1. Floor plan optimization techniques for integrated optic photonic
switching architectures
K. Malhotra*a
, S. Kara
a
Department of Electrical Engineering, Indian Institute of Technology Delhi, Hauz Khas,
New Delhi-110016, INDIA
ABSTRACT
We propose several methods by which more optimal directional-coupler based switch placement may be achieved in
integrated optic switching architectures. First, we propose a method to remove waveguide crossovers, thus making for a
planar realization. We illustrate this on two fundamental non-planar graphs K5 and K3, 3 and on the Beneš network. Next
we discuss switch placement on an annular optical substrate, and the advantage gained by this technique. Lastly, we
propose two techniques for achieving acute bends in light-paths, thus allowing fold-over architectural implementations.
Keywords: Planar layout, annular architectures, acute waveguide bends, lithium niobate, Bragg reflectors, Fresnel
lenses, integrated optic devices
1. INTRODUCTION
With Ti:LiNbO3 directional-coupler type electro-optic switches on a 6'' optical wafer, 32 × 32 architecture is the largest
order switch that can be implemented realistically on a single wafer. Architecture of this size would qualify, at most as
small scale integration. There are three major placement constraints that we address – firstly, waveguide crossovers
which lead to loss and crosstalk. We describe how to effectively eliminate all waveguide crossovers, making any
arbitrary switching architecture planar. This has several desirable consequences; for instance, a self-routing architecture
like a hypercube (of any degree) can be laid down on a wafer in planar form. Secondly, the need to butt-couple optical
fibers on the input and output waveguides requires waveguide placement on the outer periphery of a rectangular or
circular wafer. We propose alternative annular architectures which provide greater freedom in input-output waveguide
placement, thereby reducing waveguide crossovers, and for certain architectures require a relatively small real estate.
Lastly, the large real estate used in the waveguide interconnects, when acute bends in the light-paths are required. We
discuss techniques to reduce bends and eliminate waveguide arcs wherever possible, thus avoiding severe bend loss, by
incorporating slanted Bragg/blazed gratings, Fresnel lenses, grating lenses, and 3-dB couplers.
2. PLANARIZING INTEGRATED OPTIC ARCHITECTURES
A necessary and sufficient condition for a graph G to be planar is that G does not contain either of Kuratowski's two
graphs (K5 and K3, 3) or any graph homomorphic to either of them. There is exactly one crossing in the K5 and K3, 3
graphs. Any architecture, photonic or otherwise, is non-planar if and only if any of its sub-graphs are either K5 or K3, 3 (or
any graph homomorphic to them). We assert that any photonic switching architecture can be made planar by planarizing
both K5 and K3, 3 graphs embedded in that architecture.
There are two ways of dealing with a waveguide crossover. In the first, if the waveguides intersect at an angle greater
than about 7
0
, the losses and crosstalk are small
7, 8
. Fig. 1(a) illustrates one such waveguide crossing. Fig. 1(b) and 1(c)
illustrate the loss and power distribution in the “cross” and “bar” channels of ? n- as well as 2? n-crossings as a function
of angle of intersection
8
. Though the loss and the crosstalk resulting due to waveguide crossings can be reduced still
further by increasing this angle, this leads to increased losses at the corner-bends due to the corresponding reduction in
the length-to-width ratio of the crossing waveguides. On the other hand, increasing the angle of intersection for a given
bend loss necessitates a larger real estate.
For small angles of intersection, we eliminate a waveguide crossover by replacing it with a 2 × 2 directional coupler as
shown in Fig. 2(a) and 2(b). Fig. 2(a) is a complete graph of 5 nodes (vertices), and the absence of the directional coupler
would have necessitated an edge (waveguide) crossover between edges connecting nodes 2-5 and 4-3. Light from node 2
however, is made to couple into the waveguide incident on node 5, just as light from node 3 couples into the waveguide
incident on node 4.

2. Figure 1 (a) Two crossed linear waveguides. Power distribution as a function of angle of intersection a, in passive X-crossings of (b)
the ?n–type and (c) the 2 ? n–type8
Figure 2(a) Kuratowski's first graph, K5. (b) Kuratowski's second graph, K3, 3

3. To illustrate an application of this scheme, the Beneš architecture
4
is made planar in Fig. 3. From graph theory, the
architecture is capable of being represented in a plane because it contains neither K5 nor K3,3 sub-graphs. However, the
necessity of allowing for input and output waveguides, and the complexity of finding an optimum layout (which is both
free from waveguide crossovers and has low bend losses), prevents a planar layout for the Beneš and many other
photonic architectures of that family.
Figure 3(a) Planar Beneš architecture. (b) Highlighted region prior to planarization. (c) Highlighted region after planarization, with
the waveguide crossover replaced by a directional coupler
The number of directional couplers required for planarizing a photonic architecture is the same as the number of
waveguide crossovers that need to be eliminated. Our scheme renders a graph planar, with the layout as is where is. That
is, in order to eliminate a waveguide crossover, a designer must scale his layout to make way for two waveguides
running in close proximity with one another over the distance of an odd multiple of coupling length, without modifying
the relative placement of nodes.
The obvious question that arises now is which waveguide crossovers to eliminate and which ones to ignore. Waveguide
crossovers have negligible loss and crosstalk if the angle between crossed waveguides is greater than about 7 degrees
7, 8
,
though the exact angle would depend on both waveguide design and desired performance. Fig. 4(a) illustrates a

4. waveguide crossing between two S-bends. The total crossing angle is a. An S-bend can be constructed using the
following expression












+





=
x
y
x
y
l
xl
x
l
l
y π
π
2sin
2
(1)
where lx and ly are the length and width (span) of the bent waveguide. The second term on the RHS of equation (1) is
maximum for x= 3 lx /4. Choosing the center of the bend as a reference point (which is also the crossover point in this
case), this value of xis at a distance of lx /4 from the reference point along the horizontal. We denote this value of x by
x1. Substitution of x1in equation (1) yields y1 = ly /4 + ly /2p. The coordinate point (x1, y1) subtends an angle a/2 w.r.t. the
horizontal at the reference point. With some mathematical manipulations we have evolved the following expression






+⋅=
π
α
2
12/tan
x
y
l
l
(2)
Fig. 4(b) shows the dependence of real estate on the total crossing angle a in S-bends. Both bends are assumed to be
symmetrical, having a span of 250 µm. For S-bends, bend loss can be excessive for crossing angles greater than about 6
0
.
By compromising on bend loss we can reduce crosstalk as well as real estate requirement.
Figure 4(a) Schematic of intersecting S-bend waveguides. (b) Real estate plotted as a function of flare angle a
2.1 Lower bound on the number of waveguide crossovers
In any integrated optic switching architecture, where the driving concern is planarity, a floor on the number of
waveguide crossovers – the crossing number – is a useful figure of merit. While there is no closed form expression
which gives the crossing number of an arbitrary graph, we present a method for a quick estimation of the lower bound on
the number of crossings in an arbitrary graph. It is known that any non-planar graph contains either one orboth K5 and
K3, 3 sub-graphs or any graph homomorphic to them. By counting the number of K5 and K3,3 sub-graphs individually, one
can determine this lower bound. If only one of the two sub-graphs is present, the method yields the desired lower bound.
However, in the event of both sub-graphs being present, the lower bound can be determined by taking the sum of the
crossing number of both K5 and K3, 3 calculated separately. For example, by applying our quick estimation method, we
find that the (p = 3, k = 2) ShuffleNet
1, 2
, which contains only K3, 3 sub-graphs, has a lower bound of 8 crossings. A (p =

5. 2, k = 4) ShuffleNet also contains only K3, 3 sub-graphs, yielding a lower bound of 104 waveguide crossings. A (d = 5, k
= 2) Kautz graph
3
is non-planar with a minimum of 92 (50 plus 42) waveguide crossings. A (? = 4, D = 3) deBruijn
graph
3
has a minimum of 64 (4 plus 60) waveguide crossings. In some graphs, nodes may be common to more than one
sub-graph. In that case, the number of crossings may exceed the pres ented lower bound. We assert however, that our
quick estimate method yields an estimate floor on the number of waveguide crossings. Our method has the following
limitations –
(1) We are yet to provide a rigorous mathematical proof,
(2) It does not account for additional crossings arising due to nodes common to more than one sub-graph and,
(3) It does not predict the additional waveguide crossings incurred due to input-output waveguides.
3. ANNULAR ARCHITECTURES
Numerous architectures such as an 8 × 8 Banyan network are planar, but it is usually difficult to obtain a planar
placement when the input and output waveguides are required to be placed on opposite edges of a rectangular scribed
section of the wafer. We propose that an annular optical substrate offers greater possibilities for input-output waveguide
placement
6
. The network should be laid out on an annular wafer, with an opening in the center for connecting
input/output ports. The layout should thereafter be optimized in terms of bend losses, switching voltages, degree of
integration etc. This is shown in Fig. 5 for a schematic layout of an 8 × 8 Banyan network. The perimeter of the central
opening is greater than N × 250 µm, where N is the number of input-output waveguides that are incident on this
interface. This condition permits a gap of at least 250 µm between input-output ports to allow coupling through polished
edge facets. For a practical realization, this opening shall far exceed the mentioned dimensions, as shall be shown
subsequently. More than one opening can be provisioned to yield greater flexibility in input-output waveguide
placement. The number of such openings is however, limited by technological constraints such as wafer strength and
bend losses in the fiber at the fiber-wafer interface.
Figure 5 Schematic layout of 8 × 8 Banyan network on an annular optical substrate

6. 4. PLACEMENT TECHNIQUES FOR HIGHER LEVELS OF SWITCH INTEGRATION
There are a number of optical path-bending components for integrated optic devices like prisms, geodesic components
(lenses, corner reflector and deflector), taper termination, ridge, reflection type grating, and bent waveguides. These
devices exhibit either a large insertion loss, are difficult to fabricate or, in some cases, are incompatible with the desired
technology. With prisms, achieving deflection angles greater than 300
is difficult because of small index difference
between film and surrounding substrate. Geodesic element fabrication requires precise surface contouring, which calls
for ultrasonic machining, diamond grinding and polishing. This can be performed with special high-accuracy computer-
controlled machining system, but renders the fabrication of aberration-free geodesic elements both expensive and time-
consuming. Consequently, such elements are not mass producible. Ridges made out of SiO 2 on Si are not compatible
with LiNbO3 technology. Similarly, corner reflectors (also known as waveguide mirrors) made out in ridge waveguides
with aluminium metallization are incompatible with LiNbO3 fabrication technology. A reflection-type grating, butt-
coupled to a waveguide is not flexible to work with.
In order to place an entire photonic architecture on a standard LiNbO3 wafer, one needs to develop new passive and
functional waveguide devices. A major constraint to achieving high level of integration in photonic integrated circuits is
the large length-to-width ratios of waveguide devices. To counter this difficulty, we may use waveguide bends or arc
waveguides to turn the light-path back into the wafer. We quantified losses in bent waveguides through simulations using
BPM_CAD
TM
. A 4000 µm long waveguide bend, spanning a width of 125 µm, fabricated on 7 µm wide single-mode Ti:
LiNbO3 waveguide exhibits a loss of 1.08 dB. The losses in a waveguide arc are more severe – a waveguide arc with the
same waveguide specifications, as above, having a chord length of 4500 µm and a radius of curvature of 10 cm exhibits a
loss of 2.97 dB, whereas one with the same chord length but radius of curvature of 22 cm exhibits a loss of 0.59 dB.
There is therefore, a need for ways and means by which acute bends may be realized on waveguide structures.
We propose the following two methods to realize acute angled bends:
1. Slanted Bragg gratings along with a gradient-index Fresnel lens,
2. An interferometric technique with reflective gratings on the arms of a 3-dB coupler.
Our first technique utilizes a slanted Bragg grating in conjunction with a gradient-index Fresnel lens. The Bragg grating
is incorporated into a waveguide and reflects light from the waveguide into the substrate (in the plane of the waveguide)
through coplanar contra-directional coupling. The light coupled out into the substrate region propagates in the general
direction of the Fresnel lens, which is placed parallel to and at some distance from the grating as shown in Fig. 6. The
light coupled out into the substrate, diffracts in the absence of a guiding structure, and is intercepted by the Fresnel lens.
However, this diffraction is minimal because of the proximity between the slanted grating and the Fresnel lens. It should
be noted that diffraction takes place not only in the plane of the substrate, but also in its depth. For high efficiency, the
Fresnel lens should be so constructed, that it intercepts a large fraction of the light beam.
We see that an acute bend has been realized in Fig. 6, but it is important to estimate the real estate occupied by these set
of devices on an optical substrate. We may, first, estimate the length of the Bragg grating by comparable results for in-
fiber Bragg gratings. Blazed in-fiber Bragg gratings have been studied for application in an ‘optical tap’. It has been
shown that the radiation mode vector is highly directional and that the departure angle is related to the blaze angle as
follows
5
)(
)()cos(
cos
λ
λ
λ
ξ
θ
cl
eff
n
n−
Λ= (3)
where ? is the departure angle, ? is the fringe angle, ? is the fringe period, neff is the refractive index ‘seen’ by the guided
mode and ncl is the refractive index of the cladding at wavelength?. The Bragg condition is expressed mathematically as
)90sin(2 0
ξλ −Λ= effB n (4)

7. Using equations (3) and (4), one can show that for ? = 90
0
, ? must be 45
0
. The value of ? can be arbitra rily large, but
must be less than ± 90
0
. The value of reflectivity as a function of ?, for integrated optic gratings, remains to be
investigated.
Figure 6: Proposed layout of a slanted Bragg grating and Fresnel lens system to permit acute bending of light
To estimate required grating lengths, we use standard results derived for in-fiber un-blazedgratings. For peak reflectivity
of about 92% (at communication wavelength of 1.55 µm by a grating fabricated in Ti:LiNbO3, with a peak index change
of 0.16% over that of the substrate, the length of grating must be approximately 600 µm. This implies that the width (or
aperture) of the Fresnel lens must be at least 600 µm × sin ?. For ? = 90
0
, the Fresnel lens aperture length, 2XM must also
be 600 µm. Such a lens shall have a focal length f of about 2000 µm
9
. For all other angles ?, 2XM shall be less than 600
µm and so would be the corresponding focal length f. A waveguide must be placed at the focal point of the Fresnel lens.
Since, the Fresnel lens is likely to have some aberrations; it may focus light over a diffused spot. To rectify this problem,
a waveguide taper (linear or exponential) may be placed in front of the receiving waveguide, so that all the converging

8. light from the Fresnel lens may be collected. The final device dimensions depend upon angle ?, and the efficiency
required; the device dimensions increases with an increase in either parameter. The condition for the mod-|2p| phase
modulation in a Fresnel lens is given by
π2max =∆ Lnko (5)
where L is the thickness of the gradient-index Fresnel lens (measured along the guided-wave propagation). For ?nmax =
0.0016, L = 968.75 µm at ?o = 1.55 µm. Based upon Fig. 6, the real estate of the device is approximately given by
θθ 2sin
4
1
.)(sin.)]([ 2
llwglXfL M ++++ (6)
where l and w are the length and width of the slanted Bragg grating, g is the gap between the slanted Bragg grating and
the edge of the Fresnel lens, measured along the horizontal, f is the focal length of the Fresnel lens, which is a function of
XM. In our design, 2XM = l. sin ?.
Fig. 7 is a graph between the real estate of the device (in mm
2
) plotted as a function of the angle of reflection, ? (in
degrees). The slanted Bragg grating is taken to be of length l = 600 µm and width w = 7 µm, ? nmax = 0.0016, and the
operating wavelength is ? = 1.55 µm. The gap g is taken to be 50 µm and the substrate refractive index n = 2.29. The
thickness of the Fresnel lens L = 968.75 µm. The focal length f, being a function of XM, indirectly depends on the angle
of power return, ?.
Figure 7: Real estate of the device illustrated in Fig. 6, as a function of angle ?
A relief grating having an asymmetrical triangular cross-section, which makes use of the blazing effect, can be used
instead of a slanted Bragg grating. Also, we may replace the gradient-index type Fresnel lens with a gradient-thickness
type, without any change in focal length f. We may also realize a lens function by employing a chirped-grating with a
continuous-period variation
9
. The efficiency of the latter is somewhat superior to that of a Fresnel lens. Electron-beam
lithography is the preferred patterning technique for either type of lens.
The schematic of the 8 × 8 Banyan network [Fig. 5] is redrawn in Fig. 8, as a mask layout, approximately to-scale,
though the width of the waveguides is exaggerated. For purpose of clarity, only the first quadrant of the wafer is
illustrated. In addition to linear- and bent-waveguides, we employ our path-bending component described above, to yield
superior loss performance over arc-waveguides. Other than average path-loss, waveguide design parameters and
switching voltages, the final device dimensions depend strongly on the size of the central opening of the annulus.

9. Smaller openings leave more space for waveguide and device positioning. However, very small openings would
necessitate sharp bends in the fiber at the fiber-wafer interface, leading to severe bend loss in the fiber, structurally
fragile interfaces, and for extremely narrow openings, breakage of fiber. For an 8 µm core diameter single-mode fiber
with a relative refractive index difference of 0.3%, operating at wavelength of 1.55 µm, the critical radius of curvature is
about 34 mm. When the bend radius of curvature approaches this value, the bend loss becomes excessive. For a wafer
(plus supporting substrate) thickness of about 1 mm, the central opening should be at least 8.2 mm in diameter to ensure
bend radius of curvature not less than 34 mm10
. In practice, for low bend loss and ease of alignment of fiber at the fiber-
wafer interface, we recommend a relaxation factor of 2 in this case. The diameter of the central opening would thus be
about 1.6 cm.
Figure 8: To-scalelayout of the 8 × 8 Banyan network laid out on an annular wafer. Only the first quadrant of the optical substrate is
illustrated
Our second technique is an interferometric approach to achieve acute path-bending in integrated optic devices as shown
in Fig. 9. The working principle behind this technique is widely employed in bulk and fiber-optic interferometers, fiber
loop-mirrors, fiber sensors, fiber-optic gyroscopes, etc. Bragg gratings are fabricated at the output ports of a 3-dB
coupler. Power is launched into one of the input ports (say port 1), which divides equally into both output ports (ports 3
and 4), but the field in the through port (port 3) leads the field in the coupled port (port 4) by 900
. Upon reflection from
the gratings, the light-waves return to the 3-dB coupler, and combine destructively in port 1 and constructively in port 2
achieving a 180
0
path reversal. The insertion loss of the device can be less than 0.4 dB.

10. Figure 9: Interferometric-approach to achieve compact and efficient acute path-bends
For the purpose of comparison between the wafer areas occupied by the two techniques, we employ the same waveguide
and grating specifications, at 1550 nm operating wavelength. In a 3-dB coupler, with a center-to-center gap of 12 µm
between waveguides, the required interaction length is about 250 µm, excluding the S-bends (sine bends), which also
contribute to coupling. Adding to this a grating length of about 600 µm, one must now account only for the bend length
(appearing twice), which depends on the width spanned by the bend and the tolerable insertion loss. In general, the span
(width) of a bend need not be 125 µm in the interior of the wafer.
5. CONCLUSIONS
Waveguide crossovers have always been regarded as an obstacle to high performance, crosstalk-free integrated optic
photonic switching architectures. In this paper we have proposed a technique to effectively eliminate these by employing
directional couplers. In architectures employing WDM, the coupling length will differ for different wavelengths, and in
that scenario, the directional couplers would have to be replaced by 2 × 2 directional-coupler type switches. With
application of a fixed voltage bias (positive or negative), corresponding to a particular wavelength, one would be able to
achieve a coupling ratio of 100: 0 for that wavelength.
We have shown how our techniques can be used to incorporate acute bends on a wafer to allow higher levels of
integration of passive and functional devices. Lastly, we proposed alternative annular architectures, and discussed their
design issues.
ACKNOWLEDGMENTS
The authors acknowledge the Photonics group headed by Prof. E. K. Sharma, at University of Delhi South Campus for
allowing them to carry out simulation work on BPM_CADTM
. Our special thanks to Prof. K. Thyagarajan, Physics
Department, Indian Institute of Technology Delhi, for sharing with us his views onintegratedoptics.
REFERENCES
1. ShuffleNet: An Application of Generalized Perfect Shuffles to Multihop Lightwave Networks, M. G. Hluchyj and M.
J. Karol, Journal of Lightwave Technology, 9, 1386 (1991)
2. Optical Interconnection Using ShuffleNet Multihop Networks In Multi-Connected Ring Topologies, M. J. Karol,
ACM,0-89791-279-9, 25 (1988)
3. Regular Multihop Logical Topologies for Lightwave Networks, S. Banerjee, V. Jain and S. Shah,IEEE
Communications Surveys, 1 (1999)
4. Architectures for Guided-Wave OpticalSpaceSwitchingSystems, R. A. Spanke, IEEE Communications Magazine,
25,42(1987)
5. High accuracy interrogation of a WDM FBG sensor array using radiation modes from a B-FBG, A. G. Simpson, K.
Zhou, L. Zhang, and I. Bennion, Optical Society of America, 1 (2000)
6. Some novel photonic guided-wave space-switching architectures, S. Kar and A. Selvarajan,Journal of the IETE,
Special Issue on Digital Communication, 36, (1991)

11. 7. Characteristics of S-Shaped Waveguide Structures by the Annealed Proton Exchange Process in LiNbO3, I. Januar
and A. R. Mickelson,Journal of Lightwave Technology, 11, 2044 (1993)
8. A Beam Propagation Method Analysis of Active and Passive Waveguide Crossings, A. Neyer, W. Mevenkamp, L.
Thylen and B. Lagerström, Journal of Lightwave Technology, LT-3, 635 (1985)
9. Optical Integrated Circuits. Hiroshi Nishihara, Masamitsu Haruna and Toshiaki Suhara. Passive Waveguide Devices,
McGraw-Hill Book Company, United States of America (1989)
10. Optical Fiber Communications, Principles and Practice. J. M. Senior. Transmission characteristics of optical fibers.
Prentice-Hall of India Private Limited, New Delhi (2003)
*malhotra_kartikay@yahoo.co.in; phone 91-11-32010265