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Copyright: American Scientific Publishers
RESEARCH ARTICLE
Copyright © 2013 American Scientific Publishers
All rights reserved
Printed in the United States of America
Journal of
Computational and Theoretical Nanoscience
Vol. 10, 1326–1334, 2013
Design and Modeling of Titanium Indiffused
LiNbO
3
Waveguides for Optimum Coupling to
Communication Grade Fiber
Geetika Jain Saxena
1 ∗
and Enakshi K. Sharma
2
1
Department of Electronics, Maharaja Agrasen College, University of Delhi, New Delhi 110096, India
2
Department of Electronic Science, University of Delhi South Campus, New Delhi 110021, India
In this paper we report a procedure based on variational approximation, to obtain the refractive
index profile and process parameters for fabrication of Lithium Niobate waveguide from the desired
modal field. We have illustrated our procedure by the design of a diffused channel waveguide for
optimum coupling to a standard communication grade fiber. The results have been validated by
comparison with those obtained by simulation on the BPM CAD simulator.
Keywords: Optical Waveguide, Fiber Waveguide Coupling, Variational Procedure.
1. INTRODUCTION
In the design of optical waveguides and waveguide-based
devices, it is often required to synthesize waveguides with
a desired modal field. It is usually important to design the
modal field and corresponding refractive index profile of
the waveguide that compose the device, as the important
characteristics of optical waveguides such as spot-size, sin-
gle mode condition and coupling coefficients can be pre-
dicted once the index profiles and modal fields are known.
In this paper we report a procedure to obtain the refractive
index profile and in turn the process parameters for fabri-
cation of waveguide from the desired modal field. It has
been shown that the best variational separable field for
a channel waveguide corresponds to the solution of two
equivalent planar waveguides
1
in the x and y directions.
We have used this concept coupled with a variational anal-
ysis for the fields of planar waveguides to design channel
waveguide with a desired modal field.
We have illustrated the use of the procedure in the
design of waveguides with modal fields for optimum cou-
pling efficiency between a typical communication single
mode fiber and waveguide. In the optical systems that
contain integrated optical components, coupling efficiency
between the fundamental mode of the diffused channel
waveguide of an integrated optical circuit and the optical
fiber that is connected to the circuit plays an important role
in insertion loss considerations. The estimation of coupling
∗
Author to whom correspondence should be addressed.
efficiency requires the knowledge of the modal fields of
both the fiber and waveguide.
2 3
We have used appropri-
ately defined closed form expressions for modal fields of
the equivalent planar waveguides based on the variational
method, for the optimum design of the diffused channel
waveguide.
2. EQUIVALENT PLANAR WAVEGUIDES
FOR SEPARABLE MODAL FIELDS
The typical refractive index profile of a diffused channel
waveguide obtained by Titanium diffusion into LiNbO
3
substrate can be described as
n
2
xy = n
2
s
+ 2n
s
ngx/wf y/h y> 0
= n
2
c
y< 0
(1)
where n
s
, is the substrate index, n
c
is the cover index and
n is the maximum index change and the profile functions
are gx/w = exp-x
2
/w
2
and f y/h = exp-y
2
/h
2
.
Following the approach suggested by Sharma and
Bindal,
1
we first present the procedure to obtain the equiv-
alent planar waveguides. We obtain the equivalent pla-
nar waveguides
1
corresponding to a separable field for the
channel waveguide. We begin with the stationary varia-
tional expression for the propagation constant for diffused
channel waveguide as
2
=
k
2
0
n
2
xyxy
2
-xy
2
dx dy (2)
1326 J. Comput. Theor. Nanosci. 2013, Vol. 10, No. 6 1546-1955/2013/10/1326/009 doi:10.1166/jctn.2013.2850