Abstract
A deep insight into the inherent anisotropic optical properties of silicon is required to improve the performance of silicon-waveguide-based photonic devices. It may also lead to novel device concepts and substantially extend the capabilities of silicon photonics in the future. In this paper, for the first time to the best of our knowledge, we present a three-dimensional finite-difference time-domain (FDTD) method for modeling optical phenomena in silicon waveguides, which takes into account fully the anisotropy of the third-order electronic and Raman susceptibilities. We show that, under certain realistic conditions that prevent generation of the longitudinal optical field inside the waveguide, this model is considerably simplified and can be represented by a computationally efficient algorithm, suitable for numerical analysis of complex polarization effects. To demonstrate the versatility of our model, we study polarization dependence for several nonlinear effects, including self-phase modulation, cross-phase modulation, and stimulated Raman scattering. Our FDTD model provides a basis for a full-blown numerical simulator that is restricted neither by the single-mode assumption nor by the slowly varying envelope approximation.
Highlights
The microelectronics industry has thrived on the unique electrical and mechanical properties of silicon, which have enabled significant miniaturization and mass-scale integration of electronic components on a single silicon chip [1, 2]
two-photon absorption (TPA) produces a large number of free electrons and holes, which give rise to another optical-loss mechanism known as free-carrier absorption (FCA)
We have presented a comprehensive three-dimensional finite-difference time-domain (FDTD) model for studying nonlinear optical phenomena in silicon waveguides, which allows—for the first time to our knowledge—for anisotropy of the Kerr effect, two-photon absorption, and stimulated Raman scattering
Summary
The microelectronics industry has thrived on the unique electrical and mechanical properties of silicon, which have enabled significant miniaturization and mass-scale integration of electronic components on a single silicon chip [1, 2]. The strong optical nonlinearities of silicon give rise to a variety of nonlinear effects, such as stimulated Raman scattering (SRS) [10,11], self-phase modulation (SPM) [12,13], cross-phase modulation (XPM) [14], cross-absorption modulation (XAM) [15], four-wave mixing (FWM) [16,17,18], and coherent anti-Stokes Raman scattering (CARS) [9, 19, 20] These effects have been successfully utilized in a number of chip-scale photonic devices, including lasers [21, 22], amplifiers [23, 24], switchers [15, 25], modulators [26,27,28], broad-band frequency converters [20, 29], detectors [30], all-optical logic gates [25], continuum generators [31, 32], and pulse compressors [33]. We simplify these equations to obtain a computationally efficient algorithm that can be used to simulate SOI-based photonic devices.
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