  We present a study of linearized \c{hi}^((3)) based electro-optic modulation
beginning with an analysis of the nonlinear polarizability, and how to
linearize a modulator based on the quadratic third order DC-Kerr effect. Then
we perform a numerical study, designing a linearized \c{hi}^((3)) phase
modulator utilizing Silicon-rich Nitride where we show that a phase modulator
with a V_{\pi} L_{\pi} metric of 1 Vcm or a V_{\pi} L_{\pi} {\alpha} metric of
37VdB is achievable and a V_{\pi} L_{\pi} as low as 0.5Vcm in a push-pull Mach
Zehnder Interferometer. This numerical study argues that linearized modulation
exploiting the \c{hi}^((3)), and \c{hi}^((2)) as applicable, is possible and
can allow for high-speed modulation using a CMOS compatible material platform.
