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HIGH SPEED OPTICAL MODULATORS IN COMMUNICATIONS - Ubiquitous Computing and Communication Journal


UBICC, the Ubiquitous Computing and Communication Journal [ISSN 1992-8424], is an international scientific and educational organization dedicated to advancing the arts, sciences, and applications of information technology. With a world-wide membership, UBICC is a leading resource for computing professionals and students working in the various fields of Information Technology, and for interpreting the impact of information technology on society.

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                            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)
                                                 Dhaka, Bangladesh.

             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 [1]-[2], [5]-[7], 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 [7]. 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 [6]. 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 [1]-[4]. Microwave propagation losses, which
include conductor loss and dielectric loss, are the        2 THEORY
limiting factors for bandwidth determination [2].
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 [2]
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 [2] as                   Here S is the width of the central electrode and the
                                                                   gap between electrodes, G1 and G 2 are unequal.
        1             ∂φ
                                                                   As the structure is very small in size, asymmetry
C=                       dl                                  (2)
                  n                                                may occur during fabrication process. So during
        V0    S
                                                                   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 [8]

N m = (C C a )1 / 2                                         (3a)

and                                                                                                          z

Z c = 1 [v0 ⋅ (CC a )         1/ 2
                                     ]                      (3b)
                                                                   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 [9] 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)
                                                                   transverse plane.
                                                                        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 [9].                                                  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 [2]
                                                                   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

                            Ubiquitous Computing and Communication Journal                                               2
                            2.7                                                                                                                                                           2
                                                                                                             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
                                                  2                                                                                                                                   0.8
                                                                      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

                                                              44                                                                                                                          2.4

                                                              38                                                                                                                                           G1=15 µm
                                                                                                                     G1= 8 µm                                                             2.1              G1=12 µm
                                                              36                                                     G1= 12 µm
                                                                                                                                                                                                           G1=8 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
                                        2.8                                                                                                   55

                                                                                                                                G1=15 um
 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
                                        2.4                                                                                                   45
                                                           G1=8 um
                                                                                                                                G1=8 um
                                        2.2                                                                                                   40

                                                      2                                                                                       35
                                                                                                                                                                                                                     100                                       80
                                                                                                                                                                                                                               50                  40
                                        1.8                                                                                                    30                                                                                           20
                                          0.6                     0.8           1         1.2           1.4         1.6          1.8          2                                                                                     0   0
                                                                                                                                                                                                                      Y-axis                     X-axis
                                                                         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.
thickness, B.





                                                               100                                                                             80
                                                                           50                                             40
                                                                                          0     0
                                                                Y-axis                                              X-axis

Fig. 8: 3-D plot of potential distribution of the
modulator with asymmetric CPW.
                                                                                                                                                                                   Fig. 11: Potential distribution of the modulator with
                                                                                                                                                                                   asymmetric CPW.

                                                                                                                                                                                        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.
                                                                                                                                                                                   4                  CONCLUSION
                                                                                                                                         60                                             In this paper, we investigated the electric field
                                                                                50                                             40
                                                                                                                   20                                                              distribution and microwave properties, such as the
                                                                                              0     0
                                                                     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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