Coupled mode equations polarization effects

In this study we suppose nonlinear organic material shows optical Kerr effect as n = n0+n2lEl2 and n2 = X<3)/(2n0). Moreover for simplification, we suppose the waveguides allow single mode propagations and TE polarization. After appropriate handling we get the following nonlinear coupled mode equations [ 12] ... 

For the particular case of longitudinal optical modes, we found in Eq. (9-27) the electrostatic electron-phonon interaction, which turns out to be the dominant interaction with these modes in polar crystals. Interaction with transverse optical modes is much weaker. There is also an electrostatic interaction with acoustic modes -both longitudinal and transverse which may be calculated in terms of the polarization generated through the piezoelectric effect. (The piezoelectric electron phonon interaction was first treated by Meijer and Polder, 1953, and subsequently, it was treated more completely by Harrison, 1956). Clearly this interaction potential is proportional to the strain that is due to the vibration, and it also contains a factor of l/k obtained by using the Poisson equation to go from polarizations to potentials. The piezoelectric contribution to the coupling tends to be dominated by other contributions to the electron -phonon interaction in semiconductors at ordinary temperatures but, as we shall see, these other contribu-... 

Unlike ISS, the electro-optic effect (or its inverse) can occur only in noncentrosymmetric media and in general does not lead to any real material excitation. However, if there are low-frequency IR-active modes in the crystal, they may be excited impulsively [36, 59]. Such phonons couple strongly to IR radiation to form mixed modes called polaritons. Impulsive stimulated polariton scattering can be described approximately by coupled equations of motion for the polarization contributions P, and due to ionic motions (i.e., phonons) and electronic motions, respectively [9, 60] ... 

There are numerous examples of polar liquids at room temperature at least which exhibit Debye or nearly so behavior (in the sense of conformity to equation (35) over most of the frequency range of dispersion. Only a few of these are mentioned here others can be found for example in Bottcher-Bordewijk (48) and in the tables compiled by Buckley and Maryott (49). This is true of substituted methanes (50) (including methanol ) such as chloroform CHCl with = 5.7ps at 25 C. Even for these and other simple molecules there are small residual effects as indicated schematically in Figure 3(a). These seen as millimeter far infrared absorption are a resultant of inertial effects and Foley absorption variously attributed to librations coupling to translational modes and the subject of ot er contributions to these proceedings. 

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