In this paper, we present one planar graded photonic quasicrystals based on phyllotaxy structure (PSPQ) to mimic the Luneburg lens. The PSPQ is composed by discrete cylinders, which radius are determined by the index profile of Luneburg lens and Maxwell-Garnett effective medium theory, to mimic the graded index (GRIN) materials. Numerical simulations are performed to investigate the focusing features of the PSPQs by means of finite difference time domain (FDTD) methods. Numerical results show that the PSPQs-based Luneburg lens can focus the light more tightly and efficiently in comparison with conventional graded photonic crystals. Meanwhile, we also explored the focusing properties of PSPQs with different generating angle, which determined the spiral type of phyllotaxy structures, to optimize the focusing behavior of the proposed devices.
A new kind of bowtie related structures, Sierpinski complementary bowtie aperture (SCBA), is proposed for enhancing
and confining optical magnetic field. The magnetic field enhancement factor can be improved with the presence of the
fractal. Numerical simulation shows that higher iteration of the SCBA is responsible for the variation of the resonant
wavelengths. The magnetic field distributions illustrated 10nm above the output plane prove the magnetic intensity is
confined in the sub-wavelength scale. Further investigation demonstrates current can be enhanced in the center of the
apertures while electric fields are found to be easier to concentrate at the tiny fractal structures. Magnetic intensity
distributions at several resonant points in the spectrum of the third-iteration SCBA are also plotted and the longer
wavelength region in near infrared is found to be unsuited for confining magnetic field in SCBA due to weak interaction
with the fractals.