Ultrashort waveguide tapers based on Luneburg lens

Abstract: In integrated photonic circuits, silicon-on-insulator waveguides with different geometries have been employed to realize a variety of components. Therefore, efficient coupling of two different waveguides is crucial. In this paper, focusing property of the Luneburg lens is exploited to design waveguide tapers. The Luneburg lens, truncated in a shape of a parabolic taper with reduced footprint, is utilized to connect a 10 $\mu$m-wide waveguide to a 0.5 $\mu$m one with the same thickness with an average coupling loss of 0.35 dB in the entire O, E, S, C, L, and U bands of optical communications. The proposed compact taper with the length of 11 $\mu$m is implemented by varying the thickness of the guiding layer and compared with three conventional tapers with the same length. However, designing a coupler to connect waveguides with different thicknesses and widths is more challenging. By applying quasi-conformal transformation optics, we flatten the Luneburg lens and consequently increase the refractive index on the flattened side. As a result, we are able to couple two waveguides with different thicknesses and widths. The numerical simulations are used to evaluate the theoretically designed tapers. To our knowledge, this is the first study presenting ultrashort tapers based on truncated Luneburg lens.