Formation Of Localized Modes Research Articles

Nonlinear switching and solitons in PT‐symmetric photonic systems

AbstractOne of the challenges of the modern photonics is to develop all‐optical devices enabling increased speed and energy efficiency for transmitting and processing information on an optical chip. It is believed that the recently suggested Parity‐Time (PT) symmetric photonic systems with alternating regions of gain and loss can bring novel functionalities. In such systems, losses are as important as gain and, depending on the structural parameters, gain compensates losses. Generally, PT systems demonstrate nontrivial non‐conservative wave interactions and phase transitions, which can be employed for signal filtering and switching, opening new prospects for active control of light. In this review, we discuss a broad range of problems involving nonlinear PT‐symmetric photonic systems with an intensity‐dependent refractive index. Nonlinearity in such PT symmetric systems provides a basis for many effects such as the formation of localized modes, nonlinearly‐induced PT‐symmetry breaking, and all‐optical switching. Nonlinear PT‐symmetric systems can serve as powerful building blocks for the development of novel photonic devices targeting an active light control. image

Wave-packet spreading dynamics under a noninstantaneous nonlinearity: Self-trapping, defocusing, and focusing

Special localized wave modes show up in several physical scenarios including BEC in optical lattices, nonlinear photonic crystals, and systems with strong electron-phonon interaction. These result from an underlying nonlinear contribution to the wave equation that is usually assumed to be instantaneous. Here we demonstrate that the relaxation process of the nonlinearity has a profound impact in the wave-packet dynamics and in the formation of localized modes. We illustrate this phenomenology by considering the one-electron wave packet spreading in a C60 buckball structure whose dynamics is governed by a discrete nonlinear Schrödinger equation with a Debye relaxation of the nonlinearity. We report the full phase diagram related to the spacial extension of the asymptotic wave packet and unveil a complex wave-packet dynamical behavior.

Localized multibunch modes in accelerators

This paper will explore the possibility of the formation of localized modes in the coupled transverse oscillations of bunches in an accelerator. Such modes are characterized by a large amplitude excitation of one of the bunches, with little or no excitation of the other bunches. They are very similar to intrinsic localized modes predicted to appear in lattice excitations of anharmonic condensed matter systems. The existence of the phenomenon in accelerators requires long-range coupling between the bunches, and quartic terms in the effective potential experienced by the bunches. The discussion in this paper considers the specific cases of a long-range coupling due to the resistive wall impedance, and nonlinearities in the transverse force caused by octupoles. The general equations for the localized mode frequencies and amplitudes are derived. The equations are applied to the specific cases of 9 and 21 equally spaced, equally populated bunches in the Cornell electron storage ring. For both cases, with the currently available octupole strength, and with currents of 8 mA per bunch, localized modes with amplitudes of about 2 mm, and with frequency shifts of $50--100\mathrm{s}{}^{\ensuremath{-}1}$ relative to the linear coupled-bunch mode frequencies, may be possible.

Modulational Instability and Energy Localization in a Chain of Interacting Frenkel Excitons**The project supported by National Natural Science Foundation of China and the Fund of the State Education Commission of China

The modulational instability in one-dimensional molecule chain of interacting Frenkel excitons is investigated. The formation of localized modes via modulational instability is predicted and the previous numerical and analytical results are explained. The Peierls-Nabarro (PN) potential barrier for the localized modes is also discussed.

Description of resonant and localized defect vibrations

The vibrational behavior of crystals with point defects is discussed with particular emphasis on defect-induced resonant and localized modes. A method due to Krumhansl and Matthew is applied to obtain a direct description of the local vibrational properties of the defect. For low-frequency resonances an analytic expression of the Green's function of the defect is derived which has the form of the Green's function of the one-dimensional oscillator with an effective force constant ${f}^{\mathrm{eff}}$, an effective mass ${M}^{\mathrm{eff}}$, and a velocity-proportional damping $\ensuremath{\gamma}$. An exact expression for $\ensuremath{\gamma}$ in terms of ${f}^{\mathrm{eff}}$ and ${M}^{\mathrm{eff}}$ is given. Simple approximations for ${f}^{\mathrm{eff}}$ and ${M}^{\mathrm{eff}}$ are discussed, which are not based on the calculation of the perfect lattice Green's function. The method is also applied to resonances just below the maximum frequency, which are connected with the formation of localized modes. Furthermore, a simple derivation of upper and lower bounds for the frequencies of localized modes is presented.