Cascaded optical nonlinearities. The intent of this problem is to develop an understanding of the phenomenon known as cascaded optical nonlinearities. By cascaded optical nonlinearities, one means that, through propagation, a second-order nonlinearity can mimic a third-order nonlinearity. In particular, in this problem you are to calculate the phase shift acquired by an optical wave in propagating through a second-order nonlinear optical material under conditions of nearly phase-matched second-harmonic generation, and to determine the conditions under which the phase shift acquired by the fundamental wave is approximately proportional to the product of the path length and the intensity
To proceed, start for example with Eqs. (2.7.10) and (2.7.11), and show that one can eliminate A2 to obtain the equation
where is a constant (give an expression for it) and A0 is the incident value of the fundamental field. Show that under proper conditions (give specifics) the solute
n to this equation corresponds to a wave whose phase increases linearly with the length L of the nonlinear material and with the intensity I of the incident wave.
