Defect vector gap solitons in photonic lattices

The existence and general properties of different kinds of defect vector gap solitons in one dimensional optically induced photonic defect lattice with focusing saturable nonlinearity in photorefractive crystal are analyzed. The defect is well localized in a single site with two existence forms, namely repulsive and attractive defect. Propagation constants of two beams that compose defect vector gap solitons could be from same gap or from different gaps. We show that some kinds of unstable scalar defect gap solitons could be stabilized by their corresponding vector cases.     

二维单斜点阵光子晶体的第一布里渊区及带隙计算

二维单斜点阵光子晶体在光学聚焦器件及光子晶体波导中有重要的应用价值，详细讨论了二维单斜点阵光子晶体的第一布里渊区及带隙计算，并与常规方法计算得出的二维正三角形晶格光子晶体的带隙结构进行了比较.最后讨论了临界条件下二维单斜点阵光子晶体的带隙结构，证明了本方法的有效性.     

Dipole and quadrupole solitons in optically-induced two-dimensional defocusing photonic lattices

Dipole and quadrupole solitons in a two-dimensional optically induced defocusing photonic lattice are theoretically predicted and experimentally observed. It is shown that in-phase nearest-neighbor and out-of-phase next-nearest-neighbor dipoles exist and can be stable in the intermediate intensity regime. There are also different types of dipoles that are always unstable. In-phase nearest-neighbor quadrupoles are also numerically obtained, and may also be linearly stable. Out-of-phase, nearest-neighbor quadrupoles are found to be typically unstable. These numerical results are found to be aligned with the main predictions obtained analytically in the discrete nonlinear Schrödinger model. Finally, experimental results are presented for both dipole and quadrupole structures, indicating that self-trapping of such structures in the defocusing lattice can be realized for the length of the nonlinear crystal (10 mm).     

Interaction between a dark spot and a two-dimensional nonlinear photonic lattice with fully incoherent white light

We study experimentally the interaction of a dark spot with a nonlinear photonic lattice with fully incoherent white light emitted from an incandescent bulb in the self-defocussing photovoltaic media when the dark spot is aimed at different positions of lattices with different lattice spacing. In this case a host of novel phenomena is demonstrated, including dark spot induced lattice dislocation-deformation, the annihilation of the dark spot and so on. Results demonstrate that the interaction between incoherent dark spot and photonic lattice is always attraction and the large-spacing photonic lattice is analogous to the continuous medium.     

Bloch oscillations and Zener tunneling in two-dimensional photonic lattices

We report on the first experimental observation of photonic Bloch oscillations and Zener tunneling in two-dimensional periodic systems. We study the propagation of an optical beam in a square lattice superimposed on a refractive index ramp. We observe oscillations of the beam inside the first Brilloin zone and tunneling of light from the first to the higher-order bands of the lattice band gap spectrum.     

Supercontinuum generation in a two-dimensional photonic kagome crystal

We demonstrate the generation of ultrabroad spectra in a photonic crystal fiber with a kagome-lattice transverse structure. This two-dimensional periodic photonic lattice allows for strong confinement of light without employing defect states nor using photonic bandgap guiding. Light guiding is mediated by total internal reflection in the intersections of the lattice structure, similar to tapered or micro-structured fibers. The kagome lattice structure is manufactured from a soft glass with a high nonlinearity. Using a Ti:sapphire oscillator as a pump source, we observe for the first time impressive supercontinuum generation in the guided modes of a 2D photonic lattice. Supercontinuum generation is caused by fission and radiation of higher-order solitons in the anomalous dispersion range. Our spectrum encompasses the spectral range from 200 to 1750 nm. The dependence of the continuum on coupling spot location, fiber length, and pump wavelength and power as well as on pulse duration and polarization state is investigated. Using a numerical simulation for the lattice structure, pulse propagation through this structure is theoretically studied. Our model reveals the mechanism of supercontinuuum generation in the 2D photonic structure and explains the essential experimental findings.Electronic supplementary material to this article is avaiable at and accessible for authorized users.     

White-Light Nonlinear Photonic Lattices in Self-Defocusing Media

Using fully incoherent white light emitted from an incandescent lamp and amplitude mask, we experimentally investigate the influence of several factors on the fabrication of the lattice in photovoltaic self-defocusing LiNbO3：Fe crystal, the factors include the orientation of the crystalline c axis relative to the principal axis of the photonic lattice and the filament, the diameter of input dark spot and the separation of the adjacent input dark spots. Experimental results reveal that the best fabricating condition of photonic lattices is that the principal axis of lattice is tilted for 45^o relative to the crystalline c axis which is parallel to the filament of the lamp. In addition, it is necessary that the diameter of the input dark spot is larger than the half of their separation.     

Interaction of two-dimensional spatial incoherent solitons in photorefractive medium

We present a review of our recent theoretical and experimental results on the interaction of incoherent two-dimensional solitary beams in PR SBN crystals. We show that the inherent anisotropy of PR nonlinearity strongly affects the interaction between solitons. Theoretical and experimental results reveal that solitons interacting in a plane perpendicular to the direction of external biasing field always attract, whereas those colliding in a plane of the field exhibit anomalous behaviour. They may experience both attractive and repulsive forces, depending on their mutual separation. We also show that this anisotropy results in the complicated topology of soliton trajectories, featuring periodic collisions, prolonged mutual spiraling and collapse, depending on the initial conditions. Received: 16 November 1998 / Revised version: 12 February 1999 / Published online: 12 April 1999     

Tunable double-channel filter based on two-dimensional ferroelectric photonic crystals

A tunable double-channel filter is presented, which is based on a two-dimensional nonlinear ferroelectric photonic crystal made of cerium doped barium titanate. The filtering properties of the photonic crystal filter can be tuned by adjusting the defect structure or by a pump light. The influences of the structure disorders caused by the perturbations in the radius or the position of air holes on the filtering properties are also analyzed.     

Energy Squeeze of Ultrashort Light Pulse by Kerr Nonlinear Photonic Crystals

Self-phase modulation can efficiently shape the spectrum of an optical pulse propagating along an optical material with Kerr nonlinearity. In this work we show that a one-dimensional Kerr nonlinear photonic crystal can impose anomalous spectrum modulation to a high-power ultrashort light pulse. The spectrum component at the photonic band gap edge can be one order of magnitude enhanced in addition to the ordinary spectrum broadening due to self-phase modulation. The enhancement is strictly pinned at the band gap edge by changing the sample length, the intensity or central wavelength of the incident pulse. The phenomenon is attributed to band gap induced enhancement of light-matter interaction.     

Enlargement of complete two-dimensional band gap by using photonic crystal heterostructure

A two-dimensional photonic crystal heterostructure, which consists of two photonic crystals of a square lattice of circular columns with reverse dielectric configurations, is proposed. Photonic band gap properties are calculated using a plane-wave method and the transmission spectra are obtained. After optimization, the relative width of the complete band gap reached 13.8% based on the simple unit-cell shape and crystal lattice. The photonic crystal heterostructure opens up new ways of engineering photonic band gap materials and designing photonic crystal devices.     

Observation of discrete vortex solitons in optically induced photonic lattices

We report on the first experimental observation of discrete vortex solitons in two-dimensional optically induced photonic lattices. We demonstrate strong stabilization of an optical vortex by the lattice in a self-focusing nonlinear medium and study the generation of the discrete vortices from a broad class of singular beams.     

用双光束干涉制作二维光子晶体

利用双光束干涉,在光敏材料上制作光子晶体结构.通过改变两束光之间的夹角可以改变制备样品的周期.改变曝光次数以及两次曝光时干涉条纹的夹角可以分别得到一维、二维正方晶格以及二维三角晶格结构的光子晶体.     

Brillouin zone spectroscopy of nonlinear photonic lattices

We present a novel, real-time, experimental technique for linear and nonlinear Brillouin zone spectroscopy of photonic lattices. The method relies on excitation with random-phase waves and far-field visualization of the spatial spectrum of the light exiting the lattice. Our technique facilitates mapping the borders of the extended Brillouin zones and the areas of normal and anomalous dispersion within each zone. For photonic lattices with defects (e.g., photonic crystal fibers), our technique enables far-field visualization of the defect mode overlaid on the extended Brillouin zone structure of the lattice. The technique is general and can be used for photonic crystal fibers as well as for periodic structures in areas beyond optics.     

Negative refractive behavior of a two-dimensional negative-index photonic crystals using a wave vector diagram method

We have theoretically studied the negative refractive behavior and the focusing effect in a two-dimensional square-lattice photonic crystal made of air rods in a dielectric background. Detailed explanations are given for the effect of the negative refraction, and the imaging of the plano-concave lens is shown by the use of a wave vector diagram formalism. The typical negative refractive behavior is demonstrated by considering the Bloch mode with the wave vector inside the first Brillouin zone, because only those wave vectors inside the first Brillouin zone of multiple Brillouin zones have a definite meaning. The single propagating beam is analyzed by the use of the wave vector diagram formalism following the folding of the wave vectors. Good-quality focusing of a plane wave can be realized by using a photonic crystal plano-concave lens, while a plane wave is formed by a point source placed at the focal point. Our results are in good agreement with the experimental ones shown for a negative-index plano-concave lens by Vodo et al. [Appl. Phys. Lett. 86 (2005) 201108]. Finally, we also have shown the focusing behavior of a plane wave and a Gaussian pulse by a plano-concave lens structure with high-index modulation instead of air in the concave region.     

Tunable Goos-Hänchen shift for self-collimated beams in two-dimensional photonic crystals

We present finite-difference time-domain studies of the Goos-Hänchen effect observed at the reflection of a self-collimated beam from the surface of a two-dimensional photonic crystal. We describe a method of tuning the shift of the reflected beam in photonic crystals through the modification of the surface, first structurally, as a change in the radius of the surface rods, and then all-optically, with the addition of nonlinear material to the surface layer. We demonstrate all-optical tunability and intensity-dependent control of the beam shift.     

Band gap properties of two-dimensional photonic crystals with rhombic lattice

A new structure of two-dimensional photonic crystals (PCs) with rhombic lattice is proposed in this paper. It provides more flexibility in the design of photonic crystal devices and makes the designer be able to choose a more suitable lattice angle to satisfy different demands. The first Brillouin zone (1st BZ) of this structure is discussed and the general wave vectors are derived. The plane wave expansion (PWE) method is used to analyze the band gap properties. The impact of different lattice angels on the band gaps is analyzed, and the band gap map is also given.     

Discrete light bullets in two-dimensional photonic lattices: Collision scenarios

We report systematic results of collisions between discrete spatiotemporal optical solitons in two-dimensional photonic lattices. We show that the outcomes of collisions strongly depend on the initial soliton parameters, such as their input amplitudes (energies) and their transverse velocities. Four generic outcomes are identified in the study of collisions between discrete light bullets located in the corner, at the edge, and in the center of the photonic lattice: (a) merger of both low and high amplitude solitons into a single one, at small values of the kick parameter (soliton transverse velocity), (b) spreading of low amplitude solitons at intermediate values of the kick parameter, (c) bouncing of high amplitude solitons at intermediate values of the kick parameter, which is accompanied by a sharp modification of input soliton transverse velocities, and (d) quasi-elastic (symmetric) interactions of both low and high amplitude solitons at large values of the kick parameter.     

对称型单负交替一维光子晶体的能带结构

构造了(AB)^N(BA)^N对称型两种单负材料交替一维光子晶体,利用传输矩阵法进行数值模拟.结果表明：这种单负交替对称型一维光子晶体具有一种特殊带隙结构,该带隙不敏感于入射角和晶格的无序性.在该带隙内出现了两个隧穿模,该隧穿模不敏感于入射角的改变和晶格的无序性,但能带及带隙内的隧穿模却敏感于晶格标度和周期数的变化;随着入射角的改变,带隙两侧的隧穿模趋于简并.这些特性对在利用此结构光子晶体设计双重超窄带滤波器时,具有一定的参考价值. 关键词： 光子晶体 单负材料 光子带隙     

Nonlinear three-wave interaction in photonic crystals

We present a multi-scale analysis of nonlinear three-wave-interaction processes in photonic crystals. Based on photonic Bloch functions as carrier waves, we derive the effective nonlinear coupled wave equations that govern pulse propagation in these systems and obtain the corresponding effective photonic crystal parameters directly from photonic band-structure computations. As an illustration, we show how hitherto inaccessible radiation-conversion processes such as wave-front reversal of optical pulses can be realized. Furthermore, we describe a novel regime of nonlinear three-wave interaction in photonic crystals associated with the nearly degenerate case and show how these results may be utilized to study experimentally certain problems from plasma physics and hydrodynamics in the context of nonlinear photonic crystals.