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Continuous -time Fourier Transform01:11

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The Fourier series is instrumental in representing periodic functions, offering a powerful method to decompose such functions into a sum of sinusoids. This technique, however, necessitates modification when applied to nonperiodic functions. Consider a pulse-train waveform consisting of a series of rectangular pulses. When these pulses have a finite period, they can be accurately represented by a Fourier series. Yet, as the period approaches infinity, resulting in a single, isolated pulse, the...
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Transmission of Multiple Signals through an Optical Fiber Using Wavefront Shaping
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All-fiber joint-transform correlator for time-multiplexed signals.

Víctor Torres-Company1, Lawrence R Chen

  • 1Department of Electrical and Computer Engineering, McGill University, H3A 2A7 Montreal, Canada. victor.torrescompany@mail.mcgill.ca

Optics Letters
|November 3, 2009
PubMed
Summary

We developed a temporal joint-transform correlator to optically measure radio frequency spectra in real-time. This novel optical radio frequency analyzer enables all-optical pattern recognition for ultrashort pulses.

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Area of Science:

  • Optics and Photonics
  • Ultrafast Science
  • Nonlinear Optics

Background:

  • Spatial joint-transform correlators are established for pattern recognition.
  • Real-time spectral analysis is crucial for understanding complex optical signals.
  • Ultrafast pulse characterization demands advanced measurement techniques.

Purpose of the Study:

  • To introduce the temporal analog of a spatial joint-transform correlator.
  • To demonstrate real-time optical measurement of radio frequency (rf) spectra.
  • To explore applications in all-optical pattern recognition of ultrashort pulses.

Main Methods:

  • Utilized a sequence of time-multiplexed pulses to generate a spectral interferogram.
  • Employed cross-phase modulation of a continuous-wave (cw) probe in a highly nonlinear fiber.
  • Developed an optical radio frequency (rf) analyzer for spectral measurements.

Main Results:

  • Successfully measured the rf spectrum of a real-time spectral interferogram.
  • Demonstrated that the cw probe's optical spectrum encodes the electric-field cross-correlation information.
  • Validated the temporal joint-transform correlator's capability for spectral analysis.

Conclusions:

  • The presented system serves as the temporal counterpart to spatial joint-transform correlators.
  • The optical rf analyzer provides a method for real-time spectral analysis of complex optical signals.
  • This technology holds promise for advanced all-optical pattern recognition of ultrashort pulses.