HIGH SPEED OPTICAL MODULATORS IN COMMUNICATIONS
M. Rakib Uddin1, M. Shah Alam2 and Yong Hyub Won1
School of Engineering, Information and Communications University (ICU)
Daejeon, South Korea.
Department of Electrical and Electronic Engineering
Bangladesh University of Engineering and Technology (BUET)
In this paper, the microwave properties of coplanar waveguide (CPW) for Mach-
Zehnder electrooptic modulators in presence of asymmetry, has been presented by
using efficient and versatile finite element method (FEM). Two dimensional and
three dimensional electric field distributions, microwave effective index,
characteristic impedance, and microwave propagation losses of the modulator are
investigated in this work. We observed that the above properties are affected
significantly by the asymmetry of the CPW. We also observed that impedance
matching and phase velocity matching were changed significantly when the
modulator has asymmetry in its structure.
Keywords: Modulators, asymmetry, effective index, characteristic impedance.
1 INTRODUCTION In most cases -, -, the symmetric
CPW electrode are used, however, the asymmetric
Over the past decade, as the demand for CPW electrode can play a significant role in the
telecommunications services and bandwidth has design . By introducing deliberate asymmetry, the
boomed, the need for and advantages of Mach- microwave effective index, characteristic impedance,
Zehnder external modulation in fiber-optic and conductor loss can be controlled to achieve
transmission systems has been firmly established. In velocity and impedance matching, which in turn
higher speed digital communication applications, enhance optical response of the modulator. But,
fiber dispersion has limited system performance. analysis of such waveguides with asymmetry or
Mach-Zehnder external modulators provide both the arbitrary cross section is rather difficult as they do
required bandwidth and the equally important means not lend themselves to analytical solutions . In this
for minimizing the effects of dispersion. Unlike paper, by using the numerically efficient and
direct modulation of laser diode, Mach-Zehnder versatile finite element method (FEM), the analysis
external modulators can be designed for zero-chirp of asymmetric CPW for LiNbO3 Mach-Zehnder
or adjustable chirp operation. Zero-chirp or negative modulators is carried out and two dimensional and
chirp modulators help to minimize the system three dimensional electric field distributions,
degradation associated with fiber dispersion. microwave propagation characteristics such as the
The frequency response of the broad-band Mach- characteristic impedance, Z c , the microwave
Zehnder Modulators with traveling wave electrode is
restricted mainly by the electrical characteristics of effective index, N m , and the microwave
the electrode and the mismatch in velocity between propagation losses are calculated for various
the modulating microwave signals and optical carrier structural parameters.
waves -. Microwave propagation losses, which
include conductor loss and dielectric loss, are the 2 THEORY
limiting factors for bandwidth determination .
However, accurate analysis of coplanar waveguide In the quasi-static approximation, the scalar
(CPW) electrode is indispensable to the design of potential function φ ( x, y ) is governed by the
these modulators. As a mater of fact, the CPW
Laplace’s equation 
electrodes are commonly used as traveling wave
electrodes for a Ti:LN optical modulator because it
∂ 2φ ( x , y ) ∂ 2φ ( x , y )
provides a good connection to an external coaxial εx +εy =0 (1)
line. ∂x 2 ∂y 2
Ubiquitous Computing and Communication Journal 1
Where ε x and ε y are the permittivity in x and y due to dielectric loss. The dielectric loss can arise
from different lossy microwave regions, and in this
directions respectively. By discretizing the case it is comprised of losses in silica and lithium
modulator cross section with many linear triangular niobate.
elements and solving the highly sparse resultant
algebraic equation generated, the nodal values of the 3 SIMULATION AND RESULTS
potential function φ ( x, y ) can be obtained.
From the nodal potential values, the capacitance Fig. 1 shows the cross sectional view of a Mach-
per unit length of the CPW electrode can be Zehnder modulator which is an asymmetric structure.
evaluated by using the divergence theorem  as Here S is the width of the central electrode and the
gap between electrodes, G1 and G 2 are unequal.
As the structure is very small in size, asymmetry
C= dl (2)
n may occur during fabrication process. So during
analysis of the CPW optical modulator, if any
asymmetry present in the structure should be
Where C is the capacitance of the CPW line, V0 is considered very carefully. Besides, asymmetry of the
the applied voltage, S is the integration contour. By CPW Mach-Zehnder modulator may play significant
replacing the dielectric materials by free space, roles on the electric field distribution, the
characteristic impedance, the effective index, and the
capacitance of the free-space line C a can be microwave propagation losses which in turn may
calculated and from these two values the microwave affect the bandwidth of the modulators.
effective index and characteristic impedance can be
calculated using 
N m = (C C a )1 / 2 (3a)
Z c = 1 [v0 ⋅ (CC a ) 1/ 2
Fig. 1: Cross section of asymmetric CPW Mach-
Where v0 =3 × 10 m/s is the speed of light.
8 Zehnder optical modulator.
We employ a perturbation approach  to solve Buffer layer thickness and the electrode thickness
for the attenuation constants due to conductor and are the important parameters in the design of an
dielectric losses as optical modulator. To reduce the optical loss due to
the lossy metal electrodes, often a SiO2 buffer layer
α c = Pc (2 P0 ) (4a) is used, which also assists in the phase matching. The
relative dielectric constant of the SiO2 buffer layer is
and taken as 3.9. For a z-cut LiNbO3 substrate, dielectric
constants are 28 and 43 for orthogonal directions on
α d = Pd (2 P0 ) (4b)
Fig. 2 and Fig. 3 show the calculated values of
N m and Z c as functions of B , respectively. It is
Where P0 is the time average power flow along the
observed that with increasing of B , N m decreases
line, Pc and Pd are the time average powers
dissipated in the conductors and dielectrics,
but Z c increases for a certain value of electrode
respectively . width, S and electrode thickness, T . It can also
When both the conductor loss and the dielectric be observed that as G1 decreases while G 2 is
loss are considered, the total frequency dependent
constant, both N m and Z c decreases significantly.
attenuation constant may be given by 
However, Nm changes uniformly over the variation of
B from 0.6 µm to 2.0 µm, when G1≠G2. On the
α( f ) = αc f + αd f (5) other hand, Zc is more sensitive with the asymmetric
gap width at higher B.
Where αc is the attenuation constant due to
conductor loss and αd is the attenuation constant
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S = 8 µm
S = 8 µm
2.6 T = 10 µm
T = 10 µm
Microwave Propagation Loss (dB/cm)
G2 = 15 µm
G2 = 15 µm
Effective Index, N m
G1= 8 µm G1= 8 µm
G1= 12 µm G1= 12 µm
G1= 15 µm G1= 15µm
0.6 0.8 1 1.2 1.4 1.6 1.8 2 0.6 0.8 1 1.2 1.4 1.6 1.8 2
Buffer Layer Thickness, B (µm) Buffer Layer Thickness, B (µm)
Fig. 2: Variations of microwave effective index, Fig. 4: Variations of total propagation loss, α with
N m with buffer layer thickness, B. buffer layer thickness, B .
S = 8 µm
50 S = 8 µm 2.7
B = 1.2 µm
T = 10 µm
Characteristic Impedance, Z c (ohm)
G2 = 15 µm
G2 = 15 µm 2.6
46 Effective Index, N m 2.5
38 G1=15 µm
G1= 8 µm 2.1 G1=12 µm
36 G1= 12 µm
G1= 15 µm 2
34 2 4 6 8 10 12 14 16 18 20
0.6 0.8 1 1.2 1.4 1.6 1.8 2 Electrode Thickness, T ( µm)
Buffer Layer Thickness, B (µm)
Fig. 3: Variations of characteristic impedence, Fig. 5: Variations of microwave effective index,
Z c with buffer layer thickness, B. N m with electrode thickness, T.
Fig. 4 shows the total propagation loss versus the 60
buffer layer thickness, B. Here the microwave loss S=8 µm
Characteristic Impedance, Z c (ohm)
55 B=1.2 µm
decreases as B increases. However, no significant G2=15 µm
difference is observed for asymmetric structure. 50
The electrode thickness, T is also a significant
parameter for the design of optical modulators. In 45
Figs. 5 we can see the variation of effective index as
a function of electrode thickness. We observed that
effective index decreases as electrode thickness 35 G1= 15 µm
increases. We also observed that when the degree of G1= 12µm
G1= 8 µm
asymmetry increases, effective index decreases. In 30
2 4 6 8 10 12 14 16 18 20
Fig. 6 we observed that the characteristic impedance Electrode Thickness, T ( µm)
decreases for increasing of electrode thickness. We
also observed in Fig. 6 that the characteristic
Fig. 6: Variations of characteristic impedance, Zc
impedance is decreasing due to increasing of the
degree of asymmetry. with center electrode thickness, T.
To find impedance matching, we need
characteristic impedance of 50 Ω and for velocity
matching we need effective index of 2.15. For best
performance simultaneous impedance and velocity
matching is required. But, we observed in Fig. 7 that
due to asymmetry in the structure, simultaneous
velocity and impedance matching is a big problem.
Ubiquitous Computing and Communication Journal 3
Microwave effective index, N
Characteristic impedance, Z
2.6 G1=15 um 50
Electric field (E y)
G1=12 um G1=12 um 0.5
1.8 30 20
0.6 0.8 1 1.2 1.4 1.6 1.8 2 0 0
Buffer layer thickness, B (um)
Fig. 7: Variation of Nm and Zc with the buffer layer Fig. 10: 3-D plot of Ey for T= 10 µm.
Fig. 8: 3-D plot of potential distribution of the
modulator with asymmetric CPW.
Fig. 11: Potential distribution of the modulator with
Fig. 11 shows the contour plot of the potential
distribution over the cross section of the modulator
when the structure is asymmetric. As expected, the
Electric field (E )
distribution here is asymmetric and that the potential
field surrounds the central hot electrode.
60 In this paper, we investigated the electric field
20 distribution and microwave properties, such as the
Y-axis X-axis effective index, the characteristic impedance, and the
loss of asymmetric CPW for lithium niobate Mach-
Fig. 9: 3-D plot of Ex for T= 10 µm. Zehnder modulators by using the finite element
method. We observed that asymmetry of CPW
Fig. 8 shows a 3-D plot of potential distribution makes the potential distribution and hence the
over the cross section of the structure. It is seen from electric field distribution asymmetric and thus affects
the figure that the hot (center) electrode area is at the the microwave properties of the modulator
highest potential. Fig. 9 and Fig. 10 show 3-D plots significantly. To characterize the optical properties
of electric fields Ex and Ey, respectively. The electric of the optical modulators, the microwave properties
field surrounds the central electrode. In this case, we play significant roles and the further study will be
also see that Ey component of the electric field is done for investigating the optical properties of
more dominating than Ex component. different materials both for symmetric and
asymmetric CPW by using finite element method.
Ubiquitous Computing and Communication Journal 4
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