An ultrahigh-Q tunable optical filter with a FWHM bandwidth of 41 MHz is demonstrated. The filtering is produced by nondegenerate phase conjugation through four-wave mixing in atomic-sodium vapor. The filter is observed to have a maximum quantum efficiency of 4 x 10^-3. However, degenerate phase-conjugation experiments in sodium suggest that a quantum efficiency of greater than unity can be attained on a cw basis

Gluck, Natalie S.

Nilsen, Joseph

Yariv, Amnon

English

Caltech Authors - Main

380 OPTICS LETTERS / Vol. 6, No. 8 / August 1981
Narrow-band optical filter through phase conjugation by
nondegenerate four-wave mixing in sodium vapor
Joseph Nilsen, Natalie S. Gluck, and Amnon Yariv
California Institute of Technology, Pasadena, California 91125
Received March 30,1981
An ultrahigh-Q, tunable optical filter with a FWHM bandwidth of 41 MHz is demonstrated. The filtering is pro-
duced by nondegenerate phase conjugation through four-wave mixing in atomic-sodium vapor. The filter is ob-
served to have a maximum quantum efficiency of 4 X 10-3. However, degenerate phase-conjugation experiments
in sodium suggest that a quantum efficiency of greater than unity can be attained on a cw basis.
The frequency response of phase conjugation through
nondegenerate four-wave mixing has been analyzed by
several authors'- 5 and has been shown to be capable of
yielding a narrow-bandpass optical filter. The filter
bandpass is a function of both phase-mismatch con-
straints and the frequency dependence of the coeffi-
cients coupling the waves in the nonlinear process.
Optical filtering was recently demonstrated in CS2, a
transparent medium, by using high-power pulsed lasers
to provide the pump waves needed in the nonlinear
process.6 The filtering is dependent only on the
phase-mismatch constraints in this type of medium. In
this Letter we report the first known experimental
demonstration of optical filtering by phase conjugation
in a resonant system. A resonant system, sodium in this
case, has the advantage of providing much larger non-
linear coupling constants than a transparent medium,
enabling one to use low-power cw lasers to provide the
pump waves. The frequency dependence of the cou-
pling coefficients can result in a filter response that is
much narrower than in a transparent medium. An ul-
trahigh-Q filter with a FWHM bandwidth of 41 MHz
is demonstrated in our experiments.
In this experiment, a phase-conjugate signal is gen-
erated by the coupling of two counterpropagating pump
waves to a signal wave by an intensity-dependent
modulation of the atomic population. Physically, the
signal wave and one of the pump waves form an ab-
sorption grating that diffracts the second pump wave
to create the phase-conjugate wave. The output of a
passively stabilized Spectra-Physics cw ring dye laser
is circularly polarized to provide optical isolation from
the laser and is then retroreflected by a mirror to pro-
vide the counterpropagating pump waves. An actively
stabilized Coherent Radiation cw ring dye laser gener-
ates the signal wave, which intersects the pump wave
at an angle of 0.390. Sodium vapor acts as the nonlinear
medium. A 2.44-cm-long cylindrical quartz cell of
2.2-cm diameter contains sodium metal in a side arm.
The cell is heated to provide the sodium vapor. Cesium
metal is also present in the cell and provides a back-
ground pressure of 10-2 Torr of cesium vapor. The
cesium resonances are far from the sodium transition
used and do not affect the nonlinear process. The sig-
nal wave is chopped mechanically, and the phase-con-
jugate signal is detected by a P-I-N photodiode that
is connected to a lock-in amplifier to provide an excel-
lent signal-to-noise ratio. Figure 1 shows the experi-
mental setup. The pump beam has a FWHM diameter
of 0.106 cm and a maximum power of 35.2 mW at the
entrance to the cell. The signal beam has a FWHM
diameter of 0.15 cm and provides 0.3 mW of power.
Figure 2 shows the frequency dependence of degen-
erate phase conjugation in sodium when both pump and
signal waves are provided by one laser tuned to the
3S1/ 2-3P 3 /2 transition at 5890 A. The pump power is
35.2 mW. The large set of peaks on the left corresponds
to the laser tuning through the F = 2 hyperfine line of
the sodium ground state, whereas the smaller peaks are
due to tuning through the F = 1 hyperfine level of the
ground state. In the nondegenerate case, the pump
laser is tuned to the stronger peak of the 3S1/2 (F - 2)
to 3P3/2 (F = 3) transition shown in Fig. 2. The tem-
perature of the sodium cell is adjusted to provide a
saturated pump-wave transmission of 46% through the
cell. This corresponds to a sodium density of 5 X
10ll/cm 2 . The pump power is 31.5 mW. The signal
laser is then scanned in frequency through the transition
at 5890 A, and the measured phase-conjugate signal is
shown in Fig. 3. The observed signal has a FWHM
bandwidth of 48 MHz and a peak reflectivity of 4 X
10-3.
An independent photomixing experiment demon-
strates that the peak of the signal occurs when the pump
and signal lasers are degenerate. When the pump laser
is tuned to each of the other three peaks in Fig. 2 and the
pump polarizer X/4 plate
signal
loser
r i
sodium cell
beam splitter
-w
mirror
1phase conjugate signal
Fig. 1. Experimental setup for cw nondegenerate phase
conjugation.
0146-9592/81/080380-03$0.50/0 © 1981, Optical Society of America
1000MHz
Fig. 2. Reflectivity for degenerate phase conjugation versus
laser tuning for the 3S,/2-3P3/2 transition. The laser intensity
for the pump wave is 2800 mW/cm 2.
200MHz
, 
Fig. 3. Reflectivity for nondegenerate phase conjugation
versus signal laser tuning with the pump laser fixed on the
stronger peak of the 3S1 /2 (F = 2) to 3P3/2 (F = 3) transition.
The laser intensity for the pump wave is 2500 mW/cm 2 .
signal laser is scanned, we observe a similar frequency
response, but the reflectivities are smaller.
In Fig. 4, the frequency dependence of degenerate
phase conjugation is shown with the pump power at-
tenuated to 2.4 mW. The angle between the signal and
pump waves is now 0.320. There is now one peak when
the laser is tuned through the F = 2 hyperfine line.
This single peak narrows even more as the pump is re-
duced, with its bandwidth limited by the natural line-
width of sodium.7' 8 The pump laser is now tuned to the
peak of the 3S1 /2 (F = 2) to 3P3 /2 (F = 3) transition
shown in Fig. 4. The sodium density is adjusted to
provide a saturated pump-wave transmission of 48%
through the cell, which corresponds to a sodium density
of 1 X 10ll/cm 2 . The pump power is 2.5 mW. The
signal laser is frequency scanned, and the resulting
phase-conjugate signal is shown in Fig. 5. The FWHM
bandwidth is measured to be 41 MHz with a peak re-
flectivity of 6 X 10-5. The bandwidth remains basically
unchanged at the lower pump power, but the reflectivity
is greatly reduced.
We have demonstrated an optical filter with a mini-
mum FWHM bandwidth of 41 MHz. From phase-
mismatch constraints alone, one can calculate a FWHM
bandwidth of 5.2 GHz.3 The frequency response of a
resonant two-level system is limited by the T 2
transverse relaxation time.1' 2' 4' 5 If we assume that T2
= 2T 1. (T1 is the natural lifetime, 16 nsec for sodium),
then the theory for a Doppler-broadened two-level
system yields a FWHM bandwidth of 13 MHz at low
intensities.2 In our system, the frequency jitter of the
two dye lasers appears to limit our bandwidth to 40
MHz. It is important to note that we do not observe
any significant change in the filter bandwidth as the
pump power is increased. Also, the Rabi sidebands,
August 1981 / Vol. 6, No. 8 / OPTICS LETTERS 381
which are theoretically predicted,5 are not observed.
The maximum pump intensity used in these experi-
ments is already 2 orders of magnitude greater than the
saturation intensity of sodium. This suggests that
much higher pump powers can be used without seriously
affecting the filter bandwidth. A maximum reflectivity
of 4 X 10-3 is observed for the filter. However, recent
degenerate phase-conjugation experiments in sodium
vapor have demonstrated amplified reflectivity ex-
ceeding unity by using a cw dye laser with a maximum
power of 1 W.9 This suggests that a highly efficient
narrow-bandwidth filter can be constructed by using a
resonant medium such as sodium. In sodium, it should
be noted that hyperfine optical pumping transfers the
population of the ground-state hyperfine level resonant
with the laser into the other ground-state hyperfine
level. thereby diminishing the efficiency of the phase-
conjugation process. Resonant systems that do not
suffer from this effect, such as an atomic system with
zero nuclear spin, should be more efficient and should
allow much lower cw pump powers to be used. One
disadvantage of the Doppler-broadened system is the
narrow field of view of the filter. The maximum
phase-conjugate signal is observed in a collinear ge-
ometry. The acceptance angle (angle between the
signal and pump waves such that the reflectivity is re-
duced by one half from the collinear geometry) of the
filter is approximately the ratio of the natural linewidth
to the Doppler width.2
The central frequency of the filter can be selected to
coincide with that of the hyperfine transitions. The
splitting between the two components of the F = 2 hy-
1000MHz
Fig. 4. Reflectivity for degenerate phase conjugation versus
laser tuning for the 3S,/2-3P3/2 transition. The laser intensity
for the pump wave is 190 mW/cm 2 .
200MHz
Fig. 5. Reflectivity for nondegenerate phase conjugation
versus signal laser tuning with the pump laser fixed on the
3Sl/ 2 (F = 2) to 3P3/2 (F = 3) transition. The laser intensity
for the pump wave is 200 mW/cm 2.
382 OPTICS LETTERS / Vol. 6, No. 8 / August 1981
perfine transition in Fig. 2 is intensity dependent and
increases as the square root of the pump wave intensity
in our experiments, indicating that the splitting is
probably due to an ac Stark effect.'0 The filter there-
fore has a limited tuning range that is a function of
pump intensity. Additional tuning could be achieved
by detuning the pump laser from the atomic resonance
as the filter's frequency bandpass is centered at the
frequency of the pump wave. This would be at the
expense of the phase-conjugate efficiency,",2 however.
We thank William Bridges and Randy Bartman for
the loan of and advice with one of the two dye lasers
used in this experiment. We also thank Steven A.
Cohen for his assistance in constructing the sodium cell.
Joseph Nilsen thanks the Fannie and John Hertz
Foundation for support of graduate studies. Joseph
Nilsen is a Fannie and John Hertz Foundation Fellow.
This research also was supported by the U.S. Army
Research Office in Durham, North Carolina.
References
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mixing applied to optical filters," Appl. Opt. 18, 143
(1979).
2. J. Nilsen and A. Yariv, "Nondegenerate four-wave mixing
in a Doppler-broadened resonant medium," J. Opt. Soc.
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3. D. M. Pepper and R. L. Abrams, "Narrow optical band-
pass filter via nearly degenerate four-wave mixing," Opt.
Lett. 3, 212 (1978).
4. T. Fu and M. Sargent III, "Effects of signal detuning on
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5. D. J. Harter and R. W. Boyd, "Nearly degenerate four-
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Quantum Electron. QE-16, 1126 (1980).
6. L. K. Lam and R. W. Hellwarth, "A wide-angle narrow-
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7. L. M. Humphrey, J. P. Gordon, and P. F. Liao, "Angular
dependence of line shape and strength of degenerate
four-wave mixing in a Doppler-broadened system with
optical pumping," Opt. Lett. 5, 56 (1980).
8. P. F. Liao, D. M. Bloom, and N. P. Economou, "Cw optical
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9. R. C. Lind, D. G. Steel, J. F. Lam, R. K. Jain, and R. A.
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Narrow-band optical filter through phase conjugation by nondegenerate four-wave mixing in sodium vapor

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