Finite-difference complex-wavevector band structure solver for analysis and design of periodic radiative...

We demonstrate a finite-difference approach to complex-wavevector band structure simulation and its use as a tool for the analysis and design of periodic leaky-wave photonic devices. With the (usually real) operating frequency and unit-cell refractive index distribution as inputs, the eigenvalue problem yields the complex-wavevector eigenvalues and Bloch modes of the simulated structure. In a two-dimensional implementation for transverse-electric fields with radiation accounted for by perfectly matched layer boundaries, we validate the method and demonstrate its use in simulating the complex-wavevector band structures and modal properties of a silicon photonic crystal waveguide, an array-antenna-inspired grating coupler with unidirectional radiation, and a recently demonstrated low-loss Bloch-mode-based waveguide crossing array. Additionally, we show the first direct solution of the recently proposed open-system low-loss Bloch modes. We expect this method to be a valuable tool in photonics design, enabling the rigorous analysis and synthesis of advanced periodic and quasi-periodic photonic devices.