Information transfer via temporal convolution in nonlinear optics

Nonlinear parametric processes involving ultrashort pulses are typically carried out in time domain, which mathematically corresponds to a convolution of their frequency spectra. In contrast, this spectral convolution changes into a multiplication operation when performing the nonlinear interaction in frequency domain. Here, we extend the scope of frequency-domain nonlinear optics by demonstrating its ability to perform a temporal convolution. Through this approach, nonlinear optical operations that are inaccessible in time domain can be realised: specific optical information can be coherently advanced by picoseconds within a pulse sequence—a newly generated second harmonic pulse carries the amplitude and phase information of two input pulses. This central pulse is isolated when using an input field consisting of two cross-polarized input pulses in combination with type-II second harmonic generation. The effects of nonlinear temporal convolution can be viewed from the aspect of signal processing and pulse shaping, where the nonlinear interaction in the parametric crystal plays the role of a dynamic linear optical filter—in contrast to conventional static filters—with a shaping mask instantaneously adapting to the laser field.