Suppression of Nonlinear Optical Rogue Wave Formation Using Polarization-Structured Beams

A. Nicholas Black, Saumya Choudhary, E. Samuel Arroyo-Rivera, Hayden Woodworth, and Robert W. Boyd

Phys. Rev. Lett. 129, 133902 – Published 23 September 2022

Abstract

A nonlinear self-focusing material can amplify random small-amplitude phase modulations present in an optical beam, leading to the formation of amplitude singularities commonly referred to as optical caustics. By imposing polarization structuring on the beam, we demonstrate the suppression of amplitude singularities caused by nonlinear self-phase modulation. Our results are the first to indicate that polarization-structured beams can suppress nonlinear caustic formation in a saturable self-focusing medium and add to the growing understanding of catastrophic self-focusing effects in beams containing polarization structure.

Received 18 April 2022
Accepted 2 September 2022

DOI:https://doi.org/10.1103/PhysRevLett.129.133902

Physics Subject Headings (PhySH)

Nonlinear optical susceptibility Photorefractive & Kerr effects Polarization of light Spatial profiles of optical beams Third order nonlinear optical processes

Atomic gases Nonlinear waves

Four-wave mixing Kerr effect

Nonlinear DynamicsAtomic, Molecular & OpticalFluid Dynamics

Authors & Affiliations

A. Nicholas Black ^1,*, Saumya Choudhary ², E. Samuel Arroyo-Rivera ¹, Hayden Woodworth², and Robert W. Boyd ^1,2,3

¹Department of Physics and Astronomy, University of Rochester, Rochester, New York 14627, USA
²Institute of Optics, University of Rochester, Rochester, New York 14627, USA
³Department of Physics, University of Ottawa, Ottawa, Ontario, Canada K1N 6N5

^*Corresponding author. ablack18@ur.rochester.edu

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Vol. 129, Iss. 13 — 23 September 2022

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Images

Figure 1
The experimental setup for measuring spatially resolved intensity statistics. A diagonally polarized narrow-linewidth laser beam ( $+ 0.6 GHz$ above the ${}^{87}{Rb} D_{2}$ $F = 1 \to F^{'} = 2$ transition) enters a system of two spatial light modulators (SLMs) capable of generating any fully coherent polarization-structured beam (beam generation). Each SLM acts upon a different orthogonal polarization component of the beam, and the face of the first SLM is imaged onto the face of the second using a $4 f$ system. A third SLM divided into two regions, imparts the same spatially random phase to each polarization component of the beam. The face of the third SLM (dotted blue line) is imaged onto the entrance facet of a 7.5 cm-long Rb cell using a Keplerian telescope with a magnification of $- 3 / 4$ (L3 and L4). The polarization is transformed to the circular basis using a series of half- and quarter-wave plates ( $λ / 2$ and $λ / 4$ , respectively). The output facet of the Rb cell (dotted green line) is imaged onto a CCD camera (CCD) to collect pixel intensity statistics. The lens focal lengths are $f = 20 cm$ (L1), $f = 30 cm$ (L2), $f = 1 m$ (L3), $f = 75 cm$ (L4); polarizing beam splitter (PBS).
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Figure 2
The experimentally obtained intensity statistics of FP (orange diamonds), FPA (blue circles), and ${LG}_{0, 0}$ (green squares) beams after (a) linear and (b),(c),(d) nonlinear propagation. The solid, dashed, and dotted lines are Eq. (4) fitted to the FP, FPA, and ${LG}_{0, 0}$ data, respectively. The value of $γ$ obtained from fitting Eq. (4) to each dataset is shown at the bottom of the figure. The shaded area indicates the one standard deviation uncertainty in the fits. Under linear propagation, all beams have very similar intensity statistics that display no caustic formation. Under nonlinear propagation, the uniformly polarized ${LG}_{0, 0}$ and FPA beams begin to display caustic formation that increases with increasing beam power [(b) and (c)]. For the same beam powers, the polarization-structured FP beam maintains exponential intensity statistics with no caustics present. The suppression of caustics afforded by the polarization structure of the beam is no longer present at a beam power of 130 mW.
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Figure 3
Comparison of experimental and simulation results for linear and nonlinear propagation at a beam power of 90 mW. The polarization handedness in (a) and (b) is indicated by color, where red, blue, and white indicate left-circular, right-circular, and linear polarization, respectively. The same random phase mask is used in (a) and (b). The intensity structure does not change dramatically after linear propagation because the maximum phase of the phase mask is many times smaller than the maximum phase at which caustics usually develop ( $\sim 8 π rad$ ). (top). However, the intensity structure changes dramatically upon nonlinear propagation over the same distance (bottom). Nonetheless, the polarization structure remains similar to the linear result. The polarimetry simulation (b) shows good qualitative agreement with the experimental results (a). (c) In the numerical simulation of nonlinear propagation with 500 different random phase masks, the FP beam has shorter-tailed statistics than either the FPA or ${LG}_{0, 0}$ beams, in agreement with experiment (Fig. 2). The random phase masks used in obtaining (c) have the same parameters as those used in experiment.
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