Download Persistent spectral hole burning in an organic material for temporal

74
J. Opt. Soc. Am. B / Vol. 16, No. 1 / January 1999
Tian et al.
Persistent spectral hole burning in an organic
material for temporal pattern recognition
M. Tian, F. Grelet, I. Lorgeré, J.-P. Galaup, and J.-L. Le Gouët
Laboratoire Aimé Cotton, bâtiment 505, 91405 Orsay Cedex, France
Received March 31, 1998; revised manuscript received July 23, 1998
A broad-bandwidth persistent spectral hole-burning organic material is used as a fast optical processor that
compares an input temporal-frequency profile with a recorded reference spectral shape. This patternrecognition procedure relies on a subpicosecond temporal cross-correlation process. The size of the phaseencoding spectral interval exceeds 1 THz. The storage material, the spectral encoder, and the interferometric
detector are examined in detail for optimal pattern discrimination. Experimental temporal patternrecognition results are reported. © 1999 Optical Society of America [S0740-3224(99)02101-3]
OCIS codes: 090.0090, 020.1670, 070.5010, 320.5390, 200.4740, 190.4380.
1. INTRODUCTION
1
Since Mossberg’s seminal work in 1982, it has been
known that the photon-echo process opens a specific way
to optical data storage and processing. Optical storage of
data trains was demonstrated in various materials,2–5
and a rare-earth ion-doped crystal seems to be a good candidate for the practical use of an optical dynamic randomaccess memory.6 As for time-domain processing applications, several architectures were demonstrated in both
organic7,8 and inorganic9–12 persistent spectral holeburning (PSHB) materials, but the cross correlation of a
readout temporal pattern with an engraved one was effected only in ion-doped crystals,11,12 until our preliminary report.13
Indeed, the achievement of broadbandwidth temporal cross correlation in organic dyedoped amorphous materials leaves us faced with a triple
challenge. First, in order to take full advantage of the
broad spectral bandwidth of the material, one has to deal
with subpicosecond time-scale temporal patterns that one
must be able to shape and control. Second, one has to engrave a coherent spectral structure over a several terahertz interval within the absorption band of the photosensitive medium. Third, one has to detect the crosscorrelation signal with subpicosecond resolution.
In Section 2 we outline the basics of temporal cross correlation in PSHB materials, insisting upon specific features such as the white-light storage of the spectral holograms and the interferometric detection of the diffracted
signal. The experimental configuration is depicted in
Section 3, and the critical adjustment of the spectral
shaping device is detailed in Section 4. Experimental
results are presented in Section 5. We conclude in
Section 6.
tering of an input image through a reference pattern recorded in a photosensitive medium. Storage and filtering
take place in the Fourier-transform space. In the
present work, correlation is effected between temporal
shapes. The time-to-frequency Fourier transform of the
reference pattern is recorded in a persistent spectral holeburning material.
The reference image has to include phase and amplitude information. In order to record a field-amplitude
distribution in a quadratic photosensitive material, one
usually engraves the interference pattern of a known field
and the shaped field to be saved. This is the principle of
holography. We proceed in a slightly different way since
we do not really save all the information contained in the
image field. The laser beam is split into two parts. On
one arm the spectral field amplitude Ẽ( n ) is shaped by a
spectral phase factor m 1 ( n ) that changes it into the image
field Ẽ( n )m 1 ( n ). The pattern m 1 ( n ) spans a D-wide frequency interval, in the terahertz range. The field on the
other arm undergoes a delay T. The two fields propagate
along wave vectors k1 and k2 , respectively. One makes
them interfere in a low-optical-density PSHB slab. To
lowest order in the burning dose, the fields engrave the
space and frequency structure u Ẽ( n ) u 2 m 1* ( n )exp@22ipn T
1 i(k1 2 k2 ) • r# , provided the delay T is smaller than
the inverse homogeneous width G 21
hom, and D is smaller
than the absorption-band inhomogeneous width G in .
This represents the reference pattern. The phase structure of m 1 ( n ) is saved, but that of Ẽ( n ) is lost.
Let an input image, represented by its spectral amplitude Ẽ 8 ( n )m 2 ( n ), be directed to the recorded hologram
along k1 . A signal is diffracted in direction k2 . Its
spectrum, filtered by the hologram, reads as Ẽ 8 ( n )m 2 ( n )
3 (1 2 iĤ) @ u Ẽ( n ) u 2 m 1* ( n )exp(22ipnT)#, where the Hilbert operator Ĥ is defined by
2. TEMPORAL PATTERN RECOGNITION
This work is placed within the general framework of
cross-correlation pattern recognition. This procedure
can be traced back to the VanderLugt correlator, which
operates in the space domain.14 It relies on the linear fil0740-3224/99/010074-09$15.00
Ĥ @ f ~ n !# 5
1
p
© 1999 Optical Society of America
R
f~ n8!
dn 8 .
n 2 n8
(1)
Tian et al.
Vol. 16, No. 1 / January 1999 / J. Opt. Soc. Am. B
The time-dependent signal that emerges from the PSHB
plate reads as
E s~ t ! 5
E
Ẽ 8 ~ n ! m 2 ~ n ! exp~ 2i pn t !
3 ~ 1 2 iĤ !@ u Ẽ ~ n ! u 2 m 1* ~ n ! exp~ 22i pn T !# dn .
(2)
When the laser source delivers Fourier-transform-limited
short pulses, the power spectrum u Ẽ( n ) u 2 is constant over
the spectral width of the temporal images, provided that
the pulse duration is much shorter than D 21 . Then
u Ẽ( n ) u 2 can be factored out of the Hilbert operator. However, one can proceed in quite the same way with a whitelight stochastic source. Indeed, engraving is usually an
accumulation process that requires repeated interaction
with low-energy writing pulses. Therefore one can replace the quantity u Ẽ( n ) u 2 by its statistical average S
5 ^ u Ẽ( n ) u 2 & . If the coherence time of the stochastic
source is much smaller than D 21 , the spectrum is flat
over the frequency aperture D of the shaping factors and
it can be factored out of the Hilbert operator. In addition
we assume that the temporal extension of the recorded
image does not exceed the time delay T. Then the following approximation holds:15
Ĥ @ m 1* ~ n ! exp~ 22i pn T !# > im 1* ~ n ! exp~ 22i pn T ! ,
(3)
and the signal reads as
E s ~ t ! 5 2S
E
(4)
E~ t ! 5
E
dn Ẽ ~ n ! exp~ 2i pn t ! .
(5)
The fringe contrast C( t ) that is detected on a photodiode
array may be expressed as
UE
U
dn Ẽ S ~ n ! Ẽ 8 * ~ n ! exp~ 2i pn t ! ,
(6)
which, according to Eq. (4), is transformed into
C~ t ! } S
UE
duration and a 1-THz shaping window, the stochastic
background is only 1% of the correlation-peak amplitude.
For insight into the behavior of the interferometric signal,
one can regard a stochastic pulse as a sequence of uncorrelated subpulses, the duration of which is given by the
inverse width of the shaping window. Each subpulse
gives rise to an elementary response that contributes to
the interferometric signal through its interference with a
delayed replica of its parent subpulse. Summing up all
these contributions, the detector actually achieves a statistical averaging operation that tends to smooth out the
individual response fluctuations. Since the power spectrum ^ u Ẽ 8 ( n ) u 2 & is constant over the shaping window, one
finally obtains
C ~ t 5 T! }
UE
U
m 2 ~ n ! m 1* ~ n ! dn .
(8)
Except for the small stochastic background, the interferometric signal does differ from what would be obtained
with the help of a femtosecond Fourier-transform-limited
source.
Let m 1 ( n ) and m 2 ( n ) belong to a family of functions
m ( i ) ( n ) that satisfy the orthogonality condition:
E
m ~ i ! ~ n ! m ~ j ! * ~ n ! dn 5 d ij .
(9)
Ẽ 8 ~ n ! m 2 ~ n ! m 1* ~ n ! exp@ 2i pn ~ t 2 T !# dn .
The signal is expected to take on the shape of a correlation peak when the input image shape factor m 2 ( n ) coincides with the recorded reference pattern m 1 ( n ). If the
spectral width D stays in the terahertz range, the correlation signature flashes during a time interval D 21 ,
shorter than 1 ps.
Interferometric detection is appropriate to capture this
short-living burst.16 One builds the spatial interference
fringes of the signal E s (t) and a delayed replica of the
readout field E 8 (t 2 t ), where the spectral and temporal
amplitudes are linked by the Fourier-transform equation:
C~ t ! }
75
U
u Ẽ 8 ~ n ! u 2 m 2 ~ n ! m 1* ~ n ! exp@ 2i pn ~ t 2 T !# .
(7)
Let the input image be carried by a t L -long stochastic
pulse with a coherence time much smaller than D 21 .
Then C( t ) differs only by a term of order 1/(D t L ) 1/2 from a
statistical average expression, where u Ẽ 8 ( n ) u 2 is replaced
by the expectation value ^ u Ẽ 8 ( n ) u 2 & . With a 10-ns pulse
Then the correlation signal C( t ) cancels at t 5 T, except
when the input image coincides with the recorded reference pattern.
The stored reference pattern has been expressed to lowest order in the burning dose, in an optically thin sample.
Description can be extended to optically thick slabs,
where larger diffraction efficiency values are expected.
With a simple argument one can determine the validity
range of the linear dose dependence of the engraving. It
relies on the linear character of the hole-burning process
itself. As long as the incident dose is completely absorbed by the medium, the depletion of the activemolecule population is proportional to the total incident
energy. Thus the optical-density reduction is a linear
function of the dose. In other words, total bleaching near
the input side of the plate does not affect the linear behavior of the optical density as long as the dose is completely absorbed. As the accumulated dose increases,
bleaching progresses, and an important fraction of available energy ultimately reaches the exit surface. A part of
the dose passes through and does not modify the medium.
Then the optical density no longer behaves as a linear
function of the dose. Since the hologram-diffracted signal combines contributions from all the photosensitive
volume, it is expressed in terms of the optical density,
which is actually the relevant quantity to consider.
In order to build the functions m ( i ) ( n ), one can divide
the shaping spectral window into N even elementary intervals of width d. A phase factor e n ( i ) 5 61 is ascribed
to each one of these slices so that the biphase pattern
m ( i ) ( n ) reads as
76
J. Opt. Soc. Am. B / Vol. 16, No. 1 / January 1999
~i!
m ~n! 5
1
AD
N21
(
e ~ni ! P
n50
S D
n
d
2n ,
Tian et al.
(10)
where P(x) 5 1, when u x u , 1/2, and vanishes otherwise.
The pattern orthogonality is then conditioned by the following rule:
N21
(
e ~ni ! e ~n j ! 5 N d ij .
(11)
n50
Several procedures can be used to build a set of N phasefactor arrays that satisfy this condition. For instance,
the Hadamard codes are defined as the rows of matrices
generated by the recursion formula:17
H 2 ~ p11 ! 5
F
@ H 2~ p!#
@ H 2~ p!#
@ H 2~ p!#
2@ H 2 ~ p ! #
G
,
(12)
Fig. 1.
which starts from the 2 3 2 seed matrix,
H2 5
F
1
1
1
21
G
.
(13)
In the pth-order matrix, N 5 2 p rows of N elements obey
the orthogonality condition. The row number is used to
label the phase-factor array. Therefore all the phase factors are set equal to 11 in m ( 0 ) ( n ), which is uniform over
the D-wide shaping interval. Function m ( 0 ) ( n ) is named
the gate function. The product of two functions still belongs to the same function set. A function multiplied by
the gate function equals the function itself. The square
of a function equals the gate function.
3. EXPERIMENTAL CONFIGURATION
The setup is presented on Fig. 1. The light pulses are 10
ns long. They are provided by a low-repetition-rate (15Hz) broadband laser. In this demonstration experiment
the reference phase factor m 1 ( n ) and the input image
m 2 ( n ) are built by the same spectral shaper. In the recording step the shutters Sh1 and Sh2 are open and
closed, respectively. The shaped pulse, propagating
along k1 , interferes with the initial pulse that propagates
along k2 . They engrave the reference hologram in the
liquid-helium-cooled PSHB sample. In the patternrecognition step the shutter state is reversed. The spectral shaper imprints the phase factor m 2 ( n ) on the light
pulse that is directed to the sample along k1 . Fringes
built by the diffracted signal and the interferometric reference beam are detected on a CCD linear array. The
time intervals T and t are adjusted with the help of the
optical delay lines DL1 and DL 2, respectively.
The PSHB sample is a 0.5-mm-thick plate of
octaethylporphyrin-doped polystyrene. The lifetime of
the PSHB engraving is practically limited to a few hours,
as imposed by the cryostat helium-holding time. Repeated illumination by the input pulses also contributes
to the erasure of the engraved reference image, which is
not fixed.
The light pulses are spectrally shaped with the help of
a two-grating device that was originally proposed by
Froehly18 and was further experimented by Weiner.19
The frequency components of the pulse are spatially dis-
Experimental setup.
persed by the first diffraction grating, and they are focused by a lens on a linear array of liquid-crystal phase
modulators (LCM’s). After phase filtering, the different
spectral components are collimated by a second lens and
collected into a single beam by a second grating. Both
lenses have the same focal distance f 5 25 cm, and the
two gratings (Jobin–Yvon 520 12 090, 40 mm 3 60 mm,
blazed at 620 nm) have the same parameter a 5 2400
grooves/mm. The grating grooves are set in the vertical
direction so that the plane of incidence is horizontal. In
an ideal configuration, each lens is located at equal distance f from the LCM and the closest grating. Therefore
the lenses form a 21 magnification telescope and the system is symmetric with respect to the plane where the
LCM is positioned.
Maximum diffraction efficiency on the gratings is obtained when the light polarization is oriented in the plane
of incidence. It has to be made consistent with the LCM
action. The horizontally polarized field that emerges
from the grating G1 undergoes a 90° rotation provided by
a half-wave plate inserted before the liquid-crystal cell.
This device acts itself as a half-wave plate that makes polarization return to the horizontal direction. A polarizer
inserted before the second grating G2 selects this polarization component. Mechanical stresses on the glass
windows of the LCM cell induce a small birefringence.
We compensate it by inserting a properly oriented
quarter-wave plate.
The LCM delimits a 1.1-THz-wide window that is
parted into 64 independent pixels. We used the device
for building a family of 32 Hadamard orthogonal codes,
from the combination of 32 elementary intervals. Each
one spreads over two pixels, and its width d equals 35
GHz. The delay T is set equal to d 21 , so that Eq. (3) is
valid.
The shaping device requires careful adjustment. The
critical parameters are examined in Section 4.
4. ADJUSTMENT OF THE
SPECTRO-TEMPORAL SHAPING DEVICE
A. Spectral Resolution
It is commonly admitted that the finite size of the incident
light beam limits the spectral resolution of the shaping
Tian et al.
Vol. 16, No. 1 / January 1999 / J. Opt. Soc. Am. B
device.19 We show that the pattern-recognition operation in our experiment circumvents this diffraction effect.
On the first grating the incident field is represented by
its amplitude E i (x, n ) that depends on frequency n and on
transverse coordinate x (see Fig. 2). Let this function be
decoupled into the following product:
E i ~ x, n ! 5 E ~ x ! J~ n ! .
E F ~ j , n ! 5 Ẽ
F
G
j 2 b~ n 2 n0!f
J~ n ! ,
a l 0f
(15)
where Ẽ( j ) 5 * dxE(x)exp(22ipxj) and where
b5
]u
]n
U
n0
occurs at the end of the pattern-recognition process. The
detected fringe contrast can be expressed as
C~ t 5 T ! }
l 02 a
52
c cos u 0
E U S DU
UE S
D S
UE
U
dX Ẽ
3
(14)
We assume that E i (x, n ) is essentially a diaphragmlimited plane wave. Through the grating G1 and the lens
L1 the different spectral components are focused in the
plane F where the light modulator is positioned. Let the
geometric image of the central component n 0 be selected
as the origin of position coordinate j. The spectralcomponent images are affected by diffraction. Provided
its aperture is larger than the transverse size of the
beam, the lens L1 operates as a plain Fourier transformer.
Therefore in focal plane F the field distribution reads as
77
}
X
gl 0 f
m2
2
D U
aX
aX
1 n m 1*
1 n dn
gbf
gbf
m 2 ~ n ! m 1* ~ n ! dn .
(17)
Each point on the sample is affected by the same spectral
shift during the storage and readout steps. Therefore
the finite incident-beam size does not limit the spectral
resolution of pattern recognition.20 This conclusion relies on the assumption that the sample and the modulator
are optically conjugate. This position is more critical as
the incident beam diameter becomes smaller.
Despite its symmetric look, the shaping device actually
works in an asymmetric way, as illustrated on Fig. 3. In
the first section of the device the incident-beam diameter
determines the diffraction spot size on the modulator, but
this is the optics aperture in the second section that im-
stands for the angular-dispersion coefficient and where
the astigmatism coefficient
a5
]u
]w
U
n0
cos w 0
52
cos u 0
connects the diffraction angle u with the incidence angle
w. The two transverse dimensions of the beam are affected in different ways. In the plane of incidence the
beam is resized by the factor a 21 . The vertical dimension is unchanged. In the focal plane the field is shaped
by the liquid-crystal modulator that is represented by the
transmission factor m @ j /( b f ) # , as a function of the horizontal coordinate j. The sample located in plane P and
the shaping plane F are set in conjugate positions
through the lenses L2 and Lg. One assumes that the diffraction effect caused by the finite aperture D of these optics can be neglected. Practically this means that l 0 f/D
is smaller than the width d of the modulator pixels. Let
the geometric image of the central spectral component be
located at position X 5 0 on the sample. Then the geometric image of point j at frequency n is located at
X 5 2( g/ a )( j 2 n b f ), where g 5 2f L g /f is the magnification factor from F to P. Therefore the field distribution
in the sample reads as
E P ~ X, n ! 5 Ẽ
S DS
D
X
aX
1 n J~ n ! .
m
gl 0 f
gbf
Fig. 2. Spectral shaping device. The spectral components of
the incident beam are dispersed by grating G1 and focused in
plane F by lens L1. They are collimated by lens L2 and collected
by grating G2 into a single beam that is focused on the memory
element by the lens system Lg . Coordinates x, j, and X are orthogonal to the optical axis. The angles of incidence and of diffraction on G1 are represented by w 0 and u 0 , respectively.
(16)
The spectral distribution at each position on the sample
faithfully reflects the transmission profile of the spatial
modulator. However, a a X/( g b f ) frequency shift affects
the spectrum at each position X so that the different
sample points are illuminated by different spectra. As a
consequence, the space-integrated spectrum on the
sample is actually blunted by the diffraction profile
Ẽ (X/gl 0 f ). In our experiment, space integration only
Fig. 3. Asymmetric operation of the two-grating device. The
diffraction spot size on the LCM is determined by the incident
beam diameter, but, as for the imaging of the LCD on the
sample, the diffraction limit depends on the output optics aperture.
78
J. Opt. Soc. Am. B / Vol. 16, No. 1 / January 1999
Tian et al.
poses the diffraction limit of the spectral resolution. Optics aberrations have to be considered in full-aperture operation. Proper orientation of the lenses reduces the
spherical aberration that is expected to dominate under
infinite conjugate ratio conditions. As for doublet L2, its
less steeply curved surface should face the modulator.
We shall see that this orientation conflicts with the elimination of group-velocity dispersion.
B. Group-Velocity Dispersion
First, the device must not modify the spectro-temporal
properties of the incident light in the absence of the LC
modulator. The group-velocity dispersion vanishes when
the second grating coincides with the image of the first
one through the two lenses. Let u denote the distance
from exact conjugation along the optical axis of the lens
pair. Then the spectral component n undergoes a phase
shift with respect to the central component n 0 . The
phase shift is expanded in powers of n 2 n 0 . The
second-order term contributes to the group-velocity dispersion and reads as21
F ~ 2 !~ n ! 5 p
H F
u
l 0a
l 0 cos~ u 0 !
G JS
2
n 2 n0
n0
D
2
,
(18)
where u 0 represents the diffraction angle on the first grating. At u 0 5 70° and l 0 5 620 nm, a phase shift of p radians is observed at 2 THz from the central frequency
when the second-grating position is 2 mm away from exact conjugation. The intergrating distance has thus to be
adjusted with a 1023 precision.
To achieve this precision, we monitor the group-velocity
dispersion with the help of the interferometric detector.
Indeed, the output-field spectral amplitude can be expressed as Ẽ( n )exp@iF(n)#, where Ẽ( n ) stands for the input field and where F(n) represents the dispersion phase
shift. One makes the two fields interfere on the photodiode array where the fringe contrast reads as
C~ t ! }
UE
U
dn u Ẽ ~ n ! u exp@ 2i pn t 1 iF ~ n !# .
2
C. Astigmatism
The distance between lenses L1 and L2 has to be set equal
to 2 f. Then they combine into a 21 magnification telescope, and the astigmatism effects of the two gratings
compensate each other. However, special care must be
taken when the incident field differs from a plane wave.
An incident spherical wave would exhibit two focusing positions after lens L1. It would converge in F' and F i
along vertical and horizontal directions, respectively.
Let F' be located at distance h, ahead of the L1 focal
plane. Then F i stays at distance h / a 2 from this plane.
When a polychromatic beam is directed to the shaping device, the different spectral components draw a misleading
horizontal focal line at position F' . When set at the
beam waist, the sample is actually conjugate with a linear
vertical object positioned at F' . However, the horizontal
linear modulator array has to be set at F i in order to be
imaged on the sample. The distance h ( a 22 2 1) between F i and F' increases dramatically when one enlarges the diffraction angle u 0 to improve the spectral dispersion.
5. EXPERIMENTAL RESULTS
A. Testing the Spectral Shaper and the Interferometric
Detector
We test the encoding and detection systems in the same
way as we monitor the group-velocity dispersion. One
makes the initial field Ẽ( n ) and the spectrally shaped
field Ẽ m ( n ) interfere on the photodiode array, where the
fringe contrast reads as
C~ t ! }
UE
U
dn Ẽ * ~ n ! Ẽ m ~ n ! exp~ 2i pn t ! .
A transmission factor m @ j /( b f ) # is encoded by the LCM.
When the setup is correctly adjusted, the resulting
shaped amplitude reads as
Ẽ m ~ n ! 5 Ẽ ~ n ! m ~ n ! .
(19)
At optimum distance, F ( 2 ) ( n ) cancels and C( t ) is narrower. The spherical aberration of the lenses may also
contribute to the group-velocity dispersion. This effect is
reduced with the help of properly oriented doublets. The
less steeply curved surface should face the nearest grating, where the focal point is located. This is the opposite
of the condition that optimizes spectral resolution. As a
matter of fact, the spherical aberration induces negligible
dispersion in the present experiment, where the useful
bandwidth of the two-grating device is only 1.1 THz.
Therefore we select the L2 orientation that improves spectral resolution.
It should be noticed that the spectral shaper need not
be corrected for group-velocity dispersion in the patternrecognition experiment. Indeed, the correlation signal
only depends on the phase difference between the recorded pattern and the readout field. Velocity dispersion
has to be eliminated for the side experiment that was designed to check the capabilities of the shaper and of the
interferometric detector.
(20)
(21)
The laser spectral intensity is assumed to be uniform over
the shaping window. Substitution of Eq. (21) into Eq.
(20) leads to
C~ t ! }
UE
U
dn m ~ n ! exp~ 2i pn t ! ,
(22)
which is nothing but the Fourier transform of the encoding function. Figure 4 represents the spectral structures
of several biphase encoding functions, their temporal profiles calculated by Fourier transform and the optical delay
variations of the measured fringe contrast. The curve
number refers to the row position in the Hadamard matrix, which labels the encoding functions. The good
agreement between theoretical and experimental profiles
demonstrates the correct operation of the pulse shaper
and of the interferometric detector. The profiles displayed in the upper boxes of Fig. 4 correspond to the uniform phase factor m ( 0 ) ( n ) 5 1, with maximum fringe contrast at zero delay. All the other encoding functions
m ( k ) ( n ) (k Þ 0) are orthogonal to m ( 0 ) ( n ), in the sense
defined by Eq. (9). In our experiment it is crucial that
this orthogonality property be correctly transferred to the
Tian et al.
Vol. 16, No. 1 / January 1999 / J. Opt. Soc. Am. B
Fig. 4. Experiment side: contrast of the interference fringes of
the laser beam with its time-delayed, spectrally shaped replica.
Theory side: frequency-to-time Fourier transform of the spectral shapes that are drawn in insets. Function numbers refer to
their position in a 32-code Hadamard set.
79
Then the broadband source is converted into a tunable
probe by insertion of a 0.08-THz-wide moving slit in the
two-grating device. The intensity transmitted or diffracted by the exposed material is recorded as a function
of the slit position. The resulting spectra are displayed
in Figs. 5(c) and 5(d).
With a dose of ;2.7 mJ/THz on an exposed area of
;0.25 mm2, the burning depth approaches 1/3 of the initial optical density. The measured transmission results
from an average over the space- and frequency-engraved
fringes. However, even at positions where the brightest
illumination was received, the final optical density remains large enough to comply with the linear-dosedependence condition discussed in Section 1.
It should be noticed that larger dose burning is also affected by the specific properties of persistent spectral hole
burning in octaethylporphyrin. In this material the
chemical structure of the photoproducts does not differ
from that of the educts. Therefore the burnt molecules
do not leave the absorption band and ultimately hamper
the bleaching process. The model that we developed22
shows that this does not occur as long as the hole depth
does not exceed 1/3 of the initial optical density.
Linear dose dependence also requires that one avoid
transient depletion of the ground state during the laser
pulse. About 90% of the excited molecules are trapped in
the metastable triplet state during several tens of milliseconds. Therefore at the end of a laser shot the groundstate population is reduced by factor exp@2(Bw/c)#, where
B stands for the stimulated-emission Einstein coefficient
and w represents the spatial and spectral density of burning energy per shot. From available data on free-base
porphyrin,23 one obtains (B/c) 21 5 0.35 mJ/THz/cm2/
pulse spectra and correctly detected by the correlator.
According to the definition of m ( 0 ) ( n ), Eq. (22) can be rewritten as
C~ t ! }
UE
U
dn m * ~ n ! m ~ 0 ! ~ n ! exp~ 22i pn t ! ,
(23)
which means that the othogonality of m ( k ) ( n ) (k Þ 0) and
m ( 0 ) ( n ) is revealed at t 5 0. This is properly verified on
the experimental data of Fig. 4.
B. Hole Depth and Spectral Response
The reference pattern is engraved in the photosensitive
material as a space- and frequency-dependent bleaching.
In order to specify the exposure conditions, we measure
the depth of the hole that is burnt in the absorption profile. We also check the spectral response of the material.
To this end the experimental setup undergoes a temporary modification.
First, the laser bandwidth is enlarged to ;10 THz (see
upper box on Fig. 5), and the central flat region of the
spectrum is selected with the help of a 1.1-THz-wide window that replaces the LCM in the two-grating device.
The shaped beam is split into two angled arms in order to
engrave a space and frequency hologram within the photosensitive material. The delay between the two writing
pulses is adjusted to T > 70 ps. Thus the period of the
spectral interference fringes they engrave is ;15 GHz.
Fig. 5. (a) Laser spectrum. (b) Optical density of the sample
before engraving. (c) Optical density after engraving within a
1.1 T-Hz window, with an average laser energy of 0.7 mJ/THz/
shot for 6 min. (d) Diffracted-energy spectrum.
80
J. Opt. Soc. Am. B / Vol. 16, No. 1 / January 1999
shot. Experimental spectra were recorded with incident
energy density per shot w 0 5 0.2 mJ/THz/cm2/shot.
Comparing the initial and the final spectral distributions of optical density in Fig. 5, one notices that some
bleaching is effected outside the burning window, on its
red side. It corresponds to molecules that had been
burnt through the phonon sideband of the homogeneous
line. This effect contributes to optical-density reduction,
but not to the space and the frequency hologram buildup.
Indeed, the period of the recorded spectral fringes has to
be larger that the homogeneous width. On the contrary,
the 15-GHz fringe period is much smaller than the 0.5THz typical width of the phonon sideband.
Finally, the spectral distribution of the holographic signal, drawn in Fig. 5(d), is uniform, as required for the
pattern-recognition experiment.
C. Pattern Recognition
The experimental setup recovers the configuration illustrated in Fig. 1. One is faced with contradictory requirements. On the one hand, the laser spectrum must be
uniform over the storage window. On the other hand,
the detection becomes more noisy as the interferometric
reference bandwidth exceeds the width of the shaping
window. As a tentative trade-off, we equalize the laser
spectrum with the help of a Lyot filter. The spectrum is
made nearly flat within the 1.1-THz-wide LCM window
and is ;3 THz wide at half-maximum intensity. The optics are readjusted in such a way that the beam area on
the sample is ;4 times smaller than in Subsection 5.B.
The reference and the object beam intensities are balanced so that they evenly contribute to the spatial and
the spectral energy density on the sample. Dose calibration is effected by monitoring spectral hole depth. A dose
of 0.63 mJ/THz is needed to achieve a 0.5 reduction of the
optical density, which initially equals 1.5. This is consistent with previous data. The holographic storage dose is
set equal to this value, which represents the linearregime upper limit. The burning window is centered at
the top of the absorption band.
The reference pattern No 16 is stored in the PSHB material. The burning dose is provided by a 2-min pulse sequence, with a repetition rate of 15 pulses per second.
The average pulse energy on the sample amounts to 0.44
mJ/THz/shot. The 32 test functions are successively imprinted on the input beam. The result is given in Fig.
5(a). An intense correlation peak is detected when the
input pattern coincides with the reference one. False
correlation is also detected for some input functions. The
true-to-false signal ratio is larger than 15 for any input.
The most important false correlation occurs for input
phase factors Nos 0 and 24 in Fig. 6(a). The spectral
structure of the diffracted field results from the product of
the reference and the input spectral shapes. As explained in Section 2, the square of a shape function equals
the gate function (No 0), and the product of any two different shape functions is another function in the same
family. When the input pattern is the gate function, the
diffracted-field spectrum should be given by the product
of functions No 0 and 16, which coincides with the shape
factor No 16. In the same way, the emission spectrum
generated by input function No 24 should be described by
Tian et al.
function No 8, which results from the product of functions
Nos 16 and 24. The signal at the output of the interferometric detector is nothing but the frequency-to-time Fourier transform of the emitted-field spectral amplitude.
At zero delay it coincides with the integral of the spectral
amplitude over the frequency-domain storage window.
Among the 32 orthogonal shape factors, functions Nos 8
and 16 exhibit the narrowest Fourier-transform structures at zero time delay (see Fig. 4). When the diffracted
field is spectrally shaped by these functions, the correlation signal is very sensitive to the source uniformity and
to the adjustment of the delay line.
The same false-correlation feature is observed for other
reference patterns. For instance, the set of crosscorrelation signals in Fig. 6(b) have been obtained after
storage of code No 12 in the PSHB material. Then the
largest false correlation is observed when the shape No 28
is imprinted on the input pulse. The product of functions
Nos 12 and 28 again gives the function No 16.
With reference pattern No 12 stored in the PSHB material, and keeping the input function No 28, we record
the interferometric detector as a function of the time delay. The resulting profile is displayed in Fig. 7(a). The
amplitude at t 5 0 corresponds to the false correlation
with input No 28. In the same way, one records the timedelay dependence of the signal with input function No 12
[see Fig. 7(b)].
Fig. 6. Experimental cross correlation between a recorded reference pattern and 32 input codes. The interferometric signal is
detected at fixed delay t 5 T. Three different shapes (Nos 16,
12, and 1 in the 32-code Hadamard set) are successively stored in
the PSHB material.
Tian et al.
Vol. 16, No. 1 / January 1999 / J. Opt. Soc. Am. B
81
This work includes elements from two Ph.D. dissertations defended in 1997 at Université Paris XI by François
Grelet and Mingzhen Tian.
REFERENCES
1.
2.
Fig. 7. (a), (b) Interferometric detection of the diffracted field, as
a function of the time delay ( t -T). Function No 12 is stored as
the reference pattern. Readout is performed by input functions
No 28 (a) and No 12 (b). (c), (d) Interferometric detection of the
laser field shaped by the codes No 16 (c) and No 0 (d).
The optical setup and the storage material may both
contribute to the generation of the false-correlation signals. In order to elucidate the respective part they play,
we compare the diffracted field data, diagrammed in Figs.
7(a) and 7(b), with the direct interferometric detection of
functions Nos 16 and 0, as reported in Subsection 5.A.
The latter recordings do not involve any contribution from
the material. The relevant profiles are copied in Figs.
7(c) and 7(d). In Fig. 7(c) the interferometric signal at
t 5 0 for function No 16 does not vanish. Therefore the
spectral shaper, the laser spectrum, or the detector still
have some defects. The signal ratio at zero delay between code No 0 [Fig. 7(d)] and code No 16 [Fig. 7(c)] is
;16. This is consistent with the ratio of the correlation
signals, as observed in Figs. 7(a) and 7(b). Therefore in
the linear regime the material does not seem to contribute
to the false signal.
The residual distortion is at least partly attributed to
the nonuniformity and uncontrollable instability of both
spatial and spectral distributions of the laser beam. The
LCM interpixel dead zones may also contribute up to
;5%. Finally, the laser spectrum is still much broader
than the LCM window, which affects the interferometric
detection sensitivity.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
6. CONCLUSION
We have successfully engraved complex spectral shapes
in an organic PSHB material and have used them to perform temporal pattern recognition. In this experiment
the spectral definition was limited to 35 GHz, but it could
be improved to less than 10 GHz with the same shaping
technique. Comparison of the input pulse to a single reference pattern does not take full advantage of the
memory capabilities of the PSHB material. They actually open the way to the simultaneous comparison of the
input shape to a complete set of reference patterns. This
could be accomplished by combining space and frequency
selectivity, by storing each reference pattern, and by retrieving the corresponding cross-correlation signal, along
a specific k2 wave vector.24–26
16.
17.
18.
19.
20.
T. W. Mossberg, ‘‘Time-domain frequency-selective optical
data storage,’’ Opt. Lett. 7, 77–79 (1982).
A. Rebane, R. Kaarli, P. Saari, A. Anijalg, and K.
Timpmann, ‘‘Photochemical time-domain holography of
weak picosecond pulses,’’ Opt. Commun. 47, 173–176
(1983).
P. Saari, R. Kaarli, and A. Rebane, ‘‘Picosecond time- and
space-domain holography by photochemical hole-burning,’’
J. Opt. Soc. Am. B 3, 527–533 (1986).
A. Rebane, J. Aaviksoo, and J. Kuhl, ‘‘Storage and time reversal of femtosecond light signals via persistent spectral
hole burning holography,’’ Appl. Phys. Lett. 54, 93–95
(1989).
M. Mitsunaga, R. Yano, and N. Uesugi, ‘‘Time- and
frequency-domain hybrid optical memory: 1.6-kbit data
storage in Eu31:Y2SiO5,’’ Opt. Lett. 16, 1890–1892 (1991).
H. Lin, T. Wang, and T. W. Mossberg, ‘‘Demonstration of 8
Gbit/in2 areal storage density based on swept-carrier
frequency-selective optical memory,’’ Opt. Lett. 20, 1658–
1660 (1995).
A. Rebane, ‘‘Compression and recovery of temporal profiles
of picosecond light signals by persistent spectral holeburning holograms,’’ Opt. Commun. 67, 301–304 (1988).
H. Schwoerer, D. Erni, and A. Rebane, ‘‘Holography in
frequency-selective media. III. Spectral synthesis of arbitrary time-domain pulse shapes,’’ J. Opt. Soc. Am. B 12,
1083–1093 (1995).
K. D. Merkel and W. R. Babbitt, ‘‘Optical coherent transient
true-time-delay regenerator,’’ Opt. Lett. 21, 1102–1104
(1996).
T. Wang, H. Lin, and T. W. Mossberg, ‘‘Optical bit-rate conversion and bit-stream time reversal by the use of sweptcarrier frequency-selective optical data storage techniques,’’
Opt. Lett. 20, 2033–2035 (1995).
X. A. Shen, Y. S. Bai, and R. Kachru, ‘‘Reprogrammable optical matched filter for biphase-coded pulse compression,’’
Opt. Lett. 17, 1079–1081 (1992).
M. Zhu, W. R. Babbitt, and C. M. Jefferson, ‘‘Continuous coherent transient optical processing in a solid,’’ Opt. Lett.
20, 2514–2516 (1995).
M. Rätsep, M. Tian, I. Lorgeré, F. Grelet, and J.-L. Le
Gouët, ‘‘Fast random access to frequency-selective optical
memory,’’ Opt. Lett. 21, 83–85 (1996).
A. VanderLugt, ‘‘Signal detection by complex spatial filtering,’’ IEEE Trans. Inf. Theory IT-10, 139–145 (1964).
H. Sonajalg, A. Débarre, J.-L. Le Gouët, I. Lorgeré, and P.
Tchénio, ‘‘Phase-encoding technique in time-domain holography: theoretical estimation,’’ J. Opt. Soc. Am. B 12,
1448–1456 (1995).
A. Débarre, J.-C. Keller, J.-L. Le Gouët, A. Richard, and P.
Tchénio, ‘‘An amplitude correlator for broadband laser
source characterization,’’ Opt. Commun. 73, 309–313
(1989).
A. K. Jain, Fundamentals of Digital Image Processing
(Prentice-Hall, Englewood Cliffs, N.J., 1989).
C. Froehly, B. Colombeau, and M. Vampouille, ‘‘Shaping
and analysis of picosecond light pulses,’’ Prog. Opt. 20, 115–
121 (1983).
A. M. Weiner, D. E. Laird, J. S. Patel, and J. R. Wullert,
‘‘Programmable shaping of femtosecond optical pulses by
use of 128 element liquid crystal phase modulator,’’ IEEE J.
Quantum Electron. 28, 908–919 (1992).
I. Lorgeré, M. Rätsep, J.-L. Le Gouët, F. Grelet, M. Tian, A.
Débarre, and P. Tchénio, ‘‘Storage of a spectral shaped hologram in a frequency selective material,’’ J. Phys. B 28,
L565–L569 (1995).
82
21.
22.
23.
24.
J. Opt. Soc. Am. B / Vol. 16, No. 1 / January 1999
O. E. Martinez, ‘‘Grating and prism compressors in the case
of finite beam size,’’ J. Opt. Soc. Am. B 3, 929–934 (1986).
M. Tian, J. Zhang, I. Lorgeré, J.-P. Galaup, and J.-L. Le
Gouët, ‘‘Phototautomerization and broadband spectral holography,’’ J. Opt. Soc. Am. B 15, 2216–2225 (1998).
S. Volker and J. H. Van der Waals, ‘‘Laser-induced photochemical isomerization of free base porphyrin in a n-octane
crystal at 4.2 K,’’ Mol. Phys. 32, 1703–1718 (1976).
W. R. Babbitt and T. W. Mossberg, ‘‘Spatial routing of opti-
Tian et al.
25.
26.
cal beams through time-domain spatial-spectral filtering,’’
Opt. Lett. 20, 910–912 (1995).
T. Wang, H. Lin, and T. W. Mossberg, ‘‘Experimental demonstration of temporal-waveform-controlled spatial routing
of optical beams via spatial-spectral filtering,’’ Opt. Lett.
20, 2541–2543 (1995).
M. Ratsep, M. Tian, F. Grelet, J.-L. Le Gouët, C. Sigel, and
M.-L. Roblin, ‘‘Time-encoded spatial routing in a photorefractive crystal,’’ Opt. Lett. 21, 1292–1294 (1996).