Loss of phase and universality of stochastic interactions between laser beams

Sagiv, Amir; Ditkowski, Adi; Fibich, Gadi

doi:10.1364/oe.25.024387

Cited by 12 publications

(12 citation statements)

References 45 publications

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“…Through the process of self-phase modulation, the acquired nonlinear phase shift of collapsing beams becomes large and highly sensitive to small fluctuations in the input power, as predicted theoretically [21,22] and demonstrated experimentally [23]. Furthermore, as the collapsing beam evolves into a filament, the sensitivity of the nonlinear phase shift to small fluctuations increases with propagation disce, so that ultimately, the nonlinear phase shift becomes uniformly distributed in [0,2π] [24]. As a result of this loss of phase, the interference between postcollapse beams becomes chaotic [22][23][24][25][26].…”

Section: Introductionmentioning

confidence: 84%

“…Furthermore, as the collapsing beam evolves into a filament, the sensitivity of the nonlinear phase shift to small fluctuations increases with propagation disce, so that ultimately, the nonlinear phase shift becomes uniformly distributed in [0,2π] [24]. As a result of this loss of phase, the interference between postcollapse beams becomes chaotic [22][23][24][25][26].…”

Section: Introductionmentioning

confidence: 99%

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Loss of polarization of elliptically polarized collapsing beams

et al. 2019

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We show theoretically and demonstrate experimentally that collapsing elliptically-polarized laser beams experience a nonlinear ellipse rotation that is highly sensitive to small fluctuations in the input power. For arbitrarily small fluctuations in the input power and after a sufficiently large propagation distance, the polarization angle becomes uniformly distributed in [0, 2π] from shot-toshot. We term this novel phenomenon loss of polarization. We perform experiments in fused-silica glass, nitrogen gas and water, and observe a significant increase in the fluctuations of the output polarization angle for elliptically-polarized femtosecond pulses as the power is increased beyond the critical power for self-focusing. We also show numerically and confirm experimentally that this effect is more prominent in the anomalous group-velocity dispersion (GVD) regime compared to the normal-GVD regime due to the extended lengths of the filaments for the former. Such effects could play an important role in intense-field light-matter interactions in which elliptically-polarized pulses are utilized.

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Section: Introductionmentioning

confidence: 84%

Section: Introductionmentioning

confidence: 99%

Loss of polarization of elliptically polarized collapsing beams

et al. 2019

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“…In such cases, the solution of the (otherwise deterministic) model becomes random, and so one is interested in computing its statistics. This problem, sometimes known as forward uncertainty propagation (UQ), arises in various areas such as biochemistry [33,35], fluid dynamics [6,21,31,35], structural engineering [48], hydrology [7], and nonlinear optics [42].…”

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confidence: 99%

“…In many applications, one is interested in computing the probability density function (PDF) of a certain "quantity of interest" (output) of the model [1,6,7,21,33,42,54]. Often, density estimation is performed using standard uncertainty propagation methods and surrogate models [22,48], such as Stochastic Finite Element and generalized Polynomial Chaos (gPC) [23,36,47,60], hp-gPC [57], and Wiener-Haar expansion [32], since these methods can approximate moments with spectral accuracy [61,62].…”

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Density Estimation in Uncertainty Propagation Problems Using a Surrogate Model

Ditkowski¹,

Fibich²,

Sagiv³

2020

SIAM/ASA J. Uncertainty Quantification

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The effect of uncertainties and noise on a quantity of interest (model output) is often better described by its probability density function (PDF) than by its moments. Although density estimation is a common task, the adequacy of approximation methods (surrogate models) for density estimation has not been analyzed before in the uncertainty-quantification (UQ) literature. In this paper, we first show that standard surrogate models (such as generalized polynomial chaos), which are highly accurate for moment estimation, might completely fail to approximate the PDF, even for one-dimensional noise. This is because density estimation requires that the surrogate model accurately approximates the gradient of the quantity of interest, and not just the quantity of interest itself. Hence, we develop a novel spline-based algorithm for density-estimation whose convergence rate in L q is polynomial in the sampling resolution. This convergence rate is better than that of standard statistical density-estimation methods (such as histograms and kernel density estimators) at dimensions 1 ≤ d ≤ 5 2 m, where m is the spline order. Furthermore, we obtain the convergence rate for density estimation with any surrogate model that approximates the quantity of interest and its gradient in L ∞ . Finally, we demonstrate our algorithm for problems in nonlinear optics and fluid dynamics.1 g in L q , the corresponding density p g might not be a good approximation of p f . Indeed, for p g to approximate p f , then g ′ needs to be close to f ′ , and g ′ (α) should also vanish if and only if f ′ (α) does. These conditions might not be satisfied by some of the above-mentioned standard UQ methods. In contrast, spline interpolation approximates both the function and its gradient [3,25,41,45], and does not tend to produce spurious extremal points. Therefore, we construct a novel algorithm for density estimation in uncertainty-propagation problems using splines as our surrogate model. With cubic splines, our density-estimation algorithm has a guaranteed convergence rate of at least h 3 , where h is the maximal sampling spacing (resolution). More generally, with splines of order m, the convergence rate is at least h m . These rates are superior to those of the standard kernel density estimators [52,59], for noise dimension 1 ≤ d ≤ 5 2 m. Our choice of splines is motivated by the availability and efficiency of one-and multi-dimensional spline toolboxes. Nevertheless, other surrogate models can be used in this algorithm, and indeed this paper lays the theoretical framework for deriving the convergence rate of such methods (Corollaries 4.8 and 5.5). We show, essentially, that density estimation convergence can be performed with any surrogate model for which the L ∞ error of both the function and its gradient converge to zero as the spacing resolution h vanishes. Because we only rely on solving the underlying deterministic model (i.e., our method is non-intrusive), and because interpolation by spline is a standard numerical procedure, our proposed method is...

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Spectral convergence of probability densities for forward problems in uncertainty quantification

Sagiv

2022

Numer. Math.

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Loss of phase and universality of stochastic interactions between laser beams

Cited by 12 publications

References 45 publications

Loss of polarization of elliptically polarized collapsing beams

Loss of polarization of elliptically polarized collapsing beams

Density Estimation in Uncertainty Propagation Problems Using a Surrogate Model

Spectral convergence of probability densities for forward problems in uncertainty quantification

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