We propose a simple realistic two-dimensional complex parity-time-symmetric photonic structure that is described by a non-Hermitian potential but possesses real-valued eigenvalues. The concept is developed from basic physical considerations to provide asymmetric coupling between harmonic wave components of the electromagnetic field. The structure results in a nonreciprocal chirality and asymmetric transmission between in-and out-coupling channels into the structure. The analytical results are supported by a numerical study of the Bloch-like mode formations and calculations of a realistic planar semiconductor structure.

Asymmetric graded-index (GRIN) inhomogeneous medium is proposed to enable even-to-odd mode conversion. An exponential refractive index profile is implemented to induce an asymmetric refractive index distribution. A two-dimensional photonic crystal structure composed of constant dielectric radii with rectangular unit cells is deployed. Efficient mode transformation in a compact structure may promote the manipulation of light for the creation of other types of higher-order modes in asymmetric GRIN structures.

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 finitedifference 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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In this study, we report a low-symmetric photonic crystal (PhC) structure that exhibits high coupling efficiency in a broadband frequency range with a tilted self-collimating capability. First, the analytical approach is implemented as a starting point, and the ideal configuration is chosen for the self-collimation effect, which is analytically supported by group velocity dispersion and third-order-dispersion calculations. Then, numerical analyses in both time and frequency domains are performed to the ideal PhC design, which possesses a strong self-collimating characteristic, even at huge incident angles within the operating frequencies. Later, experimental measurements are conducted in microwaves, and the existing self-collimation property is still preserved at longer wavelengths in the millimeter scale. The microwave experiment as well as numerical analyses indicate that the designed PhC self-collimator allows overcoming possible misalignment problems at the PhC-source interface and enables a strong broadband beam channeling with a high transmission.

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We present a novel design of two dimensional graded index medium that provides coupling of light with high coupling efficiency between two planar dielectric waveguides of different widths (15.46 μm vs. 2.21 μm). Poor light coupling performance of butt-coupler can be mitigated by implementing tapered coupler at the expense of long coupler section. In order to reduce coupling losses, a new coupling device approach based on graded index (GRIN) concept is proposed. The refractive index distribution is in the form of modified version of the Maxwell fish-eye lens. The inhomogeneous refractive index distribution is approximated by photonic crystals (PCs) such that the positions of each PC rods are appropriately arranged. Strong electric field focusing ability of the designed GRIN PC medium provides relatively high coupling efficiency that is around 90%. Spectral region corresponding to coupling efficiency over 75% has a bandwidth of Δω = 18.56% (284 nm). Finally, we discuss the durability of the proposed coupler against the lateral displacement and angular misalignment of output waveguides.