Theoretical models for ultrashort electromagnetic pulse propagation in nonlinear metamaterials

Wen, Shuangchun; Xiang, Yuanjiang; Dai, Xiaoyu; Tang, Zhixiang; Su, Wenhua; Fan, Dianyuan

doi:10.1103/physreva.75.033815

Cited by 123 publications

(90 citation statements)

References 22 publications

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“…In particular, the various envelope equations (e.g. [19,27,30,31], and even [56,57]) all use co-moving frames and/or envelopes as a preparation for discarding inconvenient derivatives: here such steps are optional extras. In this factorization approach shown here, none of these were required, but they nevertheless may be useful.…”

Section: Modificationsmentioning

confidence: 99%

Optical pulse propagation with minimal approximations

2010

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Propagation equations for optical pulses are needed to assist in describing applications in ever more extreme situations -including those in metamaterials with linear and nonlinear magnetic responses. Here I show how to derive a single first order propagation equation using a minimum of approximations and a straightforward "factorization" mathematical scheme. The approach generates exact coupled bi-directional equations, after which it is clear that the description can be reduced to a single uni-directional first order wave equation by means of a simple "slow evolution" approximation, where the optical pulse changes little over the distance of one wavelength. It also also allows a direct term-to-term comparison of an exact bi-directional theory with the approximate uni-directional theory.

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Section: Modificationsmentioning

confidence: 99%

Optical pulse propagation with minimal approximations

2010

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“…These parameters are commonly known as the electric and magnetic plasma frequencies [38]. The kernel a(ω) of the operator a is:…”

Section: Model For Dispersionmentioning

confidence: 99%

“…The idea for dispersion compensation in transmission lines using negative-refractive media (NRM) was described in [21]. An interaction of ultrashort pulses with ordinary materials is well understood in nonlinear optics [36] and extended for metamaterals in [38].…”

Section: Introduction Researches On Metamaterialsmentioning

confidence: 99%

Directed electromagnetic wave propagation in 1D metamaterial: Projecting operators method

Ampilogov

Leble

2016

Physics Letters A

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We consider a boundary problem for 1D electrodynamics modeling of a pulse propagation in a metamaterial medium. We build and apply projecting operators to a Maxwell system in time domain that allows to split the linear propagation problem to directed waves for a material relations with general dispersion. Matrix elements of the projectors act as convolution integral operators. For a weak nonlinearity we generalize the linear results still for arbitrary dispersion and derive the system of interacting right/left waves with combined (hybrid) amplitudes. The result is specified for the popular metamaterial model with Drude formula for both permittivity and permeability coefficients. We also discuss and investigate stationary solutions of the system related to some boundary regimes.

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“…Frequency band gaps, i.e., frequency domains where linear EM waves are evanescent (e.g., for ǫ < 0 and µ > 0), also exist in metamaterials. Hence, when a nonlinearity occurs, say in the dielectric response of the medium (a physically relevant situation in nonlinear metamaterials [6,7,8,9,10,11,12]), then nonlinearity-induced localization of EM waves is possible. Such localization is indicated by the formation of gap solitons, which occur mainly in nonlinear optics [13] and Bose-Einstein condensates (BECs) [14], by means of the nonlinear Schrödinger (NLS) equation with a periodic potential.…”

mentioning

confidence: 99%

“…In doing so, we consider a metamaterial characterized by the permittivity ǫ and permeability µ of Ref. [2], as well as a weak Kerr-type nonlinearity in the medium's dielectric response [10,11,15]. Following the lines of Refs.…”

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confidence: 99%

Short pulse equations and localized structures in frequency band gaps of nonlinear metamaterials

et al. 2010

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We consider short pulse propagation in nonlinear metamaterials characterized by a weak Kerr-type nonlinearity in their dielectric response. In the frequency "band gaps" (where linear electromagnetic waves are evanescent) with linear effective permittivity ǫ < 0 and permeability µ > 0, we derive two short-pulse equations (SPEs) for the high-and lowfrequency band gaps. The structure of the solutions of the SPEs is also briefly discussed, and connections with the soliton solutions of the nonlinear Schrödinger equation are presented. . The frequency dependence of the effective permittivity ǫ and permeability µ of these media is such that there exist frequency bands where the medium displays either a right-handed (RH) behavior (ǫ > 0, µ > 0) or a left-handed (LH) behavior (ǫ < 0, µ < 0), thus exhibiting negative refraction at microwave [2,3,4] or optical frequencies [5]. Frequency band gaps, i.e., frequency domains where linear EM waves are evanescent (e.g., for ǫ < 0 and µ > 0), also exist in metamaterials. Hence, when a nonlinearity occurs, say in the dielectric response of the medium (a physically relevant situation in nonlinear metamaterials [6,7,8,9,10,11,12]), then nonlinearity-induced localization of EM waves is possible. Such localization is indicated by the formation of gap solitons, which occur mainly in nonlinear optics [13] and Bose-Einstein condensates (BECs) [14], by means of the nonlinear Schrödinger (NLS) equation with a periodic potential. Gap solitons were also predicted to occur in nonlinear metamaterials [15]. There, the approximation of slowly varying electric and magnetic field envelopes, led to a nonlinear Klein-Gordon (NKG) equation supporting gap solitons.Nonlinear models describing localization of wave packets in periodic media, e.g., the NLS equation in optics [13] and NKG equation in metamaterials [15] are usually derived in the framework of the slowly-varying envelope approximation. However, as far as ultra-short pulse propagation is concerned, i.e, for pulse widths of the order of a few cycles of the carrier

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Theoretical models for ultrashort electromagnetic pulse propagation in nonlinear metamaterials

Cited by 123 publications

References 22 publications

Optical pulse propagation with minimal approximations

Optical pulse propagation with minimal approximations

Directed electromagnetic wave propagation in 1D metamaterial: Projecting operators method

Short pulse equations and localized structures in frequency band gaps of nonlinear metamaterials

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