Temporal self-imaging effect for periodically modulated trains of pulses.

In this paper, the mathematical description of the temporal self-imaging effect is studied, focusing on the situation in which the train of pulses to be dispersed has been previously periodically modulated in phase and amplitude. It is demonstrated that, for each input pulse and for some specific values of the chromatic dispersion, a subtrain of optical pulses is generated whose envelope is determined by the Discrete Fourier Transform of the modulating coefficients. The mathematical results are confirmed by simulations of various examples and some limits on the realization of the theory are commented.

[1]  B. Kolner,et al.  Principles of parametric temporal imaging. I. System configurations , 2000, IEEE Journal of Quantum Electronics.

[2]  M. V. Berry,et al.  Integer, fractional and fractal Talbot effects , 1996 .

[3]  Reza Salem,et al.  Ultrahigh-Speed Optical Processing Using Space-Time Duality , 2011 .

[4]  Hammond,et al.  Near-field imaging of atom diffraction gratings: The atomic Talbot effect. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[5]  B. Kolner.  Space-time duality and the theory of temporal imaging , 1994 .

[6]  José Azaña,et al.  General temporal self-imaging phenomena , 2003 .

[7]  M A Muriel,et al.  Temporal Talbot effect in fiber gratings and its applications. , 1999, Applied optics.

[8]  Andrew M. Weiner,et al.  Femtosecond optical pulse shaping and processing , 1995 .

[9]  E. Treacy.  Optical pulse compression with diffraction gratings , 1969 .

[10]  Lord Rayleigh F.R.S..  XXV. On copying diffraction-gratings, and on some phenomena connected therewith , 1881 .

[11]  J. Azaña.  Design specifications of time-domain spectral shaping optical system based on dispersion and temporal modulation , 2003 .

[12]  T. Jannson,et al.  Temporal self-imaging effect in single-mode fibers , 1981 .

[13]  José Azaña,et al.  Optical frequency domain reflectometry based on real-time Fourier transformation. , 2007, Optics express.

[14]  Michal Lipson,et al.  High-speed optical sampling using a silicon-chip temporal magnifier. , 2009, Optics express.

[15]  Jianming Wen,et al.  The Talbot effect: recent advances in classical optics, nonlinear optics, and quantum optics , 2013 .

[16]  J. Azaña,et al.  Temporal self-imaging effects: theory and application for multiplying pulse repetition rates , 2001 .

[17]  Hao Hu,et al.  Silicon Photonics for Signal Processing of Tbit/s Serial Data Signals , 2012, IEEE Journal of Selected Topics in Quantum Electronics.

[18]  Andrew M. Weiner,et al.  Femtosecond pulse shaping for synthesis, processing, and time-to-space conversion of ultrafast optical waveforms , 1998 .

[19]  J. Azaña,et al.  Real-time optical spectrum analysis based on the time-space duality in chirped fiber gratings , 2000, IEEE Journal of Quantum Electronics.

[20]  Andrew M Weiner,et al.  Tunable pulse repetition-rate multiplication using phase-only line-by-line pulse shaping. , 2007, Optics letters.

[21]  B. Kolner,et al.  Principles of parametric temporal imaging. II. System performance , 2000, IEEE Journal of Quantum Electronics.

[22]  Francesco Fresi,et al.  Fiber-Based Programmable Picosecond Optical Pulse Shaper , 2010, Journal of Lightwave Technology.

[23]  K. Hinton,et al.  Energy Consumption and Energy Density in Optical and Electronic Signal Processing , 2011, IEEE Photonics Journal.

[24]  Reza Salem,et al.  Application of space–time duality to ultrahigh-speed optical signal processing , 2013 .

[25]  Tomasz P. Jannson,et al.  Information capacity of Bragg holograms in planar optics , 1981 .

[26]  Jianping Yao,et al.  Chirped Microwave Pulse Generation Based on Optical Spectral Shaping and Wavelength-to-Time Mapping Using a Sagnac Loop Mirror Incorporating a Chirped Fiber Bragg Grating , 2009, Journal of Lightwave Technology.

[27]  A. V. Mamaev,et al.  SELECTION OF UNSTABLE PATTERNS AND CONTROL OF OPTICAL TURBULENCE BY FOURIER PLANE FILTERING , 1998 .

[28]  J. Azana,et al.  Spectro-temporal imaging of optical pulses with a single time lens , 2004, IEEE Photonics Technology Letters.

[29]  B Javidi,et al.  Optical image encryption based on input plane and Fourier plane random encoding. , 1995, Optics letters.

[30]  M. Akbulut,et al.  Advanced Ultrafast Technologies Based on Optical Frequency Combs , 2012, IEEE Journal of Selected Topics in Quantum Electronics.

[31]  B H Kolner,et al.  Temporal imaging with a time lens. , 1990, Optics letters.

[32]  L.R. Chen,et al.  Tunable passive all-optical pulse repetition rate multiplier using fiber Bragg gratings , 2005, Journal of Lightwave Technology.

[33]  High-rate pulse-train generation by phase-only filtering of an electrooptic frequency comb: Analysis and optimization , 2009 .

[34]  Jianping Yao,et al.  All-Fiber Chirped Microwave Pulses Generation Based on Spectral Shaping and Wavelength-to-Time Conversion , 2007, IEEE Transactions on Microwave Theory and Techniques.

[35]  Jian Wang,et al.  Optically Efficient Nonlinear Signal Processing , 2011, IEEE Journal of Selected Topics in Quantum Electronics.

[36]  W. Talbot.  Facts relating to optical science , 1836 .

[37]  J. van Howe,et al.  Ultrafast optical signal processing based upon space-time dualities , 2006, Journal of Lightwave Technology.

[38]  M A Muriel,et al.  Real-time Fourier transformer based on fiber gratings. , 1999, Optics letters.

[39]  K. Goda,et al.  Dispersive Fourier transformation for fast continuous single-shot measurements , 2013, Nature Photonics.

[40]  Michal Lipson,et al.  Optical time lens based on four-wave mixing on a silicon chip. , 2008, Optics letters.

[41]  S. J. B. Yoo,et al.  Terahertz Information and Signal Processing by RF-Photonics , 2012, IEEE Transactions on Terahertz Science and Technology.