Simulation of strong nonlinear effects in optical waveguides

Wang, X. H.; Cambrell, G.K.

doi:10.1364/josab.10.002048

Cited by 10 publications

(3 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This form of dielectric response is appropriate for anisotropic, but uni-axial, materials having the z−axis as axis of symmetry where i z is a unit vector in the direction of that axis, [8,21,7]. This symmetry means that it is possible to seek solutions with cylindrical symmetry propagating in the direction of the z−axis.…”

Section: Introductionmentioning

confidence: 99%

A constrained minimization problem and its application to guided cylindrical TM-modes in an anisotropic self-focusing dielectric

Stuart¹,

Zhou

2003

Calculus of Variations and Partial Differential Equations

View full text Add to dashboard Cite

The first part of this paper establishes the existence of a minimizer of problem:The essential features of the integrand are that. We show that the minimizer satisfies an EulerLagrange equation and estimates are given for the Lagrange multiplier as a function of d. In the second part of the paper, we use this result to establish the existence of guided TM-modes propagating through a self-focusing anisotropic dielectric. These are special solutions of Maxwell's equations with a nonlinear constitutive relation of a type commonly used in nonlinear optics when treating the propagation of waves in a cylindrical wave-guide. In TM-modes, the magnetic field has the form B = w(r) cos(kz − ωt)i θ when expressed in cylindrical polar co-ordinates (r, θ, z). The amplitude w is given by w(r) = ω ck (kr) −1/2 η(kr) where η is a minimizer of the problem (0.1) for a function Ψ which is determined by the constitutive relation through a Legendre transformation.

show abstract

Section: Introductionmentioning

confidence: 99%

A constrained minimization problem and its application to guided cylindrical TM-modes in an anisotropic self-focusing dielectric

Stuart¹,

Zhou

2003

Calculus of Variations and Partial Differential Equations

View full text Add to dashboard Cite

show abstract

“…We also limit our investigations to planar waveguides and the range of nonlinearities over which the waveguide approximation remains valid. 2,13 This paper is devoted to studying the effects of spatiotemporal coupling on the optical field behavior in dispersive nonlinear waveguides. In Section 2 we review the multidimensional NSE and then in Section 3 discuss the special cases under which it supports solitons.…”

Section: Introductionmentioning

confidence: 99%

Spatiotemporal coupling in dispersive nonlinear planar waveguides

Ryan

Agrawal

1995

J. Opt. Soc. Am. B

View full text Add to dashboard Cite

The multidimensional nonlinear Schrödinger equation governs the spatial and temporal evolution of an optical field inside a nonlinear dispersive medium. Although spatial (diffractive) and temporal (dispersive) effects can be studied independently in a linear medium, they become mutually coupled in a nonlinear medium. We present the results of numerical simulations showing this spatiotemporal coupling for ultrashort pulses propagating in dispersive Kerr media. We investigate how spatiotemporal coupling affects the behavior of the optical field in each of the four regimes defined by the type of group-velocity dispersion (normal or anomalous) and the type of nonlinearity (focusing or defocusing). We show that dispersion, through spatiotemporal coupling, can either enhance or suppress self-focusing and self-defocusing. Similarly, we demonstrate that diffraction can either enhance or suppress pulse compression or broadening. We also discuss how these effects can be controlled with optical phase modulation, such as that provided by a lens (spatial phase modulation) or frequency chirping (temporal phase modulation).

show abstract

“…It is the aim of this paper to show that a resonance phenomenon can lead either to an increase or to a decrease of the SH efficiency, depending on the losses at the SH frequency, the key point being the existence of complex zeros of the scattered diffraction order amplitudes. 10 Several different approaches have been recently proposed to deal theoretically with NL interaction in optical waveguides with phase or surface relief gratings, [11][12][13][14] and we choose a rigorous electromagnetic theory 15 based on Maxwell's equations, with the only assumption being the undepleted pump approximation.…”

Section: Introductionmentioning

confidence: 99%

Grating-enhanced second-harmonic generation in polymer waveguides: role of losses

Popov

Nevière²,

Reinisch³

et al. 1995

Appl. Opt.

View full text Add to dashboard Cite

A numerical study of second-harmonic (SH) generation in a corrugated polymer waveguide is performed with a rigorous electromagnetic theory. Comparison with experiment reveals the role of losses inside the waveguide-small losses do not significantly affect the nonresonant response and reduce the resonant enhancement of SH generation. High losses can lead to the opposite effect-instead of enhancement, dips in the SH efficiency are observed in the vicinity of guided-wave excitation. The peculiarities of the angular dependencies of SH generation are explained from the phenomenological point of view, and the role of phase matching is discussed.

show abstract

Simulation of strong nonlinear effects in optical waveguides

Cited by 10 publications

References 18 publications

A constrained minimization problem and its application to guided cylindrical TM-modes in an anisotropic self-focusing dielectric

A constrained minimization problem and its application to guided cylindrical TM-modes in an anisotropic self-focusing dielectric

Spatiotemporal coupling in dispersive nonlinear planar waveguides

Grating-enhanced second-harmonic generation in polymer waveguides: role of losses

Contact Info

Product

Resources

About