Schematic of the major nonlinear effects in silicon. The process of TPA is accompanied by the absorption of a transverse optical phonon because silicon is an indirect-bandgap material.

Operation scheme of the (a)–(c) Kerr shutter and (d)–(f) power equalizer, based on the XPM-induced polarization rotation in SOI waveguides with principal axes $x$ and $y$. Both the pump and the signal are assumed to be linearly polarized; LBC denotes the linear birefringence compensator.

(a) Comparison of approximate analytical solution given in (8) (solid curves) with the transmittance calculated numerically using (3) and (4) (open circles) for free-carrier lifetimes of 1, 2, and 3 ns; $L = 5\ \hbox{cm}$, $I_{B0} = 1\ \hbox{MW/cm}^{2}$, $\vartheta = \pi/4$, and $\varphi = \pi/3$. (b) and (c) Contour plots of signal transmittance in the $(L, I_{A0})$ and $(\vartheta, \varphi)$ domains for $\tau_{c} = 1\ \hbox{ns}$; (b) $\vartheta = \pi/4$ and $\varphi = \pi/2$; (c) $L = 3.2\ \hbox{cm}$ and $I_{A0} = 178\ \hbox{MW/cm}^{2}$. Other parameters are specified in the text.

Schematic representation of the two roots given in (11). The elliptically polarized beams are equally transmitted through polarizers whose axis have equal maximum projections of the electric fields $E_{A}$ and $E_{B}$.

Polarizer's angles, which equalize intensities of two beams passed through a 1-cm-long SOI waveguide (a) and (b), and the corresponding output intensities (c) and (d). The function $R(z) = I_{B0}(z)/I_{A0}$ with $I_{A0} = 1\ \hbox{GW/cm}^{2}$, gives the ratio of input intensities for $z = 0$, and characterizes the output intensity for $z = L$. For all panels, $\tau_{c} = 1\ \hbox{ns}$; the other parameters' values are the same as in Fig. 3.

Polarizer's angles, which equalize powers in a two-level signal passed through a 1-cm-long SOI waveguide (a) and (b), and the corresponding output intensities (c) and (d). The function $R(z)$ is the same as in Fig. 5. For all panels, $\tau_{c} = 0.1\ \hbox{ns}$; the other parameters' values are the same as in Fig. 3.