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In integrated photonic circuits, silicon-on-insulator waveguides withdifferent geometries have been employed to realize a variety of components.Therefore, efficient coupling of two different waveguides is crucial. In thispaper, focusing property of the Luneburg lens is exploited to design waveguidetapers. The Luneburg lens, truncated in a shape of a parabolic taper withreduced 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 inthe entire O, E, S, C, L, and U bands of optical communications. The proposedcompact taper with the length of 11 $\mu$m is implemented by varying thethickness of the guiding layer and compared with three conventional tapers withthe same length. However, designing a coupler to connect waveguides withdifferent thicknesses and widths is more challenging. By applyingquasi-conformal transformation optics, we flatten the Luneburg lens andconsequently increase the refractive index on the flattened side. As a result,we are able to couple two waveguides with different thicknesses and widths. Thenumerical simulations are used to evaluate the theoretically designed tapers.To our knowledge, this is the first study presenting ultrashort tapers based ontruncated Luneburg lens.

Ultrashort waveguide tapers based on Luneburg lens