We have used a finite element method to calculate the nonlinear polarization of small nematic droplets, for both the radial and bipolar director configurations. The nonlinear polarization of droplets with a radial director is concentrated along the droplet axis, while for the bipolar droplets, the nonlinear polarization is more uniform across the droplet. The nonlinear polarization of the bipolar configuration has also been shown to be sensitive to the angle between the droplet axis and the applied field.
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Risser , S.M., Ferris , K.F. Nonlinear Optical Response of Nematic Droplets . MRS Online Proceedings Library 228, 117–121 (1991). https://doi.org/10.1557/PROC-228-117