Bloch-wave packet control in truncated modulated optical lattices

We study the reflection of Bloch wave packets at the interface of an optical lattice possessing a shallow longitudinal out-of-phase refractive index modulation in the adjacent waveguides. We show that the relation between the transmitted and reflected energy flows can be efficiently controlled by tuning the frequency and depth of the modulation. Thus, complete beam reflection may be achieved for a set of resonant modulation frequencies at which light tunneling between adjacent guides of modulated lattice is inhibited.     

Tunable soliton self-bending in optical lattices with nonlocal nonlinearity

We address the phenomenon of soliton self-bending in Kerr-type nonlocal nonlinear media with an imprinted transverse periodic modulation of the linear refractive index. We show that the imprinted optical lattice makes possible to control the mobility of soliton by varying the depth and the frequency of the linear refractive index modulation.     

Two-dimensional array of room-temperature nanophotonic logic gates using InAs quantum dots in mesa structures

We present a detailed study of the dynamics of light in passive nonlinear resonators with shallow and deep intracavity periodic modulation of the refractive index in both longitudinal and transverse directions of the resonator. We investigate solutions localized in the transverse direction (so-called Bloch cavity solitons) by means of envelope equations for underlying linear Bloch modes and solving Maxwell’s equations directly. Using a round-trip model for forward and backward propagating waves we review different types of Bloch cavity solitons supported by both focusing (at normal diffraction) and defocussing (at anomalous diffraction) nonlinearities in a cavity with a weak-contrast modulation of the refractive index. Moreover, we identify Bloch cavity solitons in a Kerr-nonlinear all-photonic crystal resonator solving Maxwell’s equations directly. In order to analyze the properties of Bloch cavity solitons and to obtain analytical access we develop a modified mean-field model and prove its validity. In particular, we demonstrate a substantial narrowing of Bloch cavity solitons near the zero-diffraction regime. Adjusting the quality factor and resonance frequencies of the resonator optimal Bloch cavity solitons in terms of width and pump energy are identified.     

Stabilization of three-dimensional light bullets by a transverse lattice in a Kerr medium with dispersion management

We demonstrate a possibility to stabilize three-dimensional spatiotemporal solitons (“light bullets”) in self-focusing Kerr media by means of a combination of dispersion management in the longitudinal direction (with the group-velocity dispersion alternating between positive and negative values) and periodic modulation of the refractive index in one transverse direction (out of the two). Assuming the usual model based on the paraxial nonlinear Schrödinger equation for the local amplitude of the electromagnetic field, the analysis relies upon the variational approximation (results of direct three-dimensional simulations will be reported in a follow-up). A predicted stability area is identified in the model’s parameter space. It features a minimum of the necessary strength of the transverse modulation of the refractive index, and finite minimum and maximum values of the soliton’s energy. The former feature is also explained analytically.     

Short chirp pulses in graded-index light guides

We consider the nonlinear process of propagation of a short chirp optical pulse in a light guide in which the refractive index of a fiber material strongly depends on the radial coordinate and weakly depends on the longitudinal coordinates. The chirped and strongly chirped pulses are distinguished by the relationship between the modulation depth and the spectrum width. The chirp-pulse propagation is simulated by a nonlinear wave equation solved asymptotically with respect to the small parameter prescribing the order of magnitude of the pulse amplitude. It is shown that the pulse propagation is three-scale. The phase of high-frequency filling and the field distribution in the fiber cross section are obtained as the eigenvalue and eigenfunction of a singular Sturm-Liouville problem, respectively. On the additional assumption of longitudinal inhomogeneity of the fiber, the general equation for the pulse envelope is reduced to the second Painlevé equation. It is shown that the linear modulation of the carrier frequency is not an independent characteristic of the propagation process, but varies in certain accordance with parameters of the transverse and longitudinal inhomogeneities of the fiber. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 49, No. 1, pp. 64–71, January 2006.     

Optical filaments and optical bullets in dispersive nonlinear media

We have investigated the evolution of picosecond and femtosecond optical pulses governed by the amplitude vector equation in the optical and UV domains. We have written this equation in different coordinate frames, namely, in the laboratory frame, the Galilean frame, and the moving-in-time frame and have normalized it for the cases of different and equal transverse and longitudinal sizes of optical pulses or modulated optical waves. For optical pulses with a small transverse size and a large longitudinal size (optical filaments), we obtain the well-known paraxial approximation in all the coordinate frames, while for optical pulses with relatively equal transverse and longitudinal sizes (so-called light bullets), we obtain new non-paraxial nonlinear amplitude equations. In the case of optical fields with low intensity, we have reduced the nonlinear amplitude vector equations governing the light-bullet evolution to the linear amplitude equations. We have solved the linear equations using the method of Fourier transform. An unexpected new result is the relative stability of light bullets and the significant decrease in the diffraction enlargement of light bullets with respect to the case of long pulses in the linear propagation regime.     

温度对铌酸锂电光相位调制特性的影响

利用折射率椭球基本理论对线性电光效应进行了分析,对单轴晶体铌酸锂电光相位调制器的温度特性进行了研究。通过计算机进行数值模拟计算,分析了加电场时光通过LiNbO3电光调制器后出射光的相位变化与温度间的关系,得出在横向和纵向调制中温度对相位改变的影响。研究发现,无论在横向还是在纵向调制下,入射光偏振方向不同但其各自受温度影响的相位变化趋势大体一致,即随着晶体中温度的增加而增大。计算结果表明,LiNbO3电光调制的最佳使用方案为：电场沿x主轴方向施加,入射光偏振方向为感应主轴x’方向,且LiNbO3电光调制器粟用横向相位调制方式。     

Bloch cavity solitons in nonlinear resonators with intracavity photonic crystals

We predict a novel type of cavity solitons, Bloch cavity solitons, existing in nonlinear resonators with the refractive index modulated in both longitudinal and transverse directions and for both focusing (at normal diffraction) and defocusing (at anomalous diffraction) nonlinearities. We develop a modified mean-field theory and analyze the properties of these novel cavity solitons demonstrating, in particular, their substantial narrowing in the zero-diffraction regime.     

Soliton modes, stability, and drift in optical lattices with spatially modulated nonlinearity

We put forward new properties of lattice solitons in materials and geometries where both the linear refractive index and the nonlinearity are spatially modulated. We show that the interplay between linear and out-of-phase nonlinear refractive index modulations results in new soliton properties, including modifications of the soliton stability and transverse mobility, as well as shape transformations that may be controlled, e.g., by varying the light intensity.     

Diffraction of light beams in media with longitudinal-transverse inhomogeneity

A theory has been developed to describe the propagation of planar wave beams in media with linear or nonlinear susceptibility modulated in the transverse and longitudinal directions. The diffraction in curved coupled waveguides and from wedge-shaped inhomogeneities is considered. Ray trajectories are found and the Schrödinger equation for the beam envelope is solved numerically. The spatial dynamics of energy redistribution in the beam cross section is described. Conditions for suppressing the beam spread due to the refractive index modulation are found.     

Slow-light optical bullets in arrays of nonlinear Bragg-grating waveguides

We demonstrate that propagation direction and velocity of optical pulses can be controlled independently in the structures with multiscale modulation of the refractive index in transverse and longitudinal directions. We reveal that, in arrays of waveguides with phase-shifted Bragg gratings, the refraction angle does not depend on the speed of light, allowing for efficient spatial steering of slow light. In this system, both spatial diffraction and temporal dispersion can be designed independently, and we identify the possibility for self-collimation of slow light when spatial diffraction is suppressed for certain propagation directions. We also show that broadening of pulses in space and time can be eliminated in nonlinear media, supporting the formation of slow-light optical bullets that remain localized irrespective of propagation direction.     

强非局域光晶格中空间孤子的脉动传播

根据强非局域结构中空间孤子的演化方程——非局域非线性薛定谔方程,采用分步傅里叶方法,对一维强非局域光晶格结构中空间孤子的脉动传播进行数值研究.分析了孤子的初始光束能量、非局域程度、光晶格调制强度、光晶格周期以及线性折射率的纵向调制率与空间孤子的脉动传播周期之间的关系,并对影响脉动传播的内在物理机制进行了讨论.同时,还研究了在线性折射率纵向调制情况下强非局域光晶格结构中空间孤子传输的开关行为. 关键词： 非局域非线性薛定谔方程 光晶格 空间孤子 光开关     

梯度折射率非局域介质中空间孤子振荡行为研究

应用等效粒子近似方法研究了光学空间孤子在带有局域和非局域非线性横向非均匀介质中的传输动力学行为.发现孤子在传播过程中横向的周期性振荡.折射率调制幅度和波导的归一化宽度决定了振荡周期的大小.介质的非局域对振荡振幅有着较小的影响.模拟了孤子传输过程,所得数值结果与理论分析符合很好.此外,模拟传输还发现多孤子束缚态能够在这个模型中稳定传播.这种振荡特性或许可以应用于光学路由器、转换器、开关等.     

Spatial soliton steering induced by weak nonlocality in optical lattices

We investigate the soliton steering in weakly nonlocal nonlinear media with harmonic modulation of the refractive index. It is shown that the weak nonlocality originated from the nonlocal nonlinear response of medium induces a transverse modulation of the refractive index, which leads to the occurrence of interplay between the weak nonlocality-induced transverse modulation and the harmonic modulation. Thus, one can control the soliton steering in weakly nonlocal medium, such as nematic liquid crystal, by employing the competition between the weak nonlocality parameter and the lattice depth.     

Parametric amplification of soliton steering in optical lattices

We report on the effect of parametric amplification of spatial soliton swinging in Kerr-type nonlinear media with longitudinal and transverse periodic modulation of the linear refractive index. The parameter areas are found where the soliton center motion is analogous to the motion of a parametrically driven pendulum. This effect has potential applications for controllable soliton steering.     

The quantum acousto-optic effect in Bose-Einstein condensate

We investigate the interaction between a single mode light field and an elongated cigar shaped Bose-Einstein condensate (BEC), subject to a temporal modulation of the trap frequency in the tight confinement direction. Under appropriate conditions, the longitudinal sound like waves (Faraday waves) in the direction of weak confinement acts as a dynamic diffraction grating for the incident light field analogous to the acousto-optic effect in classical optics. The change in the refractive index due to the periodic modulation of the BEC density is responsible for the acousto-optic effect. The dynamics is characterised by Bragg scattering of light from the matter wave Faraday grating and simultaneous Bragg scattering of the condensate atoms from the optical grating formed due to the interference between the incident light and the diffracted light fields. Varying the intensity of the incident laser beam we observe the transition from the acousto-optic effect regime to the atomic Bragg scattering regime, where Rabi oscillations between two momentum levels of the atoms are observed. We show that the acousto-optic effect is reduced as the atomic interaction is increased.     

Mode Structure and the Envelope of a Short Pulse in a Graded-Index Optical Fiber with a Longitudinal Inhomogeneity and a Spatial Bending

We consider propagation of a short optical pulse in an optical fiber whose refractive index is strongly dependent on the radial coordinate and is weakly dependent on the longitudinal coordinate with allowance for the possible weak spatial bending of the fiber axis. The three-dimensional nonlinear wave equation modelling the pulse propagation is solved asymptotically with respect to a small parameter specifying the order of magnitude of the pulse amplitude. A relationship between the propagating modes and the eigenvalues and eigenfunctions of the singular Sturm-Liouville problem is established. The pulse propagation is shown to have three scales: the high-frequency carrier is modulated by the envelope which evolves in a two-scale manner and is described by a nonlinear Schrödinger equation whose coefficients depend on the longitudinal coordinate. The transverse distribution of the wave field and the envelope soliton are obtained in terms of elementary functions for several types of transverse and longitudinal inhomogeneities of the fiber. The possibility of controlling the pulse parameters by varying the transverse and longitudinal inhomogeneities of the fiber is pointed out.     

Exact spatial soliton solution for nonlinear Schrödinger equation with a type of transverse nonperiodic modulation

In this paper, we analyze (2 + 1)D nonlinear Schrödinger (NLS) equation based on a type of nonperiodic modulation of linear refractive index in the transverse direction. We obtain an exact solution in explicit form for the (2 + 1)D nonlinear Schrödinger (NLS) equation with the nonperiodic modulation. Finally, the stability of the solution is discussed numerically, and the results reveal that the solution is stable to the finite initial perturbations.     

Broadband amplitude-modulated laser source with high output power for FM/cw lidar transmitter

We are building a long-range FM/cw nonscanning imaging lidar breadboard. This lidar system achieves ranging based on a frequency modulation/continuous wave (FM/cw) technique, implemented by an amplitude modulated mid-IR diode laser transmitter with a linear frequency modulation (LFM) of the subcarrier. Firstly, various schemes of light beam modulation are analyzed. Secondly, we put forward a laser modulation scheme whose core was formed by a 1.55 μm electro-absorption modulated laser diode (EML) and an erbium-doped optical fiber amplifier (EDFA), then a corresponding experimental system architecture and components for light beam modulation and detection are established. Finally, a corresponding experiment of laser beam modulation is completed for the first time. In our experiment, the EML amplitude is modulated by a 200 MHz to 800 MHz LFM signal, whose amplitude value is 2.05 V. The average output power of the modulated laser obtained in the experiment is 10 W, peak power is 16.4 W, and the average modulation depth is 78%. The results of tests predict that this laser modulation scheme is likely to improve the imaging range of the FM/cw lidar.     

Phase and Amplitude Characteristics of Injection Lasers with Allowance for the Effects of Nonlinear Amplification in Current Modulation

The influence of the parameter of amplitude-phase coupling for nonlinear amplification on the phase-frequency characteristics of an injection laser in the regime of pumping current modulation has been investigated theoretically. The parameter is defined as the coefficient of proportionality between changes in the real and imaginary parts of the refractive index during variation of the density of photons in the cavity. The substantial dependence of the coefficient of phase modulation on the parameter of the amplitude-phase coupling for nonlinear amplification at small modulation frequencies is shown. A technique to determine the indicated parameter based on the frequency dependence of the ratio between the coefficients of phase and amplitude modulation is suggested.