Vectorial far-field method for subwavelength grating based VCSELs

We proposed in detail a procedure for the vectorial far-field analysis of high-contrast subwavelength gratings (HCGs) for vertical cavity surface emitting lasers (VCSELs). The vectorial far-field analysis method (VFM) is based on the vectorial angular spectrum method. The transmission and reflection coefficients of the HCG are used to modulate the polarized far-field components, and the modulated far-field components are vectorially composited to obtain the final transmitted and reflected far-field distribution. The reflectance and transmittance of the HCG to a two-dimensional finite-size beam can be solved by the integral of the output beam. The near field of the transmitted and reflected beam can be solved by an inverse Fourier transform of the far-field distribution. The VFM can be effectively applied in the transmit and reflect far-field beam shaping design and polarization analysis of HCG-VCSELs. The near field reconstructed by VFM can be applied to the calculation of coupling efficiency and lens design. The results of VFM are verified by a three-dimensional finite-difference time domain based on the licensed RSoft FullWAVE tool. VFM only needs to calculate a single-period structure, and the response of HCG to various near-field distributions can be obtained by one calculation, which provides an efficient and accurate method for the design of polarized HCG-VCSELs. The VFM reveals the underlying physics of the shaping effect of subwavelength grating on polarized beams and can be easily extended to the far-field analysis of arbitrary periodical meta-surfaces.