Nearly Degenerate and Transient Wave Mixing

As pointed out before, laser-induced nonlinear polarizations amount to changes in the dielectric constant. If these dielectric constant changes are spatially coincident with the imparted intensity grating, the materials are said to possess local nonlinearity. In some situations, however, the induced dielectric constant change is spatially shifted from the optical intensity that is, there is a phase shift 4 between the dielectric constant and the intensity grating function (see Fig. 11.7). 

A phase shift between the intensity and index grating function can arise, for instance, if the frequencies of the two interference waves Ex and E2 are not equal (i.e., CO2 = i + (see Fig. 11.8). In this case the intensity grating imparted by E and E2 on the nonlinear medium is moving with time. Because of the finite response time t of the medium, the induced index grating will be delayed (i.e., a phase shift ( ) will occur between the intensity and the index grating). 

The magnitude and sign of the phase shift depend on various material, optical, and geometrical parameters. For the purpose of our present discussion on the consequence of having c ) in the wave mixing process, we will represent it generally as 4 . If the total intensity function is given by 

Consider the scattering of wave Ei or E2 from the induced index grating one can associate third-order nonlinear polarization terms of the form EIE2E, E1E2 Ej and so on. If we limit our discussion to only these two waves and follow the procedure used in deriving Equations (11.63) and (11.64), the corresponding coupled two-wave mixing equations are 

The effects of the phase shift dp on these two-wave couplings are more transparent if these equations are expressed in terms of the intensities /j and I2 and individual phases c )i and 2 of the waves. Then we have 

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