We propose a mode conversion method that enables transformation of the propagating mode from fundamental to higher-order modes by utilizing asymmetric graded index (A-GRIN) structures. Refractive index variations of two different asymmetric gradient profiles, i.e., exponential and Luneburg lens profiles, have been approximated by two-dimensional photonic crystals (PCs). The basic structure is composed of constant radii with different lattice sizes. The designed GRIN mode converters provide relatively high transmission efficiency in the spectral region of interest and achieve the transformation in compact configuration. Numerical approaches utilizing the finite-difference time-domain and plane wave expansion methods are used to analyze the mode conversion phenomenon of proposed GRIN PC media. Analytical formulation based on ray theory is outlined to explore both ray trajectories and the physical concept of a wavefront retardation mechanism.
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