IntroductionExternal travelling-wave electroabsorption modulators (TW-EAMs) are suitable components for the development of high-speed fiber optic links, with potential for a wide range of functionalities, either broadband or narrowband. Despite the limited RF waveguide length, that is always electrically short (at least for microwave frequencies), the travelling-wave design significantly overcomes the bandwidth limitation inherent to the lumped approach, providing high efficiency as well as high speed. The typical TW-EAM structure exploits a p-i-n heterojunction embedded in a non-planar microwave waveguide. Being fabricated on heavily doped substrates, the transmission line exhibits high microwave losses, strongly asynchronous coupling to the optical signal, and impedance mismatch with respect to 50 Ω. Moreover, the p-i-n junction and the significant optical absorption and photocarrier generation in the intrinsic layer make the RF behavior dependent on the applied DC bias and incident lightwave, affecting the device behavior in terms of achievable extinction ratio and bandwidth. Thus, the accurate design and optimization of TW-EAMs requires large signal modeling tools, taking into account the dispersive, nonlinear behavior of the microwave and optical waveguide as well [2,1].While a purely electromagnetic (EM) approach, modeling the semiconductor as a constant conductivity medium, gives accurate results in the analysis of metal-semiconductor transmission line (e.g. it captures the slow-wave effect), this is not appropriate at all in describing the influence of DC bias or optical power typical of distributed optoelectronic devices. A rough estimate of the capacitance of reverse biased p-i-n structures can be achieved by approximating the depleted region as a dielectric; however, an accurate evaluation of this parameter as a function of bias, especially in presence of a significant concentration of photogenerated carriers, not only requires to compute the free charge profile in the depletion region, but also to account for small-signal diffusion currents, in turn requiring a direct treatment of semiconductor transport within the EM model. In this paper a novel coupled full-wave EM and carrier transport model is applied to the analysis of the RF propagation of TW-EAMs, with relevance on the effect of optical power on the microwave loss.
Modeling approachIn the literature, a few examples of coupled full-wave EM and transport models have been presented so far. A very general frequency-domain coupled formulation, including nonlinearity, has been recently proposed in [3]. However, the computational complexity limits the treatment to a 1D cross-section, thus neglecting geometrical and fringing effects that may significantly affect the microwave propagation characteristics in realistic structures.In the present paper, we propose a simplified but computationally efficient finite-element approach that reduces the field-transport problem to a DC analysis followed by a guided-wave linearized problem, in which the full-wave EM...