Reduction of the pump power threshold in the nonlinear all-optical photonic crystal directional coupler switches

In this paper, the cross-phase modulation Kerr nonlinear effect is utilized to induce nonlinearity and a change in the coupling length by a high-intensity pump signal in the nonlinear photonic crystal directional coupler. We have analyzed and modified the nonlinear square-lattice directional couplers for the first time, to the best of our knowledge, and have improved the power consumption for inducing the nonlinear switching. We have shown that according to the slower group velocity and the increased confinement of the TM modes with lower frequency in the region with a higher dielectric constant in a square lattice, the required switching pump power of the structure is less than that of the same triangular structure.     

Kerr nonlinear coupler with varying linear coupling coefficient

Abstract

We investigate a codirectional nonlinear coupler composed of two Kerr nonlinear waveguides. Unlike the conventional device, the linear coupling between the guides is supposed to be a variable function of the propagation distance. We calculate quantum statistical and dynamical properties of the Kerr nonlinear coupler with a coherent input and analyse the influence of coupling variation on oscillations in mean photon number. The possibility to control the switching characteristics and principal squeezing effect by adjusting the form of coupling function is shown.     

Optical switching and normal mode splitting in hybrid semiconductor microcavity containing quantum well and Kerr medium driven by amplitude-modulated field

ABSTRACT

We theoretically investigate optical bistability/multistability for all optical switching signature in a hybrid semiconductor microcavity system comprising a quantum well and a Kerr nonlinear substrate. The system is essentially two optically coupled microcavities with one of the microcavity being driven by an external amplitude-modulated pump laser. We show that the switching between bistable and multistable behaviour is influenced by the modulated pump laser, Kerr nonlinearity and the optical coupling between the two microcavities. We further investigate the intracavity spectrum of quantum fluctuations which exhibit the well-known normal mode splitting (NMS). The NMS behaviour is also found to be influenced by the system parameters. These results demonstrate that the present hybrid nonlinear system can be used in designing sensitive optical devices.     

Non-classical Light in Nonlinear Symmetric and Asymmetric Couplers

Abstract

We derive the quantum-statistical properties of light beams in nonlinear symmetric and asymmetric couplers composed of linear waveguides and a nonlinear waveguide operating by the second-harmonic generation. This device can exhibit non-classical behaviour in single and compound modes and produce squeezed and/or sub-Poissonian light. Power solutions are obtained up to the twelfth order adopting a symbolic computer method. In addition, new higher-order results for the asymmetric coupler are presented.     

Two-dimensional solitons in a Kerr cavity

Abstract

We study the existence and nature of soliton-like localized states in a passive cavity containing a Kerr medium driven by a plane-wave input field. As the background intensity is increased, these structures are always created in pairs, for topological reasons. The smaller ‘soliton’ is always unstable, while in two transverse dimensions the larger ‘soliton’ usually collapses to a singularity or decays.     

Switching and self-trapping dynamics of bose-Einstein solitons

Abstract

We investigate the dynamics of two weakly coupled Bose condensates in long cigar-shaped traps. The Bose condensates are characterized by attractive mean-field interaction and consequently can be studied in terms of bright solitons. We exploit the analogy with directional fibre couplers in nonlinear fibre optics to uncover interesting dynamical regimes like switching of condensates from one trap to another and self-trapping of condensates. We also discuss the analogy between two weakly coupled Bose condensates and the Josephson junction in superfluids and superconductors.     

Phase distribution and superstructures on the phase correlation of copropagating electromagnetic fields

Abstract

The phase distribution and phase correlation of two initially coherent electromagnetic field modes copropagating through a lossless nonlinear medium are investigated. We show that the number of distinguishable components in the phase distribution depends on the set of nonlinear parameters through a simple relation and that it is connected with the number of entangled field states as well as the number of components that a single field state acquires after propagating through the medium. The phase correlation between the two field modes is shown to exhibit a rich pattern of collapses and revivals, similar to those observed in the quantum inversion of several generalizations of the Jaynes-Cummings model and is related to beats of the various eigenstates of the total Hamiltonian.     

Nonlinearity-induced Modes and the Frequency Response of Coupled Nonlinear Fabry-Pérot Cavities

Abstract

We study the frequency response of a system of two coupled Kerr nonlinear cavities with the same or opposite signs of nonlinearity. In the framework of a slowly varying envelope approximation, we show the possibility of having various hysteresis loops in the transmission characteristics of the structure. We also investigate the power-dependent modes of the structure. For large powers we demonstrate the existence of new modes which do not have any linear analogue. These nonlinearity-induced modes show up in the multistable output when the input power is varied.     

Quantum statistics and dynamics of nonlinear couplers

Abstract

We investigate both codirectional and contradirectional nonlinear couplers composed of two nonlinear waveguides operating by second-harmonic generation. We take into account possible mismatches inside the waveguides and between them. We calculate the photon number distribution, its factorial moments, quadrature and integrated intensity variances and quadrature uncertainty product taking into account the effects of transmission of light between waveguides. Incident beams are assumed to be coherent, squeezed and mixed with external noise. Second-harmonic modes are assumed to be pumped with strong coherent beams. We show that non-classical behaviour of beams generated by the nonlinear waveguides can be transferred between them and controlled by linear and nonlinear mismatches. In the contradirectional regime of propagation, asymptotic non-classical states can be generated.     

Optical solitons in nonlinear directional couplers with spatio-temporal dispersion

This paper addresses solitons in nonlinear directional couplers in non-Kerr law media, with spatio-temporal dispersion. Both twin-core couplers as well as multiple-core couplers are studied. The nonlinearities studied are Kerr law, power law, parabolic law, dual-power law and log law. Bright, dark and singular soliton solutions of the governing equation are studied.     

Spatial Chaotic Power Cross-talk in Nonlinear Multibeam Co-propagation in Optical Fibres

Abstract

We investigate spatial power coupling and chaotic cross-talk when beams co-propagate in multimode optical fibres, specifically among four beams that belong to two weakly degenerate mode families. The nonlinear mechanism responsible for the power and phase coupling is the optical Kerr effect in fibres. The power of each of the modes is theoretically demonstrated to be spatially unstable and chaotically dependent on launch conditions. It is shown that the spatial instabilities and irregular energy exchange occur over broad operating conditions as long as the system deviates from its spatial steady states.     

Waveguide confinement of cerenkov second-harmonic generation through a graded-index grating coupler: Electromagnetic optimization

Abstract

The feasibility of making a frequency doubler for integrated optics is studied with the electromagnetic theory of gratings and graded-index waveguides as a tool. The device consists of a first waveguide filled with a sol-gel nonlinear material doped or grafted with a nonlinear chromophore whose thickness is chosen to generate a second-harmonic Cerenkov radiation in a dispersive glass substrate. The Cerenkov radiation is coupled into a second waveguide through a graded-index layer produced by ion exchange into glass, lying on top of an ion-etched grating coupler. The aim of the study is to optimize the optogeometrical parameters of the device in order to obtain a resonance line of the second waveguide modes that has an angular width large enough to match the experimental constraints, and which leads to a good enough coupling coefficient. The electromagnetic theory of grating couplers is developed into an S-matrix propagation algorithm form in order to be combined with the electromagnetic analysis of the thick graded-index waveguide with a view to analysing the device.     

Influence of Kerr-like medium on the dynamics of a two-mode Raman coupled model

Abstract

We study the quantum dynamics of an effective two-level atom interacting with two modes via Raman process inside an ideal cavity in the presence of Kerr non-linearity. The cavity modes interact both with the atom as well as the Kerr-like medium. The unitary transformation method presented here, not only solves the time-dependent problem, but also provides the eigensolutions of the interacting Hamiltonian at the same time. We study the atomic-population dynamics and the dynamics of the photon statistics in the two cavity modes. The influence of the Kerr-like medium on the statistics of the field is explored and it is observed that Kerr medium introduces antibunching in mode 1 and this effect is enhanced by a stronger interaction with the non-linear medium. In the high non-linear coupling regime anticorrelated beam become correlated. Kerr medium also introduces non-classical correlation between the two modes.     

Phase Properties of Elliptically Polarized Light Propagating in a Kerr Medium

Abstract

Phase properties of elliptically polarized light propagating through a nonlinear Kerr medium are considered within the framework of the Pegg-Barnett Hermitian phase formalism. The joint phase probability distribution function for the phases of two orthogonal modes describing elliptical polarization of the field is calculated and its evolution discussed and illustrated graphically. The marginal phase probability distribution for the individual phases are also calculated and discussed. Analytical formulae for phase expectation values and variances are derived for the individual phases as well as for the phase difference. It is shown that in the course of propagation the correlation between the phases of the two modes builds up. This correlation is responsible for lowering phase difference variance. The expressions for the sine and cosine functions and their variances of the individual phases as well as the phase difference are obtained and discussed. The effect of randomization of individual phases and the phase difference, which is a purely quantum effect, is shown to appear during propagation. The relation between phase randomization and degradation of the degree of polarization of the light is established.     

Nonlinear quantum optical computing via measurement

Abstract

We show how the measurement induced model of quantum computation proposed by Raussendorf and Briegel (2001, Phys. Rev. Letts., 86, 5188) can be adapted to a nonlinear optical interaction. This optical implementation requires a Kerr nonlinearity, a single photon source, a single photon detector and fast feed forward. Although nondeterministic optical quantum information proposals such as that suggested by KLM (2001, Nature, 409, 46) do not require a Kerr nonlinearity they do require complex reconfigurable optical networks. The proposal in this paper has the benefit of a single static optical layout with fixed device parameters, where the algorithm is defined by the final measurement procedure.     

Four-mode Squeezing and Applications

Abstract

The interactions among radiation modes in optical fibres and other Kerr media can create correlations among two, four or more distinct field components. These correlations can reduce the noise levels found with various detector schemes. Some interactions produce the correlations required for quantum non-demolition detection.     

Periodic and solitary wave solutions for ultrashort pulses in negative-index materials

Abstract

We present a detailed analysis for the existence of dark and bright solitary waves as also fractional-transform solutions in a nonlinear Schrödinger equation model for competing cubic–quintic and higher-order nonlinearities with dispersive permittivity and permeability. Parameter domains are delineated in which these ultrashort optical pulses exist in negative-index materials (NIMs). For example, dark solitons exist for the case of normal second-order dispersion, anomalous third-order dispersion, self-focusing Kerr nonlinearity, and non-Kerr nonlinearities, while the bright solitons exist for the case of anomalous second-order dispersion, normal third-order dispersion, self-focusing Kerr nonlinearity, and non-Kerr nonlinearities. This is contrary to the situation in ordinary materials.     

Propagation of (2 + 1)-dimensional solitary waves in dissipative/active saturable nonlinear media

Abstract

We investigate the propagation of (2 + 1)D bright solitary waves in a saturable nonlinear medium perturbed with gain or loss. We find that in the presence of loss (gain) the amplitude and width of the (2 + 1)D bright solitary waves may both increase (decrease) with their product varying adiabatically during evolution. This is in contrast to the (1 + 1)D Kerr bright (dark) solitons or (2 + 1)D vortex solitons whose amplitude decreases (increases) at the same rate as the width increases (decreases), keeping their product unchanged with the propagation distance. For a very weak nonlinear saturation approaching Kerr nonlinearity, it is found that the amplitude and the width change at a rate faster than the (1 + 1)D Kerr bright and dark solitons, whereas their variation in highly saturable media is slower than the (1 + 1) or (2 + 1)D Kerr dark solitons. In a medium of moderate nonlinear saturation, the beam width and amplitude may vary in the way following that of high nonlinear saturation or weak nonlinear saturation or a combination of the two, depending on loss or gain and propagation distance.