| Summary: | 碩士 === 國立清華大學 === 光電工程研究所 === 106 === We present an analytical description of the modes property for a dipole emitter when put above a gold nanorods hyperbolic metamaterials slab. In the long wavelength region, we simplify the hyperbolic metamaterials as an effective anisotropic medium and show that the optimized purcell factor originates from the imaginary part of the TM mode reflection coefficients, which is not only determined by bulk hyperbolic dispersion but also the selective slab thickness due to the Fabry-Perot resonance. We characterize the plane wave propagation inside the HMM slab as ‘critical coupling mode’ and ‘resonating mode’ and explain the dipole field enhancement in a view of angular expansion. Factors of HMM slab thickness, the metal fill ratio, metal loss and quenching effect are taken into discussion. Using the rigorous coupled wave analysis with the optimized geometry, we deliberately design a silicon bullseye grating and demonstrate more than 12 folds farfield radiation enhancement. This numerical method is not only suitable for nanorods HMM material but also for multilayer HMM material and other anisotropic medium, serving as an efficient tool for the design of high speed incoherent optical source devices.
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