Integrated nonlinear optical devices play an important role in modern optical communications; however, conventional on-chip optical devices with homogeneous or periodic translation dimensions generally have limited bandwidth when applied to nonlinear optical applications. So far there lacks a general method to design compact nonlinear optical devices capable of operating over a broadband continuous frequency range. In this work we propose a general strategy based on transformation optics to design curved accelerating waveguides with spatially gradient curvatures, which can achieve broadband nonlinear frequency conversion on chip. Through rigorous analytical calculation, we show that increasing the acceleration (that is, the gradient in the waveguide curvature) broadens the output signal spectrum in the nonlinear process. In this experiment we use sum-frequency generation for infrared signal upconversion as an example and fabricated a variety of curved accelerating waveguides using thin-film lithium niobate on insulators. Efficient sum-frequency generation is observed over a broadband continuous spectrum. Our conformal mapping approach offers a platform for various nonlinear optical processes and works in any frequency range, including visible, infrared and terahertz bands. Apart from lithium niobate on insulators, our approach is also compatible with other nonlinear materials such as silicon, silicon nitride and chalcogenide glasses and so on.

集成非线性光学器件在现代光通信中发挥着重要作用；然而，具有均匀或周期性平移尺寸的传统片上光学器件在应用于非线性光学应用时通常具有有限的带宽。到目前为止，还缺乏一种通用的方法来设计能够在宽带连续频率范围内工作的紧凑型非线性光学器件。在这项工作中，我们提出了一种基于变换光学的通用策略来设计具有空间梯度曲率的弯曲加速波导，它可以在芯片上实现宽带非线性频率转换。通过严格的分析计算，我们表明增加加速度（即波导曲率的梯度）会拓宽非线性过程中的输出信号频谱。在本实验中，我们以用于红外信号上转换的和频生成为例，并使用绝缘体上的薄膜铌酸锂制造了各种弯曲加速波导。在宽带连续频谱上观察到有效的和频生成。我们的共形映射方法为各种非线性光学过程提供了一个平台，并可在任何频率范围内工作，包括可见光、红外和太赫兹频段。除了绝缘体上的铌酸锂之外，我们的方法还与其他非线性材料兼容，例如硅、氮化硅和硫系玻璃等。