Proceedings Article | 28 February 2006
KEYWORDS: Pulmonary function tests, Ultrafast phenomena, Fourier transforms, Analytical research, Prisms, Matrices, Physics, Wavefronts, Spatial frequencies, Biomedical optics
Ultrashort laser pulses are usually expressed in terms of the temporal and spectral dependences of their electric field. This approach disregards any couplings between the spatial coordinates and time and/or frequency. This assumption, however, often fails, as the generation and manipulation of ultrashort pulses require the introduction of spatio-temporal couplings. Furthermore, disregarding these couplings in ultrashort pulses also greatly limits the potential applications that could only be possible by exploiting the spatio-temporal behaviors. For these reasons, spatio-temporal couplings are receiving increased attention from researchers in recent years. Most of the work presented to date, however, focuses on a few particular couplings, lacking a general and rigorous analysis. We present a rigorous and mathematically elegant theory of first-order spatio-temporal distortions of Gaussian pulses and beams. We write pulses in four possible domains, xt, xω, kω, and kt, including the couplings. We identify couplings in intensity profiles as: pulse-front tilt, spatial dispersion, angular dispersion, and time vs. angle. We identify four new couplings that occur in phase: "wave-front rotation," "wave-front-tilt dispersion," "angular temporal chirp," and "angular frequency chirp." In addition, we provide normalized, dimensionless definitions for them, which range from -1 to 1. Finally, we show that for such parameters as pulse length, bandwidth, beam spot size and divergence angle, two separate definitions are required as "local" and "global" quantities, in presence of the couplings. Our approach completely determines the explicit relations between various spatio-temporal couplings in Gaussian pulses and beams. It can be generalized to arbitrary profiles by using computational analysis.
