Analysis of photonic crystal waveguide bends by a plane-wave transfer-matrix method

Abstract

We have developed a plane-wave transfer-matrix method ͑PWTMM͒ to analyze light propagation through sharp photonic crystal bend structures. With the aid of the supercell technique, the original aperiodic waveguide bend can be modeled by a periodic scattering problem of two semi-infinite photonic crystal waveguide arrays face to face or two semi-infinite photonic crystal waveguide arrays separated by a sandwiched slab of bend region. The proposed approach has been applied to several sharp bend structures in two-dimensional photonic crystals. The calculated transmission and reflection spectra of the waveguide mode are in good agreement with existing results made by other numerical methods, even at the frequency close to the waveguide cutoff frequency. The developed PWTMM only needs to handle a single unit-cell layer domain and is therefore numerically friendly. The proposed approach can become an efficient and accurate numerical tool to understand and design high performance sharp waveguide bends in different two-dimensional and threedimensional photonic crystals with complex geometries.

Acousto-optics studied in polaritonic photonic crystals

“…However, we want to point out that the DOS increases exponentially near the band edges in 2D and 3D photonic crystals. [45][46][47][48][49] In our calculations we did not use the value of DOS at the band edges.…”

Silicon Photonic Crystals Towards Optical Integration

“…So far, other methods have not developed such a peculiar capability. For this reason, it can calculate efficiently modal coupling with multimode PC waveguides [28], transmission efficiency through general two-dimensional (2D) and 3D waveguide bends [29], and band diagrams and field profiles of PC surface states [30]. On the other hand, this method has adopted advanced numerical and mathematical analysis tools to enhance numerical convergence and accuracy, and it has shown its superior power in dealing with some metal PC structures compared with other methods [31].…”