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414 OPTICS LETTERS / Vol. 26, No. 7 / April 1, 2001
Planar holographic optical processing devices
T. W. Mossberg*
LightSmyth Technology, Inc., Eugene, Oregon 97404
Received September 20, 2000
Time-domain optical processing implemented through linear spectral filtering offers unique potential for fu-
ture high-bandwidth communications systems. One key to realization of this potential is the development
of robust, cost-effective, fully integrated filtering devices. A new spectral filtering device concept, derived
from the unique properties of index holograms stamped or otherwise written in thin planar waveguide
slabs, is described. The holograms that are described provide for high-resolution spectral filtering while at
the same time mapping general input spatial waveforms to desired output waveforms © 2001 Optical Society
of America
OCIS codes: 200.4740, 230.7390.
Temporal-waveform processing devices
1–7
offer in-
triguing functionality that may be of use in developing
optical communication areas such as code-division
multiplexing
8,9
and optical-layer decision making. In
the following, a new type of integrated time-domain
holographic optical processing device based on focus-
ing planar waveguides is introduced. This device,
which is referred to as a planar holographic optical
processor (planar HOP), is uniquely compatible with
low-cost, robust fabrication; packs multiple transfer
functions within a single device; utilizes distinct input
and output ports, thus eliminating the need for costly
support devices such as optical circulators in process-
ing applications; and operates on time scales that are
useful in current optical communication systems.
A general optical processing (or filtering) device
(OPD) as considered here is a device that applies a
fixed or dynamically reprogrammable complex-valued
spectral transfer function to an input signal. If
E
in
共n兲
and E
out
共n兲 represent Fourier spectra of input and
output signals, respectively, and T 共y兲 is a complex-
valued spectral transfer function, the effect of the
OPD can be represented as
E
out
共y兲 苷 T共y兲E
in
共y兲 . (1)
The physical characteristics of a particular OPD deter-
mine the range and types of spectral transfer function
that it can be configured to perform. The discussion
here is restricted to OPD’s that act to apply fully co-
herent transfer functions, i.e., devices that fully control
the amplitudes and phases (except for an overall phase
factor) applied to the input signal spectrum.
Previous OPD’s have relied on free-space grating
1,2
or
coherent optical delay
3–7
structures to achieve coherent
optical f iltering. These structures tend to be align-
ment sensitive and complex and (or) to provide limited
spectral resolution. The planar HOP devices proposed
here consist of one or more focusing holographic struc-
tures within or on a thin planar waveguide. Each
holographic structure acts to accept light from a spe-
cific fiber-coupled input port, spectrally filter it, and
direct it by imaging to a specific fiber-coupled output
port. The planar HOP is completely integrated and
robust and can be expected to support multiple overlaid
holographic structures within a single device, each pro-
viding a separate spectral mapping from one or more
input ports to one or more output ports. Although the
operative optical structures have a holographic charac-
ter, fabrication can proceed by multiple means, includ-
ing electron-beam master production with replication
of copies. It is noted that spatial and spectral holo-
graphic structures have been shown to provide pro-
cessing, filtering, and waveform storage functions but
under quite different conditions.
10 – 16
Similar function
has been demonstrated in the quasi-one-dimensional
environment of fibers.
17 –21
The essentials of a two-port planar HOP are shown
schematically in Fig. 1(a). Light propagates in a
thin slab (planar waveguide) of transparent substrate
material lying in the x
y plane. The planar wave-
guide confines waves to one or a few modes along
the z direction. Optical signals are coupled into the
planar grating device along its edge or via waveguide
structures. Within the thin slab, a spatial index
hologram acts to spectrally f ilter the input signal and
spatially direct it to an output port. The constant
index contours of the index hologram may have
circular [see Fig. 1(a)], elliptical,
22
or more-complex
geometry. Control of the spacing and amplitude of
Fig. 1. (a) Schematic of planar HOP device. The arcs de-
note constant-index contours centered at C. Each arc, e.g.,
S1 and S2, images the input port to the output port. A
representative spatial index variation ´共r兲 is shown. The
actual spacing between successive contours is a multiple
of l兾2n
0
. (b) Optical path taken by a representative ray
from input to output ports. The optical path length, s,
is a function of r, the radial distance into the hologram.
(c) Impulse response from the planar HOP, assuming the
form of ´共r兲 shown in (a), except that the optical carrier is
suppressed.
0146-9592/01/070414-03$15.00/0 © 2001 Optical Society of America
April 1, 2001 / Vol. 26, No. 7 / OPTICS LETTERS 415
index variations provides required spectral filtering
function. Index variations are created by modifica-
tions in the waveguide surface profile, in the surface
profile of a thin overlaid layer, or in the actual bulk
index of the waveguide. The use of surface modifi-
cations in the waveguide itself or in overlaid layers
to create the index hologram is a possible path to
very low-cost replication-based manufacture of planar
HOP devices. Planar HOP devices complement the
wide range of planar devices that are currently under
development.
23,24
The arcs shown in Fig. 1(a) are contours of constant
index. Point C is their common center and is assumed
to lie midway along the segment, of length
DL, con-
necting the input and output ports, which are repre-
sented by filled squares. The distance from the center
of curvature, C, to an arbitrary point in the cylindri-
cally symmetrical index hologram is denoted r. View-
ing each constant-index arc as a ref lective focusing
mirror, we can see that the input and output ports
are optically conjugate; i.e., each arc images the input
port onto the output port. By making DL small, we
can minimize small imaging aberrations. Then, Fer-
mat’s principle tells us that light backscattered from
all points on a constant-index arc will have an identical
input– output-port transit time. It follows that varia-
tion in index as a function of
2s共r兲, the optical distance
between the input and output ports [see Fig. 1(b)], will
translate directly into the optical impulse response of
the device. Thus light not only is spatially mapped
from the input to the output port but also spectrally
filtered with a transfer function given by the Fourier
transform of the impulse response, and hence the in-
dex variation with s共r兲. Note that, for suitably small
DL, s共r兲艐r.
To investigate the impulse response more quantita-
tively, we use the assumed cylindrical symmetry of the
index, n共r兲, to write
n共r兲
苷 n
0
1´共r兲 , (2)
where n
0
is the average background index and it is as-
sumed that ´,, n
0
. An impulsive signal of the form
E
0
d共t兲, entering the input port and interacting with
the index grating at position r along the line shown
in Fig. 1(b), produces an output signal of amplitude
a
c
E
0
´共r兲, which is delayed from the entrance time of
the input signal by an r-dependent transit time given
by t共r兲 苷 2n
0
s共r兲兾c, where c is the vacuum light speed,
a
c
is a coupling constant, and s共r兲 is the distance shown
in Fig. 1(b). By use of the approximation
s共r兲 苷 r共1 1DL
2
兾8r
2
兲 , (3)
and with expressed r in terms of t, the output f ield
produced by an impulsive input field is found to be
E
out
共t兲 苷 a
c
E
0
´
∑
ct
2n
0
2h共t兲
∏
,
(4)
where h共t兲 苷 DL
2
n
0
兾4ct. For suitably small DL, the
output field mirrors in time the spatial variation of
refractive index as a function of r. At the bottom of
Fig. 1(a), a simple exemplary form of ´共r兲 is shown.
The spacing of index crests, actually a multiple of
l兾2n
0
, where l is the operative vacuum wavelength,
is greatly exaggerated for visualization. The impulse
response function produced by the exemplary ´共r兲 is
shown in Fig. 1(c), in which the two amplitude steps
correspond to those in ´共r兲. In Fig. 1(c), it is assumed
that DL ,, r and the optical carrier is suppressed.
The transfer function of the planar HOP, T共y兲, is the
Fourier transform of Eq. (4):
T共n兲 苷
a
c
p
2p
Z
`
2`
´
∑
ct
2n
0
2h共t兲
∏
3 exp共2piyt兲dt . (5)
In the limit that DL ,, 2共cr兾nn
0
兲
1
兾2
, throughout the
operative index hologram and frequency range the
quantity h共t兲 can be ignored. In this limit the tempo-
ral impulse response of the planar HOP is simply the
Fourier transform of ´共r兲. The index profile needed
to produce a specific transfer function is obtained by
inverse transformation of Eq. (5). Equations (4) and
(5) are valid for moderate hologram ref lectivity, since
multiple scattering and depletion are ignored.
Note that the planar HOP of Fig. 1 has a maximal
spectral resolution of c兾2n
0
D, where D is the opera-
tive length of the holographic structure. Thus a 5-cm
device in a silicon substrate offers a maximal spectral
resolution of ⬃1 GHz. Realization of maximal spec-
tral resolution for a given device size demands strin-
gent control over the planar waveguide homogeneity
and precision rendering of the holographic structure.
Imperfections in either lead to lower device resolution,
characterized by replacement of D with the distance
over which l兾2-scale optical path or positioning errors
occur. Similar fabrication constraints apply even to
simple diffraction gratings.
Parameterized as a function of transit delay, the in-
dex variation function may be represented as
´共t兲 苷 A共t兲f 关t 1 p共t兲兴 , (6)
where A共t兲 is a real-valued, slowly varying amplitude
function, f 共t兲 苷 f 共t 1t
g
兲 is a real-valued periodic
function whose minimal repeat period is t
g
and where
jp共t兲j ,t
g
is a slowly varying function representing
an r-dependent spatial phase shift in the hologram’s
quasi-periodic index variation. The index func-
tion versus r is obtained by the simple substitution
t 苷 共2rn
0
1DL
2
n
0
兾4r兲兾c. Expanding f共t兲 in a Fourier
series,
´共t兲 苷 A共t兲
`
X
m苷1
f
m
cos兵mv
g
关t 1 p共t兲兴 1w
m
其 , (7)
where v
g
苷 2p兾t
g
, we can write a transfer function
for each Fourier component of ´共t兲 as
T
m
共n兲 苷
a
c
f
m
2
p
2p
Z
`
2`
A共t兲
3 共共共exp兵2imv
g
关t 1 p共t兲兴 2 iw
m
其
1 c.c.兲兲兲exp共2pint兲dt . (8)
Thus, provided that f
m
fi 0 for a particular value of m,
the device exhibits an optical output with the indicated
transfer function T
m
共n兲 at frequencies
416 OPTICS LETTERS / Vol. 26, No. 7 / April 1, 2001
n 苷
m
t
g
⬵
mc
2n
0
L
,
(9)
where L is the minimal spatial interval over which the
index is approximately spatially periodic. The output
for m 苷 1 is first-order backdiffraction. Output fre-
quencies for higher m correspond to higher backdiffrac-
tion orders and demonstrate that the physical grating
spacing can be substantially greater than half the de-
sired output wavelength in the substrate, provided that
suitably high Fourier components are present in the in-
dex profile.
It should be noted that a planar HOP device
possesses much more general spatial wave-front pro-
cessing control capability that is apparent when simple
cylindrically symmetrical index variations are used.
The overall index structure is a two-dimensional
hologram and has all the associated spatial transfer
potential. One can engineer more-general index
profiles to optimally map a general spatial input f ield
to the desired output spatial mode, while at the same
time applying a desired spectral transfer function. It
is also important to note that planar HOP devices
are immune, by virtue of their holographic character,
to point defects introduced during use or fabrication.
This property is supportive of robustness in use and
high yield in fabrication.
The planar HOP concept supports multiple-port
devices, with optical connections between the ports
implemented with one or more focusing holographic
structures. A single holographic structure can con-
nect multiple-port pairs, provided that the elements of
each port pair are located in optically conjugate posi-
tions of the structure. As shown in Fig. 1(a), various
port pairs are simply placed symmetrically about
point C, the holographic structure’s center of symme-
try. When different transfer functions are required
for different connections, relevant ports are connected
by separate holographic structures. Since index
variations are assumed to be weak and the filtering
process is linear, multiple holographic structures can
be overlaid. As a special case of this capability, a
single input port can be connected to a family of output
ports by separate holographic structures, with each
connection having a transfer function that tests (via,
for example, cross correlation) the input signal for
specific content. Such a configuration provides the
basis for an optical packet decoder. In another special
case, one input is connected to multiple outputs, with
each connection being hologram specific to one or
more specific wavelengths. Such a configuration
represents an optical wavelength demultiplexer. In
volume holographic studies, hundreds or even thou-
sands of holograms have been written in the same
spatial volume before cross-talk and insertion loss
issues became limiting. Similar results may be an-
ticipated in the case of planar HOP devices. Another
advantage of the planar holographic approach is the
ability, through use of semiconductor materials, to in-
tegrate optical and electronic processing onto a single
substrate.
23,24
In conclusion, a powerful new planar design concept
for time-domain OPD’s has been presented. Devices
made with this design may be compatible with low-cost
replication- (stamping-)based manufacture and pro-
vide multiple transfer functions in a single device,
communications-scale frequency resolution in a small
package, and highly reliable operation. New device
concepts, together with ongoing progress in the meth-
ods of utilizing OPD’s, may lead to substantial new
capability in next-generation communication systems.
The author thanks W. R. Babbitt, T. Loftus, and
M. G. Raymer for comments. His e-mail address is
twmoss@mailaps.org.
*Also with the Department of Physics and Oregon
Center for Optics, University of Oregon, Eugene, Ore-
gon 97403.
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