Temporal zone plate.

This paper extends the investigation of zone plates to the temporal case. By exploiting the space-time duality between the paraxial diffraction of beams in space and the linear dispersion of optical pulses, we present the time-domain analog of a multiple imaging system. The temporal system is created by using a digital chirp signal generator together with two dispersive delay lines. The key motivation is the potential application of the temporal zone plate to multiple compressions of pulses in dispersive lines.

Radio-frequency spectrum analysis of a jittery train after a second-order dispersive Talbot line.

The power spectral density of the intensity of coherent Gaussian pulse trains suffering timing jitter after a dispersive line with arbitrary first- (beta(2)) and second-order (beta(3)) dispersion is computed in the small-signal approximation. Due to timing jitter noise, the initial radio-frequency spectrum shows noise bands whose bandwidth and position depend, respectively, on the jitter's standard deviation and on the jitter's pulse-to-pulse correlation. After setting the accumulated first-order dispersion to Talbot conditions, it is shown that the influence on the noise spectrum is a multiplicative factor with a multiple-bandpass structure. This factor depends on both the dispersive characteristics of the line and the pulse parameters, but not on the timing jitter's correlation properties, and represents the filtering mechanism responsible for Talbot repetition-rate multiplication. It is shown that the integer or fractional temporal Talbot effect does not worsen the timing properties of the initial train. In addition, and depending on the type of jitter correlation, the pulse width, and the total dispersion, it is shown that the temporal Talbot effect may lead to significant jitter reduction. The theory is exemplified by use of simulations. The applicability of the model to practical situations is also analyzed.