Experimental observation of nonlinear pulse compression in nonuniform Bragg gratings

Broderick, Neil G. R.; Taverner, D.; Richardson, David J.; Ibsen, M.; Laming, R.I.

doi:10.1364/ol.22.001837

Cited by 34 publications

(27 citation statements)

References 9 publications

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“…[17]. Experiments demonstrating the existence of gap solitons have been performed by Eggleton, Slusher and collaborators [13,14,15], and by Broderick and his collaborators [6,34]. In two and three dimensions, Aközbek and John have formally derived envelope equations and examined their solitary waves numerically [3].…”

Section: Introductionmentioning

confidence: 99%

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Nonlinear Propagation of Light in One-Dimensional Periodic Structures

Goodman¹,

Weinstein²,

Holmes

2001

J. Nonlinear Sci.

121

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Summary. We consider the nonlinear propagation of light in an optical fiber waveguide as modeled by the anharmonic Maxwell-Lorentz equations (AMLE). The waveguide is assumed to have an index of refraction which varies periodically along its length. The wavelength of light is selected to be in resonance with the periodic structure (Bragg resonance). The AMLE system considered incorporates the effects of non-instantaneous response of the medium to the electromagnetic field (chromatic or material dispersion), the periodic structure (photonic band dispersion) and nonlinearity. We present a detailed discussion of the role of these effects individually and in concert. We derive the nonlinear coupled mode equations (NLCME) which govern the envelope of the coupled backward and forward components of the electromagnetic field. We prove the validity of the NLCME description and give explicit estimates for the deviation of the approximation given by NLCME from the exact dynamics, governed by AMLE. NLCME is known to have gap soliton states. A consequence of our results is the existence of very long-lived gap soliton states of AMLE. We present numerical simulations which validate as well as illustrate the limits of the theory. Finally, we verify that the assumptions of our model apply to the parameter regimes explored in recent physical experiments in which gap solitons were observed.

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Section: Introductionmentioning

confidence: 99%

“…This is a shock type singularity. Specifically the results of [28] imply the following: 6 The classical relation between tension, τ and strain ∂zu, is derived via…”

mentioning

confidence: 99%

Nonlinear Propagation of Light in One-Dimensional Periodic Structures

Goodman¹,

Weinstein²,

Holmes

2001

J. Nonlinear Sci.

121

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“…The envelope soliton propagates at a velocity determined by the local gradient of the band structure and with a width determined by a balance between the nonlinearity and the effective mass, rather than the bare mass. Such "Bragg grating solitons" have been observed in recent years in optical fiber gratings at extremely high laser powers [14,24] . In the present case, the nonlinearity is much stronger and BEC grating solitons should be easier to generate.…”

Section: Soliton Solutionsmentioning

confidence: 95%

Effective mass approach for a Bose-Einstein condensate in an optical lattice

Duan

Steel

et al. 2009

Chin. Sci. Bull.

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We study the stationary and propagating solutions for a Bose-Einstein condensate (BEC) in a periodic optical potential with an additional confining optical or magnetic potential. Using an effective mass approximation we express the condensate wave function in terms of slowly-varying envelopes modulating the Bloch modes of the optical lattice. In the limit of a weak nonlinearity, we derive a nonlinear Schrödinger equation for propagation of the envelope function which does not contain the rapid oscillation of the lattice. We then consider the ground state solutions in detail in the regime of weak, moderate and strong nonlinear interactions. We describe the form of solution which is appropriate in each regime, and place careful limits on the validity of each type of solution. Finally we extend the study to the propagating dynamics of a spinor atomic BEC in an optical lattice and some interesting phenomena are revealed.

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“…Experimental and numerical investigations of all-optical switching using XPM in Bragg grating in conventional fiber were carried out in the last decade [1][2][3][4]. All optical switching based on nonlinear fiber-optic grating coupler were also reported [5][6].…”

Section: Introductionmentioning

confidence: 99%

All-optical switching based on cross-phase modulation using Bragg grating in the highly nonlinear photonic crystal fiber

Sang

Zhang

et al. 2007

SPIE Proceedings

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All-optical switching based on cross-phase modulation using Bragg grating in the highly nonlinear photonic crystal fiber (PCF) is investigated numerically. Differential method is used in the simulation process. The numerical solutions of the coupled-mode equations which describe all-optical switching are presented. Switching characteristics influenced by different pump shape and pump power are analyzed. Furthermore, switching characters of using Bragg grating in a highly nonlinear photonic crystal fiber and in a conventional one are compared.

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Experimental observation of nonlinear pulse compression in nonuniform Bragg gratings

Cited by 34 publications

References 9 publications

Nonlinear Propagation of Light in One-Dimensional Periodic Structures

Nonlinear Propagation of Light in One-Dimensional Periodic Structures

Effective mass approach for a Bose-Einstein condensate in an optical lattice

All-optical switching based on cross-phase modulation using Bragg grating in the highly nonlinear photonic crystal fiber

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