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Polarization Rotation in Silicon Waveguides: Analytical Modeling and Applications

Figure 1

Figure 1
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.

Figure 2

Figure 2
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 Formula$x$ and Formula$y$. Both the pump and the signal are assumed to be linearly polarized; LBC denotes the linear birefringence compensator.

Figure 3

Figure 3
(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; Formula$L = 5\ \hbox{cm}$, Formula$I_{B0} = 1\ \hbox{MW/cm}^{2}$, Formula$\vartheta = \pi/4$, and Formula$\varphi = \pi/3$. (b) and (c) Contour plots of signal transmittance in the Formula$(L, I_{A0})$ and Formula$(\vartheta, \varphi)$ domains for Formula$\tau_{c} = 1\ \hbox{ns}$; (b) Formula$\vartheta = \pi/4$ and Formula$\varphi = \pi/2$; (c) Formula$L = 3.2\ \hbox{cm}$ and Formula$I_{A0} = 178\ \hbox{MW/cm}^{2}$. Other parameters are specified in the text.

Figure 4

Figure 4
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 Formula$E_{A}$ and Formula$E_{B}$.

Figure 5

Figure 5
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 Formula$R(z) = I_{B0}(z)/I_{A0}$ with Formula$I_{A0} = 1\ \hbox{GW/cm}^{2}$, gives the ratio of input intensities for Formula$z = 0$, and characterizes the output intensity for Formula$z = L$. For all panels, Formula$\tau_{c} = 1\ \hbox{ns}$; the other parameters' values are the same as in Fig. 3.

Figure 6

Figure 6
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 Formula$R(z)$ is the same as in Fig. 5. For all panels, Formula$\tau_{c} = 0.1\ \hbox{ns}$; the other parameters' values are the same as in Fig. 3.