Spatio-temporal characterization of ultrashort laser beams: a tutorial

Abstract

The temporal characterization of ultrafast laser pulses has become a cornerstone capability of ultrafast optics laboratories and is routine both for optimizing laser pulse duration and designing custom fields. Beyond pure temporal characterization, spatio-temporal characterization provides a more complete measurement of the spatially-varying temporal properties of a laser pulse. These so-called spatio-temporal couplings (STCs) are generally nonseparable chromatic aberrations that can be induced by very common optical elements—for example, diffraction gratings and thick lenses or prisms made from dispersive material. In this tutorial we introduce STCs and a detailed understanding of their behavior in order to have a background knowledge, but also to inform the design of characterization devices. We then overview a broad range of spatio-temporal characterization techniques with a view to mention most techniques, but also to provide greater details on a few chosen methods. The goal is to provide a reference and a comparison of various techniques for newcomers to the field. Lastly, we discuss nuances of analysis and visualization of spatio-temporal data, which is an often underappreciated and non-trivial part of ultrafast pulse characterization.

Spatiotemporal coupling investigations for Ti:sapphire-based multi-PW lasers

“…To optimize the performance of multi-PW-class laser systems and to achieve targeted laser intensity, the examined effects should be carefully taken into consideration for the better understanding, the accurate experimental characterization and the mitigation of these detrimental effects. Further research and development efforts are required to evaluate experimentally the impact of cumulated S-T coupling effects on the focused laser intensity, particularly in the direction of adequate metrology technology for their precise characterization and control [ 24 ] .…”

Reciprocating propagation of laser pulse intensity in free space

“…where, A() is the spectral amplitude,  2 is the group-velocity dispersion (GVD) denoting the temporal chirp, w in is the beam waist, and z(r 1 ,) is the frequency-dependent wave-front denoting the longitudinal chromatism. For example, when a transmission telescope is used for generating the longitudinal chromatism, z(r 1 ,) is a quadratic function with respect to the transverse coordinate z(r 1 ,) = a()r 1 2 + b, where a() is a frequency-dependent coefficient and b is a constant-coefficient [51][52][53][54]. After the Fourier-transform, the output temporal optical field is given by…”

A Survey of Spatio-Temporal Couplings throughout High-Power Ultrashort Lasers

“…Research work on STC metrology already started about 20 years ago. But it is only recently that tractable techniques providing full amplitude and phase information on the laser field in 3D have become available and in common use [7][8][9][10][11][12]. Complete spatio-temporal characterization of ultrashort beams is thus about to be a routine metrology procedure, especially with commercial instruments now available [13].…”

“…To characterize quantitatively the chromatic curvature, we projected the spectrally-resolved wavefront on Zernike polynomials in order to compute the beam curvature as a function of optical frequency (See Ref. [12] for more details on such a procedure). This data-plotted in The linear fit of these curvatures is shown as a red dashed line and its computed slope is 0.067 fs/mm 2 .…”