William Angerer - Department of Physics and Astronomy - University ...

33
2.4.4 Calculation of the Bound Wave From the Nonlinear Wave Equation
Once the nonlinear polarization is determined from the fundamental fields, the nonlinear
waves may calculated from the nonlinear wave equation and boundary conditions.
This section outlines the calculation of the nonlinear bound wave from the
wave equation and the nonlinear polarization.
The nonlinear wave equation in frequency space is [461
(2.36)
The particular solution to the nonlinear wave equation must oscillate with the same
phase as the nonlinear polarization (equation (2.33)), i.e. eikb(w)y.
Since, kb is the
bound wavevector, we subscript the particular solution of the wave equation with
·'b" to denote it is the bound wave field. This solution has the form
(2.37)
Thus, the wave equation for Ebx is
(2.38)
vVe further simplify this expression by making a zeroth-order approximation for the
coefficients in equation (2.38). We assume that w = 2w o • In other words. we assume
that the angular frequency is identically equal to the center frequency of the Gaussian
for the coefficients in equation (2.38). This approximation leads to the following
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.