Transformation Optics in Silicon Photonics
The Luneburg lens is a gradient index lens that focuses light from all incident directions, thus being free from aberrations that affect conventional lenses. Like the Maxwell fish-eye lens or the Eaton lens, the Luneburg lens can be described via non-Euclidean transformation, where light in a medium is experiencing a curved spatial geometry. The Luneburg lens focuses light on the edge of the lens in the same direction of the incident light. The position of the focus thus indicates the direction of light corresponding to a Fourier transform in terms of light waves.
Luneburg lenses are commonly used in microwave technology and have recently been made for surface plasmons. Here we demonstrate an integrated Luneburg lens on a silicon chip that works for near-infrared light, using grey-scale lithography on a Silicon on Insulator platform. Our all-dielectric approach offers the advantage over existing technology of being naturally compatible with integrated optical circuitry and of being free of the typical plasmonic losses.
In our realization a guided planar mode optical mode (red profiles in the left panel of the figure) has a tailored effective index that replicates the luneburg profile. The effective index is controlled by the thickness of the top silicon layer, which is controlled with an accuracy of few nm. The right panel shows the experimental and theoretical profile of the lens.The resolution of the Luneburg lens is limited by the wavelength, but our manufacturing method is also sufficiently versatile for making future perfect imaging devices on silicon platforms with low losses.
We have performed a complete set of experiments to confirm that the luneburg lens effectively operates the Fourier transform of the incident light. The minimum measured size of the focused spot is limited by the experimental condition.