Abstract:In this paper, the mathematical description of the temporal selfimaging 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. 161-237 (1995). 8. A. M. Weiner and A. M. Kan'an, "Femtosecond pulse shaping for synthesis, processing, and time-to-space conversion of ultrafast optical waveforms," IEEE J. Sel. Top. Quantum Electron. 4(2), 317-331 (1998). 9. B. H. Kolner, "Space-time duality and the theory of temporal imaging," IEEE J. Quantum Electron. 30(8), 1951Electron. 30(8), -1963Electron. 30(8), (1994. (McGraw-Hill, 1968). 11. S. A. Akhmanov, A. P. Sukhoruk, and A. S. Chirkin, "Nonstationary phenomena and space-time analogy in nonlinear optics," Sov. Phys. JETP-USSR28, 748 (1969). 12. E. B. Treacy, "Optical pulse compression with diffraction gratings," IEEE J. Quantum Electron. 5(9), 454^158 (1969). 13. B. H. Kolner and M. Nazarathy, "Temporal imaging with a time lens," Opt. Lett. 14(12), 630-632 (1989).
References and links
A. Papoulis, Systems and Transforms With Applications in Optics