Computer simulation and observation of anomalous light emission from nonlinear photonic crystal with various geometry of its elements

Recently, in papers [1, 2] were described the effect of long-time emission of photonic crystal (synthetic opals) under the action of nanosecond laser pulse. The duration of the luminescence is of the order of seconds. Despite on the other phenomena, which were considered in these papers, below we focus our attention on possible explanation of long time emission from nonlinear photonic crystal. The basis of our consideration is papers [3, 4], those deal with soliton formation in several layers of 1D nonlinear photonic crystal. Because of this, the light wave can exist in photonic crystal a long time (in ideal case—infinite time interval). Taking into account a relation between soliton duration and its maximum intensity, the leaving of laser energy from the layer of photonic crystal takes place due not full reflection from boundaries of layer. The time of light emission for this case depends on nonlinear susceptibility of photonic crystal and the intensity of laser pulse. Hence, soliton formation inside the nonlinear elements of photonic crystal can be one of the reasons of long time emission. We got in computer simulation a long time emission of 1D (layered) and 2D (circular or rectangular elements) nonlinear photonic crystal under the action of laser pulse with femtosecond duration under the conditions of soliton formation in some elements of photonic crystal. Input intensity of laser pulse, at which a soliton appears in nonlinear photonic crystal, can be ten times less due to effects of enhancement of optical intensity in periodic structure [4, 5].     

双零色散光子晶体光纤结构参数的变化对其性能的影响

应用多极法,研究了正六边形结构光子晶体光纤的结构参数改变时,波长范围在0.8—1.8μm之间的双零色散光子晶体光纤的色散特性和非线系数随波长的变化规律.对具有相同结构参数的正六边形结构和正八边形结构进行比较,得到正六边形结构的双零色散光子晶体光纤的色散更加平坦,非线性系数有明显增大的结果.因此,正六边形结构更容易获得色散平坦的高非线性双零色散光子晶体光纤.最终设计了在800nm附近具有平坦色散和高非线性的正六边形双零色散光子晶体光纤.     

三种典型结构光子晶体光纤基本特性的比较和分析

应用多极法比较和分析了相同结构参数下的正六边形、正八边形和正十边形光子晶体光纤的色散系数、色散斜率、非线性系数和限制损耗.正六边形光子晶体光纤更适合用于色散补偿和高非线性的研究,在波长0.8 μm处的非线性系数达到了0.37 m^-1·W^-1;正十边形光子晶体光纤更适合用于色散平坦和低限制损耗的研究,在波长0.8 μm处的限制损耗相对正六边形光子晶体光纤减小了约3000个数量级,在1.4—1.65 μm波长范围内,正十边形光纤的色散系数介于-0.07—0.17 p     

Enhanced optical nonlinearity near the photonic bandgap edges of a cholesteric liquid crystal

The third-order Kerr nonlinear optical effect of a one-dimensional photonic bandgap structure of a cholesteric liquid crystal is investigated. In a femtosecond nonlinear transmission measurement, nonlinear optical changes in the bandgap edges are observed. From analysis of the dispersion relation, Kerr nonlinear coefficients of nematics, forming the cholesteric liquid crystal, are found to be enhanced by 1-2 orders of magnitude through the photonic bandgap structure.     

Matter-wave gap solitons in atomic band-gap structures

We demonstrate that a Bose-Einstein condensate in an optical lattice forms a reconfigurable matter-wave structure with a band-gap spectrum, which resembles a nonlinear photonic crystal for light waves. We study in detail the case of a two-dimensional square optical lattice and show that this atomic band-gap structure allows nonlinear localization of atomic Bloch waves in the form of two-dimensional matter-wave gap solitons.     

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.     

A diffractive study of optical parametric interactions in nonlinear photonic crystals

With the nonlinear diffraction concept, we present a diffractive study of optical parametric interactions in nonlinear photonic crystals. The nonlinear diffraction concept enables the design of complicated nonlinear photonic crystal structures in an intuitive way. We show that there are two basic linear sequences, the anti-stacking and the para-stacking sequences, existing in a one-dimensional structure; and we present the realization of multiple phase-matching resonances in the combination of the two basic sequences. The parameters affecting the structure factor of a two-dimensional nonlinear photonic crystal are investigated, which indicate that not only the Ewald construction but also the relative domain size determines two-dimensional nonlinear diffractions.     

光子晶体光纤非线性光谱特性的理论与实验研究

光子晶体光纤具有特殊的导光机制和结构可调性,可以产生奇异的色散特性及高非线性,为非线性光纤光学领域的研究提供了新的条件。受多种非线性光学效应的共同作用,在不同泵浦光脉冲参数条件下,不同结构参数及传输特性的光子晶体光纤能产生丰富的非线性光谱。利用分步傅里叶方法求解非线性薛定谔方程,模拟飞秒激光脉冲在光子晶体光纤中的传输过程,获得输出光谱与入射光脉冲参数(泵浦光峰值功率P、泵浦光波长λ、光脉冲形状、光脉冲宽度T_FWHM)、光纤结构参数(孔间距Λ、空气填充比d/Λ、光纤长度z)、传输特性(色散、非线性系数)的关系,分析拉曼孤子、色散波、自相位调制等非线性效应产生的光谱特性。利用光子晶体光纤包层节区进行非线性光学实验研究,获得了孤子波和色散波的宽带光谱输出。理论分析与实验测量的光谱中都包括了波长0.5 μm附近可见光波段的蓝移色散波、0.82 μm波段的剩余泵浦光、1.1 μm波段的孤子波、2 μm附近的红移宽带色散波。理论分析与实验测量结果一致,阐明光子晶体光纤中非线性光谱产生的物理原理,实现了对宽带光谱的可控输出,为高非线性光子晶体光纤的结构设计、制备及非线性光谱的应用研究奠定基础。     

Anisotropy of nonlinear optical transmission at the edge of the photonic band gap of an apodized layered medium

The effect of Kerr nonlinearity on the transmission of laser radiation in a one-dimensional photonic crystal has been investigated by the transfer-matrix method, modified to describe nonlinear effects. The crystal under study is a thin-film multilayer structure with a spatial distribution of the refractive index, which makes it possible to eliminate side bands in the transmission spectrum at each side of the photonic band gap and significantly increase the slope of the transmission curve. The transmission spectrum of such a photonic crystal structure has been studied for two opposite directions of laser radiation propagation. The anisotropy of nonlinear transmission is most pronounced near the edge of the photonic crystal band gap, which lies in the near-IR region. The proposed structure, having strong transmission anisotropy and sufficiently low reflection in the forward direction, can operate as an optical diode (analog of an electron diode).     

Determination of optical Kerr nonlinearity of a photonic bandgap structure by Z-scan measurement

Through analysis of the dispersion relation in a photonic bandgap structure, the effective optical Kerr nonlinearity that determines a Z-scan profile particularly near the stop-band edges, is derived. Near and inside the stop band, the nonlinear optical phase change that originates from an off-resonant response is converted into a change in nonlinear optical intensity through Bragg reflection. The Z-scan measurement of a cholesteric liquid-crystal photonic bandgap structure confirmed that off-resonant Kerr nonlinearity is responsible for the characteristic open-aperture Z-scan profiles near the stop-band edges.     

Analytical solution for the field in photonic structures containing cubic nonlinearity

In this work, we consider the exact solution of the stationary cubic nonlinear equation in a semi-infinite nonlinear medium in contact with a one-dimensional photonic crystal. Two kinds of analytical solutions are found for an arbitrary magnitude of the nonlinearity: a standing-wave-like one containing the inverse elliptic function Eli(?∣m), and a one-wave-type solution for transmitted TE-polarized waves. An approximate two-wave solution is proposed to describe the field propagation through the nonlinear film covering the photonic crystal. It is shown that the problem of a mixed linear-nonlinear structure may be reduced to a transcendental kernel equation determining the field inside the nonlinear part of the medium. The light reflection from a Si/SiO₂ layered structure in contact with an optically nonlinear medium is calculated. The angular-frequency photonic band diagram and power dependency are investigated. Local interface waveguide modes are considered.     

Nonlinear properties of a graded-index photonic heterostructure

The optical properties of a one-dimensional (1D) photonic heterostructure with graded-index nonlinear materials are demonstrated theoretically. The influence of the gradation profile of the graded-index nonlinear layers on the linear and nonlinear responses of the structure are analysed. It is shown that the Q-factor of the defect mode and the threshold input intensity to achieve the optical bistability in the used photonic heterostructure depend on the gradation profile of the graded-index nonlinear layers.     

二维周期光子晶格中的非线性Landau-Zener隧穿

在二维周期光子晶格中研究了Kerr型非线性Landau-Zener隧穿. 首先在六方晶系光子晶格中推导出非线性三能级Landau-Zener隧穿模型, 在特殊初值条件下将其转化为非线性二能级模型. 对于三能级隧穿模型, 选择特殊初值, 研究了隧穿率随参数的变化规律. 关键词： 光子晶格 Kerr型非线性 Landau-Zener隧穿     

Tunable femtosecond frequency doubling in random domain structure of strontium tetraborate

Efficient tunable femtosecond phase-matched noncollinear second-harmonic generation in randomized nonlinear photonic crystal of strontium tetraborate is obtained. Spatial spectrum of nonlinear photonic structure is not flat but enables tuning of the harmonic frequency in the range from 355 to 460 nm. The narrowing of the bandwidth of second harmonic is found to be of order of 10-20%.     

非线性曝光对三维全息光子晶体禁带特性的影响

从理论和实验两方面研究了非线性曝光对全息方法制作光子晶体的影响.使用低折射率材料（n=152）制作了金刚石结构光子晶体,通过控制曝光量使记录介质工作在非线性曝光区域,发现光子禁带的特性得到了明显的改善.并由此提出了用低折射率材料实现全空间禁带的设想. 关键词： 光子晶体 光学全息 非线性曝光     

Improvement of characterization accuracy of the nonlinear photonic crystals using finite elements-iterative method

We investigate nonlinear one- and two-dimensional photonic crystals by applying a finite element-iterative method. Numerical results show the essential influence of nonlinear elements embedded into a quarter-wave stack and the sharp photonic crystal waveguide bend on the spectral characteristics of these structures. We compare our results with those obtained in [21] from the discrete equation method for the case of a sharp waveguide bend. The comparison shows that neglecting the nonuniform field distribution inside the embedded nonlinear elements leads to overestimation of the waveguide bend transmissivity. PACS 42.65.-k; 42.70.Qs     

Optical vortex solitons and soliton clusters in photonic crystal fibres

We study higher-order nonlinear modes in the form of vortex solitons and soliton clusters propagating in the waveguides created in photonic crystal fibers made of a material with the focusing Kerr nonlinearity. We find numerically different families of such nonlinear modes with a nontrivial topology and study their bifurcations. We also study the soliton stability to propagation. We demonstrate that waveguides in photonic crystal fibers may support a variety of soliton clusters with the symmetries that may differ from the lattice symmetry. We also discuss briefly the case of a dual-core coupler created by two neighboring cores in a photonic crystal fiber and find numerically the profiles of symmetric and asymmetric nonlinear modes.     

Conical second harmonic generation in a two-dimensional chi(2) photonic crystal: a hexagonally poled LiTaO3 crystal

A new type of conical second-harmonic generation was discovered in a 2D chi((2)) photonic crystal-a hexagonally poled LiTaO3 crystal. It reveals the presence of another type of nonlinear interaction-a scattering involved optical parametric generation in a nonlinear medium. Such a nonlinear interaction can be significantly enlarged in a modulated chi((2)) structure by a quasi-phase-matching process. The conical beam records the spatial distribution of the scattering signal and discloses the structure information and symmetry of the 2D chi((2)) photonic crystal.     

Formation of transverse structure of CW light beams in photonic crystal fibers with saturable gain

Transverse beam dynamics in a nonlinear photonic crystal fiber is studied numerically. The field decomposition in terms of Laguerre-Gaussian functions is used to simulate the propagation of a beam along the fiber. Symmetry breakdown due to the competition of transverse modes is demonstrated. Both the few-mode photonic crystal fiber and the endlessly single-mode photonic-crystal fiber are considered. In the photonic crystal fiber with broad gain region, the resulting beam structure is shown to depend strongly upon the initial conditions.     

Nonlinear photonic crystals as a source of entangled photons

Nonlinear photonic crystals can be used to provide phase matching for frequency conversion in optically isotropic materials. The phase-matching mechanism proposed here is a combination of form birefringence and phase velocity dispersion in a periodic structure. Since the phase matching relies on the geometry of the photonic crystal, it becomes possible to use highly nonlinear materials. This is illustrated considering a one-dimensional periodic Al0.4Ga0.6As/air structure for the generation of 1.5 microm light. We show that phase-matching conditions used in schemes to create entangled photon pairs can be achieved in photonic crystals.