  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. Up today, there lacks a general
method to design compact nonlinear optical devices over a broadband continuous
frequency range. In this work, we propose a general strategy based on
transformation optics (TO) to design curved accelerating waveguides (CAWs) with
spatially gradient curvatures able to achieve broadband nonlinear frequency
conversion on chip. Through rigorous analytical calculation, we show that
increasing the acceleration (i.e. gradient in the waveguide curvature) broadens
the output signal spectrum in the nonlinear process. In the experiment, we take
the sum-frequency generation for infrared signal upconversion (SFG-ISU) as the
example and fabricated a variety of CAWs using thin-film lithium niobate on
insulator (LNOI). Efficient SFG 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 LNOI, our approach is also
compatible with other nonlinear materials, such as silicon, silicon nitride and
chalcogenide glasses etc.
