Dynamics of Airy beams in parity–time symmetric optical lattices

We investigate the dynamics of airy beams propagating in the parity–time(PT) symmetric optical lattices in linear and nonlinear regimes, respectively. For the linear propagation, the position of the channel guided by the PT lattice can be shifted by tuning the lattice frequency. The underlying physical mechanism of this phenomenon is also discussed. An interesting phenomenon is found in the nonlinear regime in that the airy beam becomes a tilt channel with several Rayleigh lengths. These findings create new opportunities for optical steering and manipulations.     

Localized nonlinear waves in combined time-dependent magnetic–optical potentials with spatiotemporally modulated nonlinearities

We construct explicit novel solutions of the nonlinear Schrödinger equation with spatiotemporal modulation of the nonlinearities and potentials. By using a modified similarity transformation we explore some localized nonlinearities and combined time-dependent magnetic–optical potentials in the form of linear-lattice ones and harmonic-lattice ones. Several families of exact localized nonlinear wave solutions in terms of Mathieu and elliptic functions corresponding to these potentials are then studied, such as snakelike solitons and breathing solitons. The stability of the obtained localized nonlinear wave solutions is investigated numerically such that some stable solutions are found.     

Millimeter-wave modulated optical pulse generated by pulse repetition rate multiplication and temporal Talbot effect

A novel scheme was proposed to generate a millimeter-wave(MMW)optical pulse by combining pulse repetition rate multiplication(PRRM)technology and temporal Talbot effect(TTE).A cascaded Mach- Zehnder interferometer(MZI)lattice was used for PRRM,and a linearly chirped fiber grating(LCFG)was used as TTE.The basic principle was analyzed by using a Gaussian input short pulse and its characteristics were discussed by numerical simulation.It is shown that the proposed scheme is feasible for MMW signal generation and has potential merits for practical application of radio over fiber(ROF)technology.     

The optical properties of two-dimensional Scarff parity–time symmetric potentials

We investigate the optical properties with two-dimensional (2D) Scarff parity–time (PT) symmetric potentials, including linear case, and self-focusing and self-defocussing nonlinear cases. For linear case, the PT-breaking points, the eigenvalues and eigenfunction for different modulated depths of 2D Scarff PT symmetry complex potential are obtained numerically. The PT-breaking points increase linearly with increasing the real part of the modulated depths of PT potential. Below the PT-breaking points, the eigenvalues of linear modes are real, however, eigenvalues of linear modes are complex above the PT-breaking points. For nonlinear cases, the existence of fundamental and multipole solitons is studied in self-focusing and self-defocussing media. The eigenvalue for linear case is equal to the critical propagation constant _bc$b_c$ of soliton existing.     

Bose–Einstein condensation in random potentials

We present a rigorous study of the perfect Bose-gas in the presence of a homogeneous ergodic random potential. It is demonstrated that the Lifshitz tail behaviour of the one-particle spectrum reduces the critical dimensionality of the (generalized) Bose–Einstein Condensation (BEC) to d=1. To tackle the Off-Diagonal Long-Range Order (ODLRO) we introduce the space average one-body reduced density matrix. For a one-dimensional Poisson-type random potential we prove that randomness enhances the exponential decay of this matrix in domain free of the BEC. To cite this article: O. Lenoble et al., C. R. Physique 5 (2004).     

Interaction of Airy–Gaussian beams in saturable media

Based on the nonlinear Schr o¨dinger equation, the interactions of the two Airy–Gaussian components in the incidence are analyzed in saturable media, under the circumstances of the same amplitude and different amplitudes, respectively. It is found that the interaction can be both attractive and repulsive depending on the relative phase. The smaller the interval between two Airy–Gaussian components in the incidence is, the stronger the intensity of the interaction. However, with the equal amplitude, the symmetry is shown and the change of quasi-breathers is opposite in the in-phase case and out-of-phase case. As the distribution factor is increased, the phenomena of the quasi-breather and the self-accelerating of the two Airy–Gaussian components are weakened. When the amplitude is not equal, the image does not have symmetry. The obvious phenomenon of the interaction always arises on the side of larger input power in the incidence. The maximum intensity image is also simulated. Many of the characteristics which are contained within other images can also be concluded in this figure.     

Fluctuations of optical phase of diffracted light for Raman–Nath diffraction in acousto–optic effect

The Raman–Nath diffraction in acousto–optic effect was studied theoretically and experimentally in the paper.Up to now,each order of diffracted light in Raman–Nath diffraction was still considered simply to be just frequency-shifted and to be a plane wave.However,we find that the phase and frequency shifts occur simultaneously and individually in Raman–Nath diffraction.The findings demonstrate that,in addition to the frequency shift,the optical phase of each order of diffracted light is also shifted by the sound wave and fluctuates with the sound wave and is related to the location in the acoustic field from which the diffracted light originates.As a result,the wavefront of each order of diffracted light is modulated to fluctuate spatially and temporally with the sound wave.Obviously,these findings are significant for applications of Raman–Nath diffraction in acousto–optic effect because the optical phase plays an important role in optical coherence technology.     

Pulse loading ~(87)Rb Bose-Einstein condensation in optical lattice:the Kapitza-Dirac scattering and temporal matter-wave-dispersion Talbot effect

<正>We study ~(87)Rb Bose-Einstein condensation(BEC) loading into the pulse of the one-dimensional(1D) optical lattice experimentally.The lattice is turned on abruptly,held constant for a variable time,and then turned off abruptly.The measurement of the depth of the optical lattice is obtained by Kapitza-Dirac scattering.The temporal matter-wave-dispersion Talbot effect with ~(87)Rb BEC is observed by applying a pair of pulsed standing waves(as pulsed phase gratings) with the separation of a variable delay.     

Gyroscopic behavior exhibited by the optical Kerr effect in bimetallic Au–Pt nanoparticles suspended in ethanol

The modification in the third-order nonlinear optical response exhibited by rotating bimetallic Au–Pt nanoparticles in an ethanol solution was analyzed. The samples were prepared by a sol–gel processing route. The anisotropy associated to the elemental composition of the nanoparticles was confirmed by high-resolution transmission electron microscopy and energy-dispersive X-ray spectroscopy measurements. The size of the nanoparticles varies in the range from 9 to 13 nm, with an average size of 11 nm. Changes in the spatial orientation of the nanomaterials automatically generated a variation in their plasmonic response evaluated by UV–Vis spectroscopy. A two-wave mixing experiment was conducted to explore an induced birefringence at 532 nm wavelength with nanosecond pulses interacting with the samples. A strong optical Kerr effect was identified to be the main responsible effect for the third-order nonlinear optical phenomenon exhibited by the nanoparticles. It was estimated that the rotation of inhomogeneous nanostructures can provide a remarkable change in the participation of different surface plasmon resonances, if they correspond to multimetallic nanoparticles. Potential applications for developing low-dimensional gyroscopic systems can be contemplated.     

Coherent manipulation and guiding of Bose–Einstein condensates by optical dipole potentials

The coherent manipulation of Bose–Einstein condensates by far blue detuned optical dipole potentials is discussed in two regimes. The local manipulation of the phase of the condensate wavefunction by temporally applied dipole potentials represents a powerful tool for the design of matter waves. We use this method in particular for the creation of dark solitons in Bose–Einstein condensates and study their dynamics. Spatially inhomogeneous dipole potentials like far blue detuned doughnut laser beams can be used for the creation of Bose–Einstein condensates within a waveguide structure.     

Propagation of an Airy–Gaussian beam in uniaxial crystals

Under the paraxial approximation, the analytical propagation expression of an Airy–Gaussian beam(Ai GB) in uniaxial crystals orthogonal to the optical axis is investigated. The propagation dynamics of the Ai GB is given for different ratios of the extraordinary index to the ordinary refractive index. It has been found that the continuity and the self-bending effect of Ai GB become weaker when the ratio increases. From the figure of the maximum intensity of Ai GB, one can see that the maximum intensity is not monotone decreasing due to the anisotropic effect of the crystals. The intensity distribution of Ai GB in different distribution factors is shown. The Ai GB converges toward a Gaussian beam as the distribution factor increases.     

The effect of perturbedk-selection and gap shrinkage on the optical transitions in III–V semiconductors

Optical transitions in direct semiconductors are governed according to simple one-electron treatment by ak-selection rule, which in doped or mixed crystals is but lifted to some extent (k) caused by 1) shallow impurities, 2) isoelectronic impurities or 3) alloy scattering. Values of k for these mechanisms are given and the implications for line shapes of optical spectra are discussed.Furthermore, as to the position of lines in the optical spectra of highly doped or highly excited crystals, gap shrinkage effects have to be considered, three main mechanisms of which can be distinguished: 1) Quadratic response of the band edges with respect to the fluctuating potential of the (screened) impurities, 2) polaron effects and 3) carrier exchange and correlation effects. Results of theoretical calculation are compared with experimental findings for GaAs and GaP. The practical importance of gap shrinkage effects for gain measurements and for the operation of (Ga, Al) As laser diodes is pointed out.From the Coulomb interaction of the carriers an additional mechanism for the lifting of thek-selection rule (especially valid for pure, but excited semiconductors) can be derived (plasmon coupling): Estimations show that the simplek-selection rule is almost never fulfilled within the energy range of emission spectra and that these spectra can be well explained simply assuming no-k-selection even for pure direct material.     

Function-lock strategy in OR/NOR optical logic gates based on cross-polarization modulation effect in semiconductor optical amplifier

We have studied a function-lock strategy for all-optical logic gate (AOLG) utilizing the cross-polarization modulation (CPM) effect in a semiconductor optical amplifier (SOA).By monitoring the power of logic light,the strategy realized controllable methods to capture OR and NOR functions and switch between them.The strategy has been successfully applied in experiment with 10-Gb/s not-return-to-zero (NRZ) signals,which has a high success-rate above 95% and ensures the high extinction ratio of result light above 11.4 dB.Every step in the strategy has definite numeric evaluation,which provides the potential of automatic implementation.     

Exciton–polaritons in a 2D hybrid organic–inorganic perovskite microcavity with the presence of optical Stark effect

This study investigates the properties of exciton–polaritons in a two-dimensional(2D) hybrid organic–inorganic perovskite microcavity in the presence of optical Stark effect. Through both steady and dynamic state analyses, strong coupling between excitons of perovskite and cavity photons is revealed, indicating the formation of polaritons in the perovskite microcavity. Besides, it is found that an external optical Stark pulse can induce energy shifts of excitons proportional to the pulse intensi...     

Accelerating Airy–Gauss–Kummer localized wave packets

A general approach to generating three-dimensional nondiffracting spatiotemporal solutions of the linear Schrödinger equation with an Airy-beam time-dependence is reported. A class of accelerating optical pulses with the structure of Airy–Gauss–Kummer vortex beams is obtained. Our results demonstrate that the optical field contributions to the Airy–Gauss–Kummer accelerating optical wave packets of the cylindrical symmetry can be characterized by the radial and angular mode numbers.     

Propagation properties of Airy–Gaussian beams

The propagation of the Airy–Gaussian beams is studied in strongly nonlocal nonlinear media analytically and numerically. The linear momentum of the analytical Airy–Gaussian beam solution of the Snyder–Mitchell model is not conservational, which is the reason that results in the disagreement between the analytical Airy–Gaussian beam solution and the numerical simulations of the nonlocal nonlinear Schr?dinger equation in the case of strong nonlocality. The quasi-Airy–Gaussian soliton in the Gaussian-shaped response material can be obtained when the parameter χ ₀ is large enough, and the patterns of Airy–Gaussian beams are variable periodically in liquid crystal material during propagation.     

Fermions in the background of mixed vector–scalar–pseudoscalar square potentials

The general Dirac equation in 1+1$1+1$ dimensions with a potential with a completely general Lorentz structure is studied. Considering mixed vector–scalar–pseudoscalar square potentials, the states of relativistic fermions are investigated. This relativistic problem can be mapped into a effective Schrödinger equation for a square potential with repulsive and attractive delta-functions situated at the borders. An oscillatory transmission coefficient is found and resonant state energies are obtained. In a special case, the same bound energy spectrum for spinless particles is obtained, confirming the predictions of literature. We showed that existence of bound-state solutions is conditioned by the intensity of the pseudoscalar potential, which possess a critical value.     

Control of a Bose–Einstein condensate on a chip by external optical and magnetic potentials

In this paper we explore the possibilities of control of a Bose–Einstein condensate on an atom chip by the use of potentials generated by photonic and magnetic components. We show that the fields produced by both types of components can be modelled by a generic exponential potential and derive analytic expressions that allow for an easy assessment of their impact on a trapped condensate. Using dynamical numerical simulations we study the transport of the condensate between the control structures on a chip. We study in detail different regimes of the condensate behaviour in an evanescent light potential generated by a photonic structure in the vicinity of the condensate and in magnetic potentials generated by a wire or a coil. The calculations are based on the reported parameters of atom chip setups and available photonic and magnetic components. Finally, the model is verified by an experiment with a condensate on an atom chip and a coil.     

Bose–Fermi mixtures in a three-dimensional optical lattice

Using the dynamical mean-field theory and the Gutzwiller method, we study the Mott transition in Bose–Fermi mixtures confined in a three-dimensional optical lattice and analyze the effect of fermions on the coherence of bosons. We conclude that increasing fermion composition reduces bosonic coherence in the presence of strong Bose–Fermi interactions and under the condition of the integer filling factors for composite fermions, which consist of one fermion and one or more bosonic holes. Various phases of the mixtures have been demonstrated including phase separation of two species, coexisting regions of superfluid bosons and fermionic liquids, and Mott regions in the phase space spanned by the chemical potentials of the bosons and the fermions.