Note: Descriptions are shown in the official language in which they were submitted.
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SEGMENTED COMPLEX DIFFRACTION GRATINGS
Field of the Invention
The invention relates to optical communication systems using segmented complex
diffraction gratings.
Background
Many optical communication systems use wavelength division multiplexing (WDM)
to increase the data rate available with a single optical fiber. Other optical
communication
systems offer increased data rates using optical code division multiple access
("OCDMA").
OCDMA systems encode different communication channels with different temporal
codes as
contrasted to WDM systems in which different channels use different
wavelengths.
Diffraction gratings can have a complex profile that includes multiple
sinusoidal
subgratings, each subgrating having a specific amplitude and spatial phase.
Such gratings can
deflect optical pulses from a specific input direction to a specific output
direction while
simultaneously multiplying the Fourier spectrum of the input pulse by a
predetermined
filtering function. The output signals are a cross-correlation between the
input waveform and
the grating encoded temporal waveform. These gratings can accept input beams
and generate
spectrally filtered output beams propagating in one or more output directions.
The filtering
function of the device is programmed by choice of grating profile. By suitable
programming,
multiple transfer functions may be realized, each having its own specific
input and output
direction.
Summary of the Invention
According to an aspect of the invention, optical apparatus (such as, for
example, a
segmented grating) are disclosed that apply a predetermined complexvalued
spectral filtering
function to an input optical field and produce a filtered version of the input
field that
propagates in an output direction. Another aspect of the invention includes
methods for
making such optical apparatus. Grating devices, comprise of one or more such
optical
apparatus, can be used, for example, in OCDMA data links to temporally code
optical signals
with specific codes such that multiple coded channels simultaneously can be
transmitted
through the same link and then be decoded into separate channels at the output
of the system.
The optical apparatus also can be used for programmable spectral filtering.
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In a further aspect of the invention, segmented gratings comprise a series of
spatially distinct subgratings arrayed end to end. Each subgrating possesses a
periodic
array of diffraction structures (lines or more general elements). The overall
transfer
function of such a segmented grating is determined by controlling (a) the
spatial
periodicity (spatial frequency) of each subgrating, (b) the amplitude of each
subgrating,
(c) the spacing between the last diffraction structure on each subgrating and
the first
diffraction structure of the successive subgrating, and (d) the optical path
length and
transparency through each subgrating, or each subgrating plus additional
material
layers utilized to control optical path length and transparency.
Brief Description of the Drawings
FIG. 1 A is a schematic diagram of a multiplexed communication system.
FIG. 1 B is a schematic diagram of an optical path of FIG. 1 A.
FIG. 2A is a plan view of a segmented grating.
FIG. 2B shows an elevational sectional view of the segmented grating of FIG.
2A.
FIG. 3A is a schematic diagram showing an input angle and an output angle for
a light beam incident to the segmented grating of FIGS. 2A-2B.
FIG. 3B is a schematic diagram showing an angle between a plane containing
an input light beam and an output beam and an x-axis wherein the angle is
measured in
an x-y plane.
FIG. 3C shows a temporally coded optical pulse having four time slices that is
incident on a segmented grating having four contiguous, equal-width
subgratings.
FIG. 4 illustrates a method for fabricating segmented gratings.
F1G. 5 illustrates another method for fabricating segmented gratings.
FIG. 6 illustrates another method for fabricating segmented gratings.
FIG. 7 is a sectional view of two subgratings of a segmented grating, the
subgratings having different optical thicknesses.
FIG. 8 is a sectional view of two subgratings of a segmented grating, the
subgratings having a saw-tooth shaped blaze.
FIG. 9 is a schematic diagram of a four-channel OCDMA system.
Detailed Description
FIG. 1 A is a schematic diagram of an OCDMA communication system 9 that
uses segmented diffraction gratings to perform optical multiplexing and
demultiplexing.
A short-pulse laser 10 generates a coherent light beam 12. A beam splitter 13
divides
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the light beam 12 into beams 15,16. The beams 15,16 are modulated by
respective
modulators 15a, 16a, thereby generating respective modulated beams 15b, 16b.
The
modulation of each of the beams 15, 16 is done in response to external data
streams, not
shown in FIG. 1A. The beams 15b, 16b consist, either by virtue of the
operative character of
the laser source 10, the action of the modulators 15a, 16a, or a combination
of the two, of a
stream of bits whose temporal character matches the designed input pulses of a
compound
grating 19.
Each of the beams 1 Sb, 16b is directed at the compound grating 19 so that it
is
incident on the compound grating 19 at an angle that differs for each beam.
The compound
grating 19 comprises two superimposed segmented gratings 1915, 1916 (not shown
in FIG. 1
A) operative on the beams 15b, 16b, respectively, to produce separate output
time codes in an
optical transport 11 (such as, for example, an optical fiber) for each of the
beams 15b, 16b.
(The coding technique and the details of the compound grating 19 are described
below). The
combined coded beam is transported to a second compound grating 19a via the
optical
transport 11.
The compound grating 19a also comprises two superimposed segmented gratings
19a15, 19a16 (not shown in FIG. l A) operative on the time codes in the beam
received from
the optical transport 11 to produce respective output beams 15c, 16c. The
beams 15c, 16c are
modulated identically to the beams 15b, 16b, respectively. (The decoding
technique and the
compound grating 19a are described below). The beams 15c, 16c are detected by
detectors
15d, 16d and converted into electrical signals that correspond to the signals
that activated the
modulators 15a, 16a.
As shown with respect to the communication system 9 of FIG. 1 A, two beams are
combined (multiplexed) into one coded beam that propagates along an optical
transport. In
other such systems, three, four, or more beams can be multiplexed into one
beam. The
combined coded beam can be transmitted over a transmission system and then the
beams can
be demultiplexed.
FIG. 1 B illustrates the transmission of the beam 16b through the
communication
system 9 of FIG. 1A. The beam 16b is collimated by a lens 6a so that the beam
16b
illuminates the entire operative width of the two-dimensional segmented
grating 1916
contained within the compound grating 19. (The compound grating 19 also
includes the
segmented grating 1915.) As shown in FIG. 1 B, the compound grating 19
comprises the
segmented gratings 1915, 1916 that correspond to different surfaces of the
compound grating
19. In other embodiments, such segmented gratings can be combined into a
single layer on a
single surface, the optical properties of the single layer determined by
summing the optical
properties of individual subgratings.
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A second lens 6b focuses the beam 16b into the optical transport 11. Spatial
filtering provided by a spatial fitter 8a (or produced by entry into the
optical transport
11 ) selects an operative angular output channel of the segmented grating
19,s. After
transmission through the optical transport 11, a lens 7a receives the beam 16b
and
illuminates the segmented grating 19a,s over its operative width and the beam
16c
transmitted through the compound grating 19a is focused by a collimating lens
7b. A
spatial filter 8b following the lens 7b selects the operative output angular
channel of
the segmented grating l9a,s. The compound grating 19a also comprises the
segmented gratings 19a,s for the beam 15b (not shown in FIG. 1 B) and the
segmented
gratings 19a,s, 19a,s can be on different surfaces or superposed. FIG. 1 B
illustrates
only the path of the beam 16b but the path of the beam 15b can be similar.
The communication system 9 includes mechanisms for collimating each of the
beams 15b, 16b, and providing for the beams to illuminate corresponding
segmented
gratings 19,s and 19,s within compound grating 19 at a different angle. A
separate
lens, such as the lens 6a, for each input beam provides an exemplary mechanism
for
collimating beams and illuminating segmented gratings. Alternatively, a single
lens and
control over the launch conditions of the input beams toward the single lens
can be
used. An example of spatial control comprises a spatial filter in the front
focal plane of
the single lens with apertures sufficiently small to provide diffractive
grating filling. At
the output of the compound grating 19a, there is a mechanism for providing a
spatial
Fourier decomposition of the angular output of the segmented gratings
comprising
compound grating 19a and appropriate spatial filtering mechanisms for
selecting the
multiple operative angular output channels, e.g., the lens 7b and the spatial
filter 8b.
A single lens provides an exemplary mechanism for providing spatial Fourier
decomposition. Apertures placed in the focal plane of the single lens then
permit
selection of operative angular channels. Other methods for selecting operative
angular
channels also can be used.
The compound gratings 19, 19a through their constituent segmented gratings
19,s, 19,s and l9a,s, l9a,s, respectively, are designed to accept light beams
from one
or more directions and to redirect the light beams into one or more output
directions in
a manner that is dependent on the temporal waveform of the light beams.
Considering
a sp8cific input direction and one of the output directions associated with
this specific
input direction, the grating's functions are summarized as follows. A portion
of each
spectral component of the input light beam is mapped into the output direction
with a
controlled amplitude and phase. The compound grating applies a designated
complex
valued spectral transfer function to the input light beam and produces a
filtered version
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of the input light beam that propagates in the output direction. The spectral
resolution of the
filtering function is determined by the physical size of the corresponding
segmented grating
and the input and output angles of the light beam relative to the grating. The
spectral mapping
between each input direction and each output direction may be programmed
substantially
independently using dedicated segmented gratings for each mapping. Such
mappings are
described in U. S. patent 5,182,394. In the communication system 9 of FIG. 1
A, the spectral
transfer functions are determined by respective segmented gratings.
FIG. 2A shows an example of a segmented grating 20 that is similar to the
segmented
gratings 19,5, 19a,5, 19,x, 19a,~. (The compound gratings 19,19a each contain
two such
segmented gratings, superimposed or summed together.) The design of a single
segmented
grating is described below and compound gratings incorporating two or more
segmented
gratings are designed through repetitive application of single segmented
grating procedures.
The segmented grating 20 has N spatially distinct subgratings 20; for i = 1 to
N, where
N = 8. In other embodiments N can be less than or greater than eight. FIG. 2B
is a sectional
view of the segmented grating 20. As shown in FIG. 2B, each of the subgratings
20; have
amplitude, phase, and period, all of which can be independently selected for
each of the
subgratings 20;. (FIG. 2B shows only six of the subgratings 20;.) The
structure of the
subgratings 20 is defined mathematically with respect to coordinate axes 22
and angles
descriptive of the segmented grating 20 and associated optical input and
output directions.
For convenience, the origin of the coordinate axes 22 is selected to be at a
center 23 of the
segmented grating 20. The segmented grating surface is taken to coincide with
the x-y plane.
With reference to FIG. 3A, an input line 31 passes through the coordinate
center 23 and is
parallel to an input direction and an output line 33 passes through the
coordinate center 23
parallel to an output direction. The input line 31 and the output line 33
define a plane,
referred to herein as the input/output plane. In the mathematical description
used herein, the
z-axis is located in the input/output plane. In other embodiments, the z-axis
is not in the
input/output plane.
FIGS. 3A and 3B show an input angle (6;n) and an output angle (6ou~) that are
in the
input/output plane. The angular separation between the input (output)
direction and the z-axis
is 0;n (8ou,), where the angles are positive as shown in FIG. 3A. FIG. 3B
shows an angle 6a
between the input/output plane and the x-axis as measured in the x-y plane.
Thus, FIGS. 3A
and 3B show the geometrical arrangement of a segmented grating relative to
particular input
and output optical field directions. For the segmented
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grating 20, a groove-normal line is defined as a line perpendicular to the
grooves lying
in the plane of the segmented grating surface and passing through the origin.
As
described above, the groove-normal line is contained within the input/output
plane and
is parallel to the x-axis. In other embodiments, the groove-normal line can be
at other
locations relative to the input/output plane.
When the input/output plane contains the z-axis, the diffractive structures
(grooves) that redirect and spectrally filter the input optical beam into the
output
direction are perpendicular to the input/output plane and are within or on the
surface of
the segmented grating 20. Multiple segmented gratings having the same or
different
values of 98 can be co-located on the same substrate with any degree of
overlap.
Compound gratings may include a single segmented grating, multiple spatially
superimposed segmented gratings, or a combination of spatially superimposed
and
spatially separated segmented gratings fabricated onto a single substrate.
The compound grating 20 uses transmissive segmented gratings, but reflective
gratings can also be used. Each input optical beam illuminates the active
width of
each segmented grating structure with which it is intended to interact.
Referring to
FIGS. 1 A-1 B, the compound grating 19 and the segmented gratings i 9,s, 19,s
are
substantially planar and arranged parallel to the x-y coordinate plane. As in
the case of
simple monospaced diffraction gratings, segmented gratings may be implemented
with
nonplanar surface geometry. For example a segmented grating could be supported
by
a nonplanar (e. g., a concave or convex) substrate. The use of non-planar
surface
geometry allows for the control over the spatial wavefront of input optical
beams in
addition to the spectral content control that is afforded by grating
segmentation.
A single segmented grating is fabricated in the form of a series of N
spatially
distinct subgratings arrayed side to side whose collective span defines the
operative
width of the segmented grating. if the input/ouput plane contains the x-axis,
each
subgrating possesses a periodic array of diffractive structures (for example,
grooves)
arranged in a plane perpendicular to the input/output plane. The spacing
between
diffractive structures within the N successive spatial subgratings is
typically but not
necessarily the same. The N subgratings are written or otherwise created such
that
each occupies a specific subsection of a compound grating surface and
subgratings
appear successively as one passes along the groove-normal line. The
subgratings of a
particular segmented grating typically (but not necessarily) have the same
span
perpendicular to the groove-normal line, i.e., height. The spatial interval
between the
last diffractive structure (groove) of each subgrating and the first
diffractive structure
(groove) of the successive subgrating can be controlled as well, as described
below.
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Control over groove positioning provides control over relative spatial phase
of
adjacent subgratings. Also controlled is the amplitude of the diffractive
structures
within a given subgrating. The manner in which subgrating spacing and
amplitude is
controlled determines the spectral transfer function of the grating. The
optical
thickness of the various subgratings comprising a segmented grating can be
controlled
by variation of substrate thickness, addition of phase masks, or other means
known in
the art to provide additional control over the spectral transfer function of
the grating.
Variation of optical thickness under a spatial subgrating or the separation
between
subgratings both act to control the relative phase of light transferred from
the input to
the output directions. Active devices can be added between the subgratings to
dynamically change subgrating-subgrating separation to allow for the dynamical
reprogramming of the spectral filtering function. Active devices to control
the optical
thickness of subgratings inclusive of overlays can be added to provide an
alternative
means of dynamical reprogramming of the spectral filtering function.
The representative segmented grating shown in FIGS. 2A-2B has eight
subgratings 20.. The subgratings 20~ have essentially equal extent along the
groove
normal line; however, subgratings of dissimilar extent can be employed. The
segmented grating 20 is a transmissive phase grating, but it could be a
reflective,
amplitude, or other generalized physical grating type.
We represent the transmissive optical phase shift versus position of a
subgrating 20~ as
h;(x~~= A;f,.(2~(x~ -x;)lA;)+~p; ffor X'a s x' s xb}, (1)
where x' represents the spatial position coordinate along the groove-normal
line, x. is
the spatial position shift of the t'" subgrating groove pattern, the function
f represents
a particular groove profile and is periodic with period 2a and modulates
between the
values of 0 and 1, ~p is an optical phase shift introduced by a variation in
substrate
thickness or superimposed phase mask, A~ is a real-valued amplitude factor, xa
and x°
are the edge positions of subgrating t, and A~ is the spatial period of the
t'" subgrating.
Outside the prescribed spatial interval, hr(x')=0. The subscript t ranges from
1 to N
30 and denotes individual subgratings. By specifying the parameters A. , ~p ,
x., and A. for
the subgratings employed, a wide range of spectral filtering functions can be
encoded.
The parameters A; , rp; , x; , and A~ necessary to produce specific,
predetermined
spectral transfer functions are chosen in a variety of ways. For example, a
segmented
grating can be constructed to provide a predetermined spectral transfer
function T(v)
(where v is the optical frequency) as approximated by N transmission
coefficients each
of which corresponding to one of N contiguous frequency channels collectively
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spanning the full non-zero width of T(vl, where T(v) is non-zero over a
specific spectral
region of width 8v centered about the frequency vo. To approximate T(v) to
accomplish
this purpose, the segmented grating requires approximately N subgratings. To
provide
filtering with a predetermined resolution, the subgratings require a spatial
width of
approximately c/[8v(sinA;° + sine°"~], where c is the vacuum
speed of light. The total
width of the grating is given approximately by Nc/[8v(sinA;°+sinA~")],
assuming that the
subgratings are contiguous. For example, if 8v=100 GHz, A;° =
0°, 0°", = 45°, and N = 8, the
complete spatial width of the segmented grating for Tlv) is approximately 3.4
cm.
The parameters (A; , ~p; , x; , and A;) for all of the N subgratings
comprising the
segmented grating determine the spectral transfer function T(vl. Given the
subgrating
parameters, the spectral transfer function of the segmented grating can be
determined.
Conversely, given a predetermined spectral transfer function, the subgrating
parameters necessary to create a corresponding segmented grating can be
determined.
It should be understood that, while the mathematics presented herein contain
certain
constraining assumptions in order to facilitate explanation, the equations can
be
generalized.
An expression for the spectral transfer function T(v) exhibited by a segmented
grating in terms of subgrating parameters is given first. Under the
assumptions that
(1) A~< < 1 or A~=A=constant, (2) the grating output is either plus or minus
first order
(m=t1 ), and (31 the N subgratings have equal spatial width (d = x6- x;'=
constantl,
equal spatial period (A; = A = constant), and are contiguous, the spectral
transfer
function T(v) of the segmented grating may be written as a sum over subgrating
parameters as follows:
where:
and
N
T(v) = F(v)~a; exp(j~;) (2a1
a; = A; exp( j(~p; -2~zx,m/A)), (2b1
~; =~(xa'~'xb)(w-m/A), (2c)
=(S1I1B;~ +SlIle°~,t)/C. (2d)
F(v) is the spatial Fourier transform of a subgrating,
F(v) = N sinc(~rd(v~3 - m l A)) , (2e1
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where j is ~ , and C is a constant dependent on the groove profile and
contains a
phase factor dependent on the choice of x'-origin. The function sinclx) =
sin(xllx. )n
writing Eqs. (2a)-(2e), it is assumed that the output signal is derived from
the plus
(m =1 ) or minus one (m =-1 ) diffractive order of the subgratings. Analogous
expressions for higher (positive and negative) orders can also be obtained.
To design a segmented grating having a specific transfer function, parameters
for each subgrating are determined. To do this, Eq. (2a) is solved for a. to
obtain
nn(~A)+1~(z~d> { )
a; _ ~d j T v exp{-j~(vtri - m / A)(x° + x" ))d v (3)
nn(~>-ti(zpd) F(v)
From Eq. (2b), A. is equal to the amplitude of a;. The quantities x. and cps
both
determine the phase of a; as seen in the above equations. An appropriate
combination
of x. and cps consistent with Eq. (2b) and Eq. (3) can be chosen at the
convenience of
the grating designer. The parameter A is chosen so the light of carrier
frequency ve is
maximally diffracted from 8~~ to 6o~c using the well-known grating equation
sin(0~~) +
sin(Ao~~) = m~.~/A where ~=c/vo is the center wavelength of the desired
transfer
function. The angles 8~~ and 8a~~ are designer inputs as is T(v).
Mathematically
speaking, A is chosen as the solution of the mathematical equation (3voA=m.
Alternatively, a more general solution for obtaining the subgrating parameters
is
to calculate the continuous grating profile that will generate the desired
continuous
transfer function. If the transmissive phase of a grating as a function of x'
is given by
+~
h(x')=-jln 2~~D JT(v)exp(-j2~rl3vx')dv , (4)
the spectral transfer function of the grating in direction 6o~s will be T(v),
where D is the
width of the grating. Again 6~n, 8o~t, and T(v) are designer inputs. It is
necessary to
convert the continuous transmissive phase profile given by Eq. (4) to a
segmented
phase profile consistent with subgrating fabrication. Parameters descriptive
of
constant phase segments which can be directly mapped onto the parameters
defining
constituent subgratings can be determined as follows: The continuous surface
phase
profile h(x'J generally consists of a carrier spatial modulation with a slowly
varying
amplitude and phase shift. A representative average of the spatial phase shift
over the
physical extent of subgrating i is determined and the values of cp; and x; are
adjusted in
a convenient combination to match the determined spatial phase shift
determined from
Eq. (4). Similarly, a representative value of the grating amplitude from Eq.
(4) within
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the physical extent of subgrating i is determined and A~ is set equal to this
grating
amplitude. The spatial period A~ is set equal to the carrier modulation period
of hfx') as
given by Eq. (4]. A variation to the approach just given is to determine a
spatial
carrier, amplitude, and phase within the extent of each subgrating separately.
This
5 procedure allows for the variation of A~ from subgrating to subgrating.
For a segmented grating to perform the function of optical cross-correlation
between optical input waveforms and a reference optical waveform, the
grating's
spectral transfer function should be the complex conjugate of the spectrum of
the
reference optical waveform. The function of optical cross correlation here
means that
10 the electric field emitted by the grating in the operative output direction
represents the
temporal cross correlation between (a) an input optical waveform incident on
the
grating along the operative input direction and (b] the specific reference
optical
waveform whose conjugated spectrum coincides with the grating's spectral
transfer
function.
15 Consider a reference optical waveform such as an optical pulse whose time
profile is represented as a sequence of M contiguous time slices within which
the
amplitude and phase of the optical field are constant. In each time slice i
(for
i = 1,..,M), the electric field has constant amplitude B. and phase ~~. The
reference
waveform is thus determined by the set of complex numbers [B,explj~,l,
20 Bzexp(j~zl,...,Bnnexplj~M1] along with the optical carrier frequency in
each time slice and
the overall temporal duration of the waveform. FIG. 3C schematically
illustrates a
temporally coded optical pulse 40 of the form [C,explj~',1, Czexp(j~'z),
Caexplj~~a),
Coexp(j~'<I1 incident to a segmented grating 42.
When an optical waveform is incident on a grating such as the segmented
25 grating 42, the segmented grating 42 spectrally filters the incident
waveform as
described by the grating spectral transfer function for the particular Bin and
6a~~
employed. If the segmented grating is to perform the function of cross-
correlation
against the reference optical waveform, the subgratings should have parameters
that
are the "time-reversed" complex conjugate of the reference optical waveform.
For
30 example, for a segmented grating having eight segments, such that
fa,, az,..., ae] _ [Beexp(-j~al, B~expl-J~~l....,B,exp(-j~,]l,
the'subgrating parameters are related to a; by equation (2b) given the
assumptions in
deriving Eqs. (2a]-(3) are met. The operation of cross-correlation may be used
to
multiplex and demultiplex optical signals.
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The diffraction efficiency of a grating segment depends upon the groove
profile
of the segmented grating. The magnitude of the spectral transfer function and
the
constant C of Eq. (2e) depend on the diffraction efficiency.
The following specifies the compound gratings 19, 19b employed in the
communication system 9 of FIG. 1 A. As noted above, the compound gratings 19,
19a
comprise two superimposed segmented gratings, 19,s, 19,s and 19a,s, l9a,s,
respectively. The compound grating 19 accepts uncoded data streams and
launches
time-coded data into a common channel. The compound grating 19a accepts time-
coded data and launches distinct time codes into distinct output directions
while
simultaneously stripping off time-coding. The compound grating 19a functions
through
the process of cross-correlation. In an example, the compound gratings 19, 19a
each
comprise two superimposed segmented gratings 19,s, 19,s and l9a,s, l9a,s,
respectively, and the net transmissive optical phase shift versus position is
consequently the sum of the transmissive optical phase shift functions for the
two
segmented gratings. In an example, the groove profile is a square (square-
wave)
groove profile with a fifty percent duty cycle. The subgrating amplitudes are
A. = n/2
for the first and second segmented gratings, the diffraction efficiencies of
the
compound gratings 19, 19a are approximately 20°r6 in the operative
output directions.
If such a transmission grating is to be etched into a substrate with optical
index
n°=1.50, the etch depth that corresponds to A. = n/2 phase modulation
is given by
0.77 pm for a carrier wavelength of 1.54 pm. In this example, the input-output
plane
contains the z-axis. The compound gratings 19, 19a have eight subgratings, and
each
subgrating has a width of 1 mm; thus the total grating width is 8 mm. The
segmented
gratings 19,s, 19,s, 19a,s, 19a,s comprising the compound grating 19, 19a have
Aa=0°
and are designed for optical data streams having the carrier frequency 195 THz
(a
carrier wavelength of about ~,= 1.54~.m).
The optical data channels controlled by a first segmented grating of the
compound grating 19 are specified to have the input and output angles
6~~=17.94° and
6°~,=0°. The grating spacing is A=5 ~m for all subgratings of
the first segmented
grating. The first segmented grating is designed to accept temporally short
input
pulses of optimal duration Aio =1 ps along 6~~ =17.94° and generate
temporally coded
pulses along the multiplexed output direction 6°~,=0°. To
produce output pulses of
approximate duration zp=8 ps with the following temporal code
(1, 1, 1, explj2n/3), exp(j4~/3),1, explj4~rt/31, exp(j4x/31]
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the corresponding subgrating xi and Bpi parameters for the first segmented
grating are
[x,, x2,..., x$] _ [O.Opm, O.Opm, O.Opm, -1.67pm, 1.67pm, O.Opm, 1.67pm,
1.67pm] and
[~, rpz,..., rpe] _ [0,0,0,0,0,0,0,0].
The second segmented grating consists of a set of eight subgratings with the
following common specifications: A=3 um, 0i~=30.89°, 0a=0°, and
A°°r=0°. The
second segmented grating, like the first, accepts temporally brief data bits
of optimal
duration eTp~1.71 ps moving along its input direction and generates temporally
coded
bits of approximate duration TP=13.7 ps into its output direction. The first
and second
segmented gratings have a common output direction. If the coded output bits
from
second segmented grating are to have the following form
[1, exp(j2a/3), exp(j4~rt/3), 1, exp(j2~/31, explj4~/31, 1, exp(j2~c/3)],
then the corresponding subgrating parameters of the second segmented grating
are [x,,
xz,...,x8}=[O.Ollm, -1.0 pm, 1.0 pm, O.Opm, -1.0 pm, 1.0 wm, O.Opm, -1.0 um]
and [rp,, ~,...,
~}=[0,0,0,0,0,0,0,0}. The filtering bandwidth of the second segmented grating
is 8v-1/ATp
or 0.6 THz.
The multiplexed beams co-propagating in the optical transport 11 are
demultiplexed by the compound grating 19a. The demultiplexing compound grating
19a in FIGS. 1 A-1 B is identical in design to the compound grating 19. For an
input
angle into grating 19a of 9~~=0° the demultiplexed output beams are
collected in
angles 0°°t =-17.94° and A°~L =-30.89° for
the first and second reference optical
waveforms respectively. With these grating specifications, the laser 10 of
FIG. 1A
preferably has a maximum temporal pulse width (FWHM) of. 1 ps Igiven by the
minimum ~Tp of the two segmented gratings).
Using lithography (optical or electron beam), surface profiles can be written
onto a substrate point by point to make segmented gratings, and compound
gratings
and segmented gratings with spatial phase shifts between the subgratings can
be
written directly onto a transmitting or reflecting surface. Control of
subgrating
amplitude is also possible using this technique. In addition, a variety of
holographic
techniques can be used to successively or simultaneously record subgratings
with
controlled surface profile properties.
FIG. 4 illustrates a method of manufacturing segmented gratings (and
compound gratings) by spatial repositioning of a grating substrate to produce
subgratings with controlled spatial phase. The angle between the two beams or
the
wavelength of the two beams used in standard holographic recording can be used
to
control the grating period A.. Spatial phase shifts may be introduced between
exposures by translating a grating substrate. Thus, the N subgratings can be
recorded,
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as shown in FIG. 4, by spatially translating an aperture mask 45 of width
d=D/N
(where D is the total grating length) by its width N times and exposing the
recording
material at each mask position. Between exposures, the grating substrate is
shifted
along the groove-normal line. The substrate shifts a distance x~ relative to a
fixed
reference prior to exposure of subgrating l. Control of writing beam intensity
between
subgrating exposures allows control of subgrating amplitudes A~.
A similar method of producing segmented gratings comprised of subgratings
with spatial phase shifts uses single exposure holography with a phase-code
mask
having the appropriate subgrating phase shifts encoded in its optical
thickness. The
mask is placed in one of the two interfering beams in close proximity to the
substrate.
If these beams are incident from opposite sides of the substrate, this phase-
mask can
be contacted directly onto the grating substrate.
FIG. 5 shows a holographic method for fabricating gratings with N subgratings
with controlled spatial phase shifts. This technique controls the phase-
difference, ~~,
between the two optical writing beams 51, 53. Control of the intensities of
the
writing beams 51, 53 permits control of subgrating amplitude as well. The
optical
phase-difference determines the position of the interference pattern on the
sample
where the beams overlap, and their intensity controls the modulation amplitude
of the
interference pattern. The subgratings are recorded by illuminating the whole
sample
region with the interference pattern, but using an aperture of width d so that
only the
region behind the aperture is exposed and recorded. By spatially shifting the
aperture
across the sample in N steps it is possible to write a series of N
subgratings, with each
grating having a phase determined by the phase-difference ~~ used during
exposure of
the l'" subgrating.
FIG. 6 illustrates a method of producing subgratings termed the
°master phase
mask" approach. In this method, a single writing beam 61 is used in
conjunction with
a master phase mask diffraction grating 63. The writing beam 61 incident to
the
master grating 63 is diffracted to yield one or more extra output beams, such
as the
beams 65, 67. The writing beam 61 and the diffracted beams interfere,
producing an
interference pattern that can be used to record a near duplicate of the master
grating.
This property of diffraction gratings makes it possible to use a master
grating to
generate the interference. pattern needed for the grating. The phase in each
subgrating
is imparted by translating the master grating or the recording substrate
between
successive masked subgrating exposures.
The phase shifts ~ can be controlled by selecting the optical thickness of the
substrate. FIG. 7 shows a two-segment grating wherein the subgratings are
written
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onto a substrate of varying thickness. Variation in substrate thickness
provides for
control over the subgrating parameter ~p; . More generally, rp; can be
controlled by any
of the means known in the art for varying the optical path length of the
subgrating
substrates. For example, index-of-refraction changes between subgrating
substrates
provide for control over g~; .
A variety of fabrication methods support control over ~p; . Lithography
provides
for changes in surface level land hence substrate thickness) as well as groove
profile.
Programmed lithographic variations in surface Isvel thus provide control over
~p; .
Holographic, lithographic, or mechanical ruling methods can be implemented on
a
substrate that has been prepared to have specified optical thickness
throughout the
spatial region occupied by each subgrating. Control over optical thickness can
be
achieved by any of the means known in the art including but not limited to
etching and
thin-film coating.
The value of rp; for each subgrating can also be controlled through use of a
separate phase mask placed over a constant thickness substrate.
A grating can also be made using a Fourier synthesis method by the
superposition of multiple periodic gratings each of which spanning the entire
width of
the segmented grating. The constituent periodic gratings have relative phases,
amplitudes, and spatial periods that, when summed, result in the segmented
grating
profile of interest. The constituent periodic gratings are the Fourier
components of the
desired grating profile. The more Fourier components used the more sharply
defined
the subgratings will be.
The gratings can be manufactured by holographic or lithographic methods. By
exposing a photosensitive substrate with multiple holographic exposures, each
of
which writing a particular constituent periodic grating, the desired grating
profile can
be recorded. Lithographic means also provide for multipass writing wherein
each pass
is employed to write one constituent periodic grating.
By using lithographic and holographic methods the gratings may have an
arbitrary modulation profile including a grating blaze such as a saw-tooth,
square
wave, sine wave, or other blaze to engineer the distribution of power into the
diffraction orders. FIG. 8 is a schematic of a grating similar to that shown
in FIG. 2B,
but tivith a saw-tooth modulation profile.
It is noted that the descriptions of the segmented gratings presented in
herein
include gain gratings as well as absorption gratings, fiber gratings, and
gratings in
frequency selective materials.
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Dynamic gratings can also be provided. In the embodiments described above,
the gratings are static. The following describes an embodiment wherein the
gratings
can be dynamically reprogrammed with respect to their spectral filtering
functions. In
the previously described embodiments, the spectral transfer function of the
compound
5 gratings (and segmented gratings) is determined by the parameters A~, gyp,
x~ , and A~ of
its constituent subgratings. Generally speaking, any means known in the art
that
provides for dynamic control of one or more of these parameters will enable
dynamic
reprogramming of gratings. A variety of construction methods allow for dynamic
reconfiguration of gratings, for example, control of gx and A. through control
of
10 substrate or overlay index of refraction. A grating created by the means
described
above may be overlaid with a material whose index of refraction can be
controlled by
any of the standard means known in the art including, for example, applied
electric
field, pressure, current, or optical irradiation. If the means of controlling
the refractive
index of the overlayer is applied to act differentially over spatial regions
essentially
15 coinciding with the subgratings comprising the grating, either ~pr or A.
can be controlled.
To control ~ alone, an overlayer may be applied to the side of the substrate
opposite
to the grooves. Variation in optical thickness in the overlayer induced by any
means
known in the art then allows one to vary for. If the overlayer is applied to
the groove
side of the grating (filling in the grooves), then both rp and A~ can be
controlled. A. may
be controlled by changing the difference in refractive index between the
grooves and
the overlayer. ~r can be controlled by controlling the optical path length of
the
overlayer (as in the case when the overlayer is applied on the substrate side
opposite
the grooved. The ratio DArlDyx may be varied by adjusting the thickness of the
overlayer. Here ~.4~ (D~r1 is the change in Ar (gyp) introduced by a given
change in
refractive index of the overlayer. Control of A. alone can be achieved by a
variety of
means including the addition of overlayers on both sides of the grating
substrate and
configuration of the overlayers so that the optical path difference introduced
by index
changes of the two layers cancels and thus so does the change in yx. On the
other
hand, the change in amplitude of the phase subgratings is sensitive to the
index
change of only one of the overlayers and does not cancel. Pure A~ control can
also be
obtained by stacking two differentially controlled overlayers on the groove
side of the
grating. Again, the optical path difference on passing through both layers is
constrained to be constant.
The complex rp~ can also be controlled through control of substrate or.overiay
transmission. We reinterpret h~(x') in Eq. (1) to define the generalized
complex
amplitude transmission function of a grating to be given by:
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16
H~(x') =exp(jh~(x')) (5)
In this representation we allow h~(x') to be complex in order to include gain
or
absorption gratings in the above presented treatment. When the amplitude
factor A~ is
considered to be complex, the imaginary part subsequently describes the loss
or gain
grating amplitude. Furthermore, by generalizing ~p to be a complex number, we
include
the possibility of subgrating absorption or gain introduced by a variation in
substrate
transmission or a superimposed amplitude mask.
A grating, as described earlier, may be overlaid with a material whose optical
intensity transmission can be controlled by any of the standard means known in
the art
including, for example, with a liquid-crystal amplitude modulator or an
electro-
absorptive material. If the means of controlling the transmission of the
overlayer is
applied to act differentially over spatial regions essentially coinciding with
the
subgratings comprising the segmented grating, the imaginary part of ~p can be
controlled. Changing r~ will effect a change in the transfer function T(v) as
described
in Eqs. (1-4).
In the communication system shown in FIG. 1 A, two optical channels are
multiplexed using OCDMA coding. As illustrated in FIG. 9, additional channels
can be
encoded, multiplexed, transmitted and then demultiplexed. In the embodiment
shown
in FIG. 9, four channels 901, 902, 903 and 904 are modulated by modulators 901
a-
904a, multiplexed by a compound grating 919, transmitted on a fiber 911,
demultiplexed by a compound grating 919a, and then detected by detectors 901 d-
904d. The compound gratings 919, 919a comprise four superimposed segmented
gratings of the type previously described.
While the invention has been described with respect to embodiments thereof, it
will be understood by those skilled in the art that various changes in format
and detail
may be made without departing from the spirit and scope of the invention.
