Owing to rapid expansion of multimedia and wireless telecommunications and explosive growth of internet population, broadband optical telecommunication technologies are getting more important. A LiNbO3
optical modulator is a core device of the high-speed optical telecommunication system, and CPW electrodes are essentially adapted for wideband modulation optical devices [1
R. A. Becker, “Traveling-wave electro-optic modulator with maximum bandwidth product,” Appl. Phys. Lett.
45, 1168–1170 (1984). [CrossRef]
The performance of optical modulators is roughly determined by 3dB modulation bandwidth and driving voltage, which can be optimized by phase velocity matching of light propagating along optical waveguides and microwave traveling along CPW electrodes. Besides phase velocity matching, other factors to consider for broadband modulation are propagation loss, characteristic impedance mismatching of CPW electrodes and RF power leakage into high-order substrate mode [2
G. K. Gopalakrishnan, W. K. Burns, and C. H. Bulmer, “Electrical loss mechanism in traveling wave LiNbO3 Optical Modulator,” Electron. Lett.
28, 207–209 (1992). [CrossRef]
]. The high-order substrate modes result from high value of the relative permittivity of LiNbO3
itself and cause signal distortion through microwave coupling with traveling CPW modes [3
Jajid riaziat, Reza Majidi-Ahy, and I-Juang Feng, “Propagation modes and dispersion characteristics of coplanar waveguides,” IEEE Trans. Microwave Theory and Technol.
38, 245–251 (1990). [CrossRef]
This work analyzes the characteristics of parasitic modes existing in LiNbO3 substrates by two-dimensional FEM (Finite Element Method) and the effect of parasitic modes on RF Power transmission characteristics of dominant zero cut-off CBCPW(Conductor-Backed Coplanar Waveguides). From simulation results, it will be discussed that the generation of the high-order substrate mode can be suppressed (to say more precisely, the frequency can be shifted toward higher frequency) by decreasing the thickness of LiNbO3 substrates and that the microwave coupling between electrode CBCPW modes and parasitic modes can be reduced by modification of the electrode structure. Some experimental results will be presented to support the above discussions.
2. Numerical analysis of parasitic modes in CBCPW structure
shows the schematic diagrams of a LiNbO3
optical modulator fabricated in this work. High relative permittivity of LiNbO3
=28) makes simultaneous matching of RF/optic phase velocity and characteristic impedance difficult in a LiNbO3
modulator with a general CPW electrode structure. This is the reason why a thick SiO2
buffer layer and thick CPW electrodes as shown in Fig. 1
Xiang Zhang and Tanroku Miyoshi, “Optimum design of coplanar waveguide for LiNbO3 optical modulator,” IEEE Trans. Microwave Theory Technol.
43, 523–528 (1995) [CrossRef]
] are frequently required.
Fig. 1. Schematic diagram of CPW electrodes in a LiNbO3 traveling wave optical modulator; (a) top view and (b) cross-section view in a interaction region
Other negative feature of the high relative permittivity of LiNbO3 substrates is to induce high-order parasitic modes at frequencies lower than the modulation bandwidth. The parasitic modes generated in the substrate can be coupled with the electrode CBCPW modes and distort consequently the signal traveling along the electrode. Since the electric field formed in the input launch region of the high speed modulator is distributed considerably broad compared with the electric field distribution formed in the interaction region for modulation, even the short length of the input launch region can significantly distort the signal.
Fig. 2. Physical structure for analysis of propagation characteristics in a launch section.
shows a physical structure for analysis of propagation characteristics in a launch section. If we assume electric field, E
, which propagate along y-axis with propagation constant β
, the scalar wave equation governing the wave behavior in the waveguide of Fig. 2
can be written as
modes are defined as given by (2) and their propagation characteristics are calculated from Eq. (1)
by FEM. Figure 3
depicts the field plots for the CBCPW and first few parasitic Ez
modes. The field components have been normalized to their maximum values. Since the field distribution in CBCPW is symmetric about the center plane, only Ez10
modes and Ez30
with even field distribution can coupled with CBCPW mode.
Fig. 3. plot of CBCPW and parasitic modes Ez at 50GHz and z=b-0.05 mm (a=1mm, b=0.5mm, W=0.2mm, S=0.3mm, h=2mm)
Fig. 4. Effective relative permittivity of the parasitic modes as a function of frequency (b=0.5mm, W=0.2mm, S=0.3mm, h=7mm)
shows the effective relative permittivity dispersion curve of the parasitic modes as a function of frequency for the given structure. The number of the substrate mode increases with frequency. Two horizontal lines indicate effective dielectric constant in launch and active regions, respectively. Strong distortion of the RF signal in a launch section occurs at the points which are marked by arrows since the coupling can be maximized under the phase velocity matching condition. Mode coupling can be occurred also in taper and active regions.
is the power transmission curve of the fabricated modulator chip, measured by a G-S-G probe with 500 µm pitch. Close investigation of the measurement results reveals that the first dip appears around 7 GHz and that the frequency gap between dips at higher frequencies gets closer. The dips in the transmission curve are attributed to the coupling of the CPW modes to the substrate modes, and this kind of leakage should be suppressed for broadband modulation.
Fig. 5. S21 of the fabricated CPW electrode to show leaky modes; W=0.15 mm, S=0.3 mm, and b=0.5 mm.
3. Methods of suppression of substrate mode coupling
3.1. Addition of low dielectric constant material to the back-side of the LiNbO3 chip [5
Jeng-Wen Huang and Ching-Kuang C. Tzuang, “Mode-coupling-avoidance of shielded conductor-backed coplanar waveguide using dielectric lines compensation,” IEEE MTT-S Digest , 149–152 (1994).
Fig. 6. Parasitic mode characteristics in multi-layered waveguide structure; (a) physical structure for analysis, (b) dispersion curve
shows the schematic of the CPW structure where a low dielectric constant material (εc
=4 for a quartz glass) is backed to the LiNbO3
chip and the simulation result of the relative permittivity of the parasitic modes as a function of frequency. While the effective dielectric constant of Ezm0
(m=1, 2, 3,…) gets lower, compared with the structure shown in fig. 4
, and the longitudinal mode, Exn1
(n=0, 1, 2, 3,…) is generated when a low dielectric constant material with εc
=4 is added to the back side of the modulator chip. A close investigation on Fig. 6
reveals that there is no point where phase velocity matching condition is satisfied in the launch section up to 30GHz. Consequently, the distortion of the RF signal arises only in the taper region or in the active region where the coupling efficiency is comparatively low. Fig. 7
shows the S21
results of the fabricated CPW electrodes with the conductor backed and the glass backed structures. In the dielectric material backed structure, the dip, resulting from coupling between the CPW mode and the substrate mode, was clearly suppressed below 17 GHz and the effect of the coupling was not remarkable at higher frequencies.
Fig. 7. The transmission characteristics of the CPW electrodes for the conductor backed (circled line) and the glass backed (solid line) structures; W=0.15 mm, S=0.3 mm, b=0.5 mm, and c=0.5 mm.
3.2. Modification of the CPW dimension at the RF power launch region[6
Rangaraj Madabhushi, Yukio Uematsu, and Mitsuhiro Kitamura, “Wide-band Ti: LiNbO3 optical modulators with reduced microwave attenuation,” ECOC 1997 , 2, 29–32 (1997).
The degree of the energy exchange between interacting modes by coupling depends on the inter-modal overlap and the overlap length. Since the electric field in the input launch region of the high speed modulator is distributed considerably broad compared with the electric field distribution in the interaction region for modulation, even the short length of the input launch region can significantly distort the signal. For this reason, the geometry and dimension of the input region can exert a conclusive effect on the modulation bandwidth. Figure 8
explains the effect of the electrode dimension in the input region on the signal transmission.
Fig. 8. The overlap integral of the CBCPW and parasitic modes Ezm0, b=0.5 mm, h=2mm, f=50GHz.
is the overlap integral of CBCPW mode and parasitic modes Ezm0
as a function of W+2S for the given structure. A close investigation on Fig. 8
reveals that the amount of overlap integral (coupling coefficient) increases with W+2S. Figure 9
is the S21
measurement results of the fabricated CPW electrodes with different dimension at the RF launch region while keeping the other conditions, such as electrode thickness and CPW dimensions in the interaction region, identical. The only difference between the measured samples is the width (W) and the separation (S) of the CPW electrodes in the RF launch region. It should be noticed that the ratio of separation to width was kept constant to match the characteristic impedance 50 Ω. As shown in the low-side figure of Fig. 9
, which shows the details of measurement results in the frequency range of 15 GHz to 30 GHz, the dips appear at similar frequencies in all the samples with different CPW dimensions, but the fall of the dip decreased with reduction of the CPW dimension. This means that the mode overlap for coupling between the CPW mode and the substrate mode can be suppressed by reduction of the CPW dimension. A close investigation on Fig. 9
says that the effect of the substrate mode on the CPW signal transmission is insignificant for the modulator sample with W=0.07 mm and S=0.16 mm, which is reasonably the smallest dimension in practice when considering wire or ribbon bonding for modulator packaging.
measurement results of the fabricated CPW electrodes with different dimensions at the RF launch region while keeping the dimension of the other area identical; εc
=4, b=0.5 mm, and c=0.5 mm in the structure shown in Fig. 4
3.3. Thinner LiNbO3 substrates
shows signal transmission characteristics of the optical modulators fabricated on LiNbO3
substrates with different wafer thickness. The first dip appears at 10 GHz, 20 GHz and 24 GHz for wafer thickness of 1.0 mm, 0.5 mm and 0.4 mm, respectively. This should be is due to the dependence of the cutoff frequency of the substrate mode on the substrate thickness. The experimental results show that the LiNbO3
substrate as thin as 0.4 mm at least should be adapted for 40Gbps modulation.
Fig. 10. S21 measurement results of the CPW electrodes fabricated on LiNbO3 substrates with different thickness, b; W=0.25 mm, S=0.5 mm, c=0.5 mm, and εc=4.
4. RF characteristics of packaged samples
shows package samples and measured s-parameter results with different structure to investigate the effect of parasitic mode in launch section and in active region. From Sections 3.1 and 3.2, we can expect that the signal distortion can be minimized by addition of low dielectric constant material, and the effect of added material is stronger in the launch section than in the active region. The result of Fig 11
(c) confirms that our trial in this paper is helpful for broadening of modulation bandwidth.
Fig. 11. Packaged samples and measured s-parameter results with different structure; (a) type A (b) type B (c) type C
5. Discussions and conclusions
This work analyzed the effect of parasitic substrate mode launching from the CPW input electrode into a LiNbO3 substrate on modulation bandwidth and proposed the methods to minimize the distortion of the RF signal. The substrate modes induced in a conventional CPW LiNbO3 modulator were characterized by approximate modeling and numerical simulation, based on which various experiments were conducted for substrate mode suppression.
The effective dielectric constant of a fundamental parasitic mode was decreased by backing a low dielectric constant material on the modulator chip, and the coupling between the CPW mode and the substrate mode was minimized by reduction of the dimension of the CPW electrode in the RF launch section. Additionally, the dependence of the cutoff frequency of the parasitic mode on substrate thickness was experimentally demonstrated. In conclusion, the methods suggested and experimentally demonstrated in this work will contribute, in practice, to realization of ultra broadband modulators.