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- Valery S Shchesnovich, Anton S Desyatnikov, Yuri S Kivshar
- Optics express
- 2008

We study, analytically and numerically, the dynamics of interband transitions in two-dimensional hexagonal periodic photonic lattices. We develop an analytical approach employing the Bragg resonances of different types and derive the effective multi-level models of the Landau-Zener-Majorana type. For two-dimensional periodic potentials without a tilt, we… (More)

The perturbation theory based on the Riemann-Hilbert problem is developed for the modified nonlinear Schrödinger equation which describes the propagation of femtosecond optical pulses in nonlinear single-mode optical fibers. A detailed analysis of the adiabatic approximation to perturbation-induced evolution of the soliton parameters is given. The linear… (More)

We derive the soliton matrices corresponding to an arbitrary number of higherorder normal zeros for the matrix Riemann–Hilbert problem of arbitrary matrix dimension, thus giving the complete solution to the problem of higher-order solitons. Our soliton matrices explicitly give all higher-order multisoliton solutions to the nonlinear partial differential… (More)

- Anton S Desyatnikov, Yuri S Kivshar, Valery S Shchesnovich, Solange B Cavalcanti, Jandir M Hickmann
- Optics letters
- 2007

We study Zener tunneling in two-dimensional photonic lattices and derive, for the case of hexagonal symmetry, the generalized Landau-Zener-Majorana model describing resonant interaction between high-symmetry points of the photonic spectral bands. We demonstrate that this effect can be employed for the generation of Floquet-Bloch modes and verify the model… (More)

- Valery S Shchesnovich, Solange B Cavalcanti, Jandir M Hickmann, Yuri S Kivshar
- Physical review. E, Statistical, nonlinear, and…
- 2006

We discuss the interband light tunneling in a two-dimensional periodic photonic structure, as studied recently in experiments for optically induced photonic lattices [Trompeter, Phys. Rev. Lett. 96, 053903 (2006)]. We identify the Zener tunneling regime at the crossing of two Bloch bands, which occurs in the generic case of a Bragg reflection when the Bloch… (More)

- Valery S Shchesnovich, Sabino Chávez-Cerda
- Optics letters
- 2007

We show that propagation of optical beams in periodic lattices induces power oscillations between the Fourier spectrum peaks, with the indices related by the Bragg resonance condition. In the spatial coordinates, this is reflected in the beam position oscillations. A simple resonant theory explains the phenomenon. The effect can be used for controlled… (More)

We use the Riemann-Hilbert problem to study the interaction of the soliton with radiation in the parametrically driven, damped nonlinear Schrödinger equation. The analysis is reduced to the study of a finite-dimensional dynamical system for the amplitude and phase of the soliton and the complex amplitude of the long-wavelength radiation. In contrast to… (More)

We investigate, analytically and numerically, families of bright solitons in a system of two linearly coupled nonlinear Schrödinger/Gross-Pitaevskii equations, describing two Bose-Einstein condensates trapped in an asymmetric double-well potential, in particular, when the scattering lengths in the condensates have arbitrary magnitudes and opposite signs.… (More)

- Valery S. Shchesnovich
- ArXiv
- 2015

We study the closeness of an experimental unitary bosonic network with only partially indistinguishable bosons in an arbitrary mixed input state, in particular an experimental realization of the Boson-Sampling computer, to the ideal bosonic network, where the measure of closeness of two networks is the trace distance between the output probability… (More)

Abstract We explore the conditions under which identical particles in unitary linear networks behave as the other species, i.e. bosons as fermions and fermions as bosons. It is found that the BosonSampling computer of Aaronson & Arkhipov can be implemented in an interference experiment with non-interacting fermions in an appropriately entangled state.… (More)