Stability criterion for Gaussian pulse propagation through negative index materials

Joseph, Ancemma; Porsezian, K.

doi:10.1103/physreva.81.023805

Cited by 20 publications

(6 citation statements)

References 33 publications

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“…Very recently, advances in the fabrication of MMs, ranging from microwave to optical frequency and from linear to nonlinear effect, have further stimulated a great deal of research including the revaluation and characterization of the classical nonlinear optical processes [17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35]. Accordingly, the wide study of self-focusing phenomena in Kerr nonlinear NIM has recently become a new and exciting field of research that has been the subject of intense investigations [25][26][27][28][29][30][31].…”

Section: Introductionmentioning

confidence: 98%

“…Accordingly, the wide study of self-focusing phenomena in Kerr nonlinear NIM has recently become a new and exciting field of research that has been the subject of intense investigations [25][26][27][28][29][30][31]. Several intriguing and counterintuitive nonlinear phenomena associated with optical collapse, optical solitons as well as modulation instability (MI) have been substantially disclosed [24][25][26][27][28][29][30][31][32][33][34][35] due to the anomalous electromagnetic properties of such materials. In particular, for MMs described by the Drude dispersive model, diffraction may be positive or negative, depending on the sign of refractive index seen by the propagating pulse in MMs [26][27][28][29][30].…”

Section: Introductionmentioning

confidence: 98%

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Collapse of optical wave arrested by cross-phase modulation in nonlinear metamaterials

Zhang

Liu

Xiang

et al. 2015

Journal of Modern Optics

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In this article, we put forward a novel strategy to realize the management of wave collapse through designing probe-pump configuration where probe wave is assumed to propagate in the positive-index region of metamaterials (MMs), while pump wave is assumed to propagate in the negative-index region. We disclose that cross-phase modulation (XPM) in MMs as a new physical mechanism that can be used to arrest the collapse of probe wave in the positive-index region by copropagating it together with pump wave in the negative-index region. Further, we observe that pump wave will evolve into a ring while probe wave will develop a side lob in the wings during the course of coupled waves propagation, different from the corresponding counterpart in the ordinary positive-index materials (OMs) where they simultaneously exhibit the catastrophic self-focusing behavior. Meanwhile, we also discuss how to control the collapse of probe wave by adjusting intensity-detuned pump wave. Our analysis is performed by directly numerically solving the coupled nonlinear Schrödinger equations, as well as using the variational approximation, both showing consistent results. The finding demonstrates XPM as a specific physical mechanism in MMs can provide us unique opportunities unattainable in OMs to manipulate self-focusing of high-power laser.

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Section: Introductionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 98%

Collapse of optical wave arrested by cross-phase modulation in nonlinear metamaterials

Zhang

Liu

Xiang

et al. 2015

Journal of Modern Optics

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“…Modulational instability (MI) is an ubiquitous phenomena in nonlinear dynamics that have been observed in a broad spectrum of systems ranging from dual-core nonlinear optical fiber [1], nonlinear LC self-dual circuits [2], fibers with random polarization mode dispersion [3], negative refractive index medium [4], discrete optical nonlinear arrays [5], Bose-Einstein condensates [6,7], deoxyribonucleic acid (DNA) chains [8], plasmas [9], among other nonlinear physical systems. In fact, MI is generally observed in systems where there is a dynamic balance between nonlinearity and dispersion, and characterized by small amplitude and phase perturbations growing exponentially.…”

Section: Introductionmentioning

confidence: 99%

Modulational Instability and Discrete Localized Modes in Two Coupled Atomic Chains with Next-Nearest-Neighbor Interactions

Nfor

Yamgoué

2022

J Nonlinear Math Phys

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A pair of one dimensional atomic chains which are coupled via the Klein-Gordon potential is considered in this study, with each chain experiencing both nearest and next-nearest-neighbor interactions. The discrete nonlinear Schrödinger amplitude equation with next-nearest-neighbor interactions is thus derived from the out-phase equation of motion of the coupled chains. This is achieved by using the rotating wave approximations perturbation method, in which both the carrier wave and envelope are explicitly treated in the discrete regime. It is shown that the next-nearest-neighbor interactions greatly modifies the region of observation of modulational instability in the atomic chain. By exploring the discrete Hirota-Bilinear method, we obtain the discrete one-soliton solution which is localized around the origin and structurally stable because it conserves it form as time evolves. However when the atomic chain is purely subjected to a symmetric coupling potential, we observe a structurally unstable discrete excitation that changes into an up-and-down asymmetric localized modes; both in the presence and absence of next-nearest-neighbor interactions. Results of numerical simulations clearly depicts the long term evolution of these discrete nonlinear excitations, that evolve from symmetric to asymmetric localized modes in the atomic chain.

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“…In this regime, low-order nonlinear coefficients in Taylor expansions as for natural nonlinear materials would be an appropriate description. Many recent papers work in this weak radiation regime [3,[5][6][7][8][9]. When radiation becomes stronger but not strong enough to damage the building materials of meta-atoms, in some cases [2,10] there may exist a scale of radiation intensity in/above which the lattice has such complex responses due to modulational instability that it can hardly be described by uniform optical constants (e.g., linear and/or nonlinear refractive index).…”

Section: Introductionmentioning

confidence: 99%

Modulational instability of magnetoelastic metamaterials

Ding,

Wang

2012

Preprint

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We study the modulational instability of recently designed magneto-elastic metamaterials composed of elastic-mediated split-ring resonators (SRR). An effective circuit model is developed. Then four cases are studied: a dimer of SRR, one-dimension (1D) dimerized array, 1D uniform array and two-dimension layered array. It is found that except for the dimer case, all the other many-body cases can present modulational instability which may disturb the bistability (if any) under uniform assumption.

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Stability criterion for Gaussian pulse propagation through negative index materials

Cited by 20 publications

References 33 publications

Collapse of optical wave arrested by cross-phase modulation in nonlinear metamaterials

Collapse of optical wave arrested by cross-phase modulation in nonlinear metamaterials

Modulational Instability and Discrete Localized Modes in Two Coupled Atomic Chains with Next-Nearest-Neighbor Interactions

Modulational instability of magnetoelastic metamaterials

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