A comprehensive theory is developed for describing the nonlinear propagation of optical pulses through silicon waveguides with nanoscale dimensions. Our theory includes not only the vectorial nature of optical modes but also the coupling between the transverse electric and magnetic modes occurring for arbitrarily polarized optical fields. We have studied the dependence of relevant nonlinear parameters on waveguide dimensions and found a class of waveguide geometries for which self-phase modulation can have a dramatic impact on the polarization state of the optical field. Self-induced polarization changes are studied for both the continuous and pulsed optical fields propagating in silicon waveguides. We also discuss the possibility of using these effects for intensity discrimination and pulse compression.

We present a theoretical model describing the dynamics of the electromagnetic field in an optical resonator undergoing refractive index changes. We use an operator formulation of Maxwell's equations with a standard timedependent perturbation theory to derive the dynamic mode-amplitude equations that govern the response of a resonator to a perturbing dipole-moment density. We show that in the case of time-dependent changes in the refractive index, a coupling matrix Γ km ðtÞ that appears in the equations accounts for all novel physical processes that can be expected to occur. In particular, the phenomenon of adiabatic wavelength conversion is governed by the diagonal elements of this matrix, and the off-diagonal elements are responsible for the transfer of energy from an excited resonator mode into its neighboring modes. Our model clearly shows that the latter process can occur only when the index changes are spatially nonuniform. We discuss the spatially uniform and nonuniform cases separately and compare the predictions of our model with experimental data available in the literature. The overall good agreement suggests that this model should be useful in the study of dynamic optical resonators. Moreover, since we do not make any assumptions about the type of dielectric cavity used, the width of input pulses, or the speed with which the refractive index is changed, this model should be applicable under most experimental situations.

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A two-input configuration for microresonators, exhibiting bistability owing to Kerr nonlinearity, could be used for the realization of optical flip-flops with switching speeds that are not limited by thermal effects. We present design considerations for such devices. The concept of phase switching is explained, and the results of numerical simulations clarify the conditions under which it will succeed. A thermal model is presented and used to understand the influence of the material properties and cavity structure on important operating parameters that will be relevant to any experimental effort to realize the device.

We study numerically the dependence of dispersive and birefringence properties of silicon nanowires on waveguide dimensions and show that they have a strong geometrical dependence when nanowire dimensions become comparable to the wavelength of light inside the device. We develop a graphical method for engineering two or more dispersion parameters simultaneously and use it to demonstrate the possibility of fabricating silicon nanowires with flattened dispersion curves over a wide spectral range with normal or anomalous nominal values. We quantify polarization-mode dispersion through the differential group delay and show that it can acquire large values for properly designed nanowires. Our analysis should help in designing silicon-based photonic integrated circuits.