Retardation and reduction of pulse distortion by group-velocity dispersion through pulse shaping

Abstract

We show that a reduction in the pulse distortion caused by chromatic dispersion can be achieved through pulse shaping. We argue that a simple binary phase mask in the Fourier plane of the laser spectrum can improve the transmission of short pulses in a dispersive channel through reduced broadening. The argument was tested experimentally, and a good agreement was found with the theory.Optically transmitted pulses in a single-mode channel can be severely distorted and broadened as the result of chromatic dispersion. Several methods have been used to overcome the distortion of the pulse envelope caused by group-velocity dispersion (GVD): a grating pair, 1 a Fabry -Perot interferometer, 2 a phase conjugator, 3 a laser modulated with a periodic injection current sweep, 4,5 and time lenses for Gaussian-shaped pulses. 6In soliton propagation self-phase modulation compensates the GVD of a hyperbolic secant pulse shape. 7With z denoted as the position along the dispersive channel, y g as the group velocity, and T t 2 z͞y g as the delayed time, the inf luence of GVD on the complex temporal pulse electric field u͑T , z͒ envelope is given bywhere U ͑v, 0͒ is the Fourier transform of u͑T , 0͒, v is the angular frequency (relative to the laser's center frequency v 0 ), Dv is the spectral width corresponding to the pulse, and b 2 ≠ 2 b͞≠v 2 j v0 is the GVD per unit length.Recently 9,10 the possibility of pulses that do not disperse by virtue of their unique shaping was introduced. Based on the time-space analogy Rosen et al.as the initial pulse envelope to reduce the effect of GVD. a, b, f , and p . 2 are real positive parameters of the pulse. This pulse ͑u u C , Dv `͒ propagates along a dispersive channel at a distance of Dz Ӎ 2 p 2p b 2 f 2 p͓4͑1 1 p͔͒ ͑22p͒/p ͞b 2 while maintaining a nearconstant peak value of ju C ͑0, z͒j.The spectrum of u C iswhere T b b 2 f ͞b, T a b 2 f ͞a, and the power p 4 has been chosen as an example.In what follows we describe an experimental investigation of the possibility of creating dispersion-resistant pulses through pulse shaping and show that it can be accomplished by use of a simple binary phase mask in the spectral plane. We find that using a binary approximation of the initial pulse spectrum [Eq. (3)], U B ͑v, 0͒ U C ͑v, 0͒͞jU C ͑v, 0͒j, still leads to a considerable reduction in pulse distortion. This approximation enables us to use a binary (0 or p) phase mask instead of a complicated amplitude and phase filter.The pulse field U B and its capability of maintaining its form without distortion when traveling through a dispersive channel depend on the ratio T b ͞T a . We find numerically that T b ͞T a p 8͞5 is suff icient in that the intensity I B ͑T 0, z͒ ju B ͑0, z͒j 2 of the center of the symmetric pulse and its shape remains at a nearly constant height over the interval Dz Ӎ 8T 2 b ͞b 2 near z 0. One may increase this interval by increasing the ratio T b ͞T a , yet increasing the interval spoils the constancy of I B ͑0, z͒ in the region of interest. At z 0 the pulse has a main lobe wid...

Space-time wave packets

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