Introduction - Optical Signal Processing by Silicon Photonics - page 8

stems because of its relatively stronger nonlinear interaction with external elec-
tromagnetic fields, wavelengths of whose lie in the region of transparent infrared
region away from 1.1 μ m. Since the telecommunication window near 1.55 μ m lies
in this region, a multitude of nonlinear optical effects inside silicon waveguides can
be used for miscellaneous useful applications. Furthermore, these nonlinear inter-
actions can be improved by employing silicon-on-insulator (SOI) waveguides in
which a tight-mode confinement provides large optical intensities even at moderate
input power levels. Therefore, it is not surprising that, to-date, almost all physical
properties of silicon have found applications in different nonlinear SOI-based pho-
tonic devices. Like, stimulated Raman scattering (SRS), which is particularly strong
in silicon, is employed to make optical modulators, amplifiers, and Raman lasers.
The Kerr effect is successfully applied for soliton formation, optical phase
modulation, and super continuum generation. The phenomenon of four-wave
mixing by itself, or in combination with SRS, has been used to make broadband
frequency converters. Although two-photon absorption by itself is undesirable, it
has been demonstrated that TPA-induced free-carrier generation and thermo optic
effects are suitable for all-optical switching, modulation, and pulse compression;
they can also be used for autocorrelation measurements. The natural compatibility
of SOI technology with the existing silicon manufacturing process opens up wide
possibilities for utilizing these and other useful functionalities in fabricating pho-
tonic integrated circuits.
To date, nonlinear propagation of optical pulses through silicon waveguides
has been studied mostly numerically by using the well-known, split-step Fourier
method. It makes use of widely deployed slowly varying envelope approximation
to separate a rapidly varying waveform (the carrier) from the signal (the enve-
lope). Another numerical method, which is often used for a direct solution of the
Maxwell's equations, is the finite-difference time-domain (FDTD) method. Since
it does not make use of the slowly varying envelope approximation, the FDTD
scheme is well suited for studying the propagation of pulses as short as a single
optical cycle. In principle, these two numerical methods can provide compre-
hensive information and model all types of nonlinear phenomena inside silicon
waveguides.
In spite of this, simple analytical solutions and semi-analytical tools are of con-
siderable value in practice because they offer a clearer view of nonlinear processes
in silicon waveguides and may open up nontrivial paths for device optimization.
Over the past few years, a number of such methods have been proposed in litera-
ture on nonlinear silicon photonics.
For an intuitive understanding of nonlinear optical phenomena in silicon wave-
guides, numerical simulations should be supported by simple analytical solutions
capable of providing a reasonable estimate of the physical quantity involved. Such
solutions provide not only a rapid way of checking simulation results but also
considerable physical insight that is often lost in voluminous data generated by
numerical simulations.
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