Nondegenerate Optical Wave Mixing Harmonic Generations

Nondegenerate Optical Wave Mixing Harmonic Generations 

Nondegenerate optical wave mixing, where the frequencies of the incident and the generated waves are different, are due to nonlinear polarization of the form given by Equation (11.35). For example, the incident frequencies cdi, CO2, and CO3 can be combined to create new frequencies 0)4 = cdi CO2 0)3 involving sums or differences. These wave mixing processes are sometimes termed sum-difference frequency generations. 

In this section we discuss two basically different sum frequency generation processes, namely, second- and third-harmonic generations. These processes are associated with nonlinear polarizations of the following  

The main fundamental difference between these two processes is that second-harmonic generations involve a polarization that is even order in the electric field (i.e., P EE), whereas third-harmonic generations involve an odd-order polarization P—EEE). Consider a centrosymmetric nonlinear medium. If we invert the coordinate system, then Equation (11.82) becomes 

Since the polarization and the electric field are vectors, they must change signs (i.e., = -P , = i. A, —A,), whereas = Xyvtsince it is a measure of 

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Nondegenerate Optical Wave Mixing Harmonic Generations... 

At second order in optical fields (x = 2), only nonquadrature passive processes, harmonic generation and parametric three-wave mixing, are possible. In fully nondegenerate second order processes, three frequency components of the field at [Pg.71]

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