The general theory of first-order spatio-temporal distortions of Gaussian pulses and beams

Abstract

We present a rigorous, but mathematically relatively simple and elegant, theory of first-order spatio-temporal distortions, that is, couplings between spatial (or spatial-frequency) and temporal (or frequency) coordinates, of Gaussian pulses and beams. These distortions include pulse-front tilt, spatial dispersion, angular dispersion, and a less well-known distortion that has been called "time vs. angle." We write pulses in four possible domains, xt, xomega, komega, and kt; and we identify the first-order couplings (distortions) in each domain. In addition to the above four "amplitude" couplings, we identify four new spatio-temporal "phase" couplings: "wave-front rotation," "wave-front-tilt dispersion," "angular temporal chirp," and "angular frequency chirp." While there are eight such couplings in all, only two independent couplings exist and are fundamental in each domain, and we derive simple expressions for each distortion in terms of the others. In addition, because the dimensions and magnitudes of these distortions are unintuitive, we provide normalized, dimensionless definitions for them, which range from -1 to 1. Finally, we discuss the definitions of such quantities as pulse length, bandwidth, angular divergence, and spot size in the presence of spatio-temporal distortions. We show that two separate definitions are required in each case, specifically, "local" and "global" quantities, which can differ significantly in the presence of spatio-temporal distortions.

Generation of Attosecond Light Pulses from Gas and Solid State Media

“…Ultrafast wavefront rotation (WFR) is a direct consequence of pulse-front tilt (PFT), a linear optic effect resulting at the focus of ultrashort laser pulses following angular dispersion, such as that introduced by slightly misaligning one of the gratings in the compressor or by introducing a prism into the beam [142]. Heyl et al [99] proposed an elegant alternative for achieving WFR.…”

Compact 200 kHz HHG source driven by a few-cycle OPCPA

“…The most prominent spatio-temporal distortion, originating from NOPA stages detuned from the magic angle configuration, should be angular dispersion, which also causes pulse front tilt and potentially spatial dispersion in the far-field. For a detailed discussion of spatio-temporal couplings and their different representations, we refer to an article by Akturk et al [24]. The analysis of our measurements concentrates on distinguishing the following spatio-temporal coupling contributions:…”

Diagnostics and controls for spatiotemporal couplings for laser-plasma accelerator drivers

“…Here, we consider a Gaussian beam, for which all the first-order STCs can be described, if beam size w 0 , spectral amplitude and phase [I(ω) and φ(ω))], angular dispersion, and spatial chirp are known [16]. For a common doublepass optical compressor, non-parallel gratings introduce angular dispersion, and the misaligned retro-reflection mirror introduces spatial chirp [17].…”