We describe semi-self-pumped photorefractive phase-conjugate mirrors based on the unidirectional ring resonator and the double phase-conjugate mirror. Their applicability to thresholding phase conjugation and one-way imaging through distortions is discussed

Cronin-Golomb, Mark

Yariv, Amnon

English

Caltech Authors - Main

714 OPTICS LETTERS / Vol. 12, No. 9 / September 1987
Semi-self-pumped phase-conjugate mirrors
Mark Cronin-Golomb
Electrooptics Technology Center, Tufts University, Medford, Massachusetts 02148
Amnon Yariv
California Institute of Technology, Pasadena, California 91125
Received April 4, 1987; accepted June 15, 1987
We describe semi-self-pumped photorefractive phase-conjugate mirrors based on the unidirectional ring resonator
and the double phase-conjugate mirror. Their applicability to thresholding phase conjugation and one-way
imaging through distortions is discussed.
In the past, four-wave mixing phase-conjugate mirrors
(PCM's) have been either externally pumped or com-
pletely self-pumped. In the first case, both pumps are
provided independently of the signal and must be ar-
ranged to be plane waves or at least good phase conju-
gates of each other. The second case is that of the
passive (self-pumped) photorefractive phase-conju-
gate mirrors (PPCM's). For the linear PPCM1 and
the cat PPCM2 both pumping beams are self-induced
as oscillation beams. For the ring PPCM1 one is self-
induced and the other is provided directly by the sig-
nal. In this Letter we introduce the concept of semi-
self-pumped PCM's in which one pump is externally
supplied to a four-wave mixing phase conjugator while
the other is self-induced as an oscillation beam. One
application is as a thresholding PCM, which would be
useful, for example, in providing nonlinear feedback
for optical associative memories.3-5 The second ap-
plication is in one-way imaging through optical distor-
tions using a phase-conjugate window6.
The first semi-self-pumped PCM (Fig. 1) is based
on the unidirectional ring resonator.7 The signal
beam pumps a photorefractive crystal to supply gain
for unidirectional ring oscillation II. This unidirec-
tional ring oscillation serves as the self-induced pump
of the semi-self-pumped phase conjugation. It is
forced into the lowest-order transverse mode by an
intracavity spatial filter. One of the resonator cavity
mirrors is partially transmitting, and the second
pumping beam I2 is injected externally through it into
the ring.
The second example of a semi-self-pumped PCM is
a special case of the ring semi-self-pumped PCM that
results if the reflectivity of the partial-feedback mirror
is reduced to zero (Fig 2). This gives us a device that
was previously studied as a double PCM.1"8 Here, we
discuss its interpretation as a semi-self-pumped PCM.
The pump labeled 1 in the figure is the self-induced
oscillation beam, while the pump labeled 2 is external-
ly supplied.
Both of these devices may be used as thresholding
PCM's finding application, for example, in optical as-
sociative memories. Associative memory devices op-
erate by using nonlinear feedback to select the stored
memory that most closely resembles the partial infor-
mation input. The parallelism of optical information
processing has made all-optical associative memories
an attractive prospect, and some of the first theoreti-
cal and experimental considerations along these lines
have involved phase-conjugate resonators in which the
memories are stored in intracavity holograms. Mem-
ory selection takes place through competitive mode
selection biased by injection of a beam bearing the
partial information.3-5 The competition is encour-
aged by the presence of a positive thresholding effect
in the reflectivities he cavity PCM's.9"10
In the semi-self-pi iiped phase conjugator of Fig. 1
the presence of the externally supplied pumping beam
I2' suppresses buildup of the self-induced pumping
beam I, until the signal reaches a certain threshold
intensity. This threshold intensity is proportional to
the intensity of the external pump. We are currently
developing a full theoretical treatment of this device,
which, because of the closed nature of the ring resona-
tor, will require the simultaneous fitting of phase and
Fig. 1. Semi-self-pumped photorefractive phase conjuga-
tor based on unidirectional ring resonator. The intracavity
aperture forces single-transverse-mode operation.
0146-9592/87/090714-03$2.00/0 © 1987, Optical Society of America
September 1987 / Vol. 12, No. 9 / OPTICS LETTERS 715
z
3 .,1~1-" 
(yla/2) + a = O. y is the photorefractive coupling
constant, and 1 is the length of the interaction region.
The theory of the double PCM gives its reflectivity R
as
R = a + 1+
q
a -) (a 1 +a+ , (2)
Fig. 2. The double PCM may be interpreted as a semi-self-
pumped phase conjugator. When barium titanate is used,
the crystal is tilted so that the c axis is neither parallel nor
perpendicular to the bisectors of the beams. This enables
extraordinarily polarized beams to use the high electro-optic
coefficient r42 -
4
_JUJ~~~~~~~1.
I -
PROBE PATIO
Fig. 3. Reflectivity of semi-self-pumped phase conjugator
versus probe ratio for three different crystal temperatures.
amplitude boundary conditions giving rise to cavity-
length-dependent oscillation frequency-detuning ef-
fects. Figure 3 shows the experimental performance
of this device, giving the reflectivity of a ring-resona-
tor barium titanate semi-self-pumped phase conjuga-
tor as a function of probe ratio, defined as signal inten-
sity normalized by the external pump intensity. The
coupling strength in barium titanate is highly tem-
perature sensitive and increases substantially near its
tetragonal to orthorhombic phase transition near 9°C,
so that temperature tuning of the device is possible, as
shown by the results for three different temperatures.
The transfer function given by this device is a sig-
moid thresholding function. Such functions have
particular importance in associative processingil and
are characterized by being zero for arguments below
threshold and then rising through an inflection toward
saturation at high-valued arguments.
The double PCM, although it is structurally simpler
and easier to analyze theoretically,', 8 does not have
this sigmoid thresholding function. Here, there is
thresholding at both high and low intensities8 because
the reflectivity is nonzero only for input beam intensi-
ty ratio q = I4(0)/I2(l) (see Fig. 2) in the range
(1a) < q < (1+a), 1
2 a) 4'
where a is given by the solution of the equation tanh
0
_0
-3 
-4
-5 1
-5 -4 -3 -2 -I 0 1 2 3 4 5
LOG PROBE RATIO
Fig. 4. Theoretical reflectivity of double phase conjugator
versus probe ratio for various coupling strengths.
A,
S D L C A
(a)
S, °
S (b)
Fig. 5. (a) Original realization of phase-conjugate window
with externally supplied pump. Beam A2 carries the picture
information T. Probe beam A4 passes through distortion D,
which must be imaged onto the crystal by lens L1. The
reflected beam A3 carries the information through the dis-
tortion, is split off at beam splitter S, and is imaged onto the
film by lens L2. (b) Semi-self-pumped phase conjugator
applied in realization of the self-pumped phase-conjugate
window. The experimental results of Fig. 6 were obtained
with a barium titanate crystal pumped at 514.5 nm by a
single-longitudinal-mode argon laser. The transparency-
information-bearing beam was frequency shifted 40 MHz by
an acousto-optic modulator to prevent the buildup of reflec-
tion gratings in the photorefractive crystal.
716 OPTICS LETTERS / Vol. 12, No. 9 / September 1987
(a) (b) (c)
Fig. 6. (a) Transparency T imaged through self-pumped phase-conjugate window without distortion in the path. (b)
Distortion alone by an equivalent non-phase-conjugating optical system. (c) Self-pumped phase-conjugate window with
distortion in the path.
plotted in Fig. 4 as a function of the probe ratio for
several values of coupling strength. That these re-
sults are similar to the experimental results for the
ring semi-self-pumped PCM is understandable, given
the devices' close relationship to each other.
We now turn to the application of semi-self-pumped
phase conjugators to the phase-conjugate window6 for
one-way imaging through thin distortions. The origi-
nal realization of the phase-conjugate window [Fig.
5(a)] was similar to an externally pumped PCM and
had the disadvantage of requiring a clean pump beam
coherent with the distorted probe. This meant that
the clean beam had either to bypass the distortion or
to be spatially filtered after passing through the dis-
tortion, thereby losing most of its intensity. In either
case, the practical utility of the device was compro-
mised. If the externally pumped PCM portion of the
device is replaced with a semi-self-pumped PCM [Fig.
5(b)], the clean beam can be self-induced as an oscilla-
tion beam. Figure 6(a) shows an image of part of
group 1 (2.52 line pairs/mm) of a U.S. Air Force resolu-
tion chart when viewed through the phase-conjugate
window without any distortion in the line of sight.
This gives a baseline reading of the general quality of
the imaging system, which could be improved with
further engineering. Figure 6(b) is an image of the
same scene when viewed through a distortion. Figure
6(c) shows the same distorted scene when corrected by
the self-pumped phase conjugate window.
Finally, we note that the double phase conjugator is
unsuitable for this application. Referring to Fig. 2, we
have beam 1 generated as the phase conjugate of input
beam 2 and beam 3 generated as the phase conjugate
of input beam 4 independently of any spatial informa-
tion on beam 2. To be useful as a one-way imaging
device, however, beam 3 would be required to pick up
the transparency information on beam 2. The ring
semi-self-pumped PCM works as a one-way imager
because beam 1 is forced, by the closed oscillation
cavity with intracavity aperture, to have a fixed spatial
profile independent of the spatial profile of beam 2.
In summary, we have introduced the concept of a
new class of PCM, joining the already established
groups of fully externally and fully self-pumped phase
conjugators. Two applications of these devices have
been described: positive thresholding phase conjuga-
tion for optical associative memory and one-way imag-
ing through thin distortions.
This research was supported by the U.S. Army Re-
search Office, Durham, North Carolina.
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Semi-self-pumped phase-conjugate mirrors

paper PD5. We note that the device described in this paper is a negative thresholder: higher inputs give lower outputs.

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Semi-self-pumped phase-conjugate mirrors

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