Nonlinear waves in saturable self-focusing thin films bounded by linear media

Al-Bader, S.J.; Jamid, H.A.

doi:10.1109/3.8541

Cited by 27 publications

(7 citation statements)

References 15 publications

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“…Both the eigenvalues and the eigenfunctions depend on these numbers. It can be shown that the property = c 0 k for some index k implies that u k = 0, since boundary condition (16) at x=0 leads to a Cauchy problem with vanishing initial conditions. Therefore, we assume that…”

Section: Governing Equationsmentioning

confidence: 99%

“…We notice that the theory of 1-frequency transverseelectric (TE) and transverse-magnetic (TM) wave propagation in layered waveguides filled with non-linear media is widely studied [6,7,[11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27]. In the 1-frequency case, the GW is characterised by one frequency and one propagation constant (PC).…”

Section: Governing Equations and Introductory Remarksmentioning

confidence: 99%

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Nonlinear multi-frequency electromagnetic wave propagation phenomena

Валовик

2017

J. Opt.

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A generalisation of the concept of monochromatic electromagnetic waves guided by layered waveguide structures filled with non-linear medium is introduced. This generalisation leads to guided waves of a novel type: a non-linear multi-frequency guided wave. The existence of such waves, in particular guide structures, is proven using the perturbation method. Numerical experiments are presented for non-linear 1- and 2-frequency guided waves in plane and cylindrical (with a circular cross-section) waveguides. Numerically, a novel non-linear effect is found for particular cases of non-linear multi-frequency guided waves. The suggested generalisation gives not only a unified approach to treat various electromagnetic wave propagation problems but also paves the way to study non-linear interactions of guided waves.

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Section: Governing Equationsmentioning

confidence: 99%

Section: Governing Equations and Introductory Remarksmentioning

confidence: 99%

Nonlinear multi-frequency electromagnetic wave propagation phenomena

Валовик

2017

J. Opt.

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“…If the propagation constant for even mode is ze k and for odd mode is zo k , then the coupling coefficient can be written as [4] zo ze k k − = κ (9) Fig. 2 shows the wavelength dependent coupling coefficient of the coupled slab waveguide for different input power.…”

Section: Resultsmentioning

confidence: 99%

“…However, the coupling issues were not addressed. For the case of a non-Kerr-like nonlinear core with linear claddings a method based on the first integral of the nonlinear Helmholtz equation is used [3,4]. But the method cannot provide accurate results.…”

Section: Introductionmentioning

confidence: 99%

Investigation of wave propagation in coupled nonlinear slab waveguide using finite element method

Khan

Chen

Brokaw³

et al. 2007

2007 IEEE Antennas and Propagation Society International Symposium

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“…In other words, Kerr nonlinearity produces a nonperturbative effect-in nitely many eigenstates that cannot be found using perturbation theory methods. One more interesting point is that for a wide range of bounded nonlinearities (that model saturable nonlinear permittivities) there arises not more than a nite number of eigenvalues [13], see also [14,15]; (c) In the case a = 0, b > 0, the problem Q has a nite number of solutions; these solutions have linear counterparts.…”

Section: Statement Of the Problem And Introductory Remarksmentioning

confidence: 99%

Asymptotic analysis of a nonlinear eigenvalue problem arising in electromagnetics

Валовик

2020

Nonlinearity

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An eigenvalue problem for Maxwell's equations with anisotropic cubic nonlinearity is studied. The problem describes propagation of transverse magnetic waves in a dielectric layer lled with (nonlinear) anisotropic Kerr medium. The nonlinearity involves two non-negative parameters a, b that are usually small. In the case a = b = 0 one arrives at a linear problem that has a nite number of solutions (eigenvalues and eigenwaves). If a > 0, b 0, then the nonlinear problem has in nitely many solutions; only a nite number of these solutions have linear counterparts. This shows that perturbation theory methods are inapplicable to study the problem in this case. For a = 0, b > 0 the nonlinear problem has a nite number of solutions; in this case each solution has a linear counterpart. Asymptotic distribution of the eigenvalues is found, periodicity of the eigenfunctions is proved and exact formula for the period is found, zeros of the eigenfunctions are determined, and a (nonlinear) eigenvalue comparison theorem is proved. Numerical experiments are presented.

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Nonlinear waves in saturable self-focusing thin films bounded by linear media

Cited by 27 publications

References 15 publications

Nonlinear multi-frequency electromagnetic wave propagation phenomena

Nonlinear multi-frequency electromagnetic wave propagation phenomena

Investigation of wave propagation in coupled nonlinear slab waveguide using finite element method

Asymptotic analysis of a nonlinear eigenvalue problem arising in electromagnetics

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