Flat lenses constructed by graded negative index-based photonic crystals with tuned configurations

Flat lenses are designed by means of graded negative refractive index-based photonic crystals （PCs） constructed using air-holes tuned with different shapes. By gradually modifying the filling factor along the transverse direction, we obtain the graded negative index-based lenses for the purpose of focusing an incident plane wave. The finite-difference and timedomain （FDTD） algorithm is adopted for numerical calculation. Our calculation results indicate that these lenses can finely focus incident plane waves. Moreover, for the same size of air-holes, the focusing properties of the lens with rectangular air-holes are better than those with the other shaped air-holes. The graded negative index PCs lenses could possibly enable new applications in optoelectronic systems.     

Tunability of graded negative index-based photonic crystal lenses for fine focusing

Graded negative refractive index-based photonic crystal (PC) lenses are designed by gradually modifying the sizes of air holes along the transverse direction for focusing the incident plane wave. To study the tunability of the graded negative index-based PC, we introduce filling factor A, gradually tune the filling factor, and use the finite-difference and time-domain (FDTD) algorithm for numerical calculation. Our calculation results indicate that the focal length and the spot size increase with A increasing. For the same A value, the focal length of a PC with elliptical air holes is the longest, and those of PC with square and rectangular air holes are the shortest. Moreover, when the focal length is greater than 1 μm, the focal parameters of the PC are highly insensitive to the variation of A. When the focal length is less than 1 μm, the PC lenses have higher transmittances and all well focus with a beam spot size breaking the diffraction limit. This feature possibly makes the graded negative index-based PC lenses have some new applications in optoelectronic systems.