Photorefractive two-wave mixing and the lambert<i>W</i>function

Rehn, Henning

doi:10.1080/09500349808231755

Cited by 5 publications

(3 citation statements)

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“…It had been first introduced by Lambert and Euler in the late 1700s. The Lambert W function has been applied to versatile branches of physics, material science and mathematics such as ecology and evolution, electronics, quantum physics, statistical and solid state physics and laser optics [2][3][4][5][6][7][8][9][10][11][12][13][14][15]. The Lambert W function [1,2,5,16,17] is defined as the solution to the transcendental equation of, W (x) e W(x) = x,…”

Section: Introductionmentioning

confidence: 99%

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Comparison of Lambert W function with Adomian decomposition method for wave propagation in saturable absorption medium

Kim¹,

Kwak²

2020

J. Opt.

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We present a comparative study to examine the performances of both the Lambert W function method and Adomian decomposition method (ADM) for solving the nonlinear optical beam propagations in a saturable absorption (SA) medium for two distinct SA models. The SA-I model describes a fast saturable absorber (in which the relaxation time is much shorter than the pulse duration of the incident laser beam and no excited state absorption occurs) for a three-level system, while the SA-II model depicts a four-level system or two-photon absorption saturation. We derive the explicit analytic solutions based on the Lambert W function as well as ADM without using thin-sample approximation, and without weak saturation limit. The two different approaches to solve the nonlinear optical wave equation for two distinct SA models are compared and discussed in detail, and show excellent agreement with each other. Finally, to validate the theoretical analysis, we provide some experimental data for nonlinear optical transmission in methyl orange-doped PVA films, revealing excellent agreement with the theory of the SA-II model.

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Section: Introductionmentioning

confidence: 99%

“…In the optics community, several researchers have used the Lambert W function to solve various optical problems such as photorefractive two-wave mixing [8], Beer-Lambert-Bouguer law for optical absorption [9], laser system range calculations [10], Q-switching in a fast saturable absorber [11][12][13][14][15], among others.…”

Section: Introductionmentioning

confidence: 99%

Comparison of Lambert W function with Adomian decomposition method for wave propagation in saturable absorption medium

Kim¹,

Kwak²

2020

J. Opt.

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“…4 Secondly, while many examples from physics where the Lambert W function arises have now been found (see, e.g., Refs. [18,[20][21][22][23][24][25][26][27][28][29][30][31][32][33][34]), the problem of determining closed-form expressions for the Wien peaks provides what is undoubtedly the simplest illustration of the use of this function in physics.…”

Section: Introductionmentioning

confidence: 99%

Wien peaks and the Lambert W function

Stewart¹

2011

Rev. Bras. Ensino Fís.

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Exact expressions for the wavelengths where maxima occur in the spectral distribution curves of blackbody radiation for a number of different dispersion rules are given in terms of the Lambert W function. These dispersion rule dependent "Wien peaks" are compared to those wavelengths obtained in a setting independent of the dispersion rule chosen where the "peak" wavelengths are taken to be those obtained on dividing the total radiation intensity emitted from a blackbody into a given percentile. The account provides a simple yet accessible example of the growing applicability of the Lambert W function in physics. Keywords: blackbody radiation, Wien peaks, Lambert W function, polylogarithm.São apresentadas em termos das funções W de Lambert as expressões exatas para os comprimentos de onda para os quais ocorrem máximos das curvas espectrais do corpo negro para algumas diferentes regras de dispersão. Estes "picos de Wien", dependentes da regra de dispersão, são comparadosàqueles obtido independentes desta regra, onde os comprimentos de onda de "pico" são obtidos dividindo-se a intensidade de radiação total emitida por um corpo negro em um dado percentil. Isto fornece um exemplo simples e acessível da crescente aplicabilidade das funções W de Lambert. Palavras-chave: radiação de corpo negro, picos de Wien, função W de Lambert, polylogarithm.

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