Ultrafast Optical Temporal Processing Using Phase-Space Signal Representations

CUADRADO LABORDE, CHRISTIAN; COSTANZO CASO, PABLO; DUCHOWICZ, RICARDO; SICRE, ENRIQUE

Optics Research Trends

Nova Science Publishers

Año: 2007; p. 477 - 522

    We start by reviewing some relevant properties of image formation with spatial optical systems based on phase-space signal representations, like the Wigner distribution function (WDF) and the fractional Fourier transform (FRT). Some imaging quality properties such as defocus and aberrations tolerance and/or apodizing effects are described here using the relationships between the normalized point-spread function and a system phase-space representation. The space-time duality theory, based on the analogy existing between the properties of quadratic phase filters in the spatial domain and the time impulse responses of different dispersive media in guided light transmission, is used for extending to the temporal domain well-known properties of spatial optical configurations. The temporal optical definitions, and implementations of some phase-space representations (like the FRT and its related Radon-Wigner transform (RWT)), are performed in such a way that several features of dispersive pulse transmission can be analyzed in the dual phase-space time vs. frequency. The spatial properties exhibited by certain optical systems referred to light focusing can be properly translated to the temporal domain as pulse conformation of time-varying signals. The optical devices proposed are based on an adequate combination of dispersion transmission and time lens action applied to the input signal. These operations can be considered as a generalization of those used to produce temporal imaging or real-time Fourier transformation. The approach is illustrated by transferring to the time domain the properties of a spatial optical imaging system having good tolerance under defocusing. Thus, an analogue temporal device is obtained which produces output optical pulses remaining almost unchanged in dispersive propagation under a small variation of the associated dispersion parameter. Then, the temporal Talbot effect or selfimaging phenomenon is analyzed by using the RWT display of an input periodic pulse train where well-conformed pulse trains having different repetition rates and duty-cycles can be produced. We compare the selfimaging formation for the cases of frequency chirped and unchirped pulses. The effect of the finite extension of the pulse train on the selfimage quality is analyzed and a condition is found for relating the required minimum pulse number with the pulse chirp parameter. Finally, the selfimaging formation is applied to aperiodic input signals by using the more general Montgomery condition. An adequate temporal filtering scheme is proposed for achieving isolate optical pulses having selfimage properties under further dispersive transmission. Some numerical simulations are carried out in order to determine the effect of the several involved parameters on both, the pulse shape and the noise level.