Coherent Transient Systems Evaluation

Abstract

This final report of contract F49620-91-C-0088 describes the development of the analytical tools required to evaluate optical coherent transient memory, triple-product correlator, and continuous signal processor systems. One key tool is a coherent transient simulator based on the optical Bloch equations. The coherent transient output signal that results from an arbitrary sequence of pulses, each having an arbitrary amplitude, duration, center frequency, chirp, phase, and timing can be calculated. The simulator was used to study excitation pulse saturation and it effects on the output signal efficiency and fidelity and to study frequency chirped reference pulse saturation. Analytical tools were developed to assess the effects of local heating and spatial crosstalk. A performance evaluation of a coherent transient continuous optical correlator is reported, along with new implementation techniques. The continuous processor's predicted time-bandwidth product, data bandwidth, and pattern storage density are 10000, 5 GHz, and 100000 patterns per square centimeter, respectively. A proof of concept demonstration of the continuous optical processor was performed in europium doped yttrium silicate in collaboration with IBM Almaden Research Center. Research into divalent ion doped crystals as photon gated materials for coherent transient systems was performed.

Full text

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193l
Final
Report
of the
C
Coherent
Transient
Systems
Evaluation
F49620-91-C-0088
Win.
Randall
Babbitt
Boeing
Defense
&
Space
Group
1993
fD~
Air
Force
Office
of
Scientific
Research
93-20266

FAC
84-56
MARCH
7,1990
53.301-298
FEDERAL
ACQUISITION
REGULATION
(FAR)
Form
Approved
REPORT
DOCUMENTATION
PAGE
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0704-0188
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20503.
1.
AGENCY USE
ONLY
(Leave
blank)
2.
REPORT
DATE
3.
REPORT
TYPE AND
OATES
COVERED
,17
Jun
1993
T
Final
Report:
1
Sep
91
-
7
Jun
93
4.
TITLE
AND
SUBTITLE
S.
FUNDING NUMBERS
Final
Report
on
the
Contract
Coherent Transients
Systems
Evaluation
F49620-91
-C-0088
6.
AUTHOR(S)
Dr.
Wm.
Randall
Babbitt
7.
PERFORMING
ORGANIZATION
NAME(S) AND
ADDRESS(ES)
B.
PERFORMING
ORGANIZATION
REPORT
NUMBER
Boeing
Defense
&
Space
Group
9-5554-WRB93-012
P.O.
Box
3999 7J-91
Seattle,
WA
98124-2499
"9.
SPONSORING/ MONITORING
AGENCY
NAME(S)
AND
ADDRESS(ES)
10.
SPONSORING/'MONITORING
•!
AGENC
REPORT
NUMBER
Air
Force
Office
of
Scientific
Research
Building
410
Boiling AFB
DC
20332-6448
_
11.
SUPPLEMENTARY
NOTES
"12a.
DISTRIBUTION
/AVAILABILITY
STATEMENT
12b.
DISTRIBUTION
CODE
13.
ABSTRACT
(Maximum
200
words)
This
final
report
of
contract
F49620-9
1
-C-0088
describes
the
development
of
the
analytical tools
required
to
evaluate
optical
coherent
transient
memory,
triple-product correlator,
and
continuous
signal
processor
systems.
One
key
tool is
a
coherent transient
simulator
based
on
the
optical
Bloch
equations. The
coherent
transient
output
signal
that
results
from
an
arbitrary
sequence
of
pulses,
each
having
an
arbitrary
amplitude,
duration,
center
frequency,
chirp, phase,
and
timing
can
be
calculated.
The
simulator
was
used
to study
excitation
pulse
saturation
and
it
effects
on
the
output
signal
efficiency
and fidelity and to
study
frequency
chirped reference
pulse
saturation.
Analytical
tools
were
developed
to
assess
the
effects
of
local
heating
and
spatial
crosstalk.
A
performance
evaluation
of
a
coherent transient continuous optical
correlator
is
reported,
along
with
new
implementation
techniques.
The continuous
processor's
predicted
time-bandwidth
product,
data
bandwidth,
and pattern
storage density are
10000,
5
GHz,
and
100000
patterns
per
square
centimeter,
respectively.
A
proof
of
concept demonstration
of
the
continuous
optical
processor
was
performed
in
europium
doped
yttrium
silicate
in
collaboration
with
IBM
Almaden
Research
Center. Research
into
divalent
ion
doped
crystals
as
photon
gated materials
for
coherent
transient systems
was
performed.
"-4..,UBCT.TERMS
...
15.
NUMBER
OF
PAGES
OP
coherent transient,
optical
memories,
triple-product
13
correlator,
continuous
signal
processor,
optical
Bloch
equations,
16.
PRICE CODE
chirped
reference
pulses,
photon
gated
materials
17.
SECURITY
CLASSIFICATION
18.
SECURITY
CLASSIFICATION
19.
SECURITY
CLASSIFICATION
20.
LIMITATION
OF
ABSTRACT
OF REPORT OF
THIS
PAGE,
OF
ABSTRACT
UNCLASSIFIED UNCLASSIFIED
UNCLASSIFIED
L
NSN
7S40-01-280"5500
Standard
Form
298
(Rev
2-89)
291.
'02
53-76

INTRODUCTION
Real-time, wideband
information
storage
and
signal
processing devices
are
critical
to
many military
and
commercial
systems
in
order
to
perform
complex
functions
such
as
secure communications, electronic
surveillance and
tracking,
target
recognition,
tactical
database
management,
and
tactical
air
reconnaissance.
Coherent transient
optical
memories
and
optical signal
processors have
been
proposed
as
technologies
capable
of
performing
the
above
functions
at data
rates
in
excess
of
10
GHz
and
with
storage
densities
on
the
order
of
1011
bits/cm
2.
Initial
calculations
indicate
that at
moderate
optical
input
power
levels,
the
output
signals
would
have
sufficiently
high
signal
to
noise
ratios
to
achieve reliable
recall
of
stored/processed
information.
However,
these
calculations
are
solely
based
on
a
shot noise
limited model and
ignore
the
non-ideal
properties
of
the
medium,
nonlinear
effects, spatial
crosstalk,
gating
efficiencies, local
heating,
the
effects
of
non-ideal
write
and
read
pulses,
and
the
characteristics
of
the
light
source,
the
modulation
technique, and
the
detector.
Compatibility
and
interfacing
issues
have
not
yet been
addressed.
A
major
obstacle to
realizing
coherent
transient
based
devices
is
the
availability
of
suitable
materials.
There
are
several
characteristics
(broad
inhomogeneous
linewidth,
narrow
homogeneous
linewidth,
long
storage
times,
operation and/or
storage
at
elevated
temperatures(>77
K),
effectively
singlet
ground
states, gateable
storage
with
high
efficiency,
and
high optical
quality)
that
a
storage
material must
possess
before coherent
transient memories
and
signal
processors become
practical.
The
absolute
and
relative
importances
of
each
these
characteristics
has
yet
to
be
examined.
The
work
performed
under
this
contract
addresses
the
above issues.
The
statement
of
work
calls
for
the
development
of
analytical tools which
are
needed
to
evaluate
the
performance
of
coherent transient
memory
and
signal
processing
systems.
The
evaluations
are
then
to
be
used
to
guide
the
development
of
coherent transient
materials.
1E

MODIFIED
STATEMENT
OF
WORK
The
contractor
shall
choose
one
coherent
transient
system
and
develop
an
appropriate
system architecture. Candidate
systems
are
a
memory
system,
a
triple
product
correlator,
and
a
continuous
optical
correlator.
The
contractor
shall
develop
a
set
of
analytical tools
for
evaluating
coherent
transient
based
systems.
These
tools will take
into
account
the
material
properties,
spatial
crosstalk,
the
characteristics
of
the
light
source
and
the
detector,
and the
detection
and
modulation
schemes. The
fidelity
loss
that
can
occur
due to
data
pulse
saturation
and
the
effects
of
local heating
of
the
material
will
be
addressed.
The system
parameters
to
be
determined
include
material
thickness, spot
sizes,
laser
powers,
and
output
signal
to
noise
ratios.
The
contractor
shall
evaluate the
chosen
system architecture
using
expected
performance
characteristics
for
the
individual
components.
The system
performance
characteristics
include
storage
times, storage
densities, access
times,
data
bandwidths,
time-bandwidth products,
bit
error
rates, and
processing
accuracies. The
contractor
shall
investigate the
dependence
of
the
systems'
performance
characteristics on
the
performance
of
the
individual components.
The
contractor
shall
determine
optimal
values
and
tolerances
for
the
system
parameters
that
are
variable
and
study
the
trade-offs between
performance
characteristics.
The
contractor
shall
provide
specifications
for
coherent transient materials
in
order
to
aid the
development
of
materials
that meet
the
requirements
of
the
chosen
coherent
transient
system.
,Accesiorl
For
/
The
contractor
shall
characterize
a
candidate
coherent transient material.
-s
CRA&/
Using the
results
of
the
material characterization,
the
contractor
will
provide
rTIC
TA3
',1Mnotnce(I
guidance
to
improve
the
material
growth.
If
an
appropriate
material becomes
available,
the
contractor
will
perform
a
proof
of
concept demonstration
of
a
coherent
transient
system
in
a
solid.
JIAr
butionI
.Availability
l
DTIC
QTTALTTY
TN.3PECTED
3p
Avdatl
and/
2
Special
, L_

STATUS
OF THE
RESEARCH
EFFORT
Previously
Reported
Progress
The work completed
up to
the end
of
1992
was
reported in
the
first
annual
report
(see
Appendix
A).
Continuous
Optical
Correlator
A
manuscript
on
the
evaluation
of
the
continuous
optical
correlator
was
submitted
to
Applied
Optics. The
submitted
version
is
in
appendix
B.
Since
the
annual
report,
the
estimation
of
the
performance
of
the
continuous
optical
correlator
was
improved
by
including
a
maximum
allowable
non-linearity
of
the
processor,
homogeneous
decay,
and
beam
overlap
efficiency.
An
optimal
effective
decay time
of
the
excited
state
is
derived.
It
was
found that
due
to
coupled
effects,
optimization
of
certain
properties
or
efficiencies
did
not
always
yield
optimal
performance.
Thus,
the
impact
of
each
adjustable
input
parameters
was
carried
through
to
the
final
result
in
order
that full
optimization
of
the
pattern
density
could
be
achieved.
The
pattern
density
calculation
was
derived
by
evaluating
the spatial
crosstalk
i
the
cases
of
1)
uncorrelated
adjacent
spots,
2)
correlated adjacent
spots, and
3)
uncorrelated
adjacent
spots
with
a
detection
aperture.
Proof
of
concept
demonstration
of
the
Continuous
Optical
Correlator
In
collaboration
with
Michael
Jefferson
and
Miao
Zhu
at
IBM
Almaden
Research
Center,
a
proof of
concept
demonstration
of
the
coherent transient
continuous
optical
processor
was
performed
in europium
doped
yttrium
silicate.
Though
hyperfine
split ground
state
transitions,
like
the
7F0-5D0
of
trivalent
europium,
are
not
ideal
for
continuous
processing
due
to
the
fact
that
the single
photon
storage leads
to
destructive
reads,
they
can be
use
for
short
term
processing.
A
phase
encoded
13-bit
parker
pattern
was
programmed
into
the
3

medium.
The
bit
rate
was
400 kHz.
A
2.5
psec
reference
pulse
was
used.
After
a
6
msec
delay
(the
upper
state
lifetime
is
2
msec),
a
stream
of
1170
phase
encoded
bits
was
processed
at
the same
400
kHz
bit
rate.
The
duration
of
the
data
stream
was
thus
2.925
msec
and
longer than
the
upper
state
decay
time
and
much
longer
than
the
coherence
lifetime
of
the
transition
(roughly
600
tsec).
The stream
consisted
of
9
repetitions
of
a
10-word
sequence.
The 10-word
sequence
was
made
up
to
13-bit
words.
Six
of
the
words
in
the
10-word sequence
matched
the 13-bit
pattern pulse. Four
of
the
words
in the
10-word
sequence
were
roughly orthogonal
to
the
barker
code and
would
not
be
expected
to
produce significant
peaks
when
correlated
with the
pattern
pulse. The resultant
output
signal
would
be expected
to
have
36
autocorrelation peaks
that
temporally
coincide
with
the
words
that match the
pattern
pulse.
The
experiment
was
performed
at
2K.
The
isolation
of
the
output
signal
from
the
"continuous"
data
stream
was
achieved
by
slightly
angling
the input
beams.
The
data
stream
and
output
signal
were
simultaneously
recorded
on
a
digitizing oscilloscope.
The
problem
of
erasing
the
spectral gratings
previously
stored
in
the
ground
state
hyperfine
levels
was
done
by
ramping
the
beam
power
up
and
down while
sweeping
the
laser
frequency
over
the
inhomogeneous
bandwidth.
After erasure,
a
single
program
and
process
experimental
run
was
performed
at
one
laser
frequency
setting
and
then
the
laser
was
tuned
1
MHz
to
a
new
"clean" area
of
the
inhomogeneous bandwidth
for
the
next experimental
run.
The term "clean"
is
relative,
since
a
hole burned
at
one
frequency creates
hole
and
anti-holes
over
a
400
MHz
bandwidth.
Several
experimental
runs
were
performed.
In
over
90%
of
the
runs,
the
resultant
output
signal was
somewhat
random.
The
reason
for
this
is
still
under
investigation,
but
could
be
due
to
excitation dependent
dephasing,
spectral diffusion,
laser
drift,
or
interference
with
previously
recorded
gratings.
Despite
this
problem,
several
recordings
of
output
signals
were made
in
which
all
but
one
of
the
36
autocorrelation peaks
were
well
above
the
background
and
the
last
autocorrelation
peak
was
present
but
comparable
to
the
background.
The
autocorrelation
peaks
temporally
corresponded
to
the
words
in
the
data stream
that
matched
the
pattern
pulse.
4

Since the
probability
of
such
a
output
signal
being
generated
randomly
is
less
than
one in
21170,
the
experiment
provided
a
proof
of
concept
demonstration
of
the
coherent
transient continuous
optical
processor.
Local
Heating
The
calculation
of
the
effects
of
local
heating
in
a
cylindrically
cooled
medium
were
enhanced
by deriving
the
equation
for
the
temperature
rise at
the
center
of
the
optical
beam
rather
than
just
at the
edge. The
effects
of
local
heating
on
the
performance
of
the
continuous
optical
correlator
were
again found
to
be
negligible.
Materials
Research
The
study
of
divalent
samarium
in
potassium
chloride
was
completed.
The
study
revealed
that
at
concentrations
that
were
high
enough
to
provide
adequate
absorption
in
a
one
centimeter
long
crystal
the
homogeneous linewidth
of
the
7F0-5D0
transition
was
significantly
broader
than
100
MHz.
The
conclusion
is
that Sm:KCL
is
bad
candidate
for
two-photon
"gated"
coherent
transient
materials.
Research
into
divalent
samarium
doped
into
other
hosts
is
incomplete
and
may
produce
better
results.
Preliminary
measurements
on
Tm:KCl
revealed
that
the
thulium
concentration
in
the
current
sample
(grown
at
the
University
of
Utah)
was
lower
than
expected. Initial
attempts
to
detect
the
florescence
of
the
2F7/2 -
215/2
transition produced
a
null
result.
Our
research
into
material
system
has
found
the
following
good
candidate
ions
for
photon
gated
coherent
transient
systems:
Sm
2+,
Tm
2+
and
Cr
3+.
For
the
triple
product correlator,
a
material
system
that
is
an
ensemble
of
effective
two-
level
absorbers
is
desirable.
Effective
two-level
systems
are
also
useful
in
experiments
to
verify
aspects
of
the
systems
analysis.
We
have
found
the
following
good
candidates
ions
for
effective two-level
systems:
Tmn
2+,
Tm
3+,
5

Sm
2+,
Cr
3+,
and
Yb
3
+.
These
ions
are
discussed
below.
Divalent
samarium
7F0 -
5D
0
(689nm)
Divalent samarium
is
a
promising
effective
two-level
system
and
gated
material
since
it
does
no
exhibit
nuclear
hyperfine splitting
and
experiments demonstrating
photon
gate
holebuming
in
Sm
2
+:BaC1F
have been
performed.
The
emphasis
is
on
host
systems
with
low
symmetry
that
will
yield
higher
oscillator
strengths
for
divalent
samarium and
thus
not
require
large
concentration which
lead
to
broadening
of
the
homogeneous
linewidth.
For
photon
gating,
sites
capable
of
trapping
2+
and
3+
ions
are
needed.
Hosts
that
shift
the
transition
above
690nm
are
preferred
in
order
to
make
the
system
more
compatible
with
Ti:Sapphire
lasers.
Divalent
Thulium
2F712 -2F512
(1120nm)
The
homogeneous linewidth
and
photoionization potential
of
divalent
thulium
has
yet to
be explored
and it
could
prove
to
be
a
promising
candidate
material.
For
photon
gating,
the
host
crystal
needs
to
have
sites
that
are
capable
of
trapping
2+
and
3+
ions.
A
host
the
shifted
the
transition
below
1100
nm would
be preferred
to
match
the
capabilities
of
Ti:Sapphire
lasers.
Trivalent
Chromium
R
lines
(694nm)
Photon
gating has
been
demonstrated
in
Cr
3
+:SrTiO
3.
However,
this
crystal
is
cubic and
the
oscillator
strength
is
very
low. Chromium
doped,
non-centrosymmetric
crystals
that
have
sites
capable
of
trapping
3+
and
4+
ions
have
the
potential
for
high
oscillator
strength
and
high
gating
efficiency.
Sufficiently
high
absorption
coefficients
can
be obtained
at
concentration
levels
that don't
induce
significant
spectral
broadening
provided
a
high
magnetic field
is
applied
to
obtain long
coherence
times.
Trivalent
thulium
3F4 -
3H6
(800nm)
The
homogeneous linewidth
of
trivalent
thulium
is
rumored
to
be
very narrow.
The
transition
wavelength
is
great
for
Ti:Sapphire
and
semiconductor
lasers.
Trivalent
ytterbium
2F712 -2F512
(1100nm)
The
homogeneous
linewidth
of
trivalent
ytterbium has
yet
to
be explored
but
has
the
potential
to
be
quite
narrow.
LIST
OF
PUBLICATIONS
A
manuscript
describing
our
results
on
the
evaluation
of
the
continuous
optical
correlator
was
submitted
to
Applied
Optics.
See
appendix
B.
6

PROFESSIONAL PERSONNEL
The
bulk of
the
work
was
performed
by
Dr.
W.
Randall
Babbitt. Dr.
John
A.
Bell
aided
in
the
laser
characterization
of
materials
and
in
the
evaluation
of
the
continuous
optical correlator.
Dr.
Bruce
Evans
has performed
excitation
and
florescence
studies
of
the
Sm:KC1
and
Tm:KC1
crystals.
Dr.
Evans and
Dr.
Rudy
L.
Prater
have
provided
expertise
on
doped
crystalline
materials
and
the
possible
adaptation
for
coherent
transients.
INTERACTIONS
Previously
Reported
Interactions
Interactions
before
December
1992
were
reported
in the
first
annual
report
(see
Appendix
A).
Joint
Study
Agreement
with
IBM
The
joint
study
agreement
between Boeing
and
IBM
resulted
in
the
proof
of
concept demonstration described
above.
7

Appendix
A
9-5554-WRB92-033
Annual
Report
of
the
Progress
on
the
Coherent
Transient
Systems
Evaluation
Wm.
Randall
Babbitt
Boeing Defense
&
Space
Group
1992
Air
Force
Office
of Scientific
Research
Al

INTRODUCTION
Real-time,
wideband information
storage
and
signal
processing
devices
are
critical
to
many
mili,:y
and
commercial
systems
in
order
to
perform
complex
functions
such
as
secure
communications, electronic
surveillance and tracking,
target
recognition,
tactical database
management,
and
tactical
air
reconnaissance.
Coheient
transient
optical memories
and
optical
signal
processors
have
been
proposed
as
technologies
capable
of
performing
the
above
functions
at
data
rates
in
excess
of
10
GHz
and
with
storage
densities
on
the
order
of
1011
bits/cm
2.
Initial
calculations
indicate
that
at
moderate
optical input
power
levels,
the
output
signals
would
have sufficiently
high
signal
to
noise
ratios
to
achieve
reliable
recall
of
stored/processed information. However,
these
calculations
are
solely
based
on
a
shot
noise
limited
model and
ignore
the
non-ideal
properties
of
the
medium, nonlinear
effects,
spatial
crosstalk,
gating
efficiencies,
local
heating,
the
effects
of
non-ideal
write
and
read
pulses,
and
the
characteristics
of
the
light
source,
the
modulation
technique,
and
the detector.
Compatibility
and
interfacing
issues
have
not
yet
been
addressed.
A
major
obstacle
to
realizing
coherent transient based devices
is
the
availability
of
suitable materials. There
are
several
characteristics
(broad
inhomogeneous
linewidth,
narrow
homogeneous linewidth, long
stor,.ge
times,
operation
and/or
storage
at
elevated
temperatures(>77
K),
effectively
singlet
ground
states,
gateable
storage
with
high
efficiency,
and
high
optical
quality)
that
a
storage
material
must possess
before
coherent
transient
memories
and
signal
processors
become
practical.
The
absolute
and
relative
importances
of
each these
characteristics
has yet
to
be
examined.
The
work
performed under
this
contract
addresses
the
above
issues.
The
statement
of
work calls
for
the
development of
analytical tools
which
are
needed
to
evaluate
the
performance
of
coherent
transient
memory
and
signal
processing
systems.
The
evaluations
are
then to
be used
to
guide
the
development
of
coherent transient
materials.
A2

STATEMENT
OF
WORK
The
contractor
shall
choose
three
coherent transient
system
architectures
to
evaluate. They
include
a
memory
system
(either
register,
cache,
RAM,
mass,
or
archival
storage),
a
triple
product correlator,
and
a
continuous
optical
correlator.
The
contractor
shall
develop
a
set
of
analytical
tools
for evaluating
coherent
transient
based
systems.
These
tools
will take
into
account
the
material
properties,
spatial
crosstalk,
the
characteristics
of
the
light
source
and
the
detector,
and
the
detection
and
modulation
schemes.
The
fidelity
loss
that
can
occur
d&,.
to
data
pulse saturation, gating
non-linearities,
fine
structure
in
the
inho!,nogeneous
profile,
and
reference
and
read
pulse imperfections
and the
effects
of
local
heating
of
the
material
will
be
addressed. The
system
parameters
to
be
determined
include
material thickness, spot
sizes,
laser powers,
and output
signal
to
noise
ratios.
The
contractor
shall
evaluate
the
three chosen
system
architectures
using
expected
performance
characteristics
for
the
individual
components.
The
system
performance characteristics
include storage
times,
storage
densities,
access times,
data
bandwidths, time-bandwidth
products,
bit
error
rates,
and
processing
accuracies.
The
contractor
shall
investigate
the
dependence
of
the
systems'
performance
characteristics
on
the
performance
of
the
individual
components.
The
contractor
shall
determine
optimal
values
and
tolerances
for
the
system
parameters that
are
variable
and
study the
trade-offs
between
performance
characteristics.
The
contractor
shall
provide specifications
for
coherent
transient
materials
in
order
to
aid
the
development
of
materials
that
meet
the
requirements for
coherent
transient
systems.
The
contractor
shall
characterize materials provided
by AFOSR.
The
materials
are
to
be
provided
at
no
expense
to
Boeing. Along
with
the
results
of
the
materials characterization,
guidance
shall
be
provided
in
the
growth
of
improved materials.
A3

If
an
appropriate
material
becomes
available,
experiments shall
be
conducted
to
verify
aspects
of
the system
analysis and/or
to
perform
a
proof
of
concept
demonstration
of
one
of
the
coherent
transient
systems
in
a
solid.
STATUS
OF
THE
RESEARCH
EFFORT
Coherent
Transient
Simulator
A
key
tool
in
our evaluation
of
coherent transient
systems
is
a
computer
program that
integrates
the
optical
Bloch
equations
and
follows
the
evolution
of
the
density
matrix
elements
during
multiple
excitation
pulses.
After
the
final
excitation
pulse,
the
density matrix
elements
contain
the
information
necessary
to
calculate
the
resultant
coherent
transient
response
of
the
absorbing medium.
Since the
Bloch
equations
take
into
account
nonlinear
effects,
the
program
is
useful
in
studying
the
effect
nonlinear
excitation
pulses.
The
program
currently
runs
on
a
Macintosh
Ilci.
It
is
written
in
C
using console
input
(i.e.
it
is
machine
independent)
and
is
thus
directly
portable
to
a
PC-compatible,
a
workstation,
or
a
mainframe
computer.
Eventually
the
computer
program
will
be
incorporated
in
the
core
of
channel
modelling
programs used
to
evaluate
the
performance
of
memory
and
processing
systems.
The
Bloch
equation
integration
program
was
originally
developed
at
Boeing
under
Independent
Research
and
Development
funds.
Under
the
current contract,
several
improvements
have
been made
to
the
program
that
greatly enhance
its
speed,
flexibility,
and
input
and
output
capabilities.
The
exact
analytical
transformation
of
the
density matrix
elements resulting from
excitation
by
a
square
pulse
of
arbitrary duration,
amplitude, center
frequency,
phase,
and
timing
was
calculated
and
incorporated
into the
program.
This
greatly
enhanced
the
programs
speed
since
integrations
of
the matrix
elements
was
no
longer
required.
For
example,
the
evaluation
of
the
exact
solutions
of
the
Bloch
equations
for
an
excitation
pulse
sequence
consisting
of
32
square
pulses
for
1025
frequency
points
takes
only
115
seconds
on
a
Macintosh
Ilci.
Chirped
pulses
of
A4

arbitrary
of
arbitrary
duration,
bandwidth, amplitude, center frequency,
phase,
and
timing
are
still
calculated
by
integration
of
the
optical
Bloch
equations.
A
typical
chirps
pulse
requires
about
2
minutes
to
calculate
the
resultant
density
matrix
elements for
1025
frequency
points
with
1
part
in
a
1000
accuracy
(7
minutes
for
1
part
in
109).
The improvements
in
input
capabilities
and
calculation
flexibility
include
options
for
32-bit
data
pulses, gating pulse, sudden losses
in
coherence,
and
homogeneous
decay
Data
pulse
up
to
32-bits long
can
be
entered
as
a
single
integer
and
can
be amplitude
or
phase
encode,
return
to
zero
(RZ)
or
non-return
to
zero
(NRZ).
Data
pulses
longer
than
32-bits
are
achieved
by
repeating
this
options
indefinitely.
The
gating
pulse
option
simulates
the
effects
of
a
gating
palse
by
eliminating
those atoms
in the
upper
state at the time
of
the
pulse,
thus
permanently
modifying
the
inhomogeneous
profile.
The
resultant
modulations
in
the
inhomogeneous
profiles
will
alter
the
effect
of
excitation pulse nonlinearities
compared
to
an
unmodulated
inhomogeneous
profile.
The
ability
to
create
a
sudden
loss
of
coherence
aids
in
simulating absorbers with
homogeneous
decay
times
much shorter
than the
upper
state
lifetimes
and
in
simulating
the
rejection
of
spurious
outputs
via
spatial
isolation (since
the
program
does
not
do spatial
integrations).
Homogeneous
decay
can
now
be
optionally
included
in
the
standard
bloch
equations
for
chirped
or
square
pulses.
The
output
now
include
direct
detection,
coherent
detection,
and
the
resultant
holeburning
spectra. The
graphical interface allows
quick
evaluation
of
the
results.
The
interface
in
achieved
via
a
different
program
that
is
simultaneously
resident
with
the
coherent transient
simulator.
This
separation
maintains
the
quick
portability
of
the
simulator
to
other
machines.
Modified
Bloch
Equations
The
implementation
in
the
simulator
of
the
modified
Bloch
equations
which
correct
the
failures
of
the
ordinary
Bloch
equations
to
predict
the
effects
of
homogeneous
decay
during strong
excitation
pulses
was
considered.
During
A5

intense pulses,
the dephasing
time
can
be
considerably
longer
than
in
the
zero
intensity
limit
in
certain
materials
and
under
certain
conditions.
However,
since
the
main
concem
for
coherent
transient memory
and
signal
processing
systems
is
the
fidelity
of
the
output
signals
which
rely
heavily
on
the
materials
response
to
the
data pulses,
it
is
the
coherence
decay
during
the
data
pulses that
is
of
greatest
concern.
However,
the
spectrum
of
the
data
pulse
is
by
necessity
complex
with
regions
of
high
and
low
spectral density.
If
the above
phenomena
were
required
to
play
a
role,
it
would
differentially
affect
the
spectral
components
of
the
data
pulses,
resulting
in
a
loss
in
output
fidelity.
There
may be
techniques
that
circumvent
these
problems
or
take
advantage
of
this
phenomenon
in
another
way
in
order
to
increase
storage
densities
or
time-bandwidth
products.
However,
it
is
not
in
the
scope
of
this
work
to
address
these issues.
Thus,
only
consider
cases
in
which
the
intensity
dependent
homogeneous
decay
is
relatively
weak
so
that
any
lengthening
of
the
dephasing
time
will
not significantly
alter
the
resultant
output
signals
were
considered.
Results
Obtained
With
Simulator
The major result
obtained
so
far
with the
simulator
was
the
effect
of
saturation
on chirped
pulses
when
used
as
reference pulses
in
time
domain
memories.
Previous
analyses
of
chirped
reference pulses
have
assumed
that
the
medium
responds
linearly
to
the
chirped reference
pulses.
However,
to
be
efficient,
reference
pulses
must
be
able
to
act
as
effective
7r/2
and
nt
pulses.
Reducing
the
amplitude
of
the
reference
pulses
to
the
linear
regime would
reduce
the
output
signal by three
to
four
order
of
magnitude.
In
studying
the
effects
of
chirped
pulses
as
reference
pulses,
it
is
not
sufficient
to
merely
study
the
chirped
pulses ability
to
invert 50%
or
100%
of
the
atoms.
The
effects
of
saturation
on
the
coherences must
be
taken into
account.
Using
the
simulator, excitation
pulse
sequences
that
contained
chirped
reference
pulses
were
compared
to
sequences
with
brief
reference
pulses.
By
optimizing
the
intensity
of
the
chirped
pulses,
it
was
shown
that
chirped
pulses
are
nearly
as
A6

intense
pulses,
the
dephasing
time
can
be considerably longer
than
in
the zero
intensity
limit
in
certain materials
and
under
certain
conditions.
However,
since
the
main
concern
for
coherent transient memory
and
signal
processing
systems
is
the
fidelity
of
the
output
signals
which
rely
heavily
on
the
materials
response
to
the data
pulses,
it
is
the
coherence
decay
during
the data
pulses
that
is
of
greatest
concern.
However,
the spectrum
of
the
data
pulse
is
by
necessity
complex with
regions
of
high
and
low
spectral density.
If
the
above
phenomena
were
required
to
play
a
role,
it
would differentially
affect
the
spectral
components
of
the
data
pulses,
resulting
in
a
loss
in
output
fidelity.
There
may
be
techniques
that
circumvent
these
problems
or
take
advantage
of
this
phenomenon
in
another
way
in
order
to
increase storage
densities
or
time-bandwidth products. However,
it
is
not
in
the
scope
of
this
work
to
address these issues. Thus,
only
consider
cases
in
which
the
intensity
dependent
homogeneous
decay
is
relatively
weak
so that
any
lengthening
of
the
dephasing
time
will
not
significantly
alter
the
resultant
output
signals
were
considered.
Results
Obtained
With
Simulator
The
major
result
obtained
so
far with
the
simulator
was
the
effect
of
saturation
on
chirped pulses
when
used
as
reference
pulses
in
time
domain
memories.
Previous
analyses
of
chirped
reference pulses have
assumed
that
the
medium
responds linearly
to
the
chirped reference
pulses.
However,
to
be
efficient,
reference
pulses
must
be able
to
act
as
effective
Rt/2
and
nr
pulses.
Reducing
the
amplitude
of
the
reference
pulses
to
the
linear
regime would
reduce
the
output
signal
by
three
to
four
order
of
magnitude.
In
studying
the
effects
of
chirped
pulses
as
reference
pulses,
it
is
not
sufficient
to
merely study
the
chirped
pulses
ability
to
invert
50%
or
100%
of
the
atoms.
The effects
of
saturation
on
the
coherences
must
be
taken
into
account.
Using
the
simulator,
excitation
pulse sequences that contained
chirped
reference
pulses
were
compared
to
sequences
with
brief
reference
pulses.
By
optimizing
the
intensity
of
the
chirped
pulses,
it
was
shown
that
chirped
pulses
are
nearly
as
A6

efficient
as
brief
pulses
in
storing and recalling
information.
Another
important
criteria
is
the
sideband
noise introduced
with
chirped
pulses
of
finite
duration.
Our results
demonstrate that
the sidebands
drop
off
rapidly
and
will
not
lead
to
intersymbol
interference
that
can
degrade
performance
in
memory or
signal
processing
systems.
These
results
are
significant since
sufficiently
intense brief
reference
pulses
are
difficult
to
produce
and
chirped
pulses
present
a
practical
alternative.
A
similar
evaluation
of
saturation
effects and efficiencies
for
phase
encoded
reference
pulses
is
planned.
Phase
encoded
reference
pulses
may
have
the
disadvantage that
they
only
work
in
the
linear
regime
and
thus
lead
to
inefficient
storage
and
recall.
For
signal
processing
applications,
coherent
transients
act
as
triple
product
correlators.
If
correlations
between
two
signals
is
desired,
the
third
pulse
previously
was
required
to
be
brief
pulse. Unlike
in
memory
applications
were
a
matched
pair
of
chirped
pulses
can
replace
the two
brief
reference
pulses,
in
the
processing
case
a
single
chirped
pulse
can
not
replace
a
brief
pulse. However,
a
technique
was
discovered
by
which
two chirped
pulses
can replace
a
single
reference
pulse
and
without
any
loss
in
efficiency. The chirped
pulses
are
the
first
two
pulses
in
a
four
pulse
sequence.
The
last
two
pulses
are
the
signals
to
be
processed.
The chirped
pulses
have
the
same
chirp
bandwidth,
but
the
second
pulse's
chirp rate
is
twice
that
of
the
first
pulse.
Employing our
simulator,
it was
found
that optimization
of
the
intensities
of
the
chirped
pulses
produced
output
signals with
the
same
efficiency
as
optimized
brief
pulses
and
with
negligible
intersymbol interference.
This
technique
works
for
both
the
triple
product
correlator
and the
continuous
optical
correlator.
Continuous
Optical
Correlator
The
performance
of
the
continuous
optical
correlator
was
evaluated.
In
carrying
out
this
evaluation,
a
technique
(discussed
above)
was
discovered
for
replacing
a
brief
reference
pulse with
two
chirped
pulses.
One
difficulty
with
the
continuous
optical
correlator
is
isolating
the
output
signal
from
the
continuous
A7

input signal
and
from the
numerous
spurious echoes
that
are
created.
This
is
especially
true
when the
brief
reference
pulse
is
replace
by
two
chirped
pulses.
Polarization
isolation
is
simple,
but
does
not
work
well
in
practice
with nonideal
systems.
Angular separation
leads
to
a
reduction
in
efficiency
and
presents
technical
alignment
difficulties
in
a
practical
system.
It
was
discovered
that
a
simple
counter-propagating configuration
provides
complete
isolation
from
spurious
coherent
transient
signal.
Polarization isolation, though
not
required,
can be
added
to
eliminate any backscattered light
and
provide additional
isolation.
The
optimized
performance
of
the
continuous
optical
correlator
was
derived
by
balancing
the
coherent
saturation
intensity
and
incoherent
saturation
intensity
and
by
balancing
the
spot
size
needed
to
maintained
a
required
signal
to
noise
with
the
diffraction limited
spot
size.
The effects
of
local
heating
were
calculated.
The
calculations confirmed
that
the
effects
were
negligible
in
the
cases
studied.
The
analysis
took
into
account the
pattern
write
efficiencies,
gating
efficiencies,
and the
signal output efficiencies including
input
signal
absorption
and
output
signal
gain
in
strongly absorbing media.
The
performance
characteristics that
were
optimized
in
the
evaluation
are
the
time-bandwidth
product
of
the
correlator
and
the
obtainable
pattern
storage
density (number
of
patterns
per
unit
area).
Though
the
optimized results
were
obtain
assuming
the
material parameters
for
Sm
2
+:KC1,
the
calculations
are
applicable
to
any
material.
Using
the
current material parameters
for
Sm
2
+:KCI,
a
time
bandwidth
products
of
800
and
a
pattern density
of
3000
per
square
centimeter
is
predicted.
By
assuming conservative estimates
of
the
material
parameters
that
could
be
obtained
for
Sm
2+
in
a
similar
hosts,
it
is
predicted
that
a
time
bandwidth
product
of
16000
could
be
achieved
with
pattern
density
of
8
x
105
pattern
per
square
centimeter.
A
paper
was
presented
on
these
results
and
a
manuscript
is
currently
being
prepared
for
publication
(see
below).
Local
Heating
The effects
of
local
heating
on
the
performance
of
the
continuous
optical
A8

correlator
were
calculated
and
found
to
be
negligible.
The
processing
medium
was
assumed
to be
cylindrical
(1
cm
in
diameter)
and
cooled only
on
the
circumference. However, for memory
applications
the
sample
area
may
be
significantly larger
and
heat
may
need
to
be
removed
from
the
back
and/or
the
front
face
of
the
sample.
To
handle
these
cases,
A
two
dimensional thermal
diffusion
modelling
program
for
axially
symmetric samples
was
written.
Spatial crosstalk
In
the
results
described
above,
in
determining
spatial
densities
the
assumption
was made
that
each
pixel
was
isolated
from
its
neighbors.
This
assumption
is
sufficiently
valid
for
beams
of
finite
extent
(i.e.
top
hat shaped).
In
practice,
the
production
of
such
beams
is
inefficient.
Gaussian
beams
are
efficiently
produced
but
have
infinite widths,
though
the
intensity in
the
wings
drops
off
dramatically.
The
maximum
storage density
depends
on how
closely
the
pixels
can
be
located
without
degrading
the
information stored.
An
equation
for
the
coherent
transient output
signal
produced when
a
gaussian
recall
pulse
of
arbitrary
waist
is
an
arbitrary
distance
from
a
pixel
written
with
two
or
more
gaussian
pulses
of
arbitrary
waist
was
derived.
The
calculation
takes
into
account
the full
two
dimensional,
nonlinear
overlap
of
the
beams.
It
assumes
a
uniform
waist
throughout
the
length
of
the
material.
A
calculation
of
the
overlap
in
mediums where
diffraction
is
significant
is
planned,
followed
by
a
study
of
the
maximum
storage
density
as
a
function
of
the
tolerable
crosstalk
and
of
the
ratio
of
the
nearest
neighbor
distance
to
the
spot
size.
Coherent
Transient
Systems
Evaluation
As
discussed
above,
the
performance
of
the
continuous
optical
correlator
has
been evaluated
using
Sm:KCI
as
the
processing
medium.
A
more
complete
study
of
the
trade-offs
is
to
follow.
During
the
evaluation
of
the
continuous correlator,
most
of
the
analytical
tools for
evaluating
the
triple
product
correlator
and
memory
systems
were
developed
as
well.
However,
evaluation
of
a
practical
and
A9

competitive memory
system
requires
knowledge
of
the
techniques
for obtaining
densities
far
beyond
the
"isolated
pixel"
and
"isolated
bit"
approach.
A
joint
study
agreement
with
IBM
to
explore these avenues
together
was
signed.
Their
expertise
in
the area
of
optimization
of
memory channels will
prove invaluable
to
this
task.
Materials
Research
Development
of
practical
coherent
transient
memory
and
signal
processing
systems
can
not
proceed without
better
materials.
There
are
several
material
systems based
on
population
storage
in
ground
state
hyperfine
levels. These
materials
provide
excellent
demonstrations
and
can
be
used
to
confirm
theoretical
predictions.
But,
hyperfine materials
have
two
disadvantages that
make
their
use
as
practical materials
improbable.
The first disadvantage
is
the
single
photon
writing
process
which
leads
to
destructive readout. Minimizing
the
effects
of
the
destructive
readout
requires
lowering
the
writing
efficiency
or lowering
the
readout
beam
intensity.
Both methods severely degrade
the
signal
to
noise.
The
second
disadvantage
is
coherent
beating.
Since
the
hyperfine splittings
are several
order
of
magnitude
less than
the
inhomogeneous linewidth
which
determines
the
ultimate
data
rate,
attempts
to
use
the
full
bandwidth
leads
to
beating between
the
levels
and
severe
modulation
of
the
output
signal.
For
these reasons, two-photon
"gated"
coherent
transient
materials
are
being
investigated.
There
has
been
some
demonstrations
of
gated
spectral
holeburning
materials, but
the
homogeneous
linewidths
of
these
materials
make
them
impractical
as
coherent transient materials.
One such
material
demonstration,
using
Sm
2
+:BaC1F,
employed
photoionization
as
the
gating
process,
transforming
Sm
2+
to
Sm
3+.
The
linewidth
of
the
burned holes
were
25
MHz.
However,
sub-
megahertz linewidths
have
been
noted
in
Sm2
+:KCl
and
photon
gating should
be
possible after
some
modifications
of
the
crystal.
A
grower
of
alkali halide
materials,
Matt
DeLong
at
the
University
of
Utah,
is
willing
to
grow
experimental
crystal
at
a
very low
cost
(=
$550
per
crystal).
Four
crystals
have
A10

been
grown
to
date.
The
first
two exhibited
very
weak lines
compared
with
earlier
studies.
This
was
probably
due to
possible contamination
of
the
SmC12
used
to
grow
the
crystals.
The
second
two
crystals
were
grown with
a
new
stock
of
SmCl
3
and
a
modified
growth
technique. Unlike
the
first two
crystal,
they
have
a
deep
purple color
indicative
of
high
Sm
2+
concentration.
Characterization
of
these
latest
materials
had
just
started
when
our
argon
laser
tube
failed. The
tube
has
just
been replaced
and
characterization
will
continue
at
the
first
of
the
year.
LIST
OF
PUBLICATIONS
A
nil-uscript
is
in
preparation
describing
our
results
on
the
evaluation
of
the
continuous
optical
correlator.
A
paper
on
the
saturation
effects
of
chirped
and
phase
encoded
reference
pulses
li
planned
for
submission
in
the
next
few
month
when the
results
on
the
phase encoded
reference
pulses
is
completed.
PROFESSIONAL
PERSONNEL
The
bulk
of
the
work
is
being
performed
by
Dr.
W.
Randall
Babbitt.
Dr.
John
A.
Bell
is
aiding
in
the
laser
characterization
of
materials
and
the
determination
of
performance
criteria
for
signal
processors. Dr.
Bruce Evans
has
performed
excitation
and
florescence
studies
of
the
Sm:KC1
crystals.
Dr.
Evans
and
Dr.
Rudy
L.
Prater
have
provided
expertise
on
doped
crystalline
materials
and possible
their
adaptation
for coherent transients.
INTERACTIONS
Papers
Presented
A
paper
was
presented
at
the
Spectral
Hole-Burning
and
Luminescence
Line
All

Narrowing:
Science
and
Application conference
in
Ascona,
Switzerland,
September
14-18,
1992.
The
paper
was
entitled
"Continuous Signal Processing
Using
Optical Coherent
Transients"
and
described the
evaluation
of
the
performance
of
the
continuous
optical correlator,
as
discussed
above.
PSHB
workshop
A
workshop
was
hosted
at
Boeing
on
persistent
spectral
holebuming.
The
participants
were
Randy
Babbitt
and
Matt
Derstine
of
the
Boeing
Company
Yu
Sheng
Bai
and
Ravinder
Kachru
of
SRI
International, Alan
Craig
of
AFOSR,
Anshel
Gorokhovsky
of
City College
of
CUNY,
Philip
Hemmer
of
ROME
Air
Dev.
Ctr.,
Mike
Jefferson
and
Roger
M.
Macfarlane
of
IBM
Almaden
Res.
Ctr.,
M.
K.
(Paul)
Kim
of
Wayne
State
University, Thomas W.
Mossberg
of
the Univ.
of
Oregon.
The topics
discussed
were
hyperfine
storage
and
beating,
homogeneous
linewidths,
spectral
diffusion,
gated
storage,
novel
storage
concepts, competitive technologies,
practical
system
considerations,
current
materials,
sources
of
materials.
A
summary
of
the
meeting
was
distributed.
Joint
Study Agreement
with
IBM
A
joint
study
agreement
was
signed between
Boeing
and
IBM
in
November.
Dr.
Babbitt
visited
IBM
for
two
weeks
in
December
to
discuss
with
Dr.
Michael
Jefferson
the
issues
we are
going
to
address
jointly.
Since
a
major
part
of
the
collaboration
will
include experimental
work
at
IBM,
the
visit
also
enabled
Dr.
Babbitt
to
familiarize
himself
with
IBM
operations.
He
had
the
opportunity
to
help
set-up
Dr.
Jefferson's
new
cryostat
and
the
associated optics
and electronics.
Photon
echoes,
optical
nutation,
and
hole-burning
were
obtained
by
the
end
of
the
visit.
A12

Appendix
B
Coherent
Transient
Continuous
Optical
Processor
Win.
Randall
Babbitt
and
John
A.
Bell
Boeing Defense
&
Space
Group
P.O.Box
3999
M/S
7J-91
Seattle,
WA
98124-2499
USA
(206)
865-3307
ABSTRACT
After
the
absorption
profile
of
an
inhomogeneously
broadened
solid is
programmed
by
two
temporally
modulated
pulses
(at
least
one
encoded
with a
pattern),
it
can
be
gated
to
permanently
fix
the
ground
state spectral
population distribution. The subsequent
illumination
of
the
solid
by
an
uninterrupted, temporally
modulated
optical
beam
results
in
a
coherent
transient
output
signal
that
represents the
correlation
of
the
signal
with
the stored
pattern.
Multiple
patterns
can
be
stored
at
different
locations
on
the
sample and
accessed
randomly,
enabling
fast
reprogramming
of
the
processor.
A
performance analysis
of
this
novel
optical
signal
processor
predicts that
real-
time
continuous
processing
is
possible
with
a
processor
bandwidth
exceeding
5
GHz,
a
time-
bandwidth
product
exceeding
104,
and
a
pattern
storage
density exceeding
105
patterns
per
cm
2.
Keywords:
optical
coherent
transients,
photon echoes,
spectral
hole-burning,
optical signal
processing,
optical
correlator.
Note
to
Publisher
(not
to
be
included
in
manuscript)
This
manuscript
is
submitted
for
publication
with
the
understanding
that
the
United States
Government
is
authorized
to
reproduce
and
distribute
reprints
for
governmental
purposes.

1.0
Introduction
The
continuous
optical
correlator
presented
here
is
based
on
the phenomena
of
coherent
transients,
also referred
to
as
photon
echoes
or
time-domain spectral
holeburning.
Long-term
coherent
transient
storage
of
temporally
modulated optical
data
pulses
1
in
cryogenic
solids
has
been
demonstrated
by
several authors.
2,3,4
The temporally
encoded
information
is
stored
as
a
spectral
interference
pattern
in
the
ground
or
excited
state
inhomogeneously
broadened
population
distribution. Permanent
storage
and non-destructive
reading
capabilities
can
be
achieved
via
a
gating
process
that
permanently fixes
the spectral
population
grating.
Such
processes
have
been
demonstrated for
frequency-domain
spectral
holeburning.
5
Optical
coherent
transient techniques
can
also
be
used
to
perform
convolutions
and
correlations
of
three
temporally
modulated
light
pulses.
6
The coherent
transient
output
signal
represents
the
cross-correlation
of
the
first
pulse's
temporal waveform
with
the
convolution
of
the
second and
third
pulses' waveforms.
The
processor
responds
to the
electric
field
amplitudes
of
the
input
pulses
and thus can
fully
process
amplitude,
phase,
and frequency
modulated
signals.
7
In
previously
proposed
implementations,
8 it
has
been
asserted
that
to
obtain
high fidelity
correlations,
the
durations
of
the
modulated
input
pulses
must
be
less than
the
homogeneous
decay
time
of
the
absorbers.
To
search
an
uninterrupted
data
stream
(data streams
longer
than
the
homogeneous
decay
time)
for
a
given
pattern
requires
that
the
signal
be
broken
up
into
overlapping
segments
that
must
be
processed
separately.
In
order
to
process
each
segment,
the
optical
pattern/reference pulses
would
have
to
be
regenerated
and
introduced into
the
medium.
Thus,
three
modulated
light
beams
with
appropriate
delays
need
to
be
generated
for
each
segment
processed.
The
resultant signals
would
then
have
to
be
additionally
processed
to
obtain
the
true correlation.
These limitations
greatly
increase
the
processor's
latency
time
and
make
real-time processing
of
continuous
signals
impossible.
In
this
paper,
we
introduce
a
novel
coherent
transient
signal-processing technique
that
enables
the
real-time processing
of
continuous
input
signals
after
a
single
programming stage.
9
The
unique
features
of
the
continuous
optical
correlator
and
the
techniques for
programming
it
and
obtaining
high
fidelity
correlation
peaks
are
discussed.
Then
a
more
detailed
analysis
of
the
continuous
processor's
potential
performance
is
presented.
Data
rates
on
the
order
of
10
GHz,
time-
bandwidth products
up to
105,
and
pattern storage
densities
in
excess
of
105
patterns per
cm
2
are
predicted.
S,

1.1
Coherent
Transient Triple
Product
Correlator
Consider
three
temporally
encoded
light
pulses.
These
light
pulses may
be
amplitude,
phase,
and/or
frequency
encoded. When
an
inhomogeneously
broadened
absorber
is
resonantly
excited
by
these
pulses
in
sequence,
the
resultant coherent
transient
output
signal
Es(t)
is
given
by
10
Es(t)
_•d
"' EIE( -")c
f
d' E2
(i')
E3(" +
t-
, (1)
where
Ej(t)
represent the
electric
field
of
the
jth
pulse.
The
output
signal
represents
the
correlation
of
the
first
data
pulses
with
the
convolution
of
the
second and
third
data pulses.
Either
the
convolution
or correlation
of
only
two
pulses
can
be
achieved
if
one
of
the
three
data
pulses
has
only
a
single subpulse
whose
duration
is
less
than
the
shortest temporal
feature
of
the
other
two
pulses.
The
above
equation
for
the
output
is
valid
regardless
of
the
modulation
characteristics
of
the
data
pulses.
Thus,
a
coherent
transient
correlator
is
capable
of
simultaneously
performing
phase
and
frequency
correlations,
as
well
as
amplitude
correlations.
The
data
bandwidth
of
the
triple
product
correlator
is
ultimately
limited
by
the
inhomogeneous
bandwidth
of
the
absorbing
transition.
For
such
transitions
in
solids, data
bandwidths
can
range
from
a
gigahertz
to
a
terahertz.
The
correlator's
time-bandwidth
product
is
limited
by the
ratio
of
the
inhomogeneous
to
homogeneous
broadening,
which
was
measured
to
be as
high
as
107
in
one
solid.
11
2.0
The
Coherent
Transient
Continuous
Optical
Processor
The
assertion
made
previously
that
all
the
pulses
must
be
less
than
the
homogeneous
decay
time
is
not
valid
in
all
cases.
Though
the
time-bandwidth
product
is
limited by
the
homogeneous
dephasing
time,
the
data
pulse
lengths
are
not.
The
duration
of
the
third
pulse
is
not
even
limited
by
the
population decay
time
and
can
actually
be
infinite. To
accomplish this
improvement,
a
step
must
be added
to
the
programming
of
the
coherent
transient
correlator
which
permanently
stores
the
ground
state
population
grating
produced
by
the
first two
data
pulses.
This
step
is
referred
to
as
the
gating.
The
programming,
gating,
and
processing
stages
of
the
coherent
transient
continuous
optical
correlator
are
illustrated
in
figure
1.
2.1
Programming
and
Gating
the
Continuous
Processor
Programming
the
continuous
processor
is
accomplished
by
illuminati,
n,
the
material
with
,.'
modulated
light
pulses:
a
pattern pulse
and
a
reference
puk•
l)c
I
'
h
,
01
I
>c
tir>1
two
pw I rc.
C,

is
identical
to
the
first
two
pulses
in
the
triple
product correlator
in
that
the
resultant
frequency
dependent
population
gratings
in
ground
and
excited
states are
equivalent.
The
next
step
is
a
gating
process
to
prevent
erasure
of
the
ground
state
population distribution during
the
processing stage.
The
gating
process
permanently
alters
a
significant
portion
of
the
atoms that
are
in
their
excited
states
after
the
first two
pulses
such
that
they can
no longer
decay
to
their
initial
ground
state.
This
can be
accomplished
by
illuminating
the
material
with
an
optical pulse
resonant
with
a
transition
from
the
excited
state
to
another
state
which
decays
into
a
metastable
state
other
than
the
initial
ground
state. The
gating
photons
could
be
of
sufficient
energy
to
photoionize
the
excited
absorbers
and,
thus,
permanently
alter
their
energy
level
structure.
The
electron from
the
photoionized
absorbers
could
be trapped
by
an
acceptor
ion
present
in
the
material. Such
a
process
has
been
demonstrated
for
holes
burned
into
an
inhomogeneous
line.
12
Other
possible
gating
methods
include
two-step
photodissociation
and
two-step
donor-acceptor electron
transfer.
5
If
the
gating
process
is
inefficient,
it
can
be
repeated until
a
sufficient
ground
state
population
grating
is
achieved.
An
example
of
the
timing
of
the
programming
and
gating
pulses
is
shown
in
figure
2a-
For
applications
requiring
temporary
processing for
a
time
duration much
longer
than
the
upper
state
lifetime
but
short
compared
to the
ground
state
storage time,
it
may
not be
necessary
to
gate
the
absorbers.
A
single photon
storage
process could
be
used.
Materials that
have
multiple
ground
states
(i.e.
hyperfine
split
ground
states) can
store
population
gratings
by
having
a
percentage
of
the
excited
state
absorbers
decay
to
a
level
other
than the
original ground
state.
In
ground
states
with
nuclear
hyperfine
splittings,
these
population
gratings
can
persist
for
days
at
liquid
helium
temperatures.
4,13
These materials
have
two
disadvantages.
The
first
is
that
the
processing
stage
is
destructive.
The
third
laser
pulse
continually
excites
the
ground
state
atoms
which can
then
decay
to
another
state
depleting
the
stored
population
grating. The available
processing
time
is
thus
limited
by
the
branching ratio
of
the
excited state
and
the
excitation
rate
required
to
obtain
a
satisfactory
signal
to
noise
ratio.
The
second
disadvantage
is
that
the
ground
state
splitting
may
be
smaller
than the width
of
the
inhomogeneous
line.
For
example,
nuclear
hyperfine
splittings
are
on
the
order
of
tens
of
megahertz
and
inhomogeneous
linewidths
are
on the
order
of
several
gigahertz.
Level
overlap
will lead
to
coherent
beating
and
undesired
modulation
of
the
output
signal.
The
data
bandwidth
would
be
severely
limited
by
the
smallest
ground
state
splitting.
In
this
paper,
only
gated
coherent
transient
processors
will
be
analyzed.

2.2
The Processing
Stage
The
gating
of
the
material
after
the
first
two
pulses
allows
non-destructive
probing
of
the
processor
by
an
uninterrupted
modulated input signal.
The
response
of
the
material
to
this
continuous input signal
is
similar
to
the
response
due
to the
third
data
pulse
in the
previously
mentioned
triple
product
correlator. The
resultant output
signal
represents
the
continuous
convolution
of
the
input
signal
with
the
cross-correlation
of
the
temporal waveforms
of
the
first
and
second
pulses
(see
figure
2b).
There
are no
restrictions
on the
duration
of
the
third
input
signal
provided
all
the
excited
absorbers
relax
to
the
previous
ground
states
(Though
the
input
signal
has
an
indefinite
duration
with
an
indefinite
number
of
breaks,
it
will
often
be
referred
to
as
the
third
pulse
throughout
the
remainder
of
this
paper).
Multi-photon
processes
may
eventually
lead
to
degradation
of
the
stored
information
and
thus impose
limits
on
the third
input
pulse.
Since
the
processor
can
accept data
continuously,
the
latency
time
if
not
reprogrammed
is
zero.
The
propagation
delay
through
the
processor
is
roughly
the
sum
of
the
durations
of
the
two
programming
pulses.
To
achieve
high
fidelity
output
signals,
the
intensity
of
the
third
pulse
must
be
reduced
to
a
level
where
saturation
effects are
negligible.
Output
direction
is
ks
=
k3 + k2 -
k
1,
where
k
1,
k2,
k3,
and
ks
are
the
wavevectors
for
the
first,
second,
and
third
pulses
and
the
output
signal,
respectively.
The output
is
optimized
when
the
phase
matching condition,
IksI
=
Ikj
,
is
satisfied.
Since
the
material
is
preprogrammed
by
pulses
I
and
2,
during
the
processing
state
the
output
signal
need
only
be
isolated
from
the
third
pulse.
This
can be
accomplished
by
introducing
slight
angular
separation between
the
two
programming
pulses
(as
illustrated
in
figure
1)
or
by
having
the
pulses
be
counter-propagating.
Large
angles
are
avoided
due
to
beam
overlap
considerations,
not
phase
matching
constraints.
2.3
Reprogramming
the
Processor
There
are
two
potential methods
for
reprogramming
the
processor.
The
old
pattern
information
could
be
erased
via
a
reversible
gating process
and
a
new
pattern
programmed
into
the
same
spatial
volume.
In
the
second method,
an
2-D
spatial
array
of
patterns
is
stored
in
the
material.
Different
patterns
are
randomly
accessed
spatially.
Access
times
of
a
few
microseconds
could
hxe
achieved
with
acousto-optic
or
clectro-optic
deflectors. The
pattern
storage
densities
are
calcilated
K,
,\x
and
can
exceed
105
patterns
per
cm
2.
Therefore,
in
most
cases
therc
\\
mild
tK
nio
ncdtl
in

introduce
the
two new
programming pulses
(pulses
I
and
2).
This
greatly
reduces
the
complexity
of
the
processing
stage
and
reduces
the
latency
time
during
reprogramming,
since
the
material
basically
acts
as
an
array
of
passive
filters.
3.0
Analysis
of
Processor's
Performance
The
following
is
an
analysis
of
the
performance
of
a
continuous
optical
processor
in
the
case
where
the
medium
is
gated
after
the
second
pulse.
The
effects
of
homogenous
and
inhomogeneous
broadening,
coherent
and
incoherent
saturation,
output
efficiency,
shot
noise,
spatial
crosstalk,
diffraction,
and
local heating
are
considered
in
evaluating
the
processor's
performance.
A
method
for
obtaining optimal
performance
is
prescribed
and
an
example
is
given.
The
determination
of
the
maximum
achievable time-bandwidth
products,
processing
bandwidths,
and
storage
densities
requires
the
following
input
parameters:
the
wavelength,
Einstein
coefficient,
inhomogeneous
bandwidth,
and
homogeneous bandwidth
of
the
absorbing
transition;
the
absorption
length
and
index
of
refraction
of
the
material;
the
maximum
permissible levels
of
distortions
and
crosstalk;
the
gating
and
detection
efficiency;
and
the
desired
number
of
photoelectons
generated
by
the
peak
of
the
output
signal.
Determining
the
performance
also
requires
limits
to
be
placed
on
the
intensities
of
the
input
signal
and
the
pattern pulse
and
on
the
characteristics
of
their
power
spectrums. These
parameters
and
limits
are
defined
and
discussed
below
3.1
Assumptions
For
convenience,
assume
1)
the
inhomogeneously
broadened
absorber
has
a
uniform
spectral
density
of
absorbers
over
the
inhomogeneous
bandwidth,
A.
Vi,
which
is
centered
around
v
=
c/A.
where
A.
is
the
wavelength
of
the
light
pulses' optical
carrier.
2)
the
inhomogeneous
bandwidth
is
much
greater
than
the
homogeneous
bandwidth,
A
Vh,
3)
the
spectrum
of
the
uninterrupted
data
stream
has
a
bandwidth
less
than
or equal
to
A'Vd,
defined
as
the
processor's
data
bandwidth,
4)
the
data
stream
has the
limitation
that,
averaged over
any
given
time
interval,
its
dynamic power
spectrum
has
the
characteristic
that
the
maximum power
of
any
frequency
component
is
less
than
some
specified
constant
times
the
average power
of
the
data stream,
and
5)
the
intensity
of
the
data stream
averaged
over
a
time
interval
equal
to
the
dephasing
time
of
the
absorbing
transition
is
fairly
constant. Making
these
assumptions
greatly
simplifies
the
analysis
while
introducing
only
a
small
error
with
respect
to
a
mlodel
that
takcs
into
accot
nt
the
trIe
shInpC
of
the
inhoniogeneous
line
and
dtta
"c',
spectiruml
\\ic
e
tice
11c'
ali.
1leatcrid
|Id
dillndata
1,trC311

properties
are
known,
the
required
modifications are
straightforward.
The
absorption
coefficient
for
a
flat
inhomogeneously broadened
line
with
an
inhomogeneous
bandwidth,
A
Vi,
is
given
by
a=
N A
A-o
(2)
87r
n2
AVi
where
N
is
the concentration
of
absorbers
in
the
material,
A10
is the
Einstein
coefficient
for
the
transition
from
the
ground
(level
0)
to
excited (level
1)
state,
/1
is
the
vacuum
wavelength
of
the
transition,
and
n
is
the
index
of
refraction
of
the
host
material.
3.2
Coherent Saturation
Assume
the
medium
responds
to
first
order
as
a
non-magnetic, linear
medium.
The intensity
Id(t)
and
electric
field
real
amplitude
Ed(t)
of
the
continuous
third data
pulse
are
related
by
Id(t)
=
,
Ed(t)1
2 (3)
41r
where
c
is
the
speed
of
light
in
a
vacuum
and
( ý&
represents
the
average
of
the
enclosed
function
over
a
time
interval
&.
The
time
interval
&
is
long
with
respect
to
an
optical
period,
but
short
with
respect
to
the
reciprocal
of
the the
data
bandwidth. The effects
of
coherent
saturation
can be evaluated
by
calculating
the
extent
to
which
the
absorbers
are
coherently
driven
in
a
time
period
equal
to
the
excitation
transition's
homogeneous dephasing time,
T2
=
1/(7r
AVh).
The
Fourier
component
of
the
electric
field
amplitudes
at
time
t
taken
over
a
time interval
T2 is
defined
as
t
+
T2/2
Ed(v)
E-
dt'
Edt)
exp(-i27rvt)
(4)
Ed(v)
is
double
peaked
with
each
peak
grouped
about
the
positive
and
negative optical carrier
frequency
(±c111),
respectively.
It
should
be
noted
that
since there
is
no
assumption
that
Ed(t)
is
repetitive,
Ed(v)
is
a
time
vwrying
quantity
and
is
thus
referred
to
as
a
dynamic
Fourier
component.
Since
Ed(t)
is
real,
Ed(-V)
=
Ed
(vM.
In
accordance
with
our
fourth
assumption
in
section
3.1,
define
Y'c
to
be
the
ratio
of
the
maximum allowable
magnitude squared
of
the
dynamic
Fourier
components
to
the
average
magnitude
squared
of
the
Fourier
components,
such
that
at
any
given
time,
t,

.Yc
Ma{
V12
(v))
K
lOd(V1
v)d
)Vd
where
(
)Avd
represents
the
frequency
average
over
AVd.
The
average
is
taken only
around
the
positive
carrier frequency.
Let
hi
be
defined
as
the maximum
intensity
of
the data stream when
averaged
over
any
time
interval
T2.
Equation
(5)
and
1d
are
limits
of
the
characteristics
of
the
data
signal
that
must
be
met
to
obtain
the
performance
predicted
below.
Assuming
that
the
power
in
the
data
stream
outside
the
data
bandwidth
is
negligible, Parseval's
theorem
yields
lK
E(V'
v),f
)d
T
22 (I[Ed(t)21r
T~2
Id
(6)
2
A
vd
nc
A
vd
The
maximum pulse
area at
time
t
at
a
given
frequency
over
the
time
interval
T2
is
given
by
14
OM=(t)
-
44rp
MaxfA(v)
-4=
p
P
2r
ycT
2
I,
<
0,
(7)
Omx
=h -h _ nC0V
where
Ot
is
defined
as
the
maximum
data
pulse
area
seen
at
any
frequency
and
at
any
time
over
a
time
interval
T2,
p
_
3AI0
h
A
3
3A
2A
(8)
827
is
the
dipole
moment,
and
h
is
Planck's
constant.
It
is
assumed that
the
unit
vectors
of
the
dipole
moment
and
electric
field are aligned.
The
maximum
allowable
photon
flux
of
the
continuous
third
data
pulse,
Fc,
is 2
Fc
= l
<
27r
01
&Av
t
(9)
hc
3
yc
AoT2
2
By establishing
an
acceptable
level
of
non-linearity
in
the
medium's
response
to
the
electric
field
amplitudes,
the
value
of
the
maximum
allowable
pulse
area
can
be
set.
At
the
onset
of
coherent
saturation,
the
medium's
response
to
the
peak
components
in
the
data
pulse's
spectrum
is
no
longer
linear,
but
is
roughly
proportional
to
the
sin
(Omax).
To
first
order,
the
non-linearity
E
is
roughly
given
by
-1.
sin(0)
If
E
<<
1,
then
01
9-E
.
The
acceptable
value
of
e,
and
thus
01,
will
depend
on
the
application
requirements.
For
example,
if
10%
non-linearity
is
accejtahle,
the
nia\li1unli
4,
,
pulse
area
is
approximately
nt/4.

3.3
Incoherent
Saturation
Since
the
duration
of
the
third
pulse
can
be
much
longer
than the
homogeneous
decay
time
of
the
excitation transition,
incoherent
saturation
of
the
transition
must
be
considered.
The
coherent
transient
output
signal's
electric
field
amplitude
is
proportional
to the
population
difference
between
the
ground state
(level
0)
and
excited
state
(level
1).
Take
the
general
case
where
the
decay
from
level
1
to
level 0
has
a
bottleneck, which
will
be labeled
level
2.
Assumption
(5)
above
assumes
the
dynamic
power
spectrum
of
the
continuous
third pulse
when
averaged
over
the
effective
decay
time
of
upper
state
population
is
roughly
uniform over
the
data
bandwidth.
The effective
decay
time
of
the
upper
state,
T,
is
discussed
below.
Define
Y,
to
be
the
maximum
allowable
ratio
of
the
peak
value
of
the time
averaged
power
spectrum
to
the
average
value
of
the
time
averaged
power
spectrum. More
precisely
Ma{
(E(v)12),
I
KK
ý
d(v)12X),.)AVd
at
any given
time
f.
This
is
a
further
limit
on
the
characteristics
of
the
input data
signal.
The
time-
varying
induced
transition
rate,
R,
between
levels
0
and
I
at
the
peak
of
the
power
spectrum
is
thus
governed
by
R
<ya
Avi
Fd
Rmax,
(12)
N
A
vd
where
Fd
is
the
incident
photon
flux
of
the
continuous
third
pulse
averaged
over
"T'.
If
the
effective
population
decay
time
is
sufficiently
greater
than
the
coherence
decay time
T2
and
the
peaks
in
the
power
spectrum
are
randomly
distributed,
then
y,
=
1.
If
the
effective decay
time
is
comparable
to
the coherence decay
time
or
if
there
are
peaks
in
the
power
spectrum
that
do
not
average
out
over
time,
then
y
can
be
as
large
as
,c.
Define
TI", T'
1
2,
and
t20 as
the
decay
times
from
levels
I
to
0,
1
to
2,
and
2
to
0,
respectively.
By
solving
the
rate
equations,
the
maximum
population
difference
is
found
to
be
proportional
to
1
(13)
1 +
2Rm,,'"
where
T' is
the
effective
decay
time
of
level
1
and
is
given
by
2'
=w
(T2
0 +
2
T1
2)
(14)
2
T1
2
+ T10

The
values
of
T'
under
various
limits
are:
For
TIO
<<
T12
and
T2 0 << T12,
T'
T10 .
(15)
For
'C
1
0
<<
T12
and
T20
>>
T12,
T'
(zloz2o)/(2"I
2).
(16)
For
"10
>>
T1
2
and
T20
<<
T12,
T'
T12.
(17)
For
T1 0
>>
T12
and
"20
>>
T12 , -'
'r20/2
(18)
In
the
section
on
coherent
saturation,
an
acceptable
level
of
nonlinearity
for
the
processor, e,
was
introduced.
The
non-linearity
due
to
incoherent
saturation
is
roughly
equal
to the
deviation
of
equation
(13)
from unity
or approximately
2Rr'
for
2Rr'<<
1.
In
order
that
incoherent
saturation does
not
introduce
non-linearities
greater
than
e,
the
condition
2R
z'
<
e
must
hold.
Thus,
the
maximum
photon
flux
of
the
continuous
third
pulse
limited
by
incoherent
saturation
is
given
by
4itn
2A
VdE
Fi
=2
A
1n2-e'dC(19)
Here (and throughout
the
paper)
it
is
assumed
that
the
non-linearites
due
to
different
effects
are
uncorrelated,
though
further
study
is
needed
to
determine
the
extent
to
which
this
is
true.
In
order
to
minimize
both
coherent
and
incoherent
saturation,
the
maximum
allowable
photon
flux
of
the
continuous
third
pulse must
be
less
than
or
equal
to
the
minimum
of
Fc
in
equation
(9)
and
Fi
in
equation
(19). In
accordance
with
assumption
(5),
the
time
average
of
the
intensity
over
an
interval
T2
is
roughly
equal
to
the
time average
over
an
interval
T'.
If
the
coherence
decay
time
were
a
fixed
property
of
the
material
but
the
population
decay
time
was
variable
(i.e.
by
optical
pumping
of
the
bottleneck
state
to
a
short
lived
state),
the
optimal
effective decay
time
is
obtained
by
setting
Fd
=
Fi
=
Fc,
which
yields
,' =
n
ye
T2
.
(20)
(2
Shorter
decay
times
lead
to
less
saturation, but
may
lower
gating efficiencies
since
in
the
programming
stage
there
is
less
time
to
gate
the
excited
absorbers.
3.4
Output
Signal
Efficiency
Define
the
peak
output efficiency,
r7peak,
as
the
ratio
of
the
intensity
of
the
output
autocorrelation
peaks
to
the
average
intensity
of
the
continuous
third
pulse.
The
dependncew
,,
7
1peak
on
1)
the
gating
efficiency,
2)
the
properties
of
the
stored
p)attern
pulk,-ý
"
the
:~R( i iIII II+

homogeneous
decay
time,
4)
the
gain
efficiency
of
the
material,
and
5)
the
spatial
profile
of
the
input
beams
are
discussed
below.
Gating
efficiency
Define
the
gating
efficiency
ligate
as
the
ratio
of
the
number
of
absorbers
that are
permanently
altered
(i.e.
photoionized)
by
the
gating
pulse
to
the number
of
absorbers
that
were
in
the
excited
state
just
before
the
gating
pulse
(for
accumulated
population
gratings,
replace
rlgate
with
an
appropriate
accumulated
grating efficiency).
The
output
signal
electric
field
amplitude
is
proportional
to
the population
difference
at
the
time
of
recall
and thus
proportional
to
7igae
.
The
maximum
obtainable
electric
field
of
a
gated
coherent
transient (when
7lgate
=
1)
is
down
by
a
factor
of
2
from that
of
a
non-gated
coherent
transient
due
to
the
elimination
of
the
excited
state
population
grating which
contains
half
of
the
information
after
the
second
pulse.
14
The
output
signal's
electric field
is
equal
to
irgatw/
2 times that
of
a
non-gated
coherent transient.
Pattern
Pulse
Efficiency
To
calculate
the
intensity
of
the
output
signal,
a
particular
processor
configuration
must
be
chosen.
The case considered
below
is
one
in
which
a
single
pattern
pulse
is
programmed
during
the
programming
stage.
Assume
the second
pulse
consists
of
a
single
subpulse
with
pulse
area
equal
to
O8.
Let
the
first
pulse
be
a
pattern
pulse
of
total
duration
opa.
The
electric
field
of
the
output
signal
in
the
limit
of
an
optically
thin
sample
(oXL
<<
1)
is
given
by
14
Es(t)
=
f+
T:pad2
7
Jgape
aL
sin(0
2) IT
J
dz
Epat(')
E('
+
t
-"C
21)
exp(-2(Q
21 -
'r)/T2)
,
(21)
where
L
is
the
interaction
length
in
the
material,
Epat(t)
is
the
real
electric
field
of
the
pattern
(first)
pulse,
and
r,2
is
the
temporal
separation
between
pulses
one
and
two.
The
timc
origin
t
=
0
is
defined
such
that
Epai(t)
is
nonzero only
from
t
=
--
rp,/2
to
t
=
+-rpa/
2.
Assuming
pulse two
immediately
follows
the
pattern
pulse,
then
r21
=
rpa/
2.
The
third
pulse Ed(t)
can
start
at
any time
after
the material
has
been
programmed
and
gated.
The
exponential
term
in
the
integral takes
into
account
the
effects
of
homogeneous
coherence
decay.
Assume
that,
over
a
time
interval
Trea
about time
t',
the
third pulse
matches
the
firs,
Qatlcrrl
pulse,
i.e.
f',i

Ed(t
+ ) -
.d(t
Epat(±z),
(22)
(Ipat(r)).pat
where
it
is
assumed
that
the
intensity
of
the
third
pulse
when
averaged
over
"rpa,
is
roughly
equal
to
Id.
This
assumption
is
valid
if (1)
rpat
is
not
significantly
less
than
T2,
(2)
Vrpat
is
much
greater
than
i/Ad
and
(3)
the
average
intensity
of
the
third
pulse
is
relatively
constant.
The
maximum
allowable
intensity
of
the
fi-st
pulse
(pat(T)),r,
is
governed
by
coherent
saturation
and
is
equivalent
to
the
expression
in
equation
(9)
if
T2
is
replaced
with
rpa
and
Yc
is
replaced
with
yc2'.
The
new
parameter
yca'
is
introduced
to
allow
for
the
case
when
the
spectral
characteristics of
the
pattern
pulse differ
significantly
from
those
of
the
continuous pulse
three.
If
the
exponential
decay
term
is
temporarily
ignored,
the
intensity
of
the
output
signal
without
homogeneous
decay
at
the
correlation
peak
is 2
[im
[s(t')]
2
2t
2
69
'pat
AVd
m
1
gate
(Ci)
sin
(02)
Id
(23)
T2
--
CI
16
ýc
at
Note
that
the
intensity
of
the
output
peak
is
proportional
to
the
product
,pat
AVd
,
the
time-
bandwidth
product
of
the
processor.
Homogeneous
Decay
Efficiency
The
effect
of
homogeneous
decay
on
the
correlatoi-'z
operation
is
to
put
less
weight
on
the start
of
the
pattern
than on
the
end
of
it
and
to
reduce
the
output
efficiency.
The
maximum
field
non-
linearity
due
to
the
homogeneous
decay
is
(I -
exp(-
2rpat/T
2)).14
By
bounding
this
value
with
the
acceptable
non-linearity
r,
a
maximum
value
for
vpaj
can
be
obtained.
For
E
<<
1,
the
constraint
on the
ratio
of
rpat/T
2
is
Ipat
=
(TpateT
2)
•5
(e
/2)
(24)
To
estimate
the
reduction
in
the
autocorrelation peak
intensity due
to
homogeneous
decay,
let
IEp
at
(t)I
be
roughly constant
(as
in
the
case
of
phase
modulated
input
pulses),
so
that
the
electric
fields
can
be taken
out
of
the integral
in
equation
(21).
The
resultant
efficiency due
to
homogeneous
decay
is
[Is((t)] (1 -
exp(-2fpat)
2
l7decay
lim
[IS(t')
-2
Ipat
(25)
where
the
above
condition
that
r21
=
r,,a/2
is
assumed
It
should
be
noted 01tI)
lih
cffecLs
of
A12

homogeneous
decay
can
be
cancelled
by
introducing
an
exponential
ramp,
exp(-4z'T2), into
the
pattern
pulse. This
would
allow
rVpat
>
T2.
However,
this would
require
higher
complexity
in
the
input devices
as
well
as
confidence
in
the
consistency
of
the
homogenous decay
rate
and
in
the
shape
of
the
decay.
For
now, assume
that
the
pattern
pulse
is
uncorrected for
homogeneous
decay.
Gain
Efficiency
In
an
optically
thick
medium
(aL
approaching
or
exceeding
unity),
the
term
(oL)
2
in
equation
(23)
must
be
replaced
by
the
gain
efficiency
of
the
material,
r/a,
which
is
a
non-linear
function
of
aL.
For optically thin
samples
(aL
<<
1),
77r,
=
(aL)
2
.14
For
optically
thick
samples,
the
optimal
gain
efficiency
is
a
balance between
the
number
of
radiating
absorbers
and
the
absorption
of
the
input
pulses
and
output
signal.
Consider
the
case
of
a
stimulated
photon
echo
in
which
all
three
excitation
pulses
are
assumed
to
undergo
linear
absorption
and
the
polarization
is
assumed
proportional
to
the
cube
of
the
excitation
pulse
electric
fields.
It
has
previously
been
shown
that
14
77a
=
(1
-
exp(-aL))
2
exp(-aL)
.
(26)
The assumption
that
all
the
pulses
undergo
linear absorption
slightly
underestimates
the
gain
efficiency
since
one
of
the
excitation
pulses
is
generally
a
it/2 pulse
which
saturates
the
medium
and
the
absorber's
response
to the
excitation
pulses
is
not
linear
but
sinusoidal
in
nature.
Beam
Overlap
Efficiency
From equations
(23),
(25),
and
(26),
an
expression
for
the peak
output
intensity
efficiency,
T
7peak,
is
obtained:
2 2
Is(t')
_7gate
77a.L
l7decay
01
Tpat
AVd
ýlPeak"
=
-J 1cat
(27)
Id
16
_at
where
is is
assumed that
02
=
7r/2
and that
(IPa
1
(T)),r,,
equals
its
maximum
allowable
value.
For
gaussian beams,
this
peak
efficiency
is
only
obtained
near
the
center
of
the
beams.
As
the
intensity
decreases
on the
wings
of
the
gaussian,
so
does
the
efficiency.
If
the
spatial
intensity
profile
of
the
jth
pulse
can
be
written
as
1l(r)
=
lj(O)
exp-
(L)2)
where
r
is
the
radial
distance
from
the
centcr
of
lh
ga'Ussian
bfam,
kh
the
i)
01C
JtlCgt;t
1L
'
J

the
jth
pulse,
Pj,
is Ira2
It0).
The
output
intensity
as
a
function
of
radial
position for
a
coherent
transient
where
the
second
pulse
is
a
brief
pulse
and
the
first
and
third
pulses
are
in
the
linear
regime
is
given
by
Is(r)
=71peak
Id(r)
sin
p
ar
12(r)
(29)
ipat(O)
12(0)
The
total
output
signal
power
is
the
spatial
integral
of
Is(r).
Define
the
overlap
efficiency,
i7overlap,
as
the ratio
of
the
actual
output
signal
power
Ps
to
the
ideal
output
signal
power,
which
is
7
lpeak
Pd
(
i.e.
Ps
=
l7overlapTlpeak
Pd
).
Efficiencies approaching
77overlap
=
1
can
be
obtained
if
variable
beam
widths
or
non-diffraction
limited
"top hat"
beams
are
used.
However,
these
techniques
lead
to
increased
spatial
crosstalk
or
increased diffraction
and,
thus,
lower
pattern
densities.
In
this paper, only gaussian
beams
of
equal width
are
considered.
The
overlap
efficiency
is
then
2
Id(r)
Ipa"(r)
S1 /
I2(r)
floverlap
2
dir
r
'()10
20
)
(30)
a
,
Id(o)
Ipai(O)120
Equation
(30)
can
be
numerically
integrated.
For
02
=
7c/2,
the
result
is
7joverlap
=
0.43.
This
compares
to
Tioverlap
=
0.5
if
the
sine term
were
ignored
(set
to
one).
By
slightly
increasing
the
peak
pulse
area
of
pulse
two,
the
overlap efficiency
can
be
optimized
to
7
7overiap
=
0.46
when
02
equals
(0.59)nt.
3.5
Required
spot
size
for
shot
noise
limited detection
Define
the
detection
efficiency
77det
as
the
ratio
of
photons
detected
to
the
photons
that
are
emitted
in
the
output
signal.
Output coupling
and
scattering
losses,
as
well
as
the
detector's
quantum
efficiency,
are
incorporated
into the
detection
efficiency.
The
number
of
detected
photons,
p,
in
a
correlation
peak
is
roughly
____
2-
[ =
hAvj)
7
ldet
7loverlap7lpeak7CY
Id
(31)
assuming
the
width
of
the
correlation
peak
is
roughly
I/AyVd.
Assuming
Id
is
roughly
equal
to
its
2
maximum
value
given
by
equation
(9),
solving
for
a
yields
2 26
3
n
pf
Pa
)C
T2
A
)/(
CY "•2 4
ýTatAVd,
77w.i''
ýr
77det
7lgate
17overlap
77decayOl
I1.

3.6
Pattern
Storage
Density
The
crosstalk
from
neighboring
spots
when
the
third
pulse
is
incident
on
a
given spatial
location
is
now
calculated
for
the
cases
in
which
the
nearest neighbors have
correlated
and
uncorrelated
patterns
and
for
the
case where
a
detection
aperture
is
introdued.
Pattern
Storage Density
for
Uncorrelated
Nearest
Neighbors
Consider
two
adjacent storage
spots.
Define
an
x-y
coordinate
system
such
that
the
two
spots
lie on
the
x-axis separated
by
xs
with
the
third
pulse
centered
at
the
origin.
We
will ignore
the
saturation
of
the
second
pulse
that
occurs
when
writing
the
adjacent
spot.
This
leads
to
an
2
overestimate
of
the
crosstalk
signal
by
at
most
02;
the
error
is
greatest
in
the
region
around
the
adjacent
spot
and
is
negligible
in
the
region
around the desired
spot.
The
estimated
peak
power
of
the
crosstalk
signal
from
a
single
adjacent spot
is
+00
+00
! f ~ ~
~
2Zpat(X-Xs'Y)
12(x-x,'Y)d(y)3)
PJ(xs)
= .
dx
f
dy
7lpeak
02
pa(O)
12(0)
Id(XY)
(33)
S-00
-0
This
calculation
does
not
take
into account
interference
between
the
crosstalk
signal
and
the
desired
output
signal.
It
assumes
that
the
adjacent
spots
will have
roughly
orthogonal patterns
stored
in
them
and,
therefore,
the
correlation
peaks
in
the
crosstalk
signal
and the
desired
output
signal
will
not
overlap
temporally
and
coherently
interfere.
It
is
also assumed
that
all
the
patterns
in
the
adjacent
spots
are
roughly mutually
orthogonal
so
that
the
peak
level
of
the
total
crosstalk
signal is
just
the peak
level
calculated
above
for
a
single
adjacent
spot.
For
gaussian
pulses,
the
ratio
of
the
crosstalk
signal
to
the
desired
signal
is
22
Pc-
02
exp
-L
.
(34)
P
s
3
overlap
The
maximum
pattern
density
is
the
reciprocal
of
the
unit
cell area
which
depends
on
the two
dimensional
packing
geometry.
Assuming
hexagonal
packing,
the
maximum
pattern density
for
uncorrelated
adjacent
patterns
is
Dmax
-
4
8
(35)
,[3xS
(
33 22
In_)
31
loverlap
PC
The results
are
illustrated
in
trace
a
of
figure
3
for
O0
=
(0.59)rt
and
1,V,.L11
=
R0.46.
In
the
1ikIure
(K•

2
the
normalized pattern
density
is
defined
as
DmanlJ
Pattern
Storage
Density
for
Correlated
Nearest Neighbors
If
the
patterns
in
the
adjacent spots
are
correlated,
the
autocorrelation
peaks
temporally
overlap
the
desired
signal's
peaks
and
the
interference
between
the
crosstalk
and desired
output
signal
must
be
considered.
The
result
depends
significantly
on
the
degree
of
correlation. The
worst
case
is
if
all
six
adjacent
spots
are
programmed
identically
to
the
central
spot,
but
in
phase
or
180
degrees
out
of
phase
with the desired
signal.
The
magnitude
of
the
change
in
the
output
signal
power
under
these
conditions
is
IAPS(xS)I
=
+00
+00
022
dy
/Ipai(XXsY)
Ipat(XY)
12(X-Xsy)
12(xY)
Id(xY)
(36)
1217
peak
02f
dxf
dyipai(O)
12(0)
l(,) (6
and
Dmax
4
-
8
(37)
V'3X,
(F
2
I
floverlap
MAPI
The
results
are
illustrated
in
trace
b
of
figure
3.
This
condition
is
to be
avoided
since the
achievable
pattern
densities
are
significantly
lower
in
the
case
of
correlated
nearest
neighbors
compared
to the
case
of
uncorrelated
nearest
neighbors
for equivalent
requirements
on
the
signal
to
noise
ratio.
Pattern
Storage
Density
with
a
Detection Aperture
The
isolation
between
adjacent
spots can
be
significantly
improved
by
placing
an
aperture
in the
image
plane
of
the
output
signal.
Since
the
stored
informatioiA
is prodluced
'by
u'l.
1 1
'Jng
of
two
gaussian
beams,
its
spatial extent
is
much
less
than that
of
the
gaussian
third
pulse
and
a
majority
of
the
crosstalk
signal comes
from
the
region
around
the
adjacent spots rather
than
from
the
region
of
the
desired spot.
The
case
where
the
output
signal
is
reimaged
and
centered
on
a
square
aperture
of
width
xscan
be
calculated numerically,
using
equation (33),
by
reducing
the
limits on
the
integral
to
±
xs/2.
The
overestimate
of
the
crosstalk
signal
and,
thus,
the
underestimate
of
the
density
due
to
ignoring
the
saturation
of
pulse
2
is
negligible
under
these
conditions.
The
rcsultr'
are
shown
for
the
case
of
uncorrelated adjacent
patterns
in
trace
c
of
figure
3.

3.7
Local
Heating
One
concern
with
a
continuous
input
beam
is
the
effect
of
localized
heating
of
the
material.
This
heating would
cause
the
temperature
dependent
homogeneous
line
to
broaden.
Consider
the case
where
the sample
is
a
rod
of
radius
r0
and
length L.
Assume
the
rod
is
only
cooled
on
its
circumference
and
the
ends
are
effectively
insulated. Assume
that
all
the
incident
power,
Pd,
is
dissipated
in
the
form
of
heat
uniformly
along
a
cylinder
of
radius
0.
and
length
L
centered
in the
rod.
The
problem
is
then
axially
symmetric
and
the
temperature
rise
at
the
center
of
the
beam
is
easily calculated
to
be
AT
-
(=
+21n(rocy))P
,
(38)
4
rcL
"where
K
is
the
thermal
conductivity
of
the
material.
In
the
section
4.1,
this
effect
will
be
shown
to
be
negligible.
4.0
Optimizing
the
Processor's
Performance
2
2
Maximizing
pattern
storage
density
requires n-iinimizing0.
. Note
that
a
is
proportional
to
(T 2
A
vi)/(Tpat
AVd).
The
limit
on
rpu
is
given
in
equation
(24).
The
limit
on
Avd
is
that
it
must
be
proportionately
smaller
thin
Avi
in
order
to
minimize
distortions
due
to
bandwidth
limitations.
For
a
given maximum
acceptable distortion
level
and
assuming
that
'rpw,
and
Avd
are
at
their
limits,
the
ratios
AvdIAvi
=-
fd
and
"p/T2
=
e/2
are
fixed.
Under
these
conditions,
the pattern
density
is
independent
of
both
the
inhomogeneous
and
homogeneous
bandwidths
of
the
medium
and,
thus,
independent
of
the
time-bandwidth
product,
which
is
governed
by the
ratio
of
these
bandwidths.
If
the
expression
in
equation
(26)
is
used
for
r7,,
then
the minimum
of
(oa
/7aL)
is
5.32/L
and
occurs
at
cx
=
.523/L.
Thus,
a.2
is
inversely
proportional
to
interaction
length,
L,
and
is
minimized
when
L
is
at
its
maximum.
The
maximum
path
length
through
the
sample
is
limited
by
diffraction.
To determine
the
maximum
acceptable
path
length
through
the
sample,
consider
the
intensity
profile
of
a
focused
gaussian
beam:
I(z,r)
1(0,0)
exp
,
(39)
Z ý2ý
2
(
_+L)2))
where
z
is
the
distance away from
focus
and
zo
=
27r
n
cr2/2
.
At
±z(ýI2.
the"
nin
main
intCj,,t\
drop
on
axis
is
20%
and
the
maximum
beam
width
is
12
.,
c
atler
thl
at
i
./
1i,

than
zo,
the
beams
will
not
remain
in
focus
through
the
sample.
This
will lead
to
loss
in
efficiency
and
increased
crosstalk
with
neighboring
spots.
Setting
L
=
z0,
neglecting
the
slight
divergence
of
the
beam
as
it
traverses
the
crystal, and
solving
for
ao2
yields
2
53
2.
3
p
-
7c
l;
(miJ
2
(40)
22
Solving
for..m
in fixes
the
value
of
the
absorbing
transition
Einstein
coefficient:
A1o
=
4
n
AV,
(0.523)
/
(N
A
C.2
in)'".
(41)
Finally,
note
that
by
increasing
the
absorption
concentration,
N,
the
pattern density
is
increased.
Unfortunately,
increased
absorber concentrations
increases
the
rate
of
intercenter
interactions
and
can
lead
to
faster
dephasing
rates
and
spectral
diffusion.
These deleterious
effects
often
occur
for
concentrations
above
1018
/cm
3.5
Equation
(40)
has
been
derived assuming
that
the
choice of
N
is
independent
of
all
other
parameters.
However,
to
obtain
the
maximum
performance
in
practice,
the
relationships
between
maximum
N
and
other
parameters
(primarily
the
inhomogeneous
and
homogeneous
bandwidths,
the
Einstein
coefficient,
and
the
gating
efficiency)
will
have
to
be
introduced into
equation
(32)
before
minimizing
u
2.
These
relationships
are
material
dependent
and
have
not
been
fully
characterized.
Thus, equation
(40)
will
be
used
to
estimate
the
maximum
pattern
density
and
assumed
valid
if
conservative values
for
the
maximum concentrations
are
chosen.
4.1
Performance
of
an
Optimized
Processor
To
estimate
the
performance
of
the
continuous
correlator
with
optimized
material
parameters,
typical
values
for
the
material
and
system
parameters
must
be
assumed.
Reasonable
material
parameters
might
be
2
=
800
nm,
n
=
1.5,
Avi
=
10
GHz,
and
AVh =
5
kHz
(T2
=
64
.tsec).
The
concentration
maximum
is
taken
to be
1018
absorbers
per
cubic
centimeter
to avoid
intercenter interactions.
/Assume
77det
=
0.75,
7
7overlap
0.46
(02
=
0.597t),
E
=
0.1,
1
7gaze
=
0.1,
and
Pd
=
0.5.
The
value
of
c
requires
01
=
.75
and
0,p,,
=
0.05
and
yields
1
7
decay
=
.91.
Values
for
y,
and
yfpat
can
be
estimated
by
examining
the
spectrum
of
random
binary
sequences.
For
sequences
up
to
8192
in
length,
the
ratio
of
the
spectral
power maximum
to
average
value
seldom
exceeds
12.
Set
y,
y,
16
to
take
into
account
that
the
patterns
n,,
signals
are
not
actually
random.
Take
yi
to
be
the
geometric
anc1
it
it4,
c\rtwlle
\'aluc
,
y.,
i.e.
yi
=
4.
In
the shot
noise
limit,
the
numbcr
,t
dtctcctd
1h,
4v:
,:ru
i
N
t
,t ,

error rate
of
10-9
is
p
=
116
if
a
50%
detection
threshold
is
assumed.
The above
input
parameters
yield
the
result
a'min
=
15
Am.
Assuming
roughly
orthogonal
(uncorrelated)
adjacent
patterns
and a
crosstalk
signal
to
noise
ratio
of
10
is
acceptable,
the
maximum
pattern
storage
density
without
a
detection
aperture
is
2.2
x
105
per
cm
2.
The
data
bandwidth
is
5
GI-lz
and
the
time-bandwidth
product
is
16000.
The
required
value
of
A10 is
180
Hz,
which
corresponds
to an
oscillator
strength
of
roughly
1.7 x
10-6.
The optimal
path
length
through
the
crystal
is
2.6
mm
and
the
optimal
effective
decay
time
of
the
excited
state
is
0.41
msec. The
maximum
input
power
is
13
AW
and
the
peak output
signal
power
is
0.19
g.tW.
(To
obtain
shot
noise
limited
detection
would
require
a
cooled
avalanche
photodiode
or
coherent
detection.) Assuming
the
sample
is
a
cylinder
of
radius
r0
=
5
cm
and
has
a
low
thermal
conductivity
of
ic=
0.1
W/K
cm, the temperature
rise
at
the
center
of
the
beam
is
0.7 mK
and,
thus,
local
heating
effects
are
negligible.
The
above
is
a
reasonable
estimate
of
the
potential
performance
of
the
correlator
with
an
optimized
material
assuming
reasonable
values for
the
input
parameters.
Consider
the
effects
of
changing
one
or
more
of
the
input parameters
has
on
the
predicted
optimized
performance.
The
gating
efficiency,
7
lg,,e
,
could
possibly
approach
100%
or
only
be
limited
to
less
than
1%,
which
would increase
or
decrease,
respectively,
the
pattern
density
by
a
factor
of
10.
The value
of
yc
and
,pat
could
be
made
smaller
with
appropriate
coding
of
the
patterns
and
signals, yielding
a
slight increase
in
the
pattern
density.
The performance
is
highly
dependent
on
the
required
linearity.
A
factor
of
2
reduction
in
epsilon
and
factor
of
2
increase
in
crosstalk
signal
to
noise
leads
to
a
factor
of
3.2
reduction
in
pattern
density
and
a
factor
of
2
reduction
in
time-bandwidth
product.
As
mentioned
before,
if
the
material's
homogeneous
decay
is
well
characterized,
its
effects
can
be
cancelled
by
appropriate
tailoring
of
the
pattern
pulse.
If
Pp3,
is
increased
from
0.05
to
1.0,
a
10-fold
increase
in
the
time-bandwidth
product
and
a
3-fold increase
in
the
pattern
storage
density
are
realized.
The
above
examples
assumed that
the
processor's
free
parameters
are
reoptimized
after
each
change
in
the
input parameters.
For
non-optimized
parameters,
equation
(32)
yields
the
required
spot size
for
any
given
configuration.
5.0
Summary
Modem communication,
radar,
and
object recognition
systenis
often
rely
01n
I)crTorlv1n
reaIl
_• (

time
convolutions
of
uninterrupted
signal
waveforms
with
multiple
fixed-pattern
waveforms.
Electronic,
acoustic,
and
fiber
optic
correlators
are
limited
by
low
time-bandwidth product,
low
bandwidth,
or
programming
difficulties.
Coherent
transient
processing
techniques
have
advantages
over
existing
technologies
due
to
their
high bandwidth
and
large
time-bandwidth
product
and
processing
density.
Coherent
transients
respond
to
the
input
pulses' field
amplitudes.
This
allows
phase
and/or
amplitude
encoding
of
the
pattern
and
input
signals.
The
continuous
processing
technique
presented
here
has
three
distinct
advantages
over
previously
presented
coherent
transient processing techniques.
First, the
continuous
data stream
does
not
need
to
be
broken
up
into
overlapping
segments
which
are
shorter
than
the
homogeneous
decay
time
and,
then,
processed
separately.
Second,
once
the
first
two
input
pulses
have
programmed
the
solid,
they
need not
be
reentered.
This
greatly
increases
the
maximum
processing
speed, allowing
real-
time
processing
of
continuous
data
streams
with
multi-gigahertz
bandwidths
and
with
propagation
delays
only
slightly greater
than
the
duration
of
the
programming
pulses.
Third, different
patterns
can
be
stored
at
multiple
locations
in
the
material
and
accessed
randomly.
Access
rates
of
tens
of
microseconds
enable
fast
reprogramming
of
the
processor
without
having
to
reintroduce
the
programming
pulses.
7.0
Acknowledgement
The
authors
gratefully
acknowledge
the
assistance
of
Rudy
L.
Prater
in
verifying
the
derivations
and
editing
the
manuscript.
This
research
is
being
sponsored
by
the
Air
Force
Office
of
Scientific
Research
(AFSC) under
Contract
F49620-91-C-0088.
8.0
References
1.
T.
W.
Mossberg,
"Time-domain
frequency-selective
optical
data storage,"
Opt.
Lett.
7,
77
(1982).
2.
W.
R.
Babbitt
and
T.
W.
Mossberg, "Time-Domain
Frequency-Selective
Optical
Data Storage
in
a
Solid-State
Material,"
Opt.
Comm.
65,
185
(1988).
3.
M. K.
Kim
and
R.
Kachru,
"Multiple-Bit
Long-Term
Data
Storage
by
Backward
Stimulated
Echo,"
Opt.
Lett.
14,
423
(1989).

4.
M.
Mitsunaga,
R.
Yano,
and
N.
Uesugi,
"Time-
and
frequency-domain
hybrid optical
memory:
1.6-kbit
data
storage
in
Eu
3+:Y
2
SiO
5,"
Optics
Letters
16,
1890
(1991).
5.
W.
E.
Moerner, "Molecular
electronics
for
frequency
domain
optical storage:
Persistent
spectral
hole-burning,"
J. Molec.
Elec.
1,
55
(1985);
Frequency
domain
optical
storage
and
other
applications
of
persistent
spectral
hole-burning,"
Chapter
7
in
Persistent
Spectral
Hole-Burning:
Science
and
Applications,
W.
E.
Moerner,
Ed.,
Topics
in
Current
Physics
Vol.
44,
Springer-
Verlag,
1988
and
references
therein.
6.
Y.
S.
Bai,
W.
R.
Babbitt,
N.
W.
Carlson, and
T.
W.
Mossberg,
"Real-time optical
waveform
convolver/cross
correlator,"
Appl. Phys.
Lett.
45,
714
(1984).
7.
J.
A.
Bell
and W.
R.
Babbitt,
"Phase
and
frequency
sensitive
signal
processing
using
stimulated
photon
echoes",
Conference
on
Lasers
and Electro-Optics,
Anaheim,
1990
Technical
Digest
Series
(Optical
Society
of
America,
Washington,
DC
1990) Vol.
7,
pp 420-421.
8. T.
W.
Mossberg,
Y.
S.
Bai,
W.
R.
Babbitt,
and
N.
W.
Carlson,
"Optical
cross-correlation
and
convolution
apparatus,"
U.
S.
Patent
No.
4,670,854
(June
2,
1987).
9.
W.
R.
Babbitt and
J.
A.
Bell,
"An
optical
signal processor
for
processing
continuous signal
data,"
U.
S.
Patent
Application
Pending.
10.
W.
R.
Babbitt,
Y.
S.
Bai,
and
T.
W.
Mossberg,
"Convolution,
Correlation,
and
Storage
of
Optical
Data
in
Inhomogeneously
Broadened Materials,"
Optical
Information
Processing
II,
P.
R.
Pape
ed.,
SPIE
639,
Bellingham,
Wa. (1986).
11.
R.M.Macfarlane
and
R.M.Shelby,
"Sub-kilohertz
optical
linewidths
of
the
7F0-5D0
transition
in Y20
3
:Eu
3
+,'"
Opt. Commun.
39,
169 (1981).
12.
A.
Winnacker,
R.
M
Shelby,
and
R.
M.
Macfarlane,
"Photon-gated
hole
hurning:
ai
nc\\
mechanism
using
two-step
photoionization,"
Opt.
leit.
10.
)5ý() ( (N
i l l l
I
:I

13.
W.
R.
Babbitt,
A.
Lezama,
and
T.
W.
Mossberg,
"Optical
Dephasing,
Hyperfine
Structure,
and
Hyperfine
Relaxation Associated
with
the
580.8nm
7F0-5D0
Transition
in
Eu
3+:Y203
,"Phys.
Rev.
BI
39,
1987
(1989).
14.
W.
R.
Babbitt,
The
Response
of
Inhomoge-neously
Broadened
Optical
Absorbers
to
Temporally
Complex
Light
Pulses,
PhD Thesis,
Harvard
University,
November
1987.
Programming
Gating
Processing
the
IBS
the
IBS
the
Input
Signal
Pattern
Gating
Input
Ple ISPulse ISSignalIBS
-wo
SI
Output
•LBS
Signal
Reference
Pulse
Figure
1.
The
three
steps
for
signal
processing:
programming
the
inhomogeneously
broadened
solid
(IBS),
gating
the
IBS,
and
processing
the
continuous
input
signal.
As
drawn,
the
output
signal
propagates
in
the
same
direction
as
the
reference
pulse.
e:
I I i I
|
f I

(a)
Reference
Pulse
Pattern
Pulse
Gating
Pulse
Time
(b)
Input
Data
SignalL W,ý
Time
Figure
2.
(a)
The
timing
of
the
programming
pulses
and
the
gating
pulse.
The
pattern
pulse
is
a
phase
encoded
13-bit
Barker
code.
(b)
Segments
of
the
continuous
input
data
signal
and
resultant
output
signal
are
shown.
The
upper
trace shows
the
amplitude
of
the
input
signal
and
the
lower
trace
shows
the
intensity
of
the
output
signal.
The
input data
signal
is
phase encoded.
The
13-bit
Barker
code
use
for
the pattern
pulse
is
repeated
six
times
in
this segment
of
the
input
data signal
with
random
bits
separating
them.
The
peaks
in
the
output
signal
intensity
correspond
to
correlations
between
the
pattern
pulse
and input
data
signal.
The
actual
output
signal
will
be
delayed
by
the
temporal
separation
between
the
pattern and
reference
pulses.

1.2
(C)
V
1.0
• 0.8
(a)
S0.6
S0.4 N
Z
(b)n
0.2
0
.0
.I I .. . . ... I
1
10
100
1000
10000
Signal
to
Crosstalk
Noise
Ratio
Figure
3:
The
normalized
pattern
density versus
the
signal
to
crosstalk
noise
ratio
for
(a)
uncorrelated nearest
neighbors
and
no
detection
aperture,
(b)
correlated nearest neighbors
and
no
d9
detection..
aperture
and--(c)
nuncoreamdneigbor
an
asqar
dtetinIpeue