Realization of a High Coupling Efficiency by Employing a Concave Lens Based on Two-Dimensional Photonic Crystals with a Negative Refractive Index

A study of the interaction of a continuous-wave Gaussian beam with a concave lens used as a spot-size converter (SSC) is presented. The lens is based on a 2-D photonic crystal (PC) structure with a negative refractive index. A numerical method based on a 2-D finite-difference time domain was employed to investigate the light propagation in a photonic integrated circuitry (PIC). The PIC consisted of a single-mode fiber, an SSC, and a PC waveguide (PCW). By employing an optimized planoconcave lens, a large spot-size area of the Gaussian beam was focused/transformed into a very small spot-size area, which is even smaller than the order of the operating wavelength. Optimization of the proposed device parameters has also been reported. A significant reduction in the device size, transmission efficiency, and coupling efficiency has been achieved by optimizing the planoconcave lens and the PCW.