Decay of a nonlinear impurity in a structured continuum from a nonlinear Fano-Anderson model

Longhi, Stefano

doi:10.1103/physrevb.75.184306

Cited by 16 publications

(10 citation statements)

References 44 publications

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“…6,7 The model attracted interest long time ago because of analytical treatment and its generality. 2,6,7,9 The main result is that the transmission coefficient of a single waveguide mode scattering from Kerr off-channel features was shown to exhibit bistability properties arising from a nonlinearity of the offchannel site. In Refs.…”

Section: Tight-binding Model Of the Nonlinear Fabry-perot Systemmentioning

confidence: 99%

“…The system attracts interest over decade because of analytical treatment and its generality. [2][3][4][5][6][7][8][9][10][11][12] On the other hand, the system can be realized in the twodimensional photonic crystals ͑PhC͒.…”

Section: Introductionmentioning

confidence: 99%

“…Then the corresponding eigenfunction becomes localized, i.e., the in-channel nonlinear defect can give rise to the bound state. 2,3,9 One may ask does exist the localized bound state with discrete eigenfrequency inside the propagation band. First, this question was formulated and positively answered by von Neumann and Wigner in 1929.…”

Section: Introductionmentioning

confidence: 99%

“…The system of one nonlinear impurity embedded in a onedimensional continuum attracted interest long time ago because of analytical treatment and its generality. 2,[5][6][7]9 The system is open and differs from closed nonlinear counterpart by that the transmission resonance properties depend on the amplitude of incident wave. Correspondingly we can govern the resonance by the field intensity at the defects to give rise to a bistability.…”

Section: Introductionmentioning

confidence: 99%

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Bound states in photonic Fabry-Perot resonator with nonlinear off-channel defects

Bulgakov

Sadreev

2010

Phys. Rev. B

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We consider a Fabry-Perot resonator ͑FPR͒ comprised of two off-channel nonlinear defects coupled to the photonic waveguide. For the linear case FPR can support bound states in the form of standing waves between the defects if a distance between them is quantized. For the nonlinear case the bound states appear for arbitrary distance between the defects if electromagnetic intensity is quantized. For transmission through the FPR we reveal additional resonances which are the result of coupling of incident wave with the bound states because of nonlinearity of the defects. The resonances are spaced at the eigenfrequencies of bound states with a width proportional to the input amplitude. The theory of the FPR based on the simple Wang and Fan model ͓Phys.Rev. E 68, 066616 ͑2003͔͒ is complemented by the tight-binding one. The results for the transmission and bound states in these models agree with computations in real two-dimensional photonic crystal waveguide coupled with two off-channel defects fabricated from a Kerr-type material.

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Section: Tight-binding Model Of the Nonlinear Fabry-perot Systemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Bound states in photonic Fabry-Perot resonator with nonlinear off-channel defects

Bulgakov

Sadreev

2010

Phys. Rev. B

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“…In this context, considerable research interest has been generated on decay dynamics of straight waveguides embedded into a linear structured continuum of waveguides. The decay dynamics was theoretically investigated [18] for a nonlinear impurity mode embedded in a linear structured continuum in the framework of a nonlinear Fano-Anderson model. It was shown that the existence of bound states embedded in the continuum acts as transient trapping states which slow down the decay.…”

Section: Introductionmentioning

confidence: 99%

Variable-coupling-induced optical trapping in optical waveguides via dressed continuum

Bayal

Dutta²,

Panchadhyayee³

et al. 2013

Journal of Modern Optics

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We have studied a photonic structure, based on a semi-classical approach, considering simultaneous interaction of two side-coupled bent waveguides having variable coupling interactions (Gaussian and exponential-type) with a dressed continuum. We have examined the condition of optical trapping in spatial domain during propagation of a light field through the waveguide. The variation in parametric conditions leading to a typical trapping (quasi-trapping) phenomenon for both the cases of exponential and Gaussian coupling interactions is discussed. Simulation of such phenomenon of trapping in our macroscopic photonic structure is possible for all even relative positions of the side waveguides coupled to the dressed continuum. As far as the onset of quasi-trapping is concerned, the coupling width in the Gaussian coupling case is smaller than that in the exponential case. In this context, the Gaussian profile is found more tolerant than the exponential one so far as the separation between the side-coupled waveguides is concerned. Perfect trapping is observed to sustain by setting proper conditions while launching initial light in the side waveguides.

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Light-Induced Breaking of Symmetry in Photonic Crystal Waveguides with Nonlinear Defects as a Key for All-Optical Switching Circuits

Bulgakov

Sadreev

Pichugin

2012

Progress in Optical Science and Photonics

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We consider light transmission in 2D photonic crystal waveguide coupled with two identical nonlinear defects positioned symmetrically aside the waveguide. We show that with growth of injected light power there is a breaking of symmetry by two ways. In the first way the symmetry is broken because of different light intensities at the defects. In the second way the intensities at the defects are equaled but phases of complex amplitudes are different. That results in a vortical power flow between the defects similar to the DC Josephson effect if the input power over the waveguide is applied and the defects are coupled. As application of these phenomena we consider the symmetry breaking for the light transmission in a T-shaped photonic waveguide with two nonlinear defects. We demonstrate as this phenomenon can be explored for all-optical switching of light transmission from the left output waveguide to the right one by application of input pulses. Finally we consider the symmetry breaking in the waveguide coupled with single defect presented however by two dipole modes.

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Decay of a nonlinear impurity in a structured continuum from a nonlinear Fano-Anderson model

Cited by 16 publications

References 44 publications

Bound states in photonic Fabry-Perot resonator with nonlinear off-channel defects

Bound states in photonic Fabry-Perot resonator with nonlinear off-channel defects

Variable-coupling-induced optical trapping in optical waveguides via dressed continuum

Light-Induced Breaking of Symmetry in Photonic Crystal Waveguides with Nonlinear Defects as a Key for All-Optical Switching Circuits

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