Optical processing waveform compression Why optical processing Waveform

Optical processing – waveform compression Why optical processing? Waveform compression Thinking about temporal processes using spatial analogues Foster 2009 Bob Peterson Waves and Optics Fall 2010 Figure: Wavelength compression illustrated using imaging analogy

Basis for spatial and temporal equivalence The wave equations governing paraxial diffraction of light and narrow-beam pulse propagation in dispersive media are formally equivalent. Spatial instruments and concepts such as a lens, telescope, focal length, etc. have temporal analogues. A 'time lens' is thus a nonlinear device which causes an appropriate phase modulation. How to make this in practice? Nonlinear terms in the power series expansion of P χ(2) devices – sum/difference frequency generation χ(3) devices – four-wave mixing techniques

Time telescope Creation of higher-frequency optical signal (270 GHz) from frequency limited electronics (10 Ghz). Allows access to the huge bandwidth available in optical systems. Foster 2009

Analog compression example Foster 2009 Resolution limit of electro-optical modulator seen in red; can reproduce waveforms at much smaller temporal resolution.

Applications and limitations Direct application of time-domain telescope in photonics and fiber-optic communication. Like spatial imaging systems, analogous resolution limits apply to these devices Wider developments in 'temporal imaging' will allow for other devices inspired by more complex optical systems.