A Luneburg lens with a gradient index distribution is an aberration-free and coma-free spherical lens. It has wide applications ranging from invisibility cloaks, illusion optics, and superlensing. However, it is challenging to realize an on-chip Luneburg lens with superior performance. In this paper, an on-chip Luneburg lens is implemented through the integration of gradient metamaterial structures and silicon waveguides. The filling ratio mapping of silicon nanorods is used to achieve the gradient index distribution. As an example of the application, a general and scalable approach for a mode size converter is demonstrated to match two waveguide modes with arbitrary widths. Benefiting from the aberration-free property, a 740 nm bandwidth is achieved in simulation. Limited by our measurement setup, the measured device bandwidth is 220 nm, covering the wavelengths of 1.26–1.36 and 1.507–1.627 μm. To the best of our knowledge, this silicon mode size converter exhibits the largest bandwidth.

中文翻译：

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基于片上基于超材料的Luneburg透镜的超宽带模式尺寸转换器

具有梯度指数分布的Luneburg透镜是无像差和无彗差的球面透镜。它具有广泛的应用，包括隐形斗篷，幻象光学和超透镜。但是，要实现性能卓越的片上Luneburg镜头是一项挑战。在本文中，通过集成梯度超材料结构和硅波导来实现片上Luneburg透镜。硅纳米棒的填充率映射用于实现梯度指数分布。作为该应用的示例，演示了一种用于模式大小转换器的通用且可扩展的方法，以匹配具有任意宽度的两个波导模式。受益于无像差特性，在仿真中实现了740 nm带宽。受我们的测量设置的限制，所测量的设备带宽为220 nm，覆盖1.26–1.36和1.507–1.627μm的波长。据我们所知，这种硅模式尺寸转换器具有最大的带宽。