2.1
Chapter 2.1
Wave theory of optical
waveguides
Okamoto
The basic concepts and equations of electromagnetic
wave theory required for the comprehension of light-
wave propagation in optical waveguides are presented.
The light confinement and formation of modes in the
waveguide are qualitatively explained, taking the case of
a slab waveguide. Maxwell’s equations, boundary condi-
tions, and the complex Poynting vector are described as
they form the basis for the following chapters.
2.1.1 Waveguide structure
Optical fibers and optical waveguides consist of a core, in
which light is confined, and a cladding, or substrate sur-
rounding the core, as shown in Fig. 2.1 .1. The refractive
index of the core n
1
is higher than that of the cladding n
0
.
Therefore the light beam that is coupled to the end face
of the waveguide is confined in the core by total internal
reflection. The condition for total internal reflection at
the core–cladding interface is given by n
1
sin(p/2 f) n
0.
Since the angle f is related with the incident angle q by
sin
q
¼ n
1
sin
f
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
n
2
1
n
2
0
q
; we obtain the critical
condition for the total internal reflection as
q
sin
1
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
n
2
1
n
2
0
q
h
q
max
: (2.1.1)
The refractive-index difference between core and clad-
ding is of the order of n
1
n
0
¼ 0.01. Then q
max
in Eq.
(2.1.1) can be approximated by
q
max
y
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
n
2
1
n
2
0
q
: (2.1.2)
q
max
denotes the maximum light acceptance angle of the
waveguide and is known as the numerical aperture (NA).
The relative refractive-index difference between n
1
and n
0
is define d as
D
¼
n
2
1
n
2
0
2n
2
1
y
n
1
n
0
n
1
: (2.1.3)
Fig. 2.1.1 Basic structure and refractive-index profile of the optical waveguide.
Fundamentals of Optical Waveguides; ISBN: 9780125250962
Copyright Ó 2006 Elsevier Inc. All rights of reproduction, in any form, reserved.
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