Methods and systems for thermal fixing and/or erasing of holograms

The invention features methods and systems for thermally fixing or erasing a laser-induced hologram in a photorefractive material, for example, by directing laser radiation having a wavelength through a thickness of the photorefractive material containing the hologram, wherein the wavelength is selected such that the photorefractive material absorbs a portion of the laser radiation and transmits another portion of the laser radiation. The transmitted laser radiation can be redirected back through the hologram, wherein both the laser radiation directed and redirected to the hologram are sufficiently absorbed by the photorefractive material to thermally fix or erase the hologram.

FIELD OF THE INVENTION 
This invention relates to holography and optical storage, and in particular 
to methods and systems for the thermal fixing of holograms. 
BACKGROUND OF THE INVENTION 
Volume holograms in photorefractive crystals have generated substantial 
interest recently for possible applications in high capacity optical 
storage and optical interconnects. In particular, optical memories based 
on such volume holograms can potentially combine very large capacities, 
e.g., greater than 1 Tbyte, with very high data rates, e.g., greater than 
1 Gbit/s, and very short access times, e.g., shorter than 1 ms. 
A volume hologram can be written in a photorefractive crystal, e.g., 
iron-doped lithium niobate (Fe:LiNbO.sub.3), by crossing laser beams, 
e.g., a signal carrying beam and a reference beam, having wavelengths that 
are absorbed by the crystal. The interference pattern formed by the 
crossed beams records a corresponding diffraction pattern, i.e., a 
hologram, in the crystal. A subsequent "read" beam incident on the crystal 
at a correct angle, e.g., an angle for Bragg diffraction, diffracts from 
the hologram and reconstructs the signal-carrying beam. A large number of 
holograms can be recorded in a photorefractive crystal by directing the 
write and read beams into the crystal at different angles, which is known 
as angle multiplexing. 
In many cases, the write beams initially produce an electronic hologram in 
which local variation in the density and/or quantum state of electrons or 
holes in the crystal form the hologram. For example, the optical intensity 
pattern produced by the write beams can generate free carriers, either 
electrons or holes, which are trapped at local defect sites to form the 
hologram. Unfortunately, the electronic grating are volatile and can 
degrade upon repeated use of reading beams and exposure to moderate 
temperatures and ambient light. However, thermal fixing of electronic 
holograms can be used to overcome such volatility. 
Thermal fixing involves exchanging electronic holograms with ionic 
holograms, i.e., holograms formed from ions. Typically, one places the 
crystal containing the electronic holograms into a high-temperature oven, 
e.g., greater than 100 degrees Celsius. At such high temperatures, ionic 
charges become mobile and migrate to the electronic charges that form the 
electronic hologram thereby compensating the refractive index variations 
caused by the trapped electronic charges. As a result, there is minimal, 
if any, diffraction of a read beam at the end of the thermal heating 
process. After the crystal is cooled, a uniform light beam illuminates the 
crystal and excites the electronic charges that form the electronic 
hologram into free carriers. These free carriers migrate uniformly over 
the crystal volume to reveal a stable ionic hologram. If desired, the 
ionic hologram can be erased by heating the crystal to even higher 
temperatures that free the ionic charges that form the ionic hologram, 
thereby "washing" away the hologram. 
Recently, B. Liu et al. (Applied Optics, 37:1342-1349, 1998)described using 
10.6 micron radiation from a CO.sub.2 laser to thermally fix a hologram 
written in a 2 mm thick Fe:LiNbO.sub.3 crystal. The crystal strongly 
absorbed the 10.6 micron radiation with the absorption constant measured 
to be between 5000 and 10,000 m.sup.-1. The laser radia ion rapidly and 
efficiently heated the crystal within its first few hundred microns of 
thickness, at which point the laser radiation was fully absorbed. 
Thereafter, thermal conduction within the crystal carried the heat through 
the thickness of the crystal, thereby thermally fixing the hologram. In 
some experiments, copper absorbers were introduced into the crystal to 
more rapidly conduct the heat through the thickness of the crystal. 
SUMMARY OF THE INVENTION 
The invention features systems and methods for thermally fixing and erasing 
holograms using laser radiation. The wavelength of the laser radiation is 
selected such that the laser radiation propagates through the entire 
thickness of the crystal without being fully absorbed. Thus, the laser 
radiation directly heats the entire thickness of the hologram to fix 
and/or erase the hologram. Furthermore, in some embodiments, laser 
radiation transmitted through the crystal is reflected back towards and 
through the hologram to further heat and fix the hologram. Such a 
reflection more efficiently converts the laser radiation into heat and 
more uniformly heats opposite ends of the crystal. 
In general, in one aspect, the invention features a method for thermally 
fixing or erasing a laser-induced hologram in a photorefractive material, 
such as a crystal of iron-doped lithium niobate. The method includes 
directing laser radiation having a wavelength .lambda..sub.F through a 
thickness of the photorefractive material containing the hologram, wherein 
the photorefractive material absorbs a portion of the laser radiation and 
transmits another portion of the laser radiation; and redirecting the 
transmitted portion of the laser radiation back through the hologram, 
wherein the laser radiation directed and redirected to the hologram are 
sufficiently absorbed by the photorefractive material to thermally fix or 
erase the hologram. 
In some embodiments, .alpha.(.lambda..sub.F)d is in the range of about 0.05 
to 2.0, and in some cases 0.1 to 1.0, or 0.2 to about 0.8, where d is the 
thickness of the photorefractive material and .alpha.(.lambda..sub.F) is 
the absorption of the photorefractive material at the wavelength 
.lambda..sub.F. 
In another aspect, the invention features an additional method for 
thermally fixing or erasing a laser-induced hologram in a photorefractive 
material. The method includes directing laser radiation having a 
wavelength .lambda. through a thickness d of the photorefractive material 
containing the hologram, wherein .alpha.(.lambda.) is the absorption of 
the photorefractive material at the wavelength .lambda., 
.alpha.(.lambda.)d is in the range of about 0.1 to 1.0, and the laser 
radiation directed to the hologram is sufficiently absorbed by the 
photorefractive material to thermally fix or erase the hologram. In some 
embodiments, .alpha.(.lambda.)d is in the range of about 0.2 to 0.8. 
Embodiments for either of the methods described above can include any of 
the following features. 
The laser radiation can be produced by a diode laser or a frequency-doubled 
CO.sub.2 laser. The wavelength of the laser radiation can be in the range 
of about 1.6 to 11 microns, and in some embodiments in the range of about 
3 to 8 microns. The photorefractive material can have a thickness d 
greater than or equal to about 0.5 cm, or 0.6, 0.8, or 1.0 cm. The methods 
can further include directing revelation laser radiation towards the 
photorefractive material, the revelation laser radiation having a 
wavelength that excites electrons within the photorefractive material to 
reveal the thermally fixed ionic hologram. 
In general, in another aspect, the invention features a system for 
thermally fixing or erasing a laser-induced hologram in a photorefractive 
material. The system includes a mount which during operation supports the 
photorefractive material; a laser source which during operation directs 
laser radiation through a thickness of the photorefractive material 
containing the hologram, the laser radiation having a wavelength 
.lambda..sub.F selected such that the photorefractive material absorbs a 
portion of the laser radiation and transmits another portion of the laser 
radiation; and a reflective optic which during operation redirects the 
transmitted portion of the laser radiation back through the hologram, 
wherein the laser radiation directed and redirected through the hologram 
are sufficiently absorbed by the photorefractive material to thermally fix 
or erase the hologram. 
In another aspect, the invention features a system for thermally fixing or 
erasing a laser-induced hologram. The system includes a mount which during 
operation supports a photorefractive material; and a laser source which 
during operation directs fixing laser radiation through a thickness of the 
photorefractive material, the fixing laser radiation having a wavelength 
.lambda..sub.F such that the photorefractive material absorbs a portion of 
the laser radiation and transmits another portion of the laser radiation, 
wherein d is the thickness of the photorefractive material, 
.alpha.(.lambda..sub.F) is the absorption of the photorefractive material 
at the wavelength .lambda..sub.F, .alpha.(.lambda..sub.F) d is in the 
range of about 0.1 to 1.0, and the laser radiation directed through the 
hologram is sufficiently absorbed by the photorefractive material to 
thermally fix or erase the hologram. In some embodiments, 
.alpha.(.lambda..sub.F)d is in the range of about 0.2 to 0.8. 
Embodiments of the systems described above can have any of the following 
features. 
The systems can include the photorefractive material, e.g., a crystal of 
iron-doped lithium niobate. The laser source can be a diode laser of a 
frequency-doubled CO.sub.2 laser. The laser radiation can deliver an 
energy density to the photorefractive material greater than or equal to 
about 1 J/mm.sup.3. The wavelength .lambda..sub.F of the laser radiation 
can be in the range of about 1.6 to 11 microns, and in some cases, in the 
range of about 3 to 8 microns. The photorefractive material can have a 
thickness greater than or equal to about 0.5 cm, or larger, e.g., 1.0 cm. 
The systems can further include a revelation laser source which during 
operation directs revelation laser radiation towards the photorefractive 
material, the revelation laser radiation having a wavelength that excites 
electrons within the material. The wavelength of the revelation laser 
radiation can be in the visible region of the electromagnetic spectrum. 
Unless otherwise defined, all technical and scientific terms used herein 
have the same meaning as commonly understood by one of ordinary skill in 
the art to which this invention belongs. Although methods and materials 
similar or equivalent to those described herein can be used in the 
practice or testing of the present invention, the suitable methods and 
materials are described below. All publications, patent applications, 
patents, and other references mentioned herein are incorporated by 
reference in their entirety. In case of conflict, the present 
specification, including definitions, will control. In addition, the 
materials, methods, and examples are illustrative only and not intended to 
be limiting. 
The invention includes a number of advantages. For example, embodiments of 
the invention provide direct heating of a hologram by laser radiation to 
sufficiently fix and/or erase the hologram. This minimizes any need to 
rely on thermal conduction within the photorefractive material, e.g., by 
introducing metal absorbers, which may be impractical. Moreover, direct 
heating by laser radiation fixes and/or erases the hologram more rapidly 
and uniformly than thermal conduction. Furthermore, by using a laser for 
thermal heating, holograms can be fixed and/or erased in situ within a 
selected volume of the photorefractive material, and holograms within even 
very large materials, e.g., a size of about 1 m.sup.2 by 1 cm, can be 
fixed and erased. In addition, by reflecting laser radiation transmitted 
through the material back toward the hologram, the hologram is more 
uniformly and efficiently heated, thereby increasing the robustness of the 
thermal fixing and/or erasing. 
Other features and advantages of the invention will be apparent from the 
following detailed description, and from the claims.

DETAILED DESCRIPTION 
The invention features methods and systems for thermally fixing and erasing 
a hologram by directly heating the hologram using laser radiation. Rather 
than relying on thermal conduction within a photorefractive crystal 
supporting the hologram, the wavelength of the laser radiation is chosen 
such that the laser radiation propagates through the entire thickness of 
the hologram and directly heats the hologram all along its path through 
the crystal. Thus, thermal fixing and/or erasing of the hologram is more 
rapid and spatially uniform, covering a volume within the crystal 
corresponding to the path of the laser radiation. To more efficiently and 
uniformly heat the hologram a reflective optic can be used to retroreflect 
the portion of the laser radiation transmitted through the thickness of 
the crystal containing the hologram back towards the hologram. 
General System 
FIG. 1 shows a schematic diagram of a system 10 for thermally fixing 
electronic holograms. A mount 11 supports a photorefractive crystal 12, 
e.g., iron-doped lithium niobate (Fe:LiNbO.sub.3), having a thickness d 
and a wavelength dependent absorption .alpha.(.lambda.). Crystal 12 
includes an electronic volume hologram 14 formed by, e.g., crossing two 
write laser beams (not shown) to form an optical interference pattern. 
Suitable write laser beams for Fe:LiNbO.sub.3 include, e.g., 514 nm laser 
beams from an Argon ion laser. The write beams excite electronic carriers, 
e.g., electrons and/or holes, in regions corresponding to the optical 
interference pattern. 
A fixing laser 16, e.g., an infrared diode laser, directs laser radiation 
18 having a wavelength .lambda..sub.F to the region of crystal 12 
containing electronic hologram 14. The wavelength .lambda..sub.F is 
typically in the range of about 1.6 to 11 microns, e.g., wavelengths at 
which many photorefractive crystals are thermally excited. In particular, 
wavelengths in the range of about, e.g., 4-6 microns, can be suitable for 
Fe:LiNbO.sub.3. Laser radiation 18 propagates through the thickness of 
crystal 12 and is partially absorbed as it propagates. The absorbed laser 
radiation generates local heating within the crystal in an amount 
proportional to the intensity of laser radiation 18, which decreases as 
the laser radiation propagates through the crystal and is absorbed. The 
relative decrease in the laser radiation at opposites ends of the crystal 
is related to the product .alpha.(.lambda..sub.F)*d. As described in the 
next section below, .lambda..sub.F is chosen such that this product is 
small enough that a significant portion, e.g., an amount in the range of 
about 40% to 80%, of laser radiation 18 is transmitted through the crystal 
producing transmitted radiation 20. Thus, the laser radiation 18 
propagates through the entire thickness of crystal 12 and directly heats 
electronic hologram 14 with a relatively uniform longitudinal intensity 
profile, e.g., one that varies by less than an order of ten. 
In some embodiments, a reflective optic 22, e.g., mirror useful for 
infrared wavelengths such as a gold, copper, or aluminum coated mirror, 
retroreflects transmitted laser radiation 20 back towards hologram 14. An 
optical isolator 30 prevents retroreflected laser radiation 26 transmitted 
through crystal 12 from reaching and destablizing fixing laser 16. 
Alternatively, the reflective mirror can introduce a small offset angle in 
the retroreflected beam that prevents the retroreflected beam from 
reaching the fixing laser. The retroreflected laser radiation 26 is 
further absorbed by the crystal, thereby further heating the crystal and 
more efficiently converting the laser radiation from fixing laser 16 into 
local heating of hologram 14. Since laser radiation 18 decreases in 
intensity from the front face 23 to the back face 24 of the crystal and 
retroreflected laser radiation 26 decreases in intensity in the opposite 
direction, retroflecting transmitted laser radiation also produces a more 
uniform longitudinal laser intensity profile, and thus more uniform 
heating of hologram 14. 
During use, fixing laser 16 directs laser radiation 18 toward hologram 14 
with an intensity and duration sufficient to heat crystal 12 to a 
temperature at which thermally-excited ions can migrate to and compensate 
for the electronic charges that form the electronic hologram. For example, 
for Fe:LiNbO.sub.3 a suitable laser intensity and duration may be on the 
order of 5 W and 60 seconds in a 5 mm spot size. A monitor beam 32 from, 
e.g., a low-power HeNe laser 34 at 633 nm, can monitor the compensation of 
electronic hologram 14 by observing its diffraction (diffracted beam 38) 
from the hologram, which is measured by a detector 36. Prior to fixing the 
diffracted signal is largest, and then, as the fixing laser generates 
sufficient heat for ions to migrate to and compensate the electronic 
hologram, the diffracted signal decreases to a minimum. Thereafter, the 
compensated hologram may be allowed to cool, and then a revelation laser 
40 illuminates hologram 14 with a uniform revelation beam 42 having a 
wavelength that excites electronic charges and washes away the electronic 
hologram revealing a more stable ionic hologram. As a results, the 
diffracted signal from monitor beam 32 increases indicating the formation 
of the ionic hologram. In some embodiments, revelation laser 40 and the 
laser source initially forming the electronic hologram are the same, e.g., 
an argon ion laser operating at 514 nm. 
System 10 can also be used to erase previously fixed ionic holograms. In 
this case, fixing laser 16 directs laser radiation with a sufficient 
intensity and duration to uniformly heat the ionic hologram to an erasing 
temperature which thermally excites the ions and washes away the ionic 
hologram. The erasing temperature is greater than the fixing temperature 
and subsequent use of revelation beam 42 is not required. Decrease in the 
diffracted signal from monitor beam 32 can be used to monitor the erasure 
of a hologram by fixing laser 16. Erasing can be performed in situ and can 
be very rapid, e.g., less than 10 s for temperatures on the order of 
300.degree. C. 
The precise parameters, e.g., wavelengths, intensities, and pulse duration 
or continuous wave (cw) fluence, for the fixing, writing, and revelation 
lasers depends on the properties of the photorefractive crystal, e.g., its 
thickness, absorption, heat capacity, damage thresholds, and fixing and 
erasing temperatures. Suitable writing lasers for generating electronic 
holograms in Fe:LiNbO.sub.3 are well known in the art, e.g., an argon ion 
laser operating at 514 nm at about 2 W/cm.sup.2 can produce electronic 
holograms in about 5 s. Also see, e.g., F. H. Mok, "Angle-multiplexed 
storage of 5000 holograms in lithium niobate" (Opt. Lett., 18:915-917, 
1993). Providing substantially uniform and direct laser heating through 
the thickness of the crystal with fixing laser 16 depends on the 
dimensionless product .alpha.(.lambda..sub.F)*d, which, as described in 
the section below, is typically in the range of about 0.05 to 2.0, and 
sometimes in the range of about 0.1 to 1.0. Under such conditions, 
especially if reflective optic 22 is used, the longitudinal profile of the 
energy absorbed from laser radiation 18 and retroreflected laser radiation 
26 is relatively uniform along the thickness of the crystal. The 
temperature increase along the thickness of the crystal depends on this 
longitudinal profile, and also on the exposure time, absorption 
.alpha.(.lambda..sub.F), heat capacity C.sub.p of the crystal, and thermal 
diffusivity of the crystal. 
The temperature required for fixing and/or erasing a hologram in a given 
crystal can be determined empirically, using, e.g., monitor beam 32, or 
estimated from literature values, see, e.g., D. L. Staebler et al. (Appl. 
Phys. Lett., 26:183, 1975). For example, for Fe:LiNbO.sub.3, a suitable 
fixing temperature is 200.degree. C. for a period of about 1 second. The 
wavelength-dependent absorption of the photorefractive crystal can be 
determined empirically using conventional optical absorption experiments 
or using literature values, e.g., for Fe:LiNbO.sub.3 see, e.g., K. Naussau 
et al. (J. Phys. Chem Solids, 27:989-996, 1966). 
System 10 provides a number of advantages. For example, since the laser 
radiation from fixing laser 16 propagates through the entire thickness of 
the crystal, the hologram is directly heated by the fixing laser 
radiation. Thus, the heating is rapid and does not depend on thermal 
conduction within the crystal to raise the temperature of the hologram to 
above a fixing or erasing temperature. Furthermore, since the heating is 
rapid, the thermal fixing and erasing is rapid and there is little 
transverse thermal conduction to regions of the crystal not illuminated by 
the fixing laser radiation. As a result, the system provides fixing and 
erasing within a selected area of the crystal, making the system suitable 
for selectively fixing and erasing multiple holograms supported in very 
large, e.g., 1 m.sup.2 by 1 cm, crystals used in large scale 
photorefractive memory systems. 
Mathematical Description 
As laser radiation 18 propagates through the thickness of crystal 12, e.g., 
along a z-axis, the intensity of the laser radiation I(z) decreases 
because of absorption .alpha..sub.F =.alpha.(.lambda..sub.F) at the fixing 
wavelength .lambda..sub.F. As a result, the longitudinal intensity profile 
of laser radiation 18 is given by I(z)=I.sub.0 *exp (-.alpha..sub.F z) 
where I.sub.0 gives the intensity emitted by fixing laser 16. The energy 
absorbed by the crystal per unit volume per unit time, .DELTA.I(z) is 
given by: 
EQU .DELTA.I(z)=.alpha..sub.F *I.sub.0 *exp(-.alpha..sub.F z) (1) 
Thus, the ratio between the energy absorbed at the front and back faces of 
the crystal is given by .DELTA.I(z=d)/.DELTA.I(z=0)=exp (-.alpha..sub.F 
d). 
The fixing laser is chosen such that the fixing wavelength .lambda..sub.F 
corresponds to an absorption .alpha..sub.F that makes the product 
.alpha..sub.F d small enough, e.g., between about 0.1 and 1.0 such as 
about 0.7, to produce a substantially uniform longitudinal profile for 
absorbed energy, e.g., variations less than a factor of 10, and large 
enough that, given the laser intensity I.sub.0, a sufficient amount of 
laser radiation is absorbed to thermally fix and/or erase a hologram. 
By using reflective mirror 22 to double pass the laser radiation, the 
double pass longitudinal laser intensity profile, I.sub.dp (z), and the 
energy absorbed by the crystal per unit volume per unit time, 
.DELTA.I.sub.dp (z), are given by, respectively: 
EQU I.sub.dp (z)=I.sub.0 *{exp[-.alpha..sub.F z]+exp[-.alpha..sub.F (2d-z)]}(2) 
EQU .DELTA.I.sub.dp (z)=.alpha..sub.F *I.sub.0 *{exp[-.alpha..sub.F 
z]+exp[-.alpha..sub.F (2d-z)]} (3) 
In this case, the ratio between the energy absorbed at the front and back 
faces of the crystal is given by: 
EQU .DELTA.I.sub.dp (z=d)/.DELTA.I.sub.dp (z=0) =2*exp(-.alpha..sub.F 
d)/[1+exp(-2.alpha..sub.F d)] (4) 
Thus, for a value of, e.g., .alpha..sub.F d=0.693 for which 
exp(-.alpha..sub.F d)=0.5, the energy absorbed per unit volume per unit 
time decreases smoothly from a value of 1.25*.alpha..sub.F *I.sub.0 at the 
front face to a value of .alpha..sub.F * I.sub.0 at the back face of the 
crystal, a variation of 20%, corresponding to a substantially uniform 
longitudinal profile for absorbed energy. Even more uniform profiles can 
be achieved by selecting .lambda..sub.F such that .alpha..sub.F d is 
smaller, e.g., .alpha..sub.F d equal to about 0.4. 
In addition, .lambda..sub.F is selected such that the laser radiation is 
absorbed into bands of the photorefractive crystal that rapidly dissipate 
the optical excitation as heat. Suitable wavelengths typically include 
those in the infrared region, e.g., 1.6 to 11 microns, and in some cases, 
in the range of about 2 to 8 microns. Such wavelengths are provided by, 
e.g., CO.sub.2 lasers, frequency-doubled CO.sub.2 lasers, or diode lasers 
known in the art, such as described in A. Rybaltowski, "High power 
InAsSb/InPAsSb/InAs mid-infrared lasers," Appl. Phys. Lett., 71:2430-2432 
(1997). 
The increase in temperature .DELTA.T is given by: 
EQU .DELTA.T(z)=.DELTA.I.sub.dp (z)*.tau./C.sub.p (5) 
where .tau. is the fixing exposure time, C.sub.p is the heat capacity of 
the crystal in units of energy per unit volume per unit temperature, 
.DELTA.I.sub.dp is known from Equ. 3 or alternatively is replaced by 
.DELTA.I from Equ. 1 for the case of a single pass, and .tau. is short 
enough to ignoring heat diffusion of the absorbed laser radiation. For 
example, for Fe:LiNbO.sub.3, an intrinsic energy of about 0.5 J/mm.sup.3 
at a selected volume can raise the temperature to about 200.degree. C. 
from room temperature, corresponding to a heat capacity C.sub.p of about 3 
mJ/.degree.mm.sup.3. Such an intrinsic energy can be achieved by, e.g., 
exposing a 1 cm thick crystal to a 20 W laser beam having a 5 mm spot size 
for about 12 seconds, assuming that the crystal absorbs about half of the 
laser radiation to which it is exposed (corresponding to .alpha..sub.F d 
equal to about 0.35). In other embodiments, pulsed rather than continuous 
wave (cw) laser radiation can be used, and in some cases, using pulsed 
radiation for thermal fixing may be preferred, see, e.g., B. Liu et al., 
ibid. 
In general, once the fixing laser is chosen such that the wavelength 
.lambda..sub.F produces a substantially uniform longitudinal laser 
intensity profile based on the value of .alpha..sub.F d, the intensity and 
exposure time required to produce the appropriate fixing and/or erasing 
temperature can be determined from Equ. 5. Since the laser radiation 
directly heats the crystal, fixing times can be shorter than those that 
rely on thermal conduction in relatively thick crystals. Moreover, the 
absorbed energy produces fixing and/or erasure before there is significant 
transverse diffusion of the heat energy thereby more efficiently 
depositing laser energy into desired portions of the crystal. For example, 
Fe:LiNbO.sub.3 has a thermal conductivity of about 0.019 cm.sup.2 /s, and 
thus for fixing and exposure times on the order of 10 s, the thermal 
diffusion length is on the order of 1 mm. 
EXAMPLE 
In the following non-limiting example, the double-pass arrangement shown in 
the FIG. 1 is used to thermally fix an electronic hologram having an area 
of about 5 mm.sup.2 written by a 488 nm argon ion laser in a 0.5 cm thick, 
Fe:LiNbO.sub.3 photorefractive crystal. 
The fixing laser is a pulsed, frequency-doubled CO.sub.2 laser emitting 12 
ns pulses at 4.6 microns at 100 KHz, and having an average power of about 
2.5 W and a 1.8 mm beam diameter. For example, such a suitable 
frequency-doubled CO.sub.2 laser is commercially available from DEOS 
DeMaria ElectroOptics Systems (Bloomfield, Conn.) as Model DEOS-IR-2. The 
revelation laser is a 1 W argon ion laser operating at 488 nm, and the 
monitor laser is a 1 mW, linearly polarized HeNe laser operating at 633 
nm. 
The absorption .alpha..sub.F of the Fe:LiNbO.sub.3 photorefractive crystal 
is estimated to be about 70 m-.sup.1 at 4.6 microns producing a value for 
.alpha..sub.F d equal to about 0.35 for the 0.5 cm thick crystal. Such a 
value results in about half of the fixing laser energy being absorbed 
following the double pass and a variation in absorption between the front 
and back faces of the crystal of about 6%. Under these conditions, an 
exposure time of 2 seconds is sufficient to bring the crystal to a fixing 
temperature of about 200.degree. C. and maintain that temperature for a 
time sufficient to fix the hologram, e.g., a time of about 1 second. 
Other Embodiments 
It is to be understood that while the invention has been described in 
conjunction with the detailed description thereof, that the foregoing 
description is intended to illustrate and not limit the scope of the 
invention, which is defined by the scope of the appended claims. For 
example, photorefractive crystals other than Fe:LiNbO.sub.3, e.g, 
BaTiO.sub.3, Bi.sub.12 SiO.sub.20, and LiTaO.sub.3, can be used as the 
photorefractive crystal. 
Other aspects, advantages, and modifications are within the scope of the 
following claims.