| dc.description.abstract | Traditionally, to focus a beam of light into a tiny spot, we need a convex lens. Recently, alternative approach based on the researches of the propagating waves in photonic crystals (PhC) has been proposed: by choosing a negative-refraction (NR) photonic pass-band as operating band, a plano-concave lens of PhC makes a beam of incident light converge. Up to now, a huge amount of research papers discussing the features of NR in PhC together with a few papers studying the focusing ability of concave lenses of PhC have been published. As a kind of nano-optical component, a concave lens of PhC has the advantage of shortening the focal length and focusing the incident light beam into a spot of sub-wavelength size. However, the design and fabrication of a PhC lens are still too complicated. We therefore propose in this thesis the new idea of ‘air lens’ to simplify the previous designs. In addition, we investigate thoroughly the focusing characteristics of this device.
In the thesis, we begin with the investigation of the NR phenomenon and imaging characteristics of plano-concave nanolens in a 2D PhC. We then replace the 2D PhC structure with a 1D PhC and explore if the same work can still be done. Finally, the idea of air lens is proposed. We hope to avoid such a complicated structure like PhC but achieve the same goal of making light converged effectively in the nanoscale environment.
We first create a plano-concave air lens in a dielectric medium, whose concave surface is cylindrical. As one of the simulation parameters, a large dielectric constant of the background medium is assumed in order to focus the incident light effectively. When light propagates from a denser medium into a less dense one and back to the denser medium, the concave air lens converges light like the convex glass lens does in air. To find better converging characteristics, we then make the concave surface non-cylindrical. We replace the cylindrical surface with several conic surfaces. Moreover, we use FDTD (the wave optics based on Maxwell equations) method as well as the ray-tracing (geometrical optics) method to simulate and predict the locations of the focal points. In addition, we compare the spot sizes and focus locations for different surfaces.
In our analysis, the second type of oblate elliptical surface has the best imaging performance, in which the geometrical prediction matches the wave phenomenon very well. As an example of application, we assemble an optical coupler of concave air lens and a photonic-crystal waveguide (PCW) and show how efficiently the light beam can be coupled into the PCW. We believe that appropriately designed air nanolens will become a commonly used component in the nanophotonics in the future.
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