Abstract
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.
Highlights
Nonlinear parametric processes involving ultrashort pulses are typically carried out in time domain, which mathematically corresponds to a convolution of their frequency spectra
In optics and electrical engineering, many devices are described as linear time-invariant systems which are characterized by their impulse response: an output signal is obtained from the temporal convolution of an input signal with the impulse response of the system[1]
The output signal, i.e. the oscilloscope trace on a nanosecond level, is insensitive to the actual laser pulse temporal profile. This situation of a dynamic signal convolved with a quasi-static response is found in the case of programmable pulse shapers such as spatial light modulators or acousto-optic m odulators[2,3]. While they can provide an adjustable impulse response to shape the temporal profile of ultrashort pulses, and even though its shaping mask can be refreshed up to hundred thousand times per s econd[4], such filters are static compared to the timescale of the laser field
Summary
Nonlinear parametric processes involving ultrashort pulses are typically carried out in time domain, which mathematically corresponds to a convolution of their frequency spectra. The output signal, i.e. the oscilloscope trace on a nanosecond level, is insensitive to the actual laser pulse temporal profile This situation of a dynamic signal convolved with a quasi-static response is found in the case of programmable pulse shapers such as spatial light modulators or acousto-optic m odulators[2,3]. We demonstrate experimentally that phase and amplitude information from the trailing pulse of the input beam are transferred to the preceding central pulse of the output sequence This surprising linear information transfer between two femtosecond laser pulses separated in time is possible upon nonlinear processing in the frequency domain. Temporal convolution between two dynamic functions is the prerequisite for this unique result
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