Temporal self-imaging effect for periodically modulated trains of pulses

Abstract

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

Programmable Retiming of an Optical Clock Signal Using the Temporal Talbot Effect

“…The proposed scheme is based on the use of an optical signal processor that enables the realization of the Discrete Fourier transform (DFT) of a repetitive sequence [11,12]. In such processor a periodic function, ( ), modulates the phase and amplitude of an input train of pulses.…”

“…If this signal is slow varying, the resulting modulation can be considered constant within the pulse duration and ( ) is transformed into a periodic sequence of complex coefficients ( ) = . Then, using a specific case of the fractional temporal Talbot effect [13] as further specified below, it was demonstrated in [11] that the relationship between the pulses' amplitudes at the output, , and the applied complex coefficients, , is determined by the DFT, allowing the Fourier synthesis of the applied sequence as a function of the desired output. Thus, if the electric field at the output of the modulating stage is given by:…”

“…where 0 is the temporal separation between two adjacent pulses in the input train of pulses, ( ) corresponds to the shape of the input optical pulses with a pulse-width determined by ∆ , corresponds to the period of the sequence , and the modulation signal period is • 0 . In order for the optical processor to operate properly the system must fulfil the two conditions presented in [11,12] overlapping of pulses at the output of the optical processor, the pulse width has to verify ∆ < 0 / . Second, equation 2was obtained in [11] when the dispersive device produces a fractional Talbot case and the coprime integers s and m defined in [13] have the values = 1 and = 2 .…”

“…In order for the optical processor to operate properly the system must fulfil the two conditions presented in [11,12] overlapping of pulses at the output of the optical processor, the pulse width has to verify ∆ < 0 / . Second, equation 2was obtained in [11] when the dispersive device produces a fractional Talbot case and the coprime integers s and m defined in [13] have the values = 1 and = 2 . This corresponds to a dispersion value given by φ̈= 11,12].…”

“…Second, equation 2was obtained in [11] when the dispersive device produces a fractional Talbot case and the coprime integers s and m defined in [13] have the values = 1 and = 2 . This corresponds to a dispersion value given by φ̈= 11,12]. Besides, it is worth emphasizing that, from equation 2, a temporal scaling factor is present at the output train of pulses.…”