Analysis of focal performances of cylindrical microlenses made of anisotropically dielectric material based on rigorous diffraction theory

Abstract

In this paper we investigated the focal performances of the refractive cylindrical micro-lenses made of anisotropic material ( uniaxial crystal ) with the use of the rigorous diffraction theory and boundary element method (BEM). The expressions of conversion from the H-field into the E-field for the TM-polarization are given. The lateral and axial intensity distributions of the E- ( H-) field for the TM- polarization and E-field of the TE-polarization are calculated. The focusing features of the micro-lenses, including the focal spot size, the focal length, and the diffractive efficiency are appraised. The focusing characteristics of both isotropically and anisotropically refractive cylindrical micro-lenses with different f-numbers have been analyzed and compared. The numerical simulations show that in the case of isotropic dielectricity the E- and H- field distributions for the TE- and TM-polarizations exhibit almost the same focusing behavior for all different f-numbers (f/4, f/2, f/1.5). However, in the case of anisotropic dielectricity, we found that the focal spot size of the E-field for the TM-polarization is quite larger than that of the E-field for the TE- polarization, for instance, the focal spot sizes of the E-field for TM- and TE-polarizations are 2.35pm and 1.98μm in the case of f/2, respectively. It is noted that the positions of the focal plane of the E-field for the TE- and TM-polarizations are shifted remarkably away from each other. The focal length of the E-field of the TE-polarization is shorter than that of the E-field of the TM-polarization. For instance, the positions of the focal plane of the E-field for the TE-and TM-polarizations are 59.35μm and 70.79μm in the case of f/2, respectively. This result can be understood from the simple argument owing to the different refraction index for two polarizations in the uniaxial crystal. These interesting features are reported here for the first time. It is anticipated that this kind of elements may serve as the ideal light switching devices with high speed in the MEMS.