We study the effects of two-photon absorption on the self-phase modulation (SPM) process in silicon waveguides while including both free-carrier absorption and free-carrier dispersion. An analytical solution is provided in the case in which the density of generated carriers is relatively low; it is useful for estimating spectral bandwidth of pulses at low repetition rates. The free-carrier effects are studied numerically with emphasis on their role on the nonlinear phase shift and spectral broadening. We also consider how the repetition rate of a pulse train affects the SPM process.
We show through numerical simulations that silicon waveguides can be used to create a supercontinuum extending over 400 nm by launching femtosecond pulses as higher-order solitons. The physical process behind continuum generation is related to soliton fission, self-phase modulation, and generation of Cherenkov radiation. In contrast with optical fibers, stimulated Raman scattering plays little role. As low-energy (approximately 1 pJ) pulses and short waveguides (<1 cm) are sufficient for continuum generation, the proposed scheme should prove useful for practical applications.
The dispersive properties of silicon-on-insulator (SOI) waveguides are studied by using the effective-index method. Extensive calculations indicate that an SOI waveguide can be designed to have its zero-dispersion wavelength near 1.5 microm with reasonable device dimensions. Numerical simulations show that soliton-like pulse propagation is achievable in such a waveguide in the spectral region at approximately 1.55 microm. The concept of path-averaged solitons is used to minimize the impact of linear loss and two-photon absorption.
We experimentally realize ultrafast all-optical switching in the 1.5-microm spectral region using cross-phase modulation inside a 5-mm long silicon waveguide. Modulation depths of up to 90% and switching window durations approximately 1 ps are achieved using 500-fs pump pulses with energies below 10 pJ.
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