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Abstract
Laser heating is known to make an important contribution to the nonlinear refraction of liquid crystals due to the large rate of change of the refractive index with temperature, dn/dT. There is a strong enhancement of dn/dT near the nematic-isotropic phase transition which is associated with the rapid variation of the nematic order parameter, S, with temperature. This has been seen to lead to a strong enhancement of the nonlinear refraction. However, if the nonlinear refraction is probed with laser pulses on the nanosecond time scale, incomplete relaxation of the order parameter during the pulse results in a reduction of the observed nonlinear refraction. The time scale for relaxation of the order parameter also shows a large peak near the phase transition temperature, so that for short laser pulses, the temperature dependence of the effective nonlinear refractive index, n 2, will be strongly influenced by the relaxation dynamics of the order parameter. This paper presents a simple model for the time evolution of the orientational order of a nematic liquid crystal subjected to heating by a gaussian laser pulse. By treating the orientational degrees of freedom with a phenomenological Landau-deGennes theory, and assuming that the other degrees of freedom equilibrate quickly compared to the pulse duration, it is possible to solve for the time dependence of the order parameter, and thus the indices of refraction. By defining an intensity weighted average of the change in index of refraction, an effective nonlinear refractive index can be extracted, such as would be measured in an experiment of the z-scan type. Using parameters which have been measured for the material 5CB, it is found that the slow relaxation completely cancels the enhancement of dn/dT near the phase transition, resulting in an effective n 2 which is nearly independent of temperature, for pulse durations less than a few tens of nanoseconds.