Inhomogenous Dielectric Metamaterials with Space-Variant Polarizability

We experimentally demonstrate for the first time the focusing of optical beams within an inhomogeneous dielectric metamaterial with space-variant polarizability, implemented by etching subwavelength structures into a Silicon slab. Light focusing is obtained by creating an artificial slab material with graded refractive index profile. The local refractive index within the slab is modulated by controlling the duty cycle of the subwavelength structures. The demonstrated metamaterial based component can be integrated with various other building blocks towards the realization of devices and systems in free space optics on a chip configuration.

Figure 1

Schematic drawing showing the geometry of the slab lens. $\Lambda$ is the period of the grating, $f$ is the local duty cycle, $n_{e\mathrm{Si}}$, $n_{\mathrm{cl}1}$, $n_{\mathrm{cl}2}$, and $n_s$ are the effective refractive index of the Si slab, the upper (typically $n_{\mathrm{cl}1}=1$) and lower cladding, and the substrate, respectively. The thick arrow shows the light propagation direction (along the $z$-axis).

Figure 2

Device layout consisting of input ridge waveguide, nonpatterned slab, slab lens, and output ridge waveguide. An overlayed finite difference time domain simulation shows the beam propagation, which is found in good agreement with the approximate design of device layout using effective medium theory. Device layout is also shown. The simulation results clearly show the focusing of light towards the output ridge waveguide.

Figure 3

Scanning electron micrograph showing the fabricated device: (a) a top view of the entire structure. (b) a magnified slanted view showing part of the slab lens and the output waveguide.

Figure 4

Finite difference time domain simulation shows the beam propagation, within the device, where the deviation of the fabricated structure from the design is taken into account. Result shows that focusing occurs about 5 mm before the output waveguide.

Figure 5

Experimental results obtained with the Heterodyne Near field Scanning Optical Microscope (H-NSOM). (a) The amplitude and (b) the phase of the optical field in the region that includes the input waveguide, the nonpatterned slab ($S$), and large portion of the slab lens section ($L$). The dashed vertical lines mark the boundaries between the various sections. Light is propagating from left to right. (c) Cross sections showing phase profile at several planes along the device. The planes are marked in Fig. 5b.