The diffraction efficiency of M holograms superimposed in the volume of the recording medium is proportional to 1/M^2. We present a method, based on nondestructive localized holograms in a doubly doped LiNbO3 crystal, that allows us to also record M holograms in the same volume without an exposure schedule or a diffraction efficiency that has 1/M dependence. We compare experimentally the final diffraction efficiency obtained with the localized and distributed recording methods

Adibi, Ali

Maravic, Irena

Moser, Christophe

Psaltis, Demetri

Schupp, Benjamin

English

Caltech Authors - Main

September 1, 2000 / Vol. 25, No. 17 / OPTICS LETTERS 1243Diffraction efficiency of localized holograms in doubly doped
LiNbO3 crystals
Christophe Moser, Irena Maravic, Benjamin Schupp, Ali Adibi, and Demetri Psaltis
Department of Electrical Engineering, California Institute of Technology, Pasadena, California 91125Received May 10, 2000
The diffraction efficiency of M holograms superimposed in the volume of the recording medium is proportional
to 1M2. We present a method, based on nondestructive localized holograms in a doubly doped LiNbO3
crystal, that allows us to also record M holograms in the same volume without an exposure schedule or a
diffraction efficiency that has 1M dependence. We compare experimentally the final diffraction efficiency
obtained with the localized and distributed recording methods. © 2000 Optical Society of America
OCIS codes: 090.0090, 210.0210.In holographic data storage, pages of information
overlap in the volume of the recording medium. As a
result of destructive readout of holograms in pho-
torefractive crystals such as LiNbO3:Fe, holograms
are recorded with an exposure schedule to equalize
diffraction efficiency, which leads to a final diffraction
efficiency that is proportional to 1M2, where M is
the number of exposures. We present a technique
that does not require an exposure schedule and that
can record M holograms with diffraction efficiency
following a 1M dependence. Our technique involves
nondestructive readout in doubly doped LiNbO3.
We consider the recording of a hologram by the in-
terference of a reference beam focused by a cylindrical
lens and a signal beam, as shown in the inset of Fig. 1.
The recording dynamics of such holograms depend
strongly on the relative power distribution between
the reference and the signal beams. The recording
slope Sl in photorefractives is given by1
Sl 
A0
tw
~
p
PrPs , (1)
where A0 and tw are the square root of the satu-
ration diffraction efficiency and the recording time
constant, respectively. Pr and Ps are the power
in the reference and the signal beams, respec-
tively. Relation (1) is subject to the constraint that
Pr 1 Ps  Plaser . Maximizing the product in rela-
tion (1) subject to this constraint yields Pr  Ps. The
square root of saturation diffraction eff iciency A0 is
proportional to the modulation depth m:
A0 ~ m  2
p
IrIs
Ir 1 Is
, (2)
where Ir Is is the ratio of the power in the reference
(signal) and the beam area. This quantity is maxi-
mized for equal intensity Ir  Is, independently of the
total power. For equal power in the reference and the
signal beams, the recording slope is optimized [rela-
tion (1)] but the saturation diffraction efficiency is low
because of the resultant low modulation depth [rela-
tion (2)]. Conversely, for equal intensities the record-
ing slope is low but the saturation diffraction efficiency
is maximized. The difference in dynamics between
equal power and equal intensity is due to the large
difference between the sizes of the reference and the
signal beams.0146-9592/00/171243-03$15.00/0 ©The following experiment illustrates this dy-
namic: We use a 90± cut LiNbO3 crystal doped with
0.01-wt. % Fe2O3. The recording beams are generated
with a frequency-doubled Nd:YAG laser (Coherent;
wavelength, 532 nm) that is linearly polarized. A
cylindrical lens focuses the reference beam (8-mm
diameter, ordinary polarization) in the crystal to a
lateral extension of 500 mm (1e2 value). The refer-
ence beam interferes with a plane-wave signal beam
(8-mm diameter, ordinary polarization) as shown
in Fig. 1. The total power is distributed into the
reference and signal beams by a half-wave plate and
a polarizing beam splitter. In the first experiment
the reference and the signal beams have equal power.
In the second experiment the intensity between the
reference and the signal beams is equalized while the
total power is kept constant. The result is shown in
Fig. 2. As predicted, the curve recorded with equal
power has a larger recording slope than the curve
recorded with equal intensities and saturates to a
much lower diffraction efficiency.
The present authors and others recently demon-
strated2 the recording of multiple holograms in
a doubly doped LiNbO3:Fe,Mn crystal with the
Fig. 1. Recording setup. The half-wave plate positioned
before the polarizing beam splitter (PB) distributes the
power between the reference and the signal beams. The
wave plate is mounted upon a rotation stage for continuous
power distribution.2000 Optical Society of America
1244 OPTICS LETTERS / Vol. 25, No. 17 / September 1, 2000Fig. 2. Recording curves of a localized hologram. The
longer curve is recorded with equal intensities in the ref-
erence and the signal beams Ir  Is  11.6 mWcm2.
The other curve is recorded with equal power Pr  Ps 
3.1 mW. The reference beam is focused to a lateral ex-
tension of 500 mm, and the signal beam is a plane wave of
8-mm diameter.
geometry of Fig. 1. This method works for any gated
recorded material.3 – 7 In what follows, we compare
the diffraction eff iciency of the localized recording
method with that of the conventional method of record-
ing superimposed holograms in the same volume.
Let a be the ratio of the power in the reference beam
to the total power:
a  PrPr 1 Ps . (3)
We take the areas of the unfocused reference beam
and of the signal beam to be equal. In the follow-
ing set of equations, the primed variables correspond
to the recording with a focused reference beam. The
square root of the diffraction eff iciency,
p
h0, of a local-
ized hologram computed as the ratio of the diffracted
power to the incident power is given by2
p
h0 
p
M A001 2 exp 2 ttw 0 . (4)
where A00 and tw 0 are the saturation diffraction
efficiency (measured as the intensity ratio between
diffracted and incident beams) and the recording-time
constant of the localized recording, respectively.
A00  A0m0L0mL, where A0 is the saturation
diffraction efficiency for the unfocused reference beam
recording (corresponding to m  1). Equation (4) rep-
resents the diffraction efficiency of a single hologram
recorded with a focused reference beam that is M
times smaller than the original plane-wave reference
(M  LL0; Fig. 1). M is also equal to the number
of localized holograms that can be recorded across a
crystal of length L. The factor
p
M that appears in
Eq. (4) accounts for the focusing of the reference beam
by a factor M . Using Eq. (3), and substituting A00
and tw 0 into Eq. (4), we obtain
p
h0  2A0
p
a1 2 a
1 1 aM 2 1
3 1 2 exp2ttw1 1 aM 2 1 , (5)
where tw is the recording-time constant that corre-
sponds to the unfocused reference beam and a takes
the value 12 for equal power in reference and signal
beams. For equal intensities, a  1M 1 1.Substituting a  1M 1 1 into Eq. (5), we find that
the saturation diffraction eff iciency of a single localized
hologram recorded with equal intensities is equal to
h0  A02M , (6)
where A02 is the saturation diffraction efficiency
of a single volume hologram. When M such holo-
grams are recorded side by side in doubly doped
LiNbO3:Fe,Mn, the efficiency of each hologram is
not reduced by the recording of the remaining holo-
grams. This result suggests that, after M strong
localized holograms are recorded, the final diffraction
efficiency of each localized hologram remains equal
to A02M [Eq. (6)]. When M volume holograms
are superimposed, the f inal diffraction efficiency is
equal to h  M#M2.1 For recording materials that
do not have read–write asymmetry in distributed
volume recording [which is the case for LiNbO3:Fe,Mn
(Ref. 8)], M#  A0. Therefore the localized recording
gains a factor of M in diffraction eff iciency compared
with distributed recording. The total recording time
for the localized recording method can be estimated
when it is assumed that each hologram is recorded for
two time constants tw 0:
Tloc total0  2Mtw 0 Mtw  Mte , (7)
where we have assumed that the erasing-time con-
stant te of the distributed volume recording is roughly
equal to the writing-time constant tw. Because the to-
tal recording time of the distributed volume method is
equal to te lnM , the total recording time for the local-
ized holograms is increased by a factor of MlnM .
To verify the 1M dependence in diffraction effi-
ciency by using localized recording in a persistent
material, we experimentally compare the f inal diffrac-
tion eff iciency obtained after recording 50 holograms
by distributed volume recording and by localized
recording in the same doubly doped LiNbO3 crystal.
We use a 0.85-mm-thick crystal doped with 0.075-wt. %
Fe2O3 and 0.01 wt. % MnO in transmission geometry.
For localized recording we use a green recording
wavelength of 532 nm with a reference beam focused
by a cylindrical lens, yielding a lateral extension of
40 mm (1e2 value). The violet sensitizing beam
(401 nm) is copropagating with the green reference
beam. The signal has a diameter of 3 mm at the
crystal. Each hologram is recorded up to saturation
for a recording time equal to two writing-time con-
stants (green intensity, 100 mWcm2; violet intensity,
10 mWcm2; extraordinary polarization). The center-
to-center spacing between adjacent holograms is
60 mm. The total spatial multiplexing is done over
3 mm. Figure 3(i) shows the diffraction eff iciency of
each recorded localized hologram immediately after
each recording. An average diffraction efficiency
of 2 3 1022 is achieved. Some of the holograms
are not recorded well because of instabilities during
the long recording time of each hologram (20 min).
Figure 3(ii) shows the final diffraction eff iciency after
the recording of all 50 holograms. It shows that
the early holograms have been significantly erased
because of recording by the green signal beam and
September 1, 2000 / Vol. 25, No. 17 / OPTICS LETTERS 1245Fig. 3. Diffraction efficiency h versus spatial location for
(i) h of each localized hologram measured immediately af-
ter each recording and (ii) h measured after recording of
50 holograms.
Fig. 4. Diffraction efficiency h versus angle for 50 angle-
multiplexed holograms.
scattering from the violet sensitizing laser. The
average diffraction efficiency is approximately 1023.
The distributed volume recording experiment is
performed with the same crystal.8 Figure 4 shows
the diffraction efficiency for 50 angle-multiplexed
holograms and ordinary polarization. The measured
diffraction eff iciency is 5 3 1025 for ordinary polariza-
tion; extrapolating from that experiment, we expect
a diffraction eff iciency for extraordinary polarization
of 10 times higher 5 3 1024 because of the higher
value of the electro-optic coeff icient for extraordinary
polarization. The diffraction efficiency obtained with
the localized method is twice that obtained with the
distributed recording method; theory predicts that it
should be a factor of 50 greater.
We can explain this discrepancy as being due to three
factors. The first factor is the finite erasing-time con-
stant of the grating stored in the manganese traps forthe green signal beam [for Eq. (6) an infinite eras-
ing time constant is assumed]. Because of the long
recording time of each localized hologram, the total
exposure becomes large enough to erase significant
numbers of early holograms. The first recorded holo-
gram is erased only by the signal beam for the remain-
der of the M1 recording. Experimentally, the ratio
of the erasing-time constant to the writing-time con-
stant is 140 at 532 nm. We expect the diffraction ef-
ficiency of the first hologram to decrease by a factor of
exp2M2tute  4.17 from the saturation diffraction
efficiency obtained after initial green erasure. The
second factor is the erasure caused by the sensitizing
beam on adjacent holograms as a result of scattering
from the crystal surface and fanning caused by the
long recording time of each localized hologram. This
factor varies with the center-to-center spacing of local-
ized holograms. In this experiment we measured a
decrease in the diffraction efficiency of adjacent holo-
grams of approximately a factor of 2.5 when the center-
to-center spacing was 1.5 times the 1e2 spot size. The
third factor is the fact that the localized holograms are
not adjacent (20-mm gap between two consecutive lo-
calized holograms). This gap causes a loss of a factor
of 2.2 in diffraction eff iciency. Overall, the saturation
diffraction efficiency of each localized hologram is de-
creased by a factor of 22.9, which agrees well with val-
ues obtained experimentally. All three factors can be
reduced or completely eliminated if the properties of
the recording material can be improved to reduce era-
sure at the recording wavelength (this is true for red
wavelengths, but recording is slow in the red) and if
coated and well-polished crystals are used.
We have shown experimentally that localized holo-
gram recording can yield a larger final diffraction effi-
ciency than distributed volume recording in nonvolatile
material (e.g., doubly doped LiNbO3). Theoretically the
final diffraction efficiency with localized recording is
proportional to 1M instead of to 1M2.
This research was supported by the U.S. Air
Force/Rome Laboratory and a Jet Propulsion Labo-
ratory research Hybrid Technology MultiThreaded
Architecture project. C. Moser’s e-mail address is
moser@sunoptics.caltech.edu.
References
1. F. H. Mok, G. Burr, and D. Psaltis, Opt. Lett. 21, 896
(1996).
2. C. Moser, B. Schupp, and D. Psaltis, Opt. Lett. 25, 162
(2000).
3. H. Guenther, G. Wittmann, R. M. Macfarlane, and R. R.
Neurgaonkar, Opt. Lett. 22, 1305 (1997).
4. L. Hesselink, S. Orlov, A. Liu, A. Akella, D. Lande, and
R. R. Neurgaonkar, Science 282, 1089 (1998).
5. D. A. Parthenopoulos and P. M. Rentzepis, Science 245,
843 (1989).
6. M. M. Wang, S. C. Esener, F. B. McCormick, I. Okgr,
A. S. Dvornikov, and P. M. Rentzepis, Opt. Lett. 22, 558
(1997).
7. K. Buse, A. Adibi, and D. Psaltis, Nature 393, 665
(1998).
8. A. Adibi, K. Buse, and D. Psaltis, Opt. Lett. 24, 652
(1999).


Diffraction efficiency of localized holograms in doubly doped LiNbO3 crystals

September 1, 2000 / Vol. 25, No. 17 / OPTICS LETTERS 1243Diffraction efficiency of localized holograms in doubly doped
LiNbO3 crystals
Christophe Moser, Irena Maravic, Benjamin Schupp, Ali Adibi, and Demetri Psaltis
Department of Electrical Engineering, California Institute of Technology, Pasadena, California 91125Received May 10, 2000
The diffraction efficiency of M holograms superimposed in the volume of the recording medium is proportional
to 1M2. We present a method, based on nondestructive localized holograms in a doubly doped LiNbO3
crystal, that allows us to also record M holograms in the same volume without an exposure schedule or a
diffraction efficiency that has 1M dependence. We compare experimentally the final diffraction efficiency
obtained with the localized and distributed recording methods. © 2000 Optical Society of America
OCIS codes: 090.0090, 210.0210.In holographic data storage, pages of information
overlap in the volume of the recording medium. As a
result of destructive readout of holograms in pho-
torefractive crystals such as LiNbO3:Fe, holograms
are recorded with an exposure schedule to equalize
diffraction efficiency, which leads to a final diffraction
efficiency that is proportional to 1M2, where M is
the number of exposures. We present a technique
that does not require an exposure schedule and that
can record M holograms with diffraction efficiency
following a 1M dependence. Our technique involves
nondestructive readout in doubly doped LiNbO3.
We consider the recording of a hologram by the in-
terference of a reference beam focused by a cylindrical
lens and a signal beam, as shown in the inset of Fig. 1.
The recording dynamics of such holograms depend
strongly on the relative power distribution between
the reference and the signal beams. The recording
slope Sl in photorefractives is given by1
Sl 
A0
tw
~
p
PrPs , (1)
where A0 and tw are the square root of the satu-
ration diffraction efficiency and the recording time
constant, respectively. Pr and Ps are the power
in the reference and the signal beams, respec-
tively. Relation (1) is subject to the constraint that
Pr 1 Ps  Plaser . Maximizing the product in rela-
tion (1) subject to this constraint yields Pr  Ps. The
square root of saturation diffraction eff iciency A0 is
proportional to the modulation depth m:
A0 ~ m  2
p
IrIs
Ir 1 Is
, (2)
where Ir Is is the ratio of the power in the reference
(signal) and the beam area. This quantity is maxi-
mized for equal intensity Ir  Is, independently of the
total power. For equal power in the reference and the
signal beams, the recording slope is optimized [rela-
tion (1)] but the saturation diffraction efficiency is low
because of the resultant low modulation depth [rela-
tion (2)]. Conversely, for equal intensities the record-
ing slope is low but the saturation diffraction efficiency
is maximized. The difference in dynamics between
equal power and equal intensity is due to the large
difference between the sizes of the reference and the
signal beams.0146-9592/00/171243-03$15.00/0 ©The following experiment illustrates this dy-
namic: We use a 90± cut LiNbO3 crystal doped with
0.01-wt. % Fe2O3. The recording beams are generated
with a frequency-doubled Nd:YAG laser (Coherent;
wavelength, 532 nm) that is linearly polarized. A
cylindrical lens focuses the reference beam (8-mm
diameter, ordinary polarization) in the crystal to a
lateral extension of 500 mm (1e2 value). The refer-
ence beam interferes with a plane-wave signal beam
(8-mm diameter, ordinary polarization) as shown
in Fig. 1. The total power is distributed into the
reference and signal beams by a half-wave plate and
a polarizing beam splitter. In the first experiment
the reference and the signal beams have equal power.
In the second experiment the intensity between the
reference and the signal beams is equalized while the
total power is kept constant. The result is shown in
Fig. 2. As predicted, the curve recorded with equal
power has a larger recording slope than the curve
recorded with equal intensities and saturates to a
much lower diffraction efficiency.
The present authors and others recently demon-
strated2 the recording of multiple holograms in
a doubly doped LiNbO3:Fe,Mn crystal with the
Fig. 1. Recording setup. The half-wave plate positioned
before the polarizing beam splitter (PB) distributes the
power between the reference and the signal beams. The
wave plate is mounted upon a rotation stage for continuous
power distribution.2000 Optical Society of America
1244 OPTICS LETTERS / Vol. 25, No. 17 / September 1, 2000Fig. 2. Recording curves of a localized hologram. The
longer curve is recorded with equal intensities in the ref-
erence and the signal beams Ir  Is  11.6 mWcm2.
The other curve is recorded with equal power Pr  Ps 
3.1 mW. The reference beam is focused to a lateral ex-
tension of 500 mm, and the signal beam is a plane wave of
8-mm diameter.
geometry of Fig. 1. This method works for any gated
recorded material.3 – 7 In what follows, we compare
the diffraction eff iciency of the localized recording
method with that of the conventional method of record-
ing superimposed holograms in the same volume.
Let a be the ratio of the power in the reference beam
to the total power:
a  PrPr 1 Ps . (3)
We take the areas of the unfocused reference beam
and of the signal beam to be equal. In the follow-
ing set of equations, the primed variables correspond
to the recording with a focused reference beam. The
square root of the diffraction eff iciency,
p
h0, of a local-
ized hologram computed as the ratio of the diffracted
power to the incident power is given by2
p
h0 
p
M A001 2 exp 2 ttw 0 . (4)
where A00 and tw 0 are the saturation diffraction
efficiency (measured as the intensity ratio between
diffracted and incident beams) and the recording-time
constant of the localized recording, respectively.
A00  A0m0L0mL, where A0 is the saturation
diffraction efficiency for the unfocused reference beam
recording (corresponding to m  1). Equation (4) rep-
resents the diffraction efficiency of a single hologram
recorded with a focused reference beam that is M
times smaller than the original plane-wave reference
(M  LL0; Fig. 1). M is also equal to the number
of localized holograms that can be recorded across a
crystal of length L. The factor
p
M that appears in
Eq. (4) accounts for the focusing of the reference beam
by a factor M . Using Eq. (3), and substituting A00
and tw 0 into Eq. (4), we obtain
p
h0  2A0
p
a1 2 a
1 1 aM 2 1
3 1 2 exp2ttw1 1 aM 2 1 , (5)
where tw is the recording-time constant that corre-
sponds to the unfocused reference beam and a takes
the value 12 for equal power in reference and signal
beams. For equal intensities, a  1M 1 1.Substituting a  1M 1 1 into Eq. (5), we find that
the saturation diffraction eff iciency of a single localized
hologram recorded with equal intensities is equal to
h0  A02M , (6)
where A02 is the saturation diffraction efficiency
of a single volume hologram. When M such holo-
grams are recorded side by side in doubly doped
LiNbO3:Fe,Mn, the efficiency of each hologram is
not reduced by the recording of the remaining holo-
grams. This result suggests that, after M strong
localized holograms are recorded, the final diffraction
efficiency of each localized hologram remains equal
to A02M [Eq. (6)]. When M volume holograms
are superimposed, the f inal diffraction efficiency is
equal to h  M#M2.1 For recording materials that
do not have read–write asymmetry in distributed
volume recording [which is the case for LiNbO3:Fe,Mn
(Ref. 8)], M#  A0. Therefore the localized recording
gains a factor of M in diffraction eff iciency compared
with distributed recording. The total recording time
for the localized recording method can be estimated
when it is assumed that each hologram is recorded for
two time constants tw 0:
Tloc total0  2Mtw 0  Mtw  Mte , (7)
where we have assumed that the erasing-time con-
stant te of the distributed volume recording is roughly
equal to the writing-time constant tw. Because the to-
tal recording time of the distributed volume method is
equal to te lnM , the total recording time for the local-
ized holograms is increased by a factor of MlnM .
To verify the 1M dependence in diffraction effi-
ciency by using localized recording in a persistent
material, we experimentally compare the f inal diffrac-
tion eff iciency obtained after recording 50 holograms
by distributed volume recording and by localized
recording in the same doubly doped LiNbO3 crystal.
We use a 0.85-mm-thick crystal doped with 0.075-wt. %
Fe2O3 and 0.01 wt. % MnO in transmission geometry.
For localized recording we use a green recording
wavelength of 532 nm with a reference beam focused
by a cylindrical lens, yielding a lateral extension of
40 mm (1e2 value). The violet sensitizing beam
(401 nm) is copropagating with the green reference
beam. The signal has a diameter of 3 mm at the
crystal. Each hologram is recorded up to saturation
for a recording time equal to two writing-time con-
stants (green intensity, 100 mWcm2; violet intensity,
10 mWcm2; extraordinary polarization). The center-
to-center spacing between adjacent holograms is
60 mm. The total spatial multiplexing is done over
3 mm. Figure 3(i) shows the diffraction eff iciency of
each recorded localized hologram immediately after
each recording. An average diffraction efficiency
of 2 3 1022 is achieved. Some of the holograms
are not recorded well because of instabilities during
the long recording time of each hologram (20 min).
Figure 3(ii) shows the final diffraction eff iciency after
the recording of all 50 holograms. It shows that
the early holograms have been significantly erased
because of recording by the green signal beam and
September 1, 2000 / Vol. 25, No. 17 / OPTICS LETTERS 1245Fig. 3. Diffraction efficiency h versus spatial location for
(i) h of each localized hologram measured immediately af-
ter each recording and (ii) h measured after recording of
50 holograms.
Fig. 4. Diffraction efficiency h versus angle for 50 angle-
multiplexed holograms.
scattering from the violet sensitizing laser. The
average diffraction efficiency is approximately 1023.
The distributed volume recording experiment is
performed with the same crystal.8 Figure 4 shows
the diffraction efficiency for 50 angle-multiplexed
holograms and ordinary polarization. The measured
diffraction eff iciency is 5 3 1025 for ordinary polariza-
tion; extrapolating from that experiment, we expect
a diffraction eff iciency for extraordinary polarization
of 10 times higher 5 3 1024 because of the higher
value of the electro-optic coeff icient for extraordinary
polarization. The diffraction efficiency obtained with
the localized method is twice that obtained with the
distributed recording method; theory predicts that it
should be a factor of 50 greater.
We can explain this discrepancy as being due to three
factors. The first factor is the finite erasing-time con-
stant of the grating stored in the manganese traps forthe green signal beam [for Eq. (6) an infinite eras-
ing time constant is assumed]. Because of the long
recording time of each localized hologram, the total
exposure becomes large enough to erase significant
numbers of early holograms. The first recorded holo-
gram is erased only by the signal beam for the remain-
der of the M1 recording. Experimentally, the ratio
of the erasing-time constant to the writing-time con-
stant is 140 at 532 nm. We expect the diffraction ef-
ficiency of the first hologram to decrease by a factor of
exp2M2tute  4.17 from the saturation diffraction
efficiency obtained after initial green erasure. The
second factor is the erasure caused by the sensitizing
beam on adjacent holograms as a result of scattering
from the crystal surface and fanning caused by the
long recording time of each localized hologram. This
factor varies with the center-to-center spacing of local-
ized holograms. In this experiment we measured a
decrease in the diffraction efficiency of adjacent holo-
grams of approximately a factor of 2.5 when the center-
to-center spacing was 1.5 times the 1e2 spot size. The
third factor is the fact that the localized holograms are
not adjacent (20-mm gap between two consecutive lo-
calized holograms). This gap causes a loss of a factor
of 2.2 in diffraction eff iciency. Overall, the saturation
diffraction efficiency of each localized hologram is de-
creased by a factor of 22.9, which agrees well with val-
ues obtained experimentally. All three factors can be
reduced or completely eliminated if the properties of
the recording material can be improved to reduce era-
sure at the recording wavelength (this is true for red
wavelengths, but recording is slow in the red) and if
coated and well-polished crystals are used.
We have shown experimentally that localized holo-
gram recording can yield a larger final diffraction effi-
ciency than distributed volume recording in nonvolatile
material (e.g., doubly doped LiNbO3). Theoretically the
final diffraction efficiency with localized recording is
proportional to 1M instead of to 1M2.
This research was supported by the U.S. Air
Force/Rome Laboratory and a Jet Propulsion Labo-
ratory research Hybrid Technology MultiThreaded
Architecture project. C. Moser’s e-mail address is
moser@sunoptics.caltech.edu.
References
1. F. H. Mok, G. Burr, and D. Psaltis, Opt. Lett. 21, 896
(1996).
2. C. Moser, B. Schupp, and D. Psaltis, Opt. Lett. 25, 162
(2000).
3. H. Guenther, G. Wittmann, R. M. Macfarlane, and R. R.
Neurgaonkar, Opt. Lett. 22, 1305 (1997).
4. L. Hesselink, S. Orlov, A. Liu, A. Akella, D. Lande, and
R. R. Neurgaonkar, Science 282, 1089 (1998).
5. D. A. Parthenopoulos and P. M. Rentzepis, Science 245,
843 (1989).
6. M. M. Wang, S. C. Esener, F. B. McCormick, I. Okgr,
A. S. Dvornikov, and P. M. Rentzepis, Opt. Lett. 22, 558
(1997).
7. K. Buse, A. Adibi, and D. Psaltis, Nature 393, 665
(1998).
8. A. Adibi, K. Buse, and D. Psaltis, Opt. Lett. 24, 652
(1999).


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Diffraction efficiency of localized holograms in doubly doped LiNbO3 crystals

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