 1s4 state, such as the line at 607.4 nm (lsq-2~~) took place only when longitudinal modes of the cavity coincided with centers of the lines. This phenomenon can be explained as a saturation interaction of the light waves propagating in opposite directions, just as seen in ordinary saturated absorption. The experimental apparatus is shown in fig. 1. The Faraday filter used in the present experiment consists of a neon discharge tube with Brewster-angle windows whose principal axes are oriented perpendicularly to each other, and a solenoid to produce a relative strong axial m$gnetic field. The principle of the Faraday filter can easily be understood by considering a simplified model *. When the light polarized vertically is incident on the Faraday filter from its left-hand side in fig. 1, the light is subjected to the optical rotation while passing through the tube. Consequently, the transmission of the Faraday filter becomes a maximum for light with a frequency for which the single-pass rotation angle is n/2, if absorption inside the Faraday filter is ignored. In this way, we see that the transmission * Strictly speaking, the effects of a Faraday filter inside a cavity should be discussed in terms of the cavity loss and polarization modes. See ref. [5]. 181
Volume
22, number
2
OPTICS COMMUNICATIONS
Ne DISCHARGE
SCOPE
MONOCHROMATOR
Fig. 1. Schematic
diagram
FILTER
of the experimental
1977
gions of magnetic field strength for the oscillations are tabulated in table 1, together with the parameters for the associated transitions [S, 91. It is important to note that all of oscillations shown in table 1 occurred on a single longitudinal mode of cavity. The most striking feature observed is that oscillations at the absorption lines of 607.4 nm (lsq-2~~) and 609.6 nm (ls,-2p,) take place only when the modes of the cavity pass just through the centers of the lines, i.e. the mean frequencies of u+ and cr_ transitions. This phenomenon can be explained as an optical saturation by two u-polarized monochromatic waves propagating in opposite directions, which is analogous to the case of ordinary saturated absorption if we do not take into account polarization’of the light. Consequently, it must be convenient to discuss this in terms of hole burning [lo]. Consider an atomic system with two optically coupled levels, both of which have a total angular momentum J= 1. As shown in fig. 2 (a), the opolarized monochromatic waves induce four transitions in the ensemble of atoms having various velocities. When the g-values of the upper and lower states are different, these four transitions have different frequencies, so that each transition may occur in a group of atoms having a particular velocity along the direction of the light propagation. These four transitions can be divided into two groups, one having a common sublevel in the upper level, and another having it in the lower level, so that these group can be considered separately, if the coupling between these groups by the processes of spontaneous emission and relaxation by atomic collisions is weak. As shown in fig. 2(b), the light waves in u-modes may burn four holes in the velocity distribution of atoms in the substates mL = 0 of the lower
TUBE
FABRY-PEROT
FARADAY
August
apparatus.
has a large frequency dependence in the vicinity of an absorption line. The discharge tube used has a bore of 6 mm and a length of 1.5 cm, and it contains neon with the pressure of 1.3 torr. The dc discharge current applied to the tube was fixed at 40 mA in the present experiment. At this current the total population in the 1s states of neon may attain 10” -lOI cmU3 [6,7]. On the other hand, the solenoid can produce magnetic fields up to 2.5 kG along the discharge tube. The active medium of the dye (Rhodamine 6G) is in the form of a free flowing jet stream, which is pumped by an argon laser with about 2 W total power. The mirror spacing of the dye laser cavity was about 1 m, which results in a mode separation of 1.50 MHz. The output frequency of this dye laser system is roughly measured with a monochromator in order to assign the absorption lines, and the oscillation mode is monitored by a scanning Fabry-Perot interferometer with a frequency resolution of 40 MHz. Keeping the discharge current at 40 mA, we increased the magnetic field strength H from zero. As a result, oscillations occurred at five absorption lines from the 1s5 and Is, states to the 2p states. The re-
Table 1 The oscillating wavelengths and related transitions of neon, together with theg-values and oscillator strengths associated with these transitions. The oscillation regions of magnetic field strengths are also shown. The asterisk means the oscillation occurring only when the mode of cavity passes through the center of the absorption line. g-factor
Transition
h
f-value
(nm) _______
_~~~
182
640.2 614.3
lss (J = 2) -
594.5 607.4 609.6
ls4(J=
1) -
~~~~ ~~~ _.~~~ ..~
2p$I (J = 3) 2pb(J= 2) 2p4(J=2) 2p3GI=O) 2p4(J=2)
1.503
1.464
1.329 1.229
0.373 0.122
1.301 _ 1.301
0.056 0.114 0.157
Magnetic (kG)
field
Oscillation mode
0.94-1.73 0.31-1.42 1.74-2.09 1.42-2.29 1.33-1.83 1.71-2.30
single single single single single* single*
OPTICS COMMUNICATIONS
Volume 22, number 2
f
-R,
0
nlm,=O)
R,
Akv
Fig. 2. (a) Allowed transitions between the states with J = 1 by the o-polarized light. (b) The positions of holes and peaks in the velocity distribution of atoms in the states with rn~ = 0 and mu = 0.
state at the velocities uz = (+ L?;2,f Aw)/k ,
(1)
where a2, is the Larmor frequency in the upper state, Ao is the detuning of the light frequency from the transition frequency between the substates mL = 0 and mu = 0, and k is the wave number. Therefore, if the detuning Aw is zero, two holes in the positive or negative region of u, overlap each other at u, = R,/k or -C12,/k, which may result in the increase of the saturation at the line center. Similarly, the velocity distribution of atoms in the substate mu = 0 in the upper state has four peaks and each peak overlaps another when Aw = 0, which also causes the saturation to increase at the line center. This saturation phenomenon in a magnetic field has been studied theoretically in the case of a gas laser amplifier [ 11,121, and was actually observed by Gorlicki and Dumont in the saturated absorption of neon irradiated by a He-Ne laser operating at 632.8 nm (3s2-2~~) [13]. We could not observe the above phenomenon in oscillations at lines originating from the ls5 state. The reason might be partially due to the fact that the Is, state and the 2p states associated with these oscillations have total angular momenta larger than 2, so that the number of Zeeman components which do not contribute to the increase of saturation at Aw = 0 is larger than that of the line from the Is4 state. For these oscillations, we observed frequency shifts of mode-jump-
August 1911
ing when the magnetic field strength H was varied. For the lowest values of Hin the oscillation regions shown in table 1, the oscillations took place at the center of the lines with the ambiguity of the mode separation of 150 MHz. As H was increased within the oscillation regions, the oscillation frequencies were shifted monotonically towards higher frequencies, the total shift being l-2 GHz. One can easily see that these frequenoy shifts come from changes in the transmission spectrum of the Faraday filter due to the variations in the magnetic field strength. Using the formula for the resonant Faraday effect [ 141, we have calculated the rotation angle 0 and the transmission of the Faraday filter, for light with its frequency in the vicinity of the lines shown in table 1. The results show that the rotation angle 0 has a maximum at the line center in the case of a weak magnetic field and the maximal value increases with H. On the other hand, in a strong magnetic field in which the u+ and u_ components of the absorption lines are well resolved, we have a minimal rotation angle at the line center, and its value decreases with H. In this way, if the population of the lower states is sufficient, there exist two values of H to get 8 = n/2 at the line center, i.e. there may be two regions of H to get oscillations near the line center. However, the light absorption in the lower region of H is generally too high to support the oscillations, so that the obtained oscillations can be considered to occur in the higher region of H, except for the oscillations at the line of 614.3 nm as shown in table 1. When the maximal value of rotation angle exceeds 7r/2 or the minimal value becomes smaller than n/2, we may have two peaks in the transmission positioned symmetrically with respect to the line center. We could ascertain that all of the oscillations at the lines originating from the Is, state occurred at one of these peaks, which shifted towards higher frequencies as increasing H. The reason why the oscillations did not take place at the other peak has not yet made clear, but we think that this fact might largely be related with the deformation of the laser beam by a mechanism such as the self-focusing or self-defocusing. It should be important to notice that the optical saturation at the absorption line from long-lived states such as the 1s states of neon takes place generally in a weak laser field compared with that for a line from the ground state or from a short-lived excited state. This results in a large power-broadening of the hole burned 183
Volume 22, number 2
OPTICS COMMUNICATIONS
in the velocity
distribution in the lower state. Consider here a nondegenerate two-level atom with the upper state la) and the lower state Ib>, which are connected to each other by a monochromatic field with the frequency w. If the decay rates of the states la> and lb) are denoted by ya and yb and the decay rate of coherence between these states by y,&, the saturation parameter [ 1.51 can easily be calculated with a semiclassical density matrix formalism as
(2) where p is the electric dipole moment, E the electric field, and (Ythe fraction of the decay rate from the state la) to the states other than lb) in the total decay rate ya. In both cases that the state lb> is the ground state to which Is is given by setting CY = 0 in (2) and that it is the short-lived excited state, the decay rate ya of the upper state plays an important role to determine the value of I,. On the other hand, when lb) is the long-lived state and o is not zero, I, becomes independent of ya and is mainly determined by the quantity o/ye. As the result, we have generally a large saturation parameter for absorption lines originating from the Is states of neon. Despite this large saturation in the light absorption, the optical rotation is not significantly af. fected by a strong laser field as discussed by Gibbs et al. [16], because the non-resonant atoms Doppler shifted away from the resonance contribute primarily to the dispersion. It should be noted that yb in (2) is mainly determined by the transit time of atoms across the laser beam for the Is, state, since it is of the order of 10P6 s while the life time of this state is of the order of 1O-4 s [17,18]. In this paper, we have reported experimental results in frequency-locking a CW dye laser to some absorption lines of neon in a discharge by means of a Faraday filter. This method is applicable to frequency-locking
184
to many other atomic or molecular
August 1977
lines, if the product
iVffor the desired line is larger than 101’ cmP3, N being the population difference between the associated states andfbeing the oscillator strength. The facility to get a single mode oscillations at many atomic or molecular transitions should promote various applications in the fields of spectroscopy, photo-chemistry and isotope separation.
References [I] RX. Grove, F.Y. Wu, L.A. Hacked, D.G. Youmans amd S. Ezekiel, Appl. Phys. Lett. 23 (1973) 442. [2] F. Schuda, M. Hercher and CR. Stroud Jr., Appl. Phys. Lett. 22 (1973) 360. [3] P.P. Sorokin, J.R. Lankard, V.L. Moruzzi and A. Lurio, Appl. Phys. Lett. 15 (1969) 179. [4] T. Endo, T. Yabuzaki, M. Kitano, T. Sato and T. Ogawa, to be published. [5] T. Yabuzaki, M. Kitano, T. Endo and T. Ogawa, Japan. J. Appl. Phys., Vol. 16, No. 5 (1977) (in press). [6] O.P. Bochkova, L.P. Razumovskaya and S.E. Frish, Opt. Spectrosk. 11 (1961) 697 [Opt. Spectrosc. 11 (1961) 3761 [7] A. Ricard, J. Phys. (Paris) 30 (1969) 560. [ 81 C.E. Moore, Atomic Energy Levels, National Bureau of Standards Circular 467 (U.S. Government Printing Office, Washington, DC., 1949), Vol. 1. [9] W.L. Wiese, M.W. Smith and B.M. Glennon, Atomic Transition Probabilities, NSRDSNBS4 (U.S. Government Printing Office, Washington, DC., 1966), Vol. 1. [IO] W.R. Bennett, Jr., Appl. Opt., Suppl. 1 (1962) 24. [ 111 A. Dienes, Phys. Rev. 174 (1968) 400. [12] A. Dienes, Phys. Rev. 174 (1968) 414. [ 131 M. Gorlicki and M. Dumont, C.R. Acad. Sci. (Paris) B 279 (1974) 55. [14] D.M. Camm and F.L. Curzon, Can. J. Phys. 50 (1972) 2866. [15] W.E. Lamb, Jr., Phys. Rev. 134 (1964) 1429. [16] H.M. Gibbs, G.G. Churchill and G.J. Salamo, Opt. Comm. 12 (1974) 396. 1171 A.V. Phelps and J.P. Molnar, Phys. Rev. 89 (1953) 1202. 118) 3.R. Dixon and F.A. Grant, Phys. Rev. 107 (1957) 118.
OF A CW DYE LASER TO SOME ABSORPTION
OF A NEON DISCHARGE BY A FARADAY T. YABUZAKI, Ionosphere
August 1977
OPTICS COMMUNICATIONS
Volume 22, number 2
LINES
FILTER
T. ENDO, M. KITANO and T. OGAWA
Research Laboratory,
Kyoto University, Kyoto, Japan
Received 18 May 1977
Single-mode oscillations of a CW dye laser at the center of five absorption lines from the 1s states to the 2p states of neon were obtained by means of a neon discharge Faraday filter, without any other frequency-selective elements. The most striking thing observed is that saturated absorption takes place at the center of several absorption lines in a Faraday filter, in addition to optical rotation.
Saturated
absorption
is now a powerful
tool for
It has also been used to lock single-mode frequencies of gaseous lasers and dye lasers to the centers of Doppler-broadened resonance lines of atoms and molecules with extremely high stability. However, in this method the laser system becomes relatively complicated, because one has to prepare a single-mode oscillation by means of a cavity system such as a Fox-Smith type cavity [e.g. l] or frequency-selective elements such as Fabry-Perot etalons [e.g. 21, before applying saturated absorption techniques. One of the more conventional methods to lock the frequency of a laser to an atomic line is to utilize a Faraday filter, by which means spectral narrowing and frequency locking can be made simultaneously. This method was first developed by Sorokin et al. [3] for frequency locking a pulsed dye laser to the sodium D lines, but they obtained oscillations only on the wings of the lines. Recently, we performed a similar experiment with a CW dye laser and obtained single-mode oscillations in the center regions of the D, and D2 lines of sodium. Details of this experiment will be reported elsewhere [4]. In this paper, we report experimental results on frequency locking of a CW dye laser to some absorption lines from the 1s states to the 2p states of neon in a discharge by means of a Faraday filter. It should be noted that, simply by inserting the Faraday filter inside the dye laser cavity without any other frequencyDoppler-free
laser spectroscopy.
selective elements, we could obtain single-mode oscillations at the center regions of absorption lines. Furthermore, the single-mode oscillations at the absorption lines originating from the 1s4 state, such as the line at 607.4 nm (lsq-2~~) took place only when longitudinal modes of the cavity coincided with centers of the lines. This phenomenon can be explained as a saturation interaction of the light waves propagating in opposite directions, just as seen in ordinary saturated absorption. The experimental apparatus is shown in fig. 1. The Faraday filter used in the present experiment consists of a neon discharge tube with Brewster-angle windows whose principal axes are oriented perpendicularly to each other, and a solenoid to produce a relative strong axial m$gnetic field. The principle of the Faraday filter can easily be understood by considering a simplified model *. When the light polarized vertically is incident on the Faraday filter from its left-hand side in fig. 1, the light is subjected to the optical rotation while passing through the tube. Consequently, the transmission of the Faraday filter becomes a maximum for light with a frequency for which the single-pass rotation angle is n/2, if absorption inside the Faraday filter is ignored. In this way, we see that the transmission * Strictly speaking, the effects of a Faraday filter inside a cavity should be discussed in terms of the cavity loss and polarization modes. See ref. [5]. 181
Volume
22, number
2
OPTICS COMMUNICATIONS
Ne DISCHARGE
SCOPE
MONOCHROMATOR
Fig. 1. Schematic
diagram
FILTER
of the experimental
1977
gions of magnetic field strength for the oscillations are tabulated in table 1, together with the parameters for the associated transitions [S, 91. It is important to note that all of oscillations shown in table 1 occurred on a single longitudinal mode of cavity. The most striking feature observed is that oscillations at the absorption lines of 607.4 nm (lsq-2~~) and 609.6 nm (ls,-2p,) take place only when the modes of the cavity pass just through the centers of the lines, i.e. the mean frequencies of u+ and cr_ transitions. This phenomenon can be explained as an optical saturation by two u-polarized monochromatic waves propagating in opposite directions, which is analogous to the case of ordinary saturated absorption if we do not take into account polarization’of the light. Consequently, it must be convenient to discuss this in terms of hole burning [lo]. Consider an atomic system with two optically coupled levels, both of which have a total angular momentum J= 1. As shown in fig. 2 (a), the opolarized monochromatic waves induce four transitions in the ensemble of atoms having various velocities. When the g-values of the upper and lower states are different, these four transitions have different frequencies, so that each transition may occur in a group of atoms having a particular velocity along the direction of the light propagation. These four transitions can be divided into two groups, one having a common sublevel in the upper level, and another having it in the lower level, so that these group can be considered separately, if the coupling between these groups by the processes of spontaneous emission and relaxation by atomic collisions is weak. As shown in fig. 2(b), the light waves in u-modes may burn four holes in the velocity distribution of atoms in the substates mL = 0 of the lower
TUBE
FABRY-PEROT
FARADAY
August
apparatus.
has a large frequency dependence in the vicinity of an absorption line. The discharge tube used has a bore of 6 mm and a length of 1.5 cm, and it contains neon with the pressure of 1.3 torr. The dc discharge current applied to the tube was fixed at 40 mA in the present experiment. At this current the total population in the 1s states of neon may attain 10” -lOI cmU3 [6,7]. On the other hand, the solenoid can produce magnetic fields up to 2.5 kG along the discharge tube. The active medium of the dye (Rhodamine 6G) is in the form of a free flowing jet stream, which is pumped by an argon laser with about 2 W total power. The mirror spacing of the dye laser cavity was about 1 m, which results in a mode separation of 1.50 MHz. The output frequency of this dye laser system is roughly measured with a monochromator in order to assign the absorption lines, and the oscillation mode is monitored by a scanning Fabry-Perot interferometer with a frequency resolution of 40 MHz. Keeping the discharge current at 40 mA, we increased the magnetic field strength H from zero. As a result, oscillations occurred at five absorption lines from the 1s5 and Is, states to the 2p states. The re-
Table 1 The oscillating wavelengths and related transitions of neon, together with theg-values and oscillator strengths associated with these transitions. The oscillation regions of magnetic field strengths are also shown. The asterisk means the oscillation occurring only when the mode of cavity passes through the center of the absorption line. g-factor
Transition
h
f-value
(nm) _______
_~~~
182
640.2 614.3
lss (J = 2) -
594.5 607.4 609.6
ls4(J=
1) -
~~~~ ~~~ _.~~~ ..~
2p$I (J = 3) 2pb(J= 2) 2p4(J=2) 2p3GI=O) 2p4(J=2)
1.503
1.464
1.329 1.229
0.373 0.122
1.301 _ 1.301
0.056 0.114 0.157
Magnetic (kG)
field
Oscillation mode
0.94-1.73 0.31-1.42 1.74-2.09 1.42-2.29 1.33-1.83 1.71-2.30
single single single single single* single*
OPTICS COMMUNICATIONS
Volume 22, number 2
f
-R,
0
nlm,=O)
R,
Akv
Fig. 2. (a) Allowed transitions between the states with J = 1 by the o-polarized light. (b) The positions of holes and peaks in the velocity distribution of atoms in the states with rn~ = 0 and mu = 0.
state at the velocities uz = (+ L?;2,f Aw)/k ,
(1)
where a2, is the Larmor frequency in the upper state, Ao is the detuning of the light frequency from the transition frequency between the substates mL = 0 and mu = 0, and k is the wave number. Therefore, if the detuning Aw is zero, two holes in the positive or negative region of u, overlap each other at u, = R,/k or -C12,/k, which may result in the increase of the saturation at the line center. Similarly, the velocity distribution of atoms in the substate mu = 0 in the upper state has four peaks and each peak overlaps another when Aw = 0, which also causes the saturation to increase at the line center. This saturation phenomenon in a magnetic field has been studied theoretically in the case of a gas laser amplifier [ 11,121, and was actually observed by Gorlicki and Dumont in the saturated absorption of neon irradiated by a He-Ne laser operating at 632.8 nm (3s2-2~~) [13]. We could not observe the above phenomenon in oscillations at lines originating from the ls5 state. The reason might be partially due to the fact that the Is, state and the 2p states associated with these oscillations have total angular momenta larger than 2, so that the number of Zeeman components which do not contribute to the increase of saturation at Aw = 0 is larger than that of the line from the Is4 state. For these oscillations, we observed frequency shifts of mode-jump-
August 1911
ing when the magnetic field strength H was varied. For the lowest values of Hin the oscillation regions shown in table 1, the oscillations took place at the center of the lines with the ambiguity of the mode separation of 150 MHz. As H was increased within the oscillation regions, the oscillation frequencies were shifted monotonically towards higher frequencies, the total shift being l-2 GHz. One can easily see that these frequenoy shifts come from changes in the transmission spectrum of the Faraday filter due to the variations in the magnetic field strength. Using the formula for the resonant Faraday effect [ 141, we have calculated the rotation angle 0 and the transmission of the Faraday filter, for light with its frequency in the vicinity of the lines shown in table 1. The results show that the rotation angle 0 has a maximum at the line center in the case of a weak magnetic field and the maximal value increases with H. On the other hand, in a strong magnetic field in which the u+ and u_ components of the absorption lines are well resolved, we have a minimal rotation angle at the line center, and its value decreases with H. In this way, if the population of the lower states is sufficient, there exist two values of H to get 8 = n/2 at the line center, i.e. there may be two regions of H to get oscillations near the line center. However, the light absorption in the lower region of H is generally too high to support the oscillations, so that the obtained oscillations can be considered to occur in the higher region of H, except for the oscillations at the line of 614.3 nm as shown in table 1. When the maximal value of rotation angle exceeds 7r/2 or the minimal value becomes smaller than n/2, we may have two peaks in the transmission positioned symmetrically with respect to the line center. We could ascertain that all of the oscillations at the lines originating from the Is, state occurred at one of these peaks, which shifted towards higher frequencies as increasing H. The reason why the oscillations did not take place at the other peak has not yet made clear, but we think that this fact might largely be related with the deformation of the laser beam by a mechanism such as the self-focusing or self-defocusing. It should be important to notice that the optical saturation at the absorption line from long-lived states such as the 1s states of neon takes place generally in a weak laser field compared with that for a line from the ground state or from a short-lived excited state. This results in a large power-broadening of the hole burned 183
Volume 22, number 2
OPTICS COMMUNICATIONS
in the velocity
distribution in the lower state. Consider here a nondegenerate two-level atom with the upper state la) and the lower state Ib>, which are connected to each other by a monochromatic field with the frequency w. If the decay rates of the states la> and lb) are denoted by ya and yb and the decay rate of coherence between these states by y,&, the saturation parameter [ 1.51 can easily be calculated with a semiclassical density matrix formalism as
(2) where p is the electric dipole moment, E the electric field, and (Ythe fraction of the decay rate from the state la) to the states other than lb) in the total decay rate ya. In both cases that the state lb> is the ground state to which Is is given by setting CY = 0 in (2) and that it is the short-lived excited state, the decay rate ya of the upper state plays an important role to determine the value of I,. On the other hand, when lb) is the long-lived state and o is not zero, I, becomes independent of ya and is mainly determined by the quantity o/ye. As the result, we have generally a large saturation parameter for absorption lines originating from the Is states of neon. Despite this large saturation in the light absorption, the optical rotation is not significantly af. fected by a strong laser field as discussed by Gibbs et al. [16], because the non-resonant atoms Doppler shifted away from the resonance contribute primarily to the dispersion. It should be noted that yb in (2) is mainly determined by the transit time of atoms across the laser beam for the Is, state, since it is of the order of 10P6 s while the life time of this state is of the order of 1O-4 s [17,18]. In this paper, we have reported experimental results in frequency-locking a CW dye laser to some absorption lines of neon in a discharge by means of a Faraday filter. This method is applicable to frequency-locking
184
to many other atomic or molecular
August 1977
lines, if the product
iVffor the desired line is larger than 101’ cmP3, N being the population difference between the associated states andfbeing the oscillator strength. The facility to get a single mode oscillations at many atomic or molecular transitions should promote various applications in the fields of spectroscopy, photo-chemistry and isotope separation.
References [I] RX. Grove, F.Y. Wu, L.A. Hacked, D.G. Youmans amd S. Ezekiel, Appl. Phys. Lett. 23 (1973) 442. [2] F. Schuda, M. Hercher and CR. Stroud Jr., Appl. Phys. Lett. 22 (1973) 360. [3] P.P. Sorokin, J.R. Lankard, V.L. Moruzzi and A. Lurio, Appl. Phys. Lett. 15 (1969) 179. [4] T. Endo, T. Yabuzaki, M. Kitano, T. Sato and T. Ogawa, to be published. [5] T. Yabuzaki, M. Kitano, T. Endo and T. Ogawa, Japan. J. Appl. Phys., Vol. 16, No. 5 (1977) (in press). [6] O.P. Bochkova, L.P. Razumovskaya and S.E. Frish, Opt. Spectrosk. 11 (1961) 697 [Opt. Spectrosc. 11 (1961) 3761 [7] A. Ricard, J. Phys. (Paris) 30 (1969) 560. [ 81 C.E. Moore, Atomic Energy Levels, National Bureau of Standards Circular 467 (U.S. Government Printing Office, Washington, DC., 1949), Vol. 1. [9] W.L. Wiese, M.W. Smith and B.M. Glennon, Atomic Transition Probabilities, NSRDSNBS4 (U.S. Government Printing Office, Washington, DC., 1966), Vol. 1. [IO] W.R. Bennett, Jr., Appl. Opt., Suppl. 1 (1962) 24. [ 111 A. Dienes, Phys. Rev. 174 (1968) 400. [12] A. Dienes, Phys. Rev. 174 (1968) 414. [ 131 M. Gorlicki and M. Dumont, C.R. Acad. Sci. (Paris) B 279 (1974) 55. [14] D.M. Camm and F.L. Curzon, Can. J. Phys. 50 (1972) 2866. [15] W.E. Lamb, Jr., Phys. Rev. 134 (1964) 1429. [16] H.M. Gibbs, G.G. Churchill and G.J. Salamo, Opt. Comm. 12 (1974) 396. 1171 A.V. Phelps and J.P. Molnar, Phys. Rev. 89 (1953) 1202. 118) 3.R. Dixon and F.A. Grant, Phys. Rev. 107 (1957) 118.