Optical Directional Coupler with Tunable Coupling Coefficient
Monireh Moayedi Pour Fard
Department of Electrical and Computer Engineering, McGill University, Montreal, Quebec, Canada.
e-mail address: monireh.moayedipourfard@mail.mcgill.ca
I.
INTRODUCTION
Optical directional coupler is one of the most
fundamental components in integrated photonic
circuits and widely applies in photonic systems as
optical power combiner and splitter. It consists of
two straight waveguides which are close to each
other and optical power can couple from one to
another. Fig. 1 shows the top view (a) and cross
section (b) of the Optical directional coupler with
two identical waveguides. Coupling coefficient is
the ratio of electric field coupled in cross
waveguide and is given by the following equation:

W
X
G
Z
Output B
Coupler Length Lc
(a)
Air
Si
   asym
Pcross
 sin( sym
Lc )
P in
2
Y
G
W
Si
220 nm
SiO2, n = 1.45
X
(b)
Where Lc is the coupler length and  sym and  asym
are the propagation coefficient of symmetric and
anti-symmetric modes in two waveguides,
respectively.
Since the propagation coefficient  , is wavelength
dependent, coupling coefficient also changes with
wavelength. Longer coupler length is more
sensitive than the shorter one, so in order to design
the broadband directional coupler for specific
coupling coefficient, the coupler length should be
as short as possible.
II.
Output A
Input
Fig. 1. Top view of the optical directional coupler (a), the cross
section of the optical directional coupler (b).
The thermal conductivity of the silica and silicon
are low and also the variation of the refractive
index of silicon with temperature is about
n 2 104 1/ K , which means that changing
temperature may not give the wide range of tuning.
By increasing the length of coupling, coupling
coefficient becomes more sensitive to the
temperature as well as wavelength.
III.
TUNABLE COUPLING COEFFICIENT
OBJECTIVES
In this project I am going to design and simulate
directional couplers with different structural
properties and study their coupling coefficient
changes with temperature variation and their
wavelength dependence property. Structural
properties such as coupler length, coupler gap
distance (G in Fig. 1), waveguide structure, and
cladding material. The directional coupler can
consist of two strip waveguides with air cladding
(Fig. 1-b), or two Asymmetric ridge waveguides
with air cladding (Fig. 2-a), or two ridge
For a manufactured optical directional coupler,
variation of refractive indices of waveguides
changes the coupling coefficient  . Carrier
injection and/or temperature variation change the
refractive indices of the waveguides and can be
used for tuning the coupling coefficient. The
technology which will be used for this project
cannot deposit doped silicon and metal, so there is
no way for applying carrier injection technique.
Another potential way for tuning the coupling
coefficient is heating up the whole chip.
1
Air
G
si
Y
Table 1. Primary estimation of the waveguide size for different
waveguide structure with air and SiO2 cladding and the gap (G)
distance of 100 nm in wavelength of 1550 nm.
Air
W
Si
G
220 nm
si
Y
SiO2, n = 1.45
X
(a)
W
Si
220 nm
Type of
waveguide
Strip
Ridge
AsymmetricRidge
SiO2, n = 1.45
X
(b)
Air
Polymer
Si
Y
G
W
Si
Si
220 nm
SiO2 cladding
COCL*(µm)
14.6
8.3
2.9
Width (W)
(µm)
0.5
0. 5
0.45
* COCL, “Cross-over Coupler length” is the length which the
coupling coefficient is equal to 1
SiO2, n = 1.45
X
(c)
Fig. 2. Cross section of different waveguide structures.
Asymmetric ridge waveguide with air cladding (a), symmetric
ridge waveguide with air cladding (b), Strip waveguide with
polymer cladding (c).
waveguides with air cladding (Fig. 2-b), or using
another material such as polymer or SiO2 as
cladding (Fig. 2-c). Applying polymer with more
sensitivity to the temperature can increase the range
of tuning.
IV.
Air cladding
COCL*(µm)
32
8.15
2.85
DESIGN METHODALOGY
At first step by using Lumerical mode solver the
supermode effective indices are found and the
required length for coupling coefficient   1 is
calculated. In next step the temperature effect will
be studied by sweeping the effective indices
changes based on temperature variation. The
wavelength-dependence property of directional
coupler will be studied by sweeping the effective
indices changes based on wavelength variation. The
whole process will repeat for directional couplers
with different structural properties. Table 1 has
been summarized the primary estimation of the
waveguide size for wavelength of 1550 nm.
As it is expected and has been shown in the table,
the strip waveguide is much more sensitive to the
refractive index of the cladding.
2