**Optical pattern recognition with microlasers**

Eung Gi Paek

Optical pattern recognition has existed for approximately 45 years. The
computational power of optics to perform 2-D (two-dimensional) Fourier
transform, convolution and correlation at the speed of light is
certainly unique over other technologies. Many different system
architectures have been demonstrated to utilize the merits of optics.

However, the evolution of optical pattern recognition has been rather
slow and its performance often has been challenged by its counterpart,
digital computers. This was mainly due to the lack of suitable input
/output devices such as SLMs (spatial light modulators) and detectors
available in the market. Most of the input/output devices were developed
for other consumer applications and their speeds were usually limited to
conventional video rates (30 frames per second). With the rapid advances
in digital computers that can perform near-video-rate 2-D Fourier
transformation, higher speed devices are desperately needed in optical
information processing.

New device possibilities exist in optical pattern recognition and
information processing. Recent advances in optoelectronic device
technology include surface emitting microlaser arrays, among others,
which have a great potential for ultra-high speed (more than two orders
of magnitude faster than video rate) optical pattern recognition and ATM
header recognition due to their parallel computing capability.

The current status of the microlaser technology will be briefly reviewed
and possible applications of new devices for optical pattern recognition
and information processing will be described. Advances in these
technologies would contribute to the underlying device infrastructure
needed for advanced communications services, such as those sketched by
the National Information Initiative or "information superhighway".

12.1 Introduction: microlasers, surface emitting laser diode arrays, or
vertical-cavity surface emitting lasers

12.1.1 What is a surface emitting laser ?

Fig. 12.1 compares the surface emitting laser (SEL) diode \[Fig.
12.1(a)\] with the conventional edge emitting semiconductor diode laser
in a compact-disc player \[Fig. 12.1(b)\]. In a conventional edge
emitting laser diode, the laser beam emerges parallel to the active
layer. Therefore a two-dimensional (2-D) arrangement of lasers is
difficult. In contrast, the light from a SEL diode emerges perpendicular
to the active layer, allowing a 2-D stack of many lasers on a planar
wafer substrate. Iga and his co-workers first proposed and demonstrated
the feasibility of such SEL diodes in the late 1970's \[1,2\].

Fig. 12.1. (a) Vertical cavity surface emitting microlaser, (b) edge
emitting diode laser. (Reprinted from Ref. \[4\] by Jewell et al.)

12.1.2. What is a microlaser?

The original SEL's had a relatively large active volume (typically 10
μm^3^), requiring a large driving current. In May 1989, a miniaturized
surface emitting microlaser with a very small active volume (typically
0.05 μm^3^) than that of previous SEL's was developed \[3-7\]. As can be
seen in Fig. 12.2, a small hairlike structure with a diameter of only
1.5 μm is an independent laser. The hairlike structure consists of an
active layer surrounded by a pair of high-reflectivity mirrors on both
sides. The laser cavity is formed along the direction normal to the
wafer surface and laser light is emitted in either the top or the bottom
direction. Therefore such lasers are often called vertical cavity
surface emitting lasers (VCSEL's) to differentiate them from other
surface emitting lasers that have the cavity along the wafer surface.

The small size of the active layer of the device, which consists of very
thin (approximately 100 Α^0^) quantum well layers, requires a very low
driving current to turn on the laser. To compensate for the low gain
through the thin active region, the resonators at both ends of the
active medium should have extremely high reflectivity to minimize
losses, typically 99.9% or a finesse of 3000. This high-reflectivity
mirror and the efficient confinement of both electrons and photons
within a waveguide define the two major difficulties in fabricating
microlasers. We call such an array of microlasers a surface emitting
laser diode array (SELDA), or microlasers, in addition to the more
commonly used term, VCSEL.

Fig. 12.2. Scanning electron micrographs of vertical cavity surface
emitting microlasers. (VCSEL's, SELDA's or microlasers) (Reprinted from
Ref. \[4\] by Jewell et al.)

12.1.3 Why microlasers?

The microlaser has many good features that make it an excellent
candidate for optical information processing. Some of the important
features include:

-   Individual microlasers can be as small as a few micrometers. In
    addition, the surface emitting features allow 2-D integration of
    many lasers. Therefore approximately 10^6^ lasers can be arranged in
    a 1 cm^2^ chip area.

-   Because of the small volume of the active medium, the threshold
    current can be very low (up to a few microamperes), greatly reducing
    the power requirements of a system (compared with edge emitters,
    whose threshold currents are 5 mA to 20 mA).

-   The spectral linewidth of a microlaser is very narrow, typically
    less than 0.01 nm, for reasons that are explained below. Therefore a
    microlaser has a longer coherence length than a conventional Fabry
    Perot laser diode.

-   The beam profile of a microlaser is naturally circular. Therefore
    the beam can be directly used to illuminate optical components or
    spatial light modulators (SLM's) without requiring anamorphic prisms
    or lenses as in edge emitting lasers. In this way, a conventional
    gas laser and a pinhole spatial filter can be replaced by a simple
    microlaser, making a compact and robust system.

-   The manufacturing and test process of a microlaser is simple, once
    the crystal growth step is completed. Millions of microlasers can be
    obtained simultaneously. Moreover, microlasers can be easily tested
    in wafer form, whereas edge emitters must be cleaved before testing.
    Therefore microlasers have a potential for low-cost mass production.

Table 12.1 lists some of the differences between edge emitters and
surface emitters.

However, current microlasers have the following limitations:

-   The wavelengths of the microlasers are mostly limited to 0.75 μm -
    1.0 μm. Therefore a holographic recording with a microlaser is
    currently difficult because most of the holographic recording
    materials are sensitive to visible wavelengths.

-   Polarization of a microlaser is random or uncontrollable. This
    problem can be solved in a controllable manner by use of various
    methods, as explained in subsection 12.2.5.

-   The output power of a microlaser is not as high as that of an edge
    emitting laser diode.

-   The microlaser is still in its infancy; therefore extensive studies
    of packaging, addressing, and reliability are few compared with
    those of edge emitters.

Nonetheless, the microlaser is certainly one of the most important
photonic devices developed in this decade and will play an increasingly
important role in the future of optical information processing.
Currently, active research is being pursued over the world to overcome
these problems.

**12.2 Status of microlasers**

Below, the current status of microlasers related to optical information
processing is summarized.

12.2.1 Low threshold current

An important parameter used to characterize the power requirements of
any diode laser is its threshold current, the minimum current needed for
lasing. A low threshold current of 8.7 mA single quantum well \[8\] and
a low threshold voltage 1.33V VCSEL grown by metal-organic chemical
vapor deposition (MOCVD) were demonstrated \[9\]. An extremely large
power conversion efficiency of over 50% was also achieved \[10\]. Also,
a microlaser with a threshold current density of 80 A/cm^2^ was
demonstrated.\[11\]. An ultralow low threshold operation can be expected
with reduction in the active region volume until we meet the limitation
that is due to nonradiative recombination, and optical and electrical
confinement \[11,12\].

A thresholdless microlaser that does not have a threshold current like a
light emitting diode (LED) but still possesses narrow linewidths by
photon recycling has also been reported \[13\].

12.2.2 Coherence

Coherence is one of the most important attributes of a light source for
optical information processing and pattern recognition. The spectral
linewidth of a microlaser is very narrow \[14-16\]. This narrow
linewidth is attributed to the short cavity length of the microlaser
that can support only a single longitudinal mode, an effect similar to
that of a distributed-feedback (DFB) laser or a gas laser with a Fabry
Perot etalon. In addition, the high reflectivity of the reflector
functions as a spectral filter. Therefore a microlaser has a longer
coherence length than a conventional Fabry Perot laser diode (See Table
12.1). A short linewidth of 65 MHz has been measured with heterodyne
techniques for a microlaser (850 nm to 865 nm wavelengths) operated near
threshold \[15\]. This corresponds to a coherence length of 5 m
(0.00014nm linewidth) and is comparable with that of an Ar-ion laser
with an etalon.

Although microlasers operate inherently at a single longitudinal mode,
the coherence length still decreases at high current levels. This is due
to the multiple transverse modes at high currents. Fig. 12.3 illustrates
output light power versus current (L-I) and voltage versus current (V-I)
curves for a typical top-surface emitting gain-guiding microlaser
\[18\]. The apparent kinks in both curves are associated with changes in
the optical mode and corresponding carrier distributions. The first
threshold corresponds to the TEM~00~ lasing mode. The first plateau in
the L-I characteristic is associated with the saturation of the TEM~00~
mode. The subsequent threshold corresponds to the onset of the TEM~01\*~
mode. Lasing begins in the TEM~00~ mode, but further increases in the
current result in the occurrence of additional higher order transverse
modes. These higher-order transverse modes generates additional spectral
modes that are typically separated by approximately 0.7 nm, which
greatly reduces the coherence length and the beam profile of an expanded
beam.

Such a problem was solved with a spatial filtering technique, which was
achieved by a simple reduction in the contact aperture size with respect
to the width of the confinement (surrounded by the implantation) \[18\].
In this way, the kinks were eliminated and a single transverse mode
operation leading to a high coherence length was achieved even at high
current levels without sacrificing the output power (approximately 63%)
too much.

Also, each laser of the array operates independently; they are not phase
locked with each other \[19\].

Fig. 12.3. Light output power versus current and voltage versus current
curves of a typical microlaser. (Reprinted with permission from Ref.
\[18\] by Morgan et al., © 1993 IEEE.)

12.2.3 Visible microlasers

Current microlasers operate mainly in the wavelength range of 0.75
μm-1.0 μm which can be achieved with GaAs-based alloys. However,
researchers are developing shorter-wavelength microlasers. This is
motivated by the fact that the shorter wavelength would allow a larger
capacity of an optical storage medium as well as easy alignment. The
visible operation is crucial particularly for holographic information
processing because most holographic recording materials are sensitive to
only visible wavelengths.

The main difficulty in the fabrication of visible microlasers lies in
the creation of mirrors with high reflectance and low loss in the
visible region. Room-temperature lasing to wavelengths as short as 0.63
μm was demonstrated with InGaAlP alloys \[20-23\].

Recently an electrically pumped blue microlaser array was also
demonstrated \[24,25\]. Laser action was achieved at a wavelength of 484
nm under a pulsed-current injection at 77 K. The microlaser structure
was composed of a CdZnSe/ZnSe multiple-quantum-well active layer, ZnSe
cladding layers, and SiO~2~TiO~2~ distributed Bragg reflectors (DBR's).
This result shows promise of the microlaser for holographic information
processing based on photorefractive crystals, many of which are
sensitive at blue-green wavelengths. Likewise, additional work on
blue-green lasers with homoepitaxial deposition of ZnSe is currently
being pursued.

The recent demonstration of a blue laser diode by Nakamura at Nichia
Chemical Ind. Ltd. (Tokushima, Japan) \[26\] shows great promise in the
blue-green operation of the microlaser. The laser is II-VI based (GaN
material with InGaN multiple quantum wells) and is currently operated at
room temperature in a pulsed mode at 390 nm to 440 nm for an edge
emitting structure.

12.2.4 Two-dimensional addressing schemes

In a SELDA, more than 10^6^ lasers are available in a 1 cm X 1 cm area.
A major issue in operating such devices is their addressing scheme.
Three different approaches have been developed for 2-D addressing:
individual addressing, matrix addressing, and optical addressing.

Individual addressing is the most straightforward method and uses an
independent wire for each microlaser. This requires a tremendous amount
(N^2^, where N is the number of lasers along one direction) of wires and
pads and becomes impractical as N becomes large. Several individual
addressing schemes have been demonstrated \[27\].

Matrix addressing is the scheme most commonly used to address 2-D
devices such as liquid crystal displays or dynamic random access
memories (DRAM's). All the SEL's in the same row (or column) are
connected together with their common external wire pad. These rows and
columns are on the opposite side of the SEL's. To turn on a particular
SEL at (i, j), a voltage is applied across the i-th row and the j-th
column pad. This point-by-point addressing can be easily extended to
line-by-line addressing by the simultaneous application of voltages
across all the columns and a row. Such a matrix-addressing scheme
requires only 2N electrodes and is easy to fabricate. A monolithic 32 X
32 matrix addressable SELDA has been demonstrated by Orenstein et al.,
as shown in Fig. 12.4 \[28\]. Recently a high-density array of
microlasers with a spacing of 30 μm between neighboring lasers was
demonstrated \[29\].

Fig. 12.4. Matrix addressing of a microlaser array. (Reprinted with
permission from Ref. \[28\] by Orenstein et al., © 1991 IEE.)

Finally, an optical addressing scheme of a SELDA is shown in Fig. 12.5.
In this device, a 2-D image illuminating one side of a SELDA is detected
by an array of heterojunction photo-transistors (HPT's), and the current
generated by each HPT turns on the corresponding laser. This method
allows a complete parallel load of an image, without the need for
electrical connections. A monolithic array of such an optically
addressable SELDA has been demonstrated \[30\]. A similar concept had
been developed for LED's by various groups and was used for optical
information processing \[31-33\]. The output-light versus input-light
relationship is described below in Subsection 12.5.2.

Fig. 12.5. Optically addressable integrated SELDA: (a) structure of the
device, (b) light-output versus light-input relationship. (Reprinted
with permission from Ref. \[30\] by CHAN ET AL, APPLIED PHYSICS LETTERS,
**58,** 2342-2344, 1991. © 1991 American Institute of Physics.)

12.2.5 Polarization control

The output light from a microlaser is not linearly polarized. Therefore
polarization control is one of the most important subjects to be
resolved, especially for polarization-sensitive applications such as
magneto-optic disks and coherent detection systems. Recently it was
theoretically and experimentally predicted that the polarization of a
microlaser grown on an (n11)-oriented substrate could be simply
controlled by use of its intrinsic in-plane anisotropic gain
distribution characteristics \[34\]. Stable polarization characteristics
based on the prediction were realized for a conventional microlaser
structure \[35\].

12.2.6 Multiple wavelengths

Multiple wavelengths and tuning are highly desirable in optical
information processing and communications. A 2-D multicolor SELDA
(MC-SELDA) is a 2-D array of microlasers, each with its own wavelength.
Fig. 12.6(a) shows a monolithic 2-D MC-SELDA originally demonstrated by
Chang-Hasnain et al. \[36\]. The 7 X 20 array has a total of 140
microlasers, and each laser has a unique wavelength that is uniformly
separated from its neighbors by 0.3 nm, spanning a total wavelength of
43 nm. Such a wavelength variation was obtained by varying the laser
cavity lengths when growing the wafers as shown in Fig. 12.6 (b).

More recently, the same group demonstrated a record wavelength span of
62.7 nm by using a modified patterned-substrate growth technique in a
molecular beam epitaxy system \[37\]. The authors claim highly uniform
threshold currents with an average of approximately 2 mA with a high
repeatability of wavelength spacing and a sharp wavelength-shift rate of
117.14 nm/mm.

Fig. 12.6. 2-D MC-SELDA: (a) device, (b)wafer. (Reprinted with
permission from Ref. \[36\] by Chang-Hasnain et al., © 1991 IEEE.)

12.2.7 Wavelength tuning

Continuously tunable lasers have a huge number of potential
applications. These range from free-space optical interconnects and
wavelength-division multiplexing for communications to holographic data
storage and spectroscopy. The microlasers can be tuned in the same way
as for edge emitting lasers by varying the drive current applied to
them. Recently a new method of wavelength tuning based on a deformable
membrane mirror has been demonstrated \[38\]. As shown in Fig. 12.7, the
mirror is fabricated at the end of a light emitting cavity, with a small
air gap separating the two. As the mirror moves back and forth, the
length of the cavity changes, resulting in a change in the resonant
wavelength. A tuning range of 15 nm has been demonstrated using the
method. Currently, the device requires extremely high threshold current,
37 mA to 64 mA and thus had to be operated in pulsed mode, rather than
continuous wave.

Fig. 12.7. Wavelength tuning of a microlaser by a deformable membrane
mirror. (Reprinted with permission from Ref. \[38\] by Wu et al, © 1991
IEE.)

12.2.8 Efficiency

High electrical-to-optical power conversion (wall-plug) efficiency is
one of the most important parameters for estimating power consumption.
Microlasers suffer from poor wall-plug efficiencies because of excessive
voltage drops across the DBR's. However, recent overall cw power
efficiencies have approached 20% \[39\]. Also, dramatic improvements in
microlaser power conversion efficiency of up to 50% at low currents have
been realized \[40\] with an index-guided top-emitting structure based
on selective oxidation. The efficiencies demonstrated are at least
comparable with those of edge emitting lasers.

12.2.9 Modulation speed

The injection current modulation bandwidth of small microlasers has been
predicted to be very high (\>100 GHz) for the following reasons \[41\] :

-   For a give injection current, the small volume of a microlaser leads
    to a large photon density and hence a short stimulated lifetime.

-   Cavity quantum electrodynamic effects have been expected to increase
    the differential gain, because of an enhancement of the emission
    rate into the lasing mode. Recent measurements indicate a fast
    intrinsic response, with a 3-dB modulation bandwidth of more than 50
    GHz \[42\].

-   Recent analyses indicate that a microlaser, under the constraint of
    nonlinear gain or current density limitations, has the same
    intrinsic modulation bandwidth as conventional edge emitting lasers
    with the same cavity losses and photon density \[43\]

12.2.10 High power output

In spite of the small size of the microlaser, it can be operated at
reasonably high power levels. A cw output of more than 100 mW with a
wall plug efficiency of 20% has been demonstrated by a group at the
University of California at Santa Barbara; they tailored the laser's
operation to increased temperatures \[44\]. Also, 1-W pulsed operation
has been demonstrated with a top-surface emitting 100μm X 100 μm
broad-area laser with a grid contact segregating the laser into a 10 X
10 array of 8 μm X 8 μm emission windows \[45\].

**12.3 Optical correlators with microlasers**

**12.3.1 Introduction**

Pattern recognition has long been one of the major applications of
optics. The capability of computing a complicated operation, such as a
2-D Fourier transform, convolution, and correlation based on the wave
nature of optics, has provided a strong tool for this application.
Correlation is an operation that calculates the similarity of two
patterns and is widely used for pattern recognition. It is represented
by an equation $g(x,y) = \iint_{}^{}{f(x,h) \cdot h(x - x,h - y)dxdh}$,
where $f,h$ and $g$refer to an input, a filter, and a correlation
output, respectively. Therefore summation and shift are two basic
operations in calculating correlations.

**12.3.2 Classification of optical pattern recognition systems**

Optical correlators have been around since the early 1950's. Although
most of the current optical correlators are based on the coherent
optical processors (either the VanderLugt or the joint transform
correlator), there are many other types of correlators, as is shown in
Fig. 12.8. Below, a brief description of each of the systems is
provided. More detailed analyses can be found in various Ref's
\[46-48\].

Fig. 12.8. Classification of optical correlators. TDI, time delay and
integration.

\(1\) Kretzmer-type correlator \[49\]: This is probably the oldest and
most straightforward correlator developed in the early 1950's. In the
system, summation is achieved spatially by an optical lens and is
detected by a single detector. Also, a shift operation is achieved by
one (or both) of the inputs is mechanically moved along both the x and
the y directions. Such a movement can be achieved by an acousto-optic
beam deflector in which the signal flows through the one-dimensioal
medium. Unfortunately, there are no fast 2-D image shifters, currently.

\(2\) Shadow casting \[50-52\]: In this system architecture, both
shift-and-add operations are done in an all-optical fashion
simultaneously. The problems with such a system are diffraction effects
and no room for the spatial filtering operation. Microlasers, even with
their natural 2-D nature, can find limited application for this type of
correlator because of the diffraction effect that is due to the high
coherence of the light from microlasers.

\(3\) Electro-optic correlator with a time-delay-and-integration-mode
CCD \[53,54\]: In this system, an input signal $f(t)$is temporal and is
emitted from a point source such as an LED or a laser diode. The
reference signal $h(x)$ is recorded in an SLM that is in contact with
(or imaged to) a time-delay-and-integration-mode CCD sensor. Both the
input signal and the CCD are synchronized and systolically perform the
shift-and-add operation to calculate the correlation.

\(4\) Electro-optic correlator with a normal CCD: This system is
equivalent to the system in (3) except that the
time-delay-and-integration-mode CCD is replaced by a moving reference
signal and a normal CCD.

\(5\) VanderLugt correlator \[55\]: This architecture has probably been
the most commonly used architecture for optical pattern recognition.
Pattern recognition is achieved in two steps: (1) holographic filter
fabrication and (2) processing. In the first holographic filter
fabrication step, a matched filter for a given reference image is
holographically fabricated with the Fourier transform holographic
recording technique. In the processing step, if an input matches the
reference image, the wave-front distortion generated by an input pattern
is canceled out and a plane wave is generated. The plane wave is then
focused to a point at the focal plane of the second lens.

The system has been successful because of the high signal-to-noise ratio
(SNR) that can be achieved with additional spatial filtering that can be
easily achieved in the system. Also, once a holographic filter is
fabricated, it is fully nonblocking without requiring a
photon-to-electron conversion process that can lead to speed bottleneck.

However, the system requires an input from high-optical-quality
recording materials and a holographic filter to preserve shift-invariant
recognition. The filter has to be positioned exactly in the original
position in which it was recorded. Also, the holographic filter must be
positioned exactly in the focal plane of the Fourier transform lens.
Recent advances in high-quality SLM's and in situ holographic recording
materials allow a convenient implementation of such an optical
correlator with high performance.

\(6\) Joint transform correlator \[56,57\]: The joint transform
correlator has become popular these days because it is simple to
implement and real-time operation is possible with currently available
devices (SLM's and 2-D CCD's) \[58\].

The operation of the joint transform correlator can be considered a
two-step Fourier spectrum (modulus square of a Fourier transform)
generation. At first, both an input and a reference image are located in
the input plane (spatial domain) side by side. The Fourier spectrum of
the two inputs is recorded in a high-resolution recording material. The
Fourier spectrum of the two inputs is Fourier transformed again by the
second Fourier spectrum generator. The first order diffraction outputs
from the second Fourier spectrum generator are the correlations of the
input and the reference images.

Optics can perform a real-time Fourier spectrum generation quite well in
a simple and low-cost setup consisting of a laser, an SLM, a 2-D image
sensor, such as a CCD, and a spherical lens.

The advantages of the system are that it allows easy real-time
implementation of a correlator with currently available devices and it
does not require accurate filter positioning. Also, as in a VanderLugt
correlator, various spatial filtering operations such as bipolar
phase-only filtering can be incorporated \[59-61\]. Moreover, one can
use different wavelengths for hologram recording and readout without
requiring careful alignment.

The disadvantages are that it requires a fast and high resolution
holographic recording material and the correlator is not all-optical,
requiring intermediate photon-to-electron conversion processes.

The recent photorefractive semi-insulating multiple-quantum-well SLM
developed by A. Partovi et al. \[62\] has many desirable features
suitable for such correlators. It has high speed (a several microseconds
for 280 mW/cm^2^ at 600nm - 850 nm), high sensitivity (0.8 μJ/cm^2^ to
allow the use of a low power laser diode), high efficiency (3%), low
operational voltage (20 V), a large index change (0.06), and a
reasonable resolution (50 lines/mm). A high-speed joint transform
correlator that uses this device has been successfully demonstrated
\[63\]. The system uses a low power laser diode (3 mW) and is capable of
3 X 10^5^ correlations/s. When the system is incorporated with a fast
ferroelectric liquid crystal SLM and a fast detector, several thousand
correlations can be achieved within a second. This speed is about two
orders of magnitude faster than that of digital computers.

Although the above correlators are described in one-dimensional terms,
many combinations of the above architectures are possible \[64,65\]. The
classical holographic pattern recognition system in (5) has had limited
application because it is bulky and is too sensitive to misalignment,
input recording materials, and filters. Such problems can be greatly
alleviated with a SELDA. Two recently developed correlators based on
microlasers are introduced below.

**12.3.3 Multichannel optical correlator based on a mutually incoherent
microlaser array**

Yang and Gregory \[66\] demonstrated a multichannel optical correlator
by using the mutually incoherent property of a microlaser array to
improve the performance of an optical correlator with respect to
immunity to coherent noise and a high SNR as well as high light
throughput. As shown in Fig. 12.9, an optical correlator is incoherently
duplicated by an array of light sources to increase the SNR.

Fig. 12.9. Multichannel optical correlator with a mutually incoherent
microlaser array. FT, Fourier transform. (Reprinted from Ref. \[66\] by
Yang and Gregory, © 1995 Optical Society of America.)

In the system, the Fourier spectra due to different microlasers can
overlap one another if the separations between neighboring microlasers
are adjusted to match the period of an SLM in the filter plane. Although
a matched filter was synthesized with a single reference pattern, it is
duplicated at many periodic locations in the Fourier plane and matches
the multiple input spectra. In this way, an efficient space-bandwidth
product in the filter plane is increased and sharper correlation peaks
are obtained.

Such an approach would be extremely useful for increasing the
reliability of a conventional optical correlator. The only practical
issues here are generation of reference beams that are coherent with
object beams to record holograms and the removal of undesired fringes in
an autocorrelation peak. The authors suggested a
time-division-multiplexing (TDM) scheme as a way to eliminate
interference fringes.

**12.3.4 Compact and robust incoherent correlator**

As explained above, the light from a microlaser is highly monochromatic.
However, the phases of the light from the microlasers are not locked
with each other. These two unique coherence properties (temporally
highly coherent and spatially incoherent) make a SELDA an ideal light
source for implementing a compact and robust incoherent correlator.

Fig. 12.10. Compact and robust incoherent correlator: (a) system, (b)
experimental results.

Fig. 12.10 (a) shows an example of the microlaser-based incoherent
correlator \[67\]. The light from each SEL is collimated by lens L1 and
illuminates the hologram to reconstruct holographic images on the output
plane which is located at the focal plane of lens L2. The image
generated by each SEL is shifted by the amount that corresponds to the
position of the SEL. The reconstructed images generated by the light
from different SEL\'s are added up incoherently because each laser
operates independently, averaging out the phase-sensitive interference
terms. The eventual summation of all the reconstructed images generated
by all the SEL\'s in the input plane gives the correlation between the
input and the reference image stored on the hologram. Because the system
does not involve any moving parts (e.g., rotating diffuser) or bulky
optical components, the whole system can be miniaturized and integrated
with semiconductor technologies.

Fig. 12.10 (b) shows the correlation output obtained from the SELDA
correlator. A holographic filter was fabricated for the input pattern
(Bell logo) and was tested for the two input patterns (the Bell logo and
a Chinese character meaning light). For the correct input \[Bell logo
(middle)\], a bright autocorrelation peak appears at the center of the
correlation output (middle, right). On the other hand, for the incorrect
input \[Chinese character (bottom)\], a cross-correlation is obtained
(bottom, right). As shown in the figure, the cross-correlation signal is
much weaker than the autocorrelation peak, allowing a satisfactory
discrimination between the two input patterns.

**12.4 Holographic memory readout with microlasers**

12.4.1 Introduction

Volume holographic memory has been extensively investigated in the past
as a way of massively storing media to allow fast random access
page-organized memory \[68-72\]. This volume holographic memory has
reawakened its interest recently because of the immense demand for
storage media with fast access and a large storage capacity for
applications such as multimedia. However, the holographic system
normally requires bulky and complicated beam deflectors to steer the
beam direction from one to another, corresponding to the desired page.
Moreover, speed and resolution of a beam deflector are quite limited.

12.4.2 Compact and ultrafast holographic memory with a SELDA

Such traditional problems can be solved with a SELDA\[73\]. As is
explicitly shown in Fig. 12.11, a SELDA combined with a simple
collimating lens can function as an efficient multiple beam steerer to
change the beam direction from one to the other. Such beam steering can
be achieved within one nanosecond, compared to the switching speed of
the microlasers. This ultrafast beam steering is used to reconstruct
angular-multiplexed holographic memories in which each image is recorded
using the second beam (reference beam) propagating along a different
angle. By using this simple and compact optical setup, any frame can be
randomly accessed within one billionth of a second.

Fig. 12.11. Compact and ultrafast holographic memory with a microlaser
array.

In the experimental results shown in Fig. 12.11, memories are recorded
in a volume hologram (LiNbO3 crystal, 0.01% Fe doped) that can provide a
large storage capacity of around ten billion bits because of the third
dimension available in a volume storage medium. The figures on the
right-handed side show the images retrieved from the volume hologram by
the light from a SELDA. Each laser is separated from the adjacent one by
70 μm, corresponding to an angular separation of about 0.04^0^. As can
be seen in the figure, the two independent lasers separated by only 70
μm reconstruct totally different images. In this way, each tiny
microlaser can be matched to a separate page, allowing the array to form
a selective address generator.

12.4.3 Combined angular and wavelength multiplexing with a
two-dimensional MC-SELDA

In general, angular multiplexing can be achieved along one direction in
a plane formed by both reference and object beam directions because of
the degeneracy effect. As can be seen in Fig. 12.12 (a), the Bragg
condition is satisfied by waves that have any of the directions that
form the surface of a cone (the shaded area in the figure) whose axis is
normal to the grating planes \[74\]. This degeneracy causes cross-talk
along the direction perpendicular to the Bragg direction. However, this
cross-talk can be greatly reduced by use of different wavelengths along
the degenerate directions, as shown in Fig. 12.12(b). Such a concept has
been recently demonstrated with five different wavelengths to record a
total of 2000 holograms: five different wavelengths with 400 angularly
multiplexed images for each wavelength \[75\].

Fig. 12.12. Breaking degeneracy by use of multiple wavelengths.

The concept can also be implemented in a compact and ultrafast fashion
by a 2-D MC-SELDA, as shown in Fig. 12.13. The SELDA has the same
wavelength along the angular-multiplexing direction and different
wavelengths along the degeneracy direction. In addition, such a
combinational multiplexing with a MC-SELDA has an additional angular
separation effect along the degenerate direction because each microlaser
lies in a different position. In this way, the storage capacity of a
volume hologram can be greatly increased in a compact and ultrafast
readout system within the total limit imposed by the available number of
charge carriers in a medium and the theoretical limit of V/l^3^ , as is
proved by Lee et al. \[76\] and Psaltis et al. \[77\].

Fig. 12.13. Compact and ultrafast holographic memory readout with 2-D
(Angle + Wavelength) multiplexing by a 2-D MC-SELDA.

12.4.4 Incoherent /coherent multiplexing with a SELDA

An incoherent /coherent multiplexing approach to reduce the noise due to
multiplexing by use of an array of microlasers has been developed by
Jenkins and Tanguay \[78\]. The concept of the method can be understood
as follows:

When multiple gratings are recorded simultaneously by a coherent light
source, all the cross terms are added coherently. In other words, the
amplitudes of all the gratings are summed first and squared later. As a
result, the number of noise gratings (or the number of cross-talk terms)
becomes N^2^ , where N is the number of gratings. On the other hand, as
in this proposed method, if each grating is recorded sequentially one by
one, the cross-terms are incoherently added (each grating amplitude is
squared first and summed over all the gratings later), and thus the
number of noise gratings becomes N; therefore cross-talk can be greatly
reduced. Such an incoherent recording can be achieved simultaneously
with an array of independent (not phase locked with each other) coherent
light sources, such as an SELDA. Jenkins and Tanguay applied this noise
reduction method to photonic interconnection and holographic optical
elements for 2-D wavelength-division multiplexing applications.

This technology of using microlasers for holographic storage will be
extremely useful when suitable holographic recording materials become
available in the future. Recent developments in biological holographic
recording materials, such as bacterial rhodopsin, show a great new
promise for future computers \[79\].

**12.5 Microlasers for holographic associative memory**

12.5.1 Introduction

Recent advances in neural networks opened many new possibilities for
optical information processing for broad application areas \[80-82\].
Optics, especially coherent optics, has found an excellent match in
implementing the neural networks that require parallel and analog
computing.

Fig. 12.14 illustrates an associative memory for word-break recognition
to generate a readable text from a continuous string of words. In the
system, an input word stream is presented at the input plane of the
system. Autocorrelation peaks that appear at places where there is a
match between the input and the memory words pre-recorded in a hologram
are detected. All the spurious sidelobes are removed by a threshold
operation in the correlation plane. Next, the separation between the
peaks is magnified along the word direction. This stretched correlation
output is reflected back to illuminate the hologram and reconstruct the
whole memory at the output plane. The output through a window that is
situated at the origin of the output plane is the desired readable text,
with all the errors corrected and spaces inserted between words.

Fig. 12.14. Holographic associative memory for word-break recognition.

12.5.2 Holographic neurons

Such a neural network system normally consists of three parts: (1) a
recognition part to compare an input with all the memories, (2) a
reconstruction part to retrieve the corresponding memory, and (3)
nonlinear thresholding elements to make decisions. Recognition (pattern
recognition in subsection 12.3.2) and reconstruction (holographic memory
in 12.3.1.) have already been described. Below, we focus on the third
part, nonlinear thresholding elements, or so called optical neurons.

There has been much research done on optical neurons. Recently an
integrated vertical-cavity surface emitting microlaser array with HPT's
to yield optically controlled lasers has been demonstrated by Chan et
al.\[30\]. The structure of the device is shown in Fig. 12.5, as
explained above. Fig. 12.5(b) shows the output vesus input optical power
relationship for various bias voltages. As shown in the figure, the
device displays a suitable nonlinear threshold function as an optical
neuron with the threshold input optical power of 0.1 mW (at the
wavelength of 855 nm). It also provides an optical gain of approximately
5, making it an excellent candidate for an optical neuron array.

Besides its nonlinear threshold function, the output light from the
optical neuron is coherent. It is a laser; therefore, it can reconstruct
any type of hologram. In Fig. 12.15(a), the neuron with an input power
above threshold is fired to reconstruct the corresponding memory. Fig.
12.15(b) shows an experimental result. If the output light signal is
below threshold, nothing appears in the output plane (left). On the
other hand, as soon as the input light is increased above the threshold
level, the neuron is fired and the corresponding holographic memory is
retrieved (right).

Fig. 12.15. Holographic memory readout with an array of holographic
neurons: (a) system, (b) experimental results.

12.5.3 Microlaser-based holographic associative memory

When the optical neurons are combined with both recognition and
reconstruction parts, which were demonstrated above, in a simple
two-lens system, a compact, ultrafast, and highly efficient neural
network system may be implemented in the future. Furthermore, the bulk
lenses can be replaced by planar zone plates, allowing the integration
of the whole system into the smallest scale possible.

12.5.4 Holographic associative memory with time-division multiplexing

In previous work on holographic memory readout with a SELDA, it has been
shown that the memory is capable of retrieving a 2-D information with
approximately 10^5^ bits within 1 ns, with a total storage capacity of
10^11^ - 10^12^ bits in 1 cm^3^. However, the question is how to detect
such ultrafast information, 10^14^ bits/s or 100 Tbits/s. This is
certainly difficult, first because the speed of the current 2-D image
sensor is much slower than one billion frames pre second, and second
because the light emitted from each microlaser for only 1 ns has to be
distributed over a 2-D image, creating a light budget problem.

However, whether one can detect it or not, the retrieved information
exists in the output plane. So the question is how to utilize that fast
information. Fig. 12.16 shows one possible example of utilizing the
ultrafast information with currently available devices. In this figure,
an input transparency is placed on the plane where memories are
retrieved, and the light passing through the input is collected by a
single detector with a lens to obtain the inner product of the input and
the retrieved memory. The speed of the single detector matches that of a
microlaser. Furthermore, because a significant portion of the light from
a microlaser is focused to the single detector, serious light budget
problems can be avoided.

Fig. 12.16. Time division multiplexing-based holographic associative
memory with a SELDA.

Such a TDM system can be extended to an associative memory by the
addition of a feedback loop, as in Fig. 12.16. Let us assume that a
whole encyclopedia is recorded in the volume holographic memory and
partial information on one of the pages is presented in the input plane.
As each microlaser is turned on, the corresponding page is retrieved and
is instantly compared with the input. As soon as the memory that matches
the input appears, the inner product value reaches above a certain
threshold level and latches the microlaser, The light from the matched
microlaser reconstructs the complete information on the corresponding
page on the output plane. In this way, the advantages of optics can be
fully utilized even with currently available devices.

12.6 Integration and packaging

To answer the issue of how to align and package a complex optical system
in free space optics, a planar integration technology has been developed
\[86-90\]. As can be seen in Fig. 12.17, the free-space coherent optical
processor in Fig. 12.17 (a) can be integrated to a planar module as
shown in Fig. 12.17 (b).

Fig. 12.17. Planar integration of a coherent optical processor (a)
coherent optical processor; (b) planar integration. (Reprinted from Ref.
\[86\] by Jahns et al.© 1995 Optical Society of America.)

The main motivation for this approach is to culminate the
well-established high-precision lithographic technology that has been
extremely successful in leading to the mass production of semiconductor
components. In this way, optical systems may be designed with a
computer-aided-design tool and mass produced by a foundry with the same
or a similar technology as that of conventional semiconductors. The main
benefits of using such an integrated module are

-   Compatibility with semiconductor fabrication technology

-   A compact and robust system that does not require any alignment.

-   Because all components are on a common substrate, the whole system
    is very stable with respect to changes in temperature, dust,
    humidity, etc.

-   High-precision (close to 1-μm accuracy) prealignment that can avoid
    time-consuming alignments each time.

-   Possibility of placing all alignment-critical components on one side
    of the substrate.

-   Easy integration with other semiconductor components that share the
    same technology.

-   Easy mass production.

However, the approach also raises several issues to be resolved, i.e.,

-   Aberrations that are due to the oblique angles of light propagation,
    or off-axis holographic optical elements.

-   Limited optical path lengths are available on a thin substrate.

-   A high resolution lithographic technique is required for fabricating
    high-quality (large space-bandwidth product) diffractive optical
    elements to replace conventional bulk lenses in this approach. This
    is even more serious in this case than in conventional diffractive
    optical components in free-space optics because the light path
    length is short and all the other components need to be scaled down
    accordingly.

A hybrid integration of a microlaser chip and a planar optics substrate
has been implemented \[89\]. In the system, a top-surface emitting
microlaser array (9μm diameter, 85μm spacing, and 850nm wavelength) was
bonded to a single quartz glass substrate by the flip-chip bonding
technique with indium solder bumps. The lenses were lithographically
fabricated by the diffractive optical element technique with four phase
levels. They have a square shape with a size of 500μm X 500μm. Their
focal lengths match the thickness of the glass substrate, which is 3 mm.
Surrounding areas are coated with a Ge film to absorb any undesired
stray light. The deflection angle relative to the normal is limited by
the resolution of the lithographic process; it was 6.2^o^ in this
experiment.

Various other approaches along similar lines have been proposed and
implemented \[91-93\].

**12.7 Conclusion**

Optical pattern recognition has often been superseded by the rapidly
growing digital computer technology that approaches near-real-time
processing. However, it should be noted that the computational power of
optics to compute 2-D Fourier transformation, convolution, and
correlation at the speed of light is still unique and is not expected to
be surpassed by other technologies. Even with current device
technologies, optical pattern recognition can achieve more than 1,000
image comparisons per second. Extrapolating the developmental speed of
digital computers doubling every two years, 1000 high resolution image
comparisons per second (about two orders of magnitude faster than what
is available now) would require another 15 years or so and will not be
attained by the year 2010. Before then, the explosion of information in
the form of multimedia through the internet will increasingly demand
faster and faster image comparisons and understanding, for which optical
pattern recognition can provide many opportunities.

Fortunately photonic technology forms the backbone of the current
communication technology. The current transmission speed of an optical
signal is moving beyond 1 THz, much faster than the clock speed of a
digital computer. Total available optical bandwidths can be as high as
25 THz at the communication wavelengths. These bandwidths give a clear
edge to optics-based information technology for storage, displays, and
processing. In this regard, optical pattern recognition has a bright
future if it is closely tied to other photonic technologies and takes
advantage of new photonic devices. For example, the developmental speed
of SLM's has been much slower than that of photonic devices for
communications.

Undoubtedly, surface emitting microlasers will have rich new
possibilities for pattern recognition as the device technology becomes
mature enough to allow low (of the order of microwatts) power
consumption per laser, high reliability, integration with other devices,
and suitable addressing schemes for high density arrays, etc.

Current optical pattern recognition systems need to be greatly improved
in terms of not just speed but of accuracy. This accuracy requires the
development of elaborate measurement methods to calibrate and test
performances. Such test and measurement issues need to be seriously
addressed in the future before any optical systems are to be used for
practical purposes.

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  ----------------- -------------------------- ---------------------------
                    Edge Emitter               Surface Emitter

  Size (μm)         300 X 3 X 3                10 X 10 X 5

  Active layer (μm) 300 X 3 X 0.1              10 X 10 X 0.01

  Threshold current 5 - 20 mA                  A few microamperes to
                                               several milliamperes

  Reflector         Cleaved, 30 % reflectivity High reflectivity (99.9%)

  Fabry Perot       Long cavity, small spacing Short cavity, large spacing
  spacing                                      

  Single mode       Transverse easier          Single longitudinal mode

  Beam profile      Elliptical                 Circular

  Output power      up to 4 W (cw)             up to 100 mW (CW), 1 W
                                               (pulsed)

  Polarization      Easy control               Requires special control

  2-D Integration   Difficult                  Easy

  Fabrication and   Requires cleave before     Easy on-chip testing
  testing           test                       
  ----------------- -------------------------- ---------------------------

Table 12.1. Comparison of edge emitting laser diodes and surface
emitting laser diodes

**Figure captions**

Fig. 12.1. (a) Vertical cavity surface emitting microlaser, (b) edge
emitting diode laser. (Reprinted from Ref. \[4\] by Jewell et al.)

Fig. 12.2. Scanning electron micrographs of vertical cavity surface
emitting microlasers. (VCSEL's, SELDA's or microlasers) (Reprinted from
Ref. \[4\] by Jewell et al.)

Fig. 12.3. Light output power versus current and voltage versus current
curves of a typical microlaser. (Reprinted with permission from Ref.
\[18\] by Morgan et al., © 1993 IEEE.)

Fig. 12.4. Matrix addressing of a microlaser array. (Reprinted with
permission from Ref. \[28\] by Orenstein et al., © 1991 IEE.)

Fig. 12.5. Optically addressable integrated SELDA: (a) structure of the
device, (b) light-output versus light-input relationship. (Reprinted
with permission from Ref. \[30\] by CHAN ET AL, APPLIED PHYSICS LETTERS,
**58,** 2342-2344, 1991. © 1991 American Institute of Physics.)

Fig. 12.6. 2-D MC-SELDA: (a) device, (b)wafer. (Reprinted with
permission from Ref. \[36\] by Chang-Hasnain et al., © 1991 IEEE.)

Fig. 12.7. Wavelength tuning of a microlaser by a deformable membrane
mirror. (Reprinted with permission from Ref. \[38\] by Wu et al, © 1991
IEE.)

Fig. 12.8. Classification of optical correlators. TDI, time delay and
integration.

Fig. 12.9. Multichannel optical correlator with a mutually incoherent
microlaser array. FT, Fourier transform. (Reprinted from Ref. \[66\] by
Yang and Gregory, © 1995 Optical Society of America.)

Fig. 12.10. Compact and robust incoherent correlator: (a) system, (b)
experimental results.

Fig. 12.11. Compact and ultrafast holographic memory with a microlaser
array.

Fig. 12.12. Breaking degeneracy by use of multiple wavelengths.

Fig. 12.13. Compact and ultrafast holographic memory readout with 2-D
(Angle + Wavelength) multiplexing by a 2-D MC-SELDA.

Fig. 12.14. Holographic associative memory for word-break recognition.

Fig. 12.15. Holographic memory readout with an array of holographic
neurons: (a) system, (b) experimental results.

Fig. 12.16. Time division multiplexing-based holographic associative
memory with a SELDA.

Fig. 12.17. Planar integration of a coherent optical processor (a)
coherent optical processor; (b) planar integration. (Reprinted from Ref.
\[86\] by Jahns et al.© 1995 Optical Society of America.)