Fourier methods are widely used in optical information processing for time domain waveform synthesis and detection. In such approaches an input pulse is spectrally decomposed and modulated by an appropriately designed spectral filter. In general, various ultrafast applications may need either generation or characterization of waveforms depending whether their frequency response is or is not known a priori. Ultrafast pulses prove useful in driving or probing such systems because their broad, deterministic complex spectral amplitude âseesâ a large continuous portion of the system transfer function. Traditionally, space domain spectral decomposition is used to perform optical Fourier processing, where pairs of gratings and lenses are used to decompose the spectral content of the pulsed, optical waveforms. Liquid crystal and acousto-optic (AO) modulators provide a means for introduction of somewhat arbitrary system transfer functions. More recently, compact waveguide-based approaches have used arrayed waveguide gratings (AWGs) to perform an analogous spectral decomposition to those achieved with traditional, free-space coupled gratings. Information processing arrangements using the space domain for transverse spectral decomposition benefit from the maturity of such techniques, with respect to basic understanding, component quality, and the excellent phase control that free-space manipulations provide. Component insensitivity to optical power permits the shaping and detecting of high peak power pulses used to drive nonlinear optical systems. Furthermore, nonlinear optical elements can be introduced directly into these processors to provide unique ultrafast waveform synthesis capabilities with response times in the range of femtoseconds. Drawbacks to free-space approaches include scaling in volume to achieve large time bandwidth products (TBWPs) and limiting the temporal extent of waveforms coupled back into a single-mode fiber (SMF). The origin of this last restraint is the timeâspace interrelation inherent in traditional pulse shaping devices. AWG approaches rely on complex waveguide elements to circumvent large processor volumes and timeâspace coupling issues, but they too are practically limited by fabrication requirements. The number of resolvable spots in the output waveform for both Fourier synthesis and direct space-to-time AWG approaches is equal to the number of waveguide channels. An alternative approach to Fourier processing relying on a single transverse spatial mode can better integrate with fiber systems and photonic lightwave circuits and will scale in length only for the achievement of large TBWPs. Fiber-based and fiber-integrated processors can manipulate optical waveforms in the time domain exploiting chromatic dispersion for longitudinal spectral decomposition and applying to it Fourier synthesis techniques. Drawing on the identical mathematical treatments of diffraction in space and dispersion in time, an approximate Fourier transform (FT) of an incident optical signal is achieved via chromatic dispersion after reaching the so-called âfar-field approximation.â With such an amount of dispersion, the temporal waveform closely resembles the spectrum. Such a waveform is called a longitudinal spectral decomposition wave (SDW). A time-variant element (e.g., modulator) filters this SDW. And it is possible to recompose the pulse waveform through propagation in a conjugate dispersion source matched (i.e., of opposite sign but equal magnitude) to the first dispersive element. The number of resolvable spots that such a processor offers relies on a suitable modulation scheme and the experimental ability to disperse a sub-picosecond pulse using second-order dispersion.
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