A Rigorous Analytic Model For T!raveling Wave Optical Modulators With Conventional And Resonant Electrodes

Recently, traveling wave (TW) LiNb03 optical modulators, in the coplanar waveguide ( CPW) configuration, with performance extending well into the millimeter-wave frequency spectrum have been fabricated by engineering a near velocity match between microwave and optical signals [1,2]. In these devices, the characteristic impedance (Zv) of the active section of the CPW electrode is designed to be between 35 and 40 Ω, as it is difficult to design a CPW line on LiNb03 to simultaneously achieve microwave-optical velocity match with 50 Ω characteristic impedance [1]. Further, to obtain a low drive voltage (V π) with good overlap between microwave and optical fields, the active section of the CPW electrode must be very narrow; for the device reported in ref. 1, the center strip width (w) = 8 µm and gap width (g) = 15 µm. Therefore, to facilitate external microwave and optical access to the modulator, CPW tapers and bends are designed in conjunction with the active section. This is illustrated in the inset of fig. 2 where the layout of the complete device [1] is shown. Previously, high frequency operation of TW modulators, in the velocity matched condition, has been believed to be limited by only the conductor loss of the electrode. However, reflections due to impedance mismatches and other losses such as dielectric loss that stems from the loss tangent of the material and radiative loss that stems from radiation from discontinuities such as tapers and bends may also become significant. Since these losses and reflections are factors intrinsic to the device, they affect the overall device response and hence should be taken into consideration. In this paper, we first investigate losses that occur in different sections of a TW modulator [1). Then, by using the loss coefficients obtained and by allowing for reflections due to impedance mismatches, we develop an accurate model that is applicable to modulators with both conventional and resonant electrodes.