Method and apparatus for energy transfers between optical beams using near-bandgap electrorefractive effect

Enhanced energy transfers are achieved between optical beams by operating at wavelengths in the near-bandgap region of a photorefractive material, and employing an electrorefractive effect previously proposed only for single beams. An electric field is applied across a photorefractive medium of sufficient intensity to induce an electrorefractive coupling and consequent energy transfer between the beams. Gain enhancements are possible by orienting the photorefractive medium to obtain an electro-optic as well as an electrorefractive effect, and by a moving grating technique. The direction of energy transfer between the beams is controlled by the electric field direction, and can be reversed by reversing the field. Operation in the infrared region is made possible with semi-insulating materials. Applications include optical switches, amplifiers and phase conjugators.

BACKGROUND OF THE INVENTION 
1. Field of the Invention 
This invention relates to the photorefractive transfer of energy between 
optical beams. 
2. Description of the Related Art 
Photorefractive materials have been used in a number of different 
applications involving the processing of optical beams. (The terms "light" 
and "optical" as used herein are not limited to the visible spectrum, but 
are used in their broader sense to include other regions of the spectrum 
such as the infrared). One principle application is in phase conjugate 
mirrors (PCMs). Other applications include optical switching, holography, 
image processing and the performance of optical mathematical functions 
such as image amplification, pattern substraction, and pattern 
recognition. 
In general, a photorefractive (PR) material is one in which the index of 
refraction changes under the influence of applied light, such as a laser 
beam. The light causes charges within the PR material to migrate and 
separate, producing an internal electrostatic field. This field produces a 
change in the crystal's refractive index by the linear electro-optic (EO) 
effect (the Pockels effect). The theory of the EO effect is described in a 
text by A. Yariv, "Introduction to Optical Electronics, 2d ed.", pages 
246-253 (1976). The PR index grating, or periodic variation in the 
crystal's index of refraction, is a measure of the change in the index. PR 
materials generally comprise III-V and II-VI semiconductor combinations 
within the periodic table, and other crystals such as BaTiO.sub.3, 
Bi.sub.12 SiO.sub.20 and KTa.sub.1-x NB.sub.x O.sub.3. 
The formation of a PR index grating is illustrated in FIG. 1, in which the 
horizontal axis represents distance within the PR medium. The upper graph 
illustrates the pattern of light with a spatially periodic intensity I 
within the medium, while the next graph illustrates the resulting charge 
density. The mobile charges, illustrated as being of positive polarity, 
tend to accumulate in the dark regions of the light intensity pattern. The 
resulting periodic charge distribution produces a periodic electrostatic 
field E by Poisson's equation. This electric field, illustrated in the 
third graph of FIG. 1, then causes a change in the refractive index of the 
crystal by the linear EO effect. The index change is proportional to the 
EO coefficient and the space charge electrostatic field within the PR 
medium. The PR effect, illustrated in the last graph of FIG. 1, is 
nonlocal in that the maximum refractive index change does not occur at the 
peak of the light intensity. In FIG. 1 the spatial shift between the 
refractive index change and the intensity patter is 90.degree. with 
respect to the grating period; in general, however, this shift can be any 
fraction of the grating period. 
Large energy transfers between optical beams are important in applications 
such as high contrast optical switches, and efficient self-pumped phase 
conjugators for laser power combining or aberration correction. The 
necessary degree of energy transfer has been possible previously using 
conventional EO photorefractivity in materials such as BaTiO.sub.3. These 
materials, however, have an undesirably slow response time. Furthermore, 
their sensitive wavelength region is in the visible, which is 
technologically less attractive than the near-infrared spectral region of 
diode and Nd:YAG lasers. Semi-insulating semiconductors, on the other 
hand, have a much faster response time and are compatible in wavelength 
with diode and Nd:YAG lasers. However, these semi-insulators do not 
exhibit sufficient photorefractivity to be useful, compared to 
BaTiO.sub.3, because of their small EO coefficient. Some photorefractivity 
enhancement in these materials has recently been reported using a DC 
electric field and moving gratings, or an AC electric field, as in Imbert 
et al., "High Photorefractive Gain in Two-Beam Coupling with Moving 
Fringes in GaAs:Cr Crystals", Optics Letters, Vol. 13, pages 327-329 
(1988). The best reported net gain coefficient in semiconductors, however, 
has been only about 10 cm.sup.-1. 
Another optical phenomenon of interest is the electrorefractive (ER) 
effect, also known as the FranzKeldysh effect. This is the change in 
absorption and refractive index of a semiconductor in the spectral region 
slightly smaller than the material's band gap. This effect has been 
measured in materials such as bulk InP and GaAs, as discussed in Van Eck, 
et al., "Franz-Keldysh Electrorefraction and Electroabsorption in Bulk InP 
and GaA", Applied Physics Letters, Vol. 48, No. 7, Feb. 17, 1986, pages 
451-453. An earlier treatment of the ER effect in germanium and GaAs is 
given in Seraphin and Bottka, "Franz-Keldysh Effect of the Refractive 
Index in Semiconductors", Physical Review, Vol. 139, No. 2A, July 19, 
1965, pages A560-A565. 
The phenomenon is illustrated in simplified form in FIG. 2. The horizontal 
axis represents the photon energy of an applied optical beam (the beam 
energy varies inversely with its wavelength), while the vertical axis 
represents the material's absorption coefficient at each particular photon 
energy or wavelength. At an energy region E.sub.g, corresponding to the 
material's bandgap energy between the conduction and valence bands, the 
curve turns abruptly upward to become totally absorbing. If an electric 
field is imposed across the material, the absorption curve shifts to one 
of the modified curves 2 in the area just below E.sub.g, such that the 
transition becomes more gradual. The degree of shift from the basic 
absorption curve varies in accordance with the electric field strength. 
The region of variance near the absorption edge of the curve has been 
referred to as the "near-bandgap" region. This shift in absorption in the 
near-bandgap region is accompanied by a shift in the material's refractive 
index. 
While of interest, investigations into the Franz-Keldysh effect have 
involved single optical beams, and have not been applicable to the current 
implementations described above for multiple-beam mixing. The 
investigations have been concerned with a region of high optical 
absorption, which further limits their application to practical systems. 
SUMMARY OF THE INVENTION 
The present invention seeks to provide a method to perform multiple-wave 
mixing that is applicable to fast response materials such as 
semi-insulators and to the near-infrared spectral region of diode and 
semiconductor lasers, and yet achieves an energy transfer between beams 
sufficient for devices such as high contrast switches and phase 
conjugators. Rather than using a bulk ER effect to obtain a refractive 
index shift in the near-bandgap region for a single beam, the present 
invention uses the ER effect to form a grating which is large compared to 
the linear EO grating employed in conventional photorefraction, and to 
employ the ER grating in an energy transfer between a plurality of 
mutually coherent optical beams. Because the ER grating is phase shifted 
with respect to the sinusoidal optical intensity pattern produced by 
interference between the two beams, an energy transfer is achieved from 
one beam to the other. This energy transfer can be large because the 
variation in refractive index in the near-bandgap region is large. By 
orienting the PR medium so that EO photorefraction also occurs, the ER and 
EO photorefractive effects can be combined to increase the beam coupling 
gain. Other techniques, such as the employment of moving gratings, can 
also be employed to further increase the energy transfer. 
The sensitivity and short response times of the PR effect in semiconductors 
are thus combined with the large ER properties of these materials in the 
near-bandgap region to produce superior inter-beam energy transfers. By 
simply controlling the applied field direction, the direction of energy 
transfer between the beams can be controlled, making bi-directional 
switching possible. The method is also applicable to materials which do 
not exhibit a conventional PR effect, for example, silicon or 
polycrystalline materials or materials with zero electro-optic 
coefficients. Applications for the technique include both self-pumped and 
four wave mixing phase conjugators, and optical switches and amplifiers. 
These and other features and advantages of the invention will be apparent 
to those skilled in the art from the following detailed description of 
preferred embodiments.

DETAILED DESCRIPTION OF THE INVENTION 
It has been discovered that, by generating an optical intensity pattern 
associated with optical beams transmitted through a PR medium with an 
externally applied electric field, and by carefully selecting the beams 
and PR medium such that operation takes place within the near-bandgap 
region, an ER grating results through which greater transfers of energy 
from one beam to another can be achieved than has previously been 
attainable. This finding has many important consequences for beam 
processing, particularly for fast response materials capable of operating 
in the near-infrared region of the spectrum, such as semi-insulating 
compound semiconductors. Employing the invention, these materials can now 
be used successfully for applications such as phase conjugation and 
optical switching and amplification. 
An implementation of the invention is shown in simplified form in FIG. 3. 
The optical energy transfer takes place within a PR medium 4. In general, 
some degree of energy transfer should be attainable with virtually any 
material having a partially populated defect or dopant level between the 
valence and conduction bands, with a capability of photoionizing charge 
from this region (the "midgap center"). By using semiconductors such as 
GaAs, InP, CdTe and other III-V and II-VI compounds and their alloys, much 
faster response times are possible than previously. Semi-insulators, which 
are semiconductors in which the Fermi level is near midgap, are 
particularly suitable. The invention is also applicable to materials, such 
as silicon and polycrystalline substances, which do not exhibit an EO 
effect. Like conventional PR materials, these non-EO materials have defect 
states which produce charge separation and internal electric fields that 
result in a PR effect. If a particular semiconductor's near-bandgap region 
is close to but not precisely matched with the wavelength of a desired 
source, it may be possible to achieve a more precise matching by tuning 
the near-bandgap region with an alloy of the semiconductor material. 
A plurality of optical beams are mixed within the PR medium to produce an 
energy transfer between them. In FIG. 3 the beams are illustrated as being 
produced by a pair of laser diodes 6 and 8. One of the advantages of the 
invention is that, by making operation possible with semiconductor lasers, 
the beam sources and the PR medium can be monolithically integrated 
together on the same chip. 
Lasers 6, 8 are selected such that their beams 10, 12 are mutually 
coherent, with a wavelength in the near-bandgap region of the PR medium 4. 
An electric field is induced through the PR medium by a DC voltage source 
14 whose positive and negative terminals are connected to electrode plates 
16 on opposite faces of the PR medium 4. A net DC electric field is 
required to establish an ER grating suitable for energy transfer within 
the PR medium 4. If desired, an AC ripple can be superimposed upon the DC 
field and employed as an encoding mechanism or the like. 
If the beams 10, 12 are kept within the near-bandgap region of the PR 
medium 4, it has been found that an energy transfer between beams will 
result. Thus, the system of FIG. 3 can be used to amplify one of the beams 
at the expense of the other. If the amplification is great enough, the 
system can function as an optical switch, with the beam receiving the 
energy transfer being "off" in the absence of an electric field when there 
is no energy transfer, and "on" when the field is applied. A distinct 
advantage of this arrangement is that the direction of energy transfer can 
be controlled by the direction of the electric field. For a given field 
direction, the direction of energy transfer between beams 10 and 12 is 
determined by the orientation of the beams relative to the field, and by 
whether the dominant photo carriers in the PR medium 4 are electrons or 
holes. Whatever the direction of energy transfer turns out to be, it can 
be easily reversed by simply reversing the field direction. A reversing 
switch 18 which interchanges the terminals of DC source 14 is illustrated 
for this purpose. 
When the applied field is reversed, the refractive index variation within 
medium 4 shifts by 180.degree., so that the direction of energy transfer 
is reversed. Without the applied field, there is no energy transfer. When 
the field is reduced to zero, the field inside the crystal varies about 
zero and the refractive index, which depends upon the magnitude of the 
field in the near-bandgap region, varies with a spatial period half that 
of the intensity pattern; this variation will not transfer energy. 
The intersection of the two mutually coherent optical beams 10, 12 within 
the PR crystal 4 generates a sinusoidal intensity grating pattern, 
illustrated in FIG. 4a. This optical intensity variation results in a 
space charge field E.sub.sc, illustrated in FIG. 4b, through the usual 
diffusion and drift processes. When a DC electric field is applied, the 
total electric field E.sub.o within the crystal is equal to the sum of the 
externally applied field and the internally generated space charge field. 
In general, the application of an external field will increase the 
magnitude of the space charge field and change the phase shift between the 
intensity and space charge field patterns. For applied field magnitudes 
substantially greater than the limiting space charge field that the PR 
material can sustain, this phase shift is approximately 90.degree.; under 
these conditions the component of E.sub.sc in phase with the optical 
intensity pattern can be ignored. A 90.degree. phase shift produces 
optimum energy transfer between beams. 
The ER-induced change in the index of refraction n typically varies with 
the square of the electric field for photon energies below the bandgap 
level. FIG. 4c shows the ER change in refractive index for two directions 
of applied field, and for a zero applied field. The relative phase shift 
of the ERPR grating with respect to the optical intensity pattern can be 
seen to depend upon the direction of the applied field, but in both cases 
the ER grating is 90.degree. out of phase with respect to the intensity 
pattern and can thus transfer energy. Since the relative phase shift 
determines the direction of energy transfer, the direction of energy 
transfer thus depends uniquely upon the electric field direction (and the 
dominant photocarrier species). Thus, a system such as that shown in FIG. 
3, which is based upon such a grating, can act as an optical switch with 
the output determined by the direction of electric field. This is in 
direct contrast to conventional PR devices, in which an applied field 
increases the energy transfer without effecting its direction. With 
conventional EOPR energy transfer, the transfer direction is determined 
solely by the crystal orientation and the dominant photocarrier species. 
When no external field is applied, the space charge field is created 
through diffusion and has a zero average value. As illustrated in FIG. 4c, 
the induced ERPR grating in this case will have twice the spatial 
frequency of the space charge field pattern, and thus cannot transfer 
energy. 
The "near-bandgap" region can be defined empirically as that region in 
which there is a sufficient ER effect to produce a significant energy 
transfer between mutually coherent energy beams. The region was determined 
experimentally for GaAs. The important result is that the near-bandgap 
region extended sufficiently far away from the absorption edge so that 
substantial energy transfers could be realized between beams for 
wavelengths at which most of the beams were transmitted, rather than 
absorbed in the crystal. This leads to the conclusion that the ER effect 
might be useful for optical energy transfers in practical devices. 
The results of the experiments are summarized in FIG. 5, in which the 
optical gain coefficient is plotted as a function of wavelength for 
different values of applied field. The crystal bandgap energy was about 
1.43 eV, corresponding to an absorption edge of about 870 nm. The 
experimental setup is illustrated in FIG. 6. An ER grating 20 was formed 
in the GaAs crystal 22 by applying a voltage source V.sub.o to an 
electrode plate on one side of the crystal, and grounding an electrode 
plate on the opposite side of the crystal. An incident pump beam I.sub.po 
and an incident signal beam I.sub.so were applied to the crystal at an 
angle of 15.3.degree. to each other. An argon-pumped Ti:Sapphire laser 
tunable between 900 and 1,000 nm was used to generate the beams. The 
I.sub.po and I.sub.so intensities were respectively 17 and 1.2 
mW/cm.sup.2, and were kept constant for different wavelengths. The 
geometric orientation of the crystal, indicated by diagram A, was selected 
so that there was no EO grating for beams polarized perpendicular to the 
plane of incidence. 
Without an applied field, no energy transfer was observed. The data 
displayed in FIG. 5 was obtained by fixing the wavelength and increasing 
the field, then shifting to a different wavelength and repeating the field 
variation. Results in the general range of 920-940 nm, corresponding to 
photon energies of 1.35-1.32 eV, are displayed. Large gain coefficients 
were also observed below 910 nm, but the increased photoconductivity 
resulted in large currents and crystal heating that prevented accurate 
measurements. In addition to the data displayed in FIG. 5, a gain 
coefficient of 2.8 cm.sup.-1 was observed with a wavelength of 922 nm and 
an applied field of 14 kV/cm. 
The direction of energy transfer changed when the field direction was 
reversed. This reversal of energy transfer direction, along with the 
spectral shape of the gain coefficient, indicates that the energy transfer 
was indeed due to an ER mechanism. The particular crystal material 
employed was GaAs:EL2, which is dominated by electrons at wavelengths 
smaller than a micron. A positive value of V.sub.o resulted in gain for 
the signal beam I.sub.so, which is consistent with electrons as the 
dominant charge carrier species. No energy transfer was observed when the 
pump beam I.sub.po was cross-polarized with respect to the signal beam 
I.sub.so, ruling out the possibility of bulk absorption modulation within 
the pump beam. Experiments conducted with other crystals, crystal 
geometries and beam polarizations ruled out the possibility of the energy 
transfer being the result of an EO effect. 
The near-bandgap region for the experimental crystal illustrated in FIGS. 5 
and 6 can thus be defined as the area down to about 0.11 eV below the 
bandgap level, or about 60-80 nm above the absorption edge. Similar 
determinations of the near-bandgap range for other materials can be 
determined empirically. 
Even greater degrees of energy transfer were achieved by combining the ERPR 
and EOPR effects. This was accomplished with the crystal geometry 
indicated by diagram B in FIG. 6, at which the crystal was oriented for 
EOPR signal gain and the electric field was oriented for ERPR signal gain. 
A gain of 7.6 cm.sup.-1 was observed with a grating spacing of 5.4 
microns, an applied field of 10 kV/cm, and an optical wavelength of 937 
nm. Reversing the electric field direction resulted in a very small gain 
for the signal beam, apparently indicating that the EOPR effect was 
slightly larger than the ERPR effect under these conditions. 
Additional gain has been achieved by using the invention in conjunction 
with the previously developed moving grating technique. The set-up is 
illustrated in FIG. 7. The same laser 24 was used as in the experiments 
described above. A 939 nm laser beam was generated and divided by an 
unbalanced beam splitter 28 into pump and signal beams I.sub.po and 
I.sub.so, rated at 140 and 0.029 mW/cm.sup.2, respectively. There was a 
grating spacing of 7.0 microns, and an applied field of 10 kV/cm was 
employed. 
The pump beam I.sub.po was directed onto a piezomirror 30, which was driven 
by a sawtooth control voltage. The periodic movement of the piezomirror 30 
created a similar periodic variation in the path length for I.sub.po, 
thereby developing a moving grating within the PR crystal 22. A very large 
gain of 16.3 cm.sup.-1 was obtained with a piezomirror velocity of 30 
microns/sec. Since this gain was not optimized with respect to either the 
grating spacing or beam ratio, significant additional enhancements and 
gains should be obtainable. 
The very high gains experienced with a semi-insulating semiconductor such 
as GaAs at infrared wavelengths indicates that new devices of this type 
may be used to perform tasks which have previously been done with 
BaTiO.sub.3, but with much faster response times and at more desirable 
wavelengths; GaAs is at least 50,000 times faster than BaTiO.sub.3 in the 
infrared region. Potential applications include two-wave mixing with gain 
for optical interconnects, signal processing and logic gates. 
Phase conjugators are a primary application for the invention. Basically, a 
phase conjugate mirror (PCM) produces a retro-reflection of an incident 
beam, with the phase of the reflected beam reversed from that of the 
incident beam at the point of reflection. A typical PCM known in the art 
is depicted in FIG. 8. It is illustrated as a four-wave mixer, in which a 
pair of contradirected laser beams 32 and 34 are directed into a PR medium 
36. An initializing laser beam 38, equal in frequency to beams 32 and 34, 
is directed into the mixing medium from the side. A reflected beam 40 is 
returned from the medium in a direction opposite to that of incident beam 
38. Since power is pumped into the system by beams 32 and 34, the PCM may 
produce an amplification of return beam 40 over incident beam 38. In 
addition to being retroreflected, the phase conjugated beam 40 also 
undergoes a phase reversal with respect to the incident beam at the point 
of reflection. 
In accordance with the invention, an electric field is applied across the 
PR medium 36. For example, a voltage differential can be applied to 
electrode plates 42, 44 on opposite sides of the medium. By selecting a PR 
medium 36 and incident beam 38 such that the beam's wavelength is within 
the near-bandgap region of the medium, an enhanced energy transfer from 
the pump beams to the reflected beam can be achieved by means of the ER 
effect. 
The invention has particular application to self-pumped PCMs. This type of 
device does not employ external pump beams, and therefore does not produce 
amplification. An incident signal beam generates noise waves within a PR 
medium. These noise waves are then amplified by the input beam in a 
two-wave amplification process that builds up until the weak noise waves 
are strong enough to produce a conjugate beam contra-directional to the 
input signal beam. 
To achieve self-pumping operation, the product of the PR medium's gain 
coefficient and its length must exceed a factor on the order of 5. By 
applying the present invention to a self-pumped PCM, self-pumping 
operation can be achieved with smaller PR crystal dimensions and simpler 
geometries than previously, and may make self-pumped operation possible at 
previously unattainable wavelengths. A simplified self-pumped PCM 
employing the invention is illustrated in FIG. 9. An input signal beam 46 
is applied to a PR medium 48, with the beam wavelength within the 
near-bandgap region of the PR medium. ERPR gratings are formed within the 
medium by an electric field established between opposed electrodes 50 and 
52. The conjugated return beam is indicated by arrow 54. In the case of a 
self-pumped PCM, the energy transfer takes place between the externally 
applied signal beam 46 and an internally noise generated wave which 
results in the conjugate beam 54. In the particular implementation 
illustrated in FIG. 9, the signal beam 46 is reflected by mirrors 56 and 
58 behind the PR medium 48 back into the medium. The reflected beam 60 
produces a contra-directed noise generated wave within the PR medium, 
represented by dashed arrow 62, with which it cooperates as a pump for 
conjugated beam 54. Several other self-pumped PCM designs are also 
currently known. 
The invention can thus be seen to have numerous applications where a 
greater degree of optical energy transfer is desirable, particularly in 
the infrared and near-infrared regions. While several illustrative 
embodiments of the invention have been shown and described, numerous 
variations and alternate embodiments will occur to those skilled in the 
art. Such variations and alternate embodiments are contemplated, and can 
be made without departing from the spirit and scope of the invention as 
defined in the appended claims.