Formation of nonlinear holographic images in a system of periodically located nonlinear mediums

Abstract

Abstract. The formation of nonlinear holographic images in a system of periodically located nonlinear mediums is studied. Analytical expressions which describe the magnitudes and locations of intensity maximums depending on the corresponding image number are derived. Comparison with numerical calculation results is presented.Dependence of a refraction index on intensity leads to beam self-focusing [1], transverse instability [2] and to formation of nonlinear holographic images (NHI) of obstacles in the optical path of powerful laser systems [3]. In Ref.[4] it has been shown that at value of B-integral of only 0.2 rad a round opaque obscuration increases the intensity peak which exceeds the average level by almost 1.5 times, and for a phase obstacle the peak excess is 2.5. One can present a disk amplifier as a system of periodically located (SPL) nonlinear mediums (NM). Formation of NHI in SPLNM differs from the NHI formation in continuous media with the same value of B-integral.For the first time this problem has been considered in Ref. [3]. However, these authors [3] focused only on the analysis of the intensity dependence upon the size of an obscuration at a single point of space. Accidentally for SPLNM configuration considered in Ref. [3], the intensity in the chosen point is not a peak one. The locations of the NHI and their intensity were not explored. In Refs [5, 6] the results of peak intensity calculations for the various elements of the NIF laser chain with account for NHI formation were published. In Refs [7-9] the process of the NHI formation in a SPLNM was viewed in more details and it was shown that for KNM there are K NHI. However the chosen model parameters (number of NM, increment of B-integral for one NM, thickness of NM, size of the beam) are far from the parameters of typical disk amplifiers.In this paper, we are considering the simplified system of infinitely thin NM without energy gain and losses. According to expression (39) in Ref. [3], when the powerful plane wave and spherical scattered wave incident on the single NM, the new wave is generated. For the infinitely thin NM the complex amplitude A 1 of this wave in the plane of NHI is equal towhere A s is the complex amplitude of the scattered wave in the plane of obstacle.After passage of a NM the incident scattered wave changes toLet us note that upon the derivation of Eq. (39) in Ref.[3], it was not assumed that the incident scattered wave is diverging. Therefore expressions (1) and (2) remain valid for a converging incident wave. In This is an Open Access article distributed under the terms of the Creative Commons Attribution License 2.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.