Super-narrow frequency conversion

The spectral width of a nonlinear converter is usually thought to be inversely proportional to the length of the nonlinear crystal. We present a method to overcome this limitation using the concept of super-oscillations, thus creating an arbitrarily narrow converter. A “super-narrow” frequency doubler was fabricated by appropriate modulation of its quadratic nonlinear coefficient, showing spectral and thermal response that are narrower by 39% and 69% compared to the side lobes and main lobe of the sinc function response of a standard frequency doubling crystal with the same length. This is accompanied by corresponding reduction of the efficiency to 14% and 0.79% with respect to those of the first side lobe and the main lobe. We propose more advanced modulation patterns, and discuss implications such as nonlinear filtering with higher resolution than the standard crystal.