Implementation of amplitude–phase analysis of complex interferograms for measurement of spontaneous magnetic fields in laser generated plasma

Abstract

Generation of spontaneous magnetic fields (SMFs) is one of the most interesting phenomena accompanying an intense laser–matter interaction. One method of credible SMFs measurements is based on the magneto-optical Faraday effect, which requires simultaneous measurements of an angle of polarization plane rotation of a probe wave and plasma electron density. In classical polaro-interferometry, these values are provided independently by polarimetric and interferometric images. Complex interferometry is an innovative approach in SMF measurement, obtaining information on SMF directly from a phase–amplitude analysis of an image called a complex interferogram. Although the theoretical basis of complex interferometry has been well known for many years, this approach has not been effectively employed in laser plasma research until recently; this approach has been successfully implemented in SMF measurement at the Prague Asterix Laser System (PALS). In this paper, proprietary construction solutions of polaro-interferometers are presented; they allow us to register high-quality complex interferograms in practical experiments, which undergo quantitative analysis (with an original software) to obtain information on the electron density and SMFs distributions in an examined plasma. The theoretical foundations of polaro-interferometric measurement, in particular, complex-interferometry, are presented. The main part of the paper details the methodology of the amplitude–phase analysis of complex interferograms. This includes software testing and examples of the electron density and SMF distribution of a laser ablative plasma generated by irradiating Cu thick planar targets with an iodine PALS laser at an intensity above about 1016 W/cm2.

Complex interferometry of magnetized plasma: accuracy and limitations

“…Among them the most significant are: (i) a probe beam depolarization in plasma, (ii) an influence of plasma self-luminosity, and (iii) a shot-to-shot instability of energy distribution in a cross-section of the probing beam. Hence the intensity, registered on a detector, can be described (see [19] ) by an equation:…”

“…12B) can not be abelized by Gegenbauer polynomial approximation method [6,23] -the required even polynomial degree can not be simulated taking into account width of the abelized function. The Fourier [19] and Mach-Shardin [6,23] methods work better, however it is known that the latter one is sensitive to data irregularities, it's error is lowest at the boundary and raises to the center of considered function, increasing with the function length increase. Thus all of the data presented in this paper is calculated using the Fourier method, whose accuracy increases with the number of measured experimental points.…”

“…Use of ultra-fast probe beam can fix the first problem, good control over laser parameters and additional interferometric filters can reduce contribution of other factors. Note that the implementation of the complex interferometry setup presented in [5,19] corresponds to this situation. Thus the interferometry accuracy is limited mainly by the limited resolution of the CCD and depends on spatial frequency of fringes.…”

“…The standard approach for SMF measurements implies usage of two separate diagnostics -polarimetry and interferometry, and subsequent combination of experimental data, which may cause certain accuracy and interpretation problems due to difference in optical paths and magnifications. The complex interferometry, which combines classic interferometry and polarimetry in a one diagnostic tool, allows to record and subsequently reconstruct several sets of independent data from a single data object named complex interferogram [7,[17][18][19][20] . Despite its complexity the complex interferometry method possess certain advantages due to fewer sources of errors, leading to increased accuracy, and the setup relative compactness.…”

“…The complex interferometry concept dates back to first SMF studies, and provides excellent spatial resolution [19][20][21] . However, due to setup and data processing complexity it was not widely used until recently, when a femtosecond complex interferometry system had been tested and implemented at the PALS facility in a single-frame regime [7] , and later was upgraded to 3-frame system [5] .…”