随机性对部分随机介质激光器阈值的影响

基于速率方程和Maxwell方程相结合的模型，采用时域有限差分法(FDTD)研究了介质的随机性和层数对部分随机介质激光器阈值的影响.模拟结果显示，当抽运速率超过阈值时，出现一个或者多个振荡模；随机性或者系统的尺度增加时，振荡模数量也增加；部分随机介质激光器的阈值在一定的随机强度和层数下将达到最小值，它与完全随机情况下的结论有所不同.对所得到的结论给出了物理解释.这些结果对于制作随机激光器和光集成潜在应用价值. 关键词： 激光物理 随机激光器 阈值 时域有限差分法     

Localized mode hybridization by fine tuning of two-dimensional random media

We study numerically the interaction of spatially localized modes in strongly scattering two-dimensional (2D) media. We move eigenvalues in the complex plane by changing gradually the index of a single scatterer. When spatial and spectral overlap is sufficient, localized states couple, and avoided level crossing is observed. We show that local manipulation of the disordered structure can couple several localized states to form an extended chain of hybridized modes crossing the entire sample, thus changing the nature of certain modes from localized to extended in a nominally localized disordered system. We suggest such a chain in 2D random systems is the analog of one-dimensional necklace states, the occasional open channels predicted by Pendry [Physics 1, 20 (2008).] through which the light can sneak through an opaque medium.     

Photon localization laser: low-threshold lasing in a random amplifying layered medium via wave localization

We demonstrate low-threshold lasing in random amplifying layered medium via photon localization. Lasing is facilitated by resonant excitation of localized modes at the pump laser wavelength, which are peaked deep within the sample with greatly enhanced intensity. Emission occurs into long-lived localized modes overlapping the localized gain region. This mechanism overcomes a fundamental barrier to reducing lasing thresholds in diffusive random lasers, in which multiple scattering restricts the excitation region to the proximity of the sample surface.     

Light transport and correlation length in a random laser

A random laser is a strongly disordered, laser‐active optical medium. The coherent laser feedback, which has been demonstrated experimentally to be present in these systems beyond doubt, requires the existence of spatially localized photonic quasimodes. However, the origin of these quasimodes has remained controversial. We develop an analytical theory for diffusive random lasers by coupling the transport theory of the disordered medium to the semiclassical laser rate equations, accounting for (coherent) stimulated and (incoherent) spontaneous emission. From the causality of wave propagation in an amplifying, diffusive medium we derive a novel length scale which we identify with the average mode radius of the lasing quasi‐modes. We show that truly localized modes do not exist in the system without photon number conservation. However, we find that causality in the amplifying medium implies the existence of a novel, finite intensity correlation length which we identify with the average mode volume of the lasing quasimodes. We show further that the surface of the laser‐active medium is crucial in order to stabilize a stationary lasing state. We solve the laser transport theory with appropriate surface boundary conditions to obtain the spatial distributions of the light intensity and of the occupation inversion. The dependence of the intensity correlation length on the pump rate agrees with experimental findings.     

Time evolution of power spectra from two-dimensional passive random media with different shapes

For a set of two-dimensional passive random media that have the same randomness and different shapes, the effects of morphology on the time evolution of the power spectrum of the localized modes supported by the media are investigated. The results demonstrate that the evolving process of the spectrum, the lifetime of short-lived modes and the amount of long-lived modes are morphological-dependent, while the lifetime of long-lived modes is morphological-independent. The denser the medium is, the quicker the evolving process and the shorter the lifetime of the short-lived modes are. Single-mode operation is more possible and occurs more early for a denser medium, which is of practical importance for proposing a mode-selecting technique for random lasers.     

二维随机介质中准态模的频谱时间演化特性

采用时域有限差分法数值求解Maxwell方程组，分析了平面随机介质中光波模式的频谱时间演化特性.随机介质的特征可以用散射颗粒的随机构形、介质参数（如颗粒的尺寸和填充率等）以及介质形态等因素来描述.这些因素决定了随机介质在准稳态下模式的频率特性与数量，但具有不同因素的随机介质中模式的产生、选择与演化，具有大致相同的特征与速度.平面随机介质的这些冷腔特性，与传统光腔中模式的产生、选择和演化的特征非常相似. 关键词： 激光物理 随机激光器 无序介质中的光学特性     

Diffusion in layered random flows,polymers, electrons in random potentials,and spin depolarization in random fields

Several related models are studied in a common framework. We first reconsider the model of Matheron and de Marsilly for (anomalous) tracer dispersion in a stratified porous medium. In each horizontal layer the flow velocity is constant, parallel to the layer, and depends randomly on the vertical coordinate z. This model is mapped onto ad=1 localization problem in a random potential and, equivalently, onto ad=1 polymer. At larget theaveraged distribution of horizontal displacementsx takes the scaling form [P(x, t, z=0)]=at ^–5/4 Q(bxt ^–3/4), whereQ(y) is independent of the details of the model.Q(y),a, andb are obtained exactly for a large class of models. From the Lifschitz tails of the localization problem we find in the regionxt ^3/4, i.e.,y, thatQ(y)¦y¦ exp(–C¦y¦^4/3). We also obtain exactly ind=1 the scaling functions for the local and total average magnetization of spins diffusing in a random magnetic field, by mapping onto a polymer problem, as well as the average local concentration for diffusion in the presence of random sources and sinks. These mappings are then used to study higher-dimensional extensions of these models.     

Spatial structure and stability based on random walks

A general expression for a recursion formula which describes a random walk with coupled modes is given. In this system, the random walker is specified by the jumping probabilities P⁺ and P^– which depend on the modes. The transition probability between the modes is expressed by a jumping probabilityR ^(ij) (orr _ij). With the aid of this recursion formula, spatial structures of the steady state of a coupled random walk are studied. By introducing a Liapunov function and entropy, it is shown that the stability condition for the present system can be expressed as the principle of the extremum entropy production.On leave of absence from Tohoku University, Department of Applied Science, Faculty of Engineering, Sendai, 980 Japan.     

Synthesis, morphology and random laser action of ZnO nanostructures

Three-dimensional (3-D) ZnO random-wall nanostructures and one-dimensional (1-D) ZnO nanorods were prepared on silicon substrates by a simple solid-vapour phase thermal sublimation technique. Optical pumped random lasing has been observed in the ZnO random-wall arrays with a threshold intensity of 0.38 MW/cm² in the emission wavelength from 380 to 395 nm. The optical gain was attributed to the closed-loop scattering and light amplification of the ZnO random-wall. The experimental result suggests that the morphology of nanostructure is the key factor to effect random lasing.     

Surface-enhanced Raman spectroscopy of semiconductor nanostructures

We review our recent results concerning surface-enhanced Raman scattering (SERS) by confined optical and surface optical phonons in semiconductor nanostructures including CdS, CuS, GaN, and ZnO nanocrystals, GaN and ZnO nanorods, and AlN nanowires. Enhancement of Raman scattering by confined optical phonons as well as appearance of new Raman modes with the frequencies different from those in ZnO bulk attributed to surface optical modes is observed in a series of nanostructures having different morphology located in the vicinity of metal nanoclusters (Ag, Au, and Pt). Assignment of surface optical modes is based on calculations performed in the frame of the dielectric continuum model. It is established that SERS by phonons has a resonant character. A maximal enhancement by optical phonons as high as 730 is achieved for CdS nanocrystals in double resonant conditions at the coincidence of laser energy with that of electronic transitions in semiconductor nanocrystals and localized surface plasmon resonance in metal nanoclusters. Even a higher enhancement is observed for SERS by surface optical modes in ZnO nanocrystals (above 10⁴). Surface enhanced Raman scattering is used for studying phonon spectrum in nanocrystal ensembles with an ultra-low areal density on metal plasmonic nanostructures.     

随机光纤激光器中光纤与随机介质匹配问题的研究

降低阈值是随机激光实用化的前提, 随机光纤激光器是将随机增益介质填充到空芯光子晶体光纤中利 用其光子禁带来降低阈值的一种随机激光器. 理论分析表明: 在光子晶体光纤光子禁带的约束下, 随机光纤激光器中的大部分能量被集中在芯区传播, 这使局域在芯区的光与随机介质相互作用得到增强, 激发效率得以提高. 然而, 光纤填充介质后, 纤芯等效折射率发生了改变, 光子带隙也会随之移动, 因此当选用带隙光纤来降低阈值时, 只考虑光纤本身的带隙是不够的, 应考虑到介质的增益频率和填充后的光子带隙之间的匹配问题, 合理选择光纤或介质的材料, 如果匹配得当, 光子禁带对激光的调控能力会更强, 激光阈值有望得到更大程度的降低. 关键词： 随机激光 光子晶体光纤 光子禁带 阈值     

Waveguiding behavior of VLS-grown one-dimensional Ga-doped In2O3 nanostructures

Highly crystalline undoped and Ga-doped indium oxide nanorods with square-shaped faceted morphology were fabricated through the vapor-liquid-solid process at moderate temperature. Effects of Ga incorporation on the growth rate, morphology, and crystallinity of the nanostructures were evaluated by scanning electron microscopy, transmission electron microscopy, and X-ray diffraction. Defect structure and waveguiding behavior of the 1-D In₂O₃ nanostructures have been studied using microRaman and micro photoluminescence spectroscopies. The appearance of several resonant modes superposed over the broad room temperature micro-photoluminescence spectra of the nanostructures demonstrates their waveguiding behaviors. While the pristine or undoped In₂O₃ nanostructures of 20–150 nm widths revealed Fabry-Pérot resonance modes, the Ga-incorporated nanostructures of 20–100 nm width revealed whispering gallery modes due to their smaller widths. The quality factor (Q) of the resonators was estimated to be about 20.86 and 188.79 for the pristine and Ga-incorporated nanostructures, respectively, indicating a huge enhancement due to Ga incorporation. The increment in the Q factor on Ga incorporation in In₂O₃ nanorods opens up the possibility of their utilization for the development of new optical transmitters and resonators, and fabrication of nanoscopic lasing devices.     

光子晶体晶粒尺寸和排列结构对随机激光辐射特性的影响

研究了光子晶体对随机激光器的输出特性的调控,并分析了光子晶体的晶粒尺寸和排列结构等对调控作用的影响.对于同一随机介质而言,上下表面用同种材料不同晶粒尺寸的光子晶体覆盖,结果显示:晶粒尺寸合适的光子晶体会使光在系统中来回振荡从而得到很好的放大,使系统中的光与随机增益介质的相互作用加强,激光阈值降低;同时还对激光模式有较强的调制能力,能在一定程度上抑制自发辐射,使之向所需要的频率内辐射.但如果光子晶体的晶粒尺寸与随机增益介质结构匹配不当,则光子晶体对激光模式调制能力较弱,光场能量不能有效地被局域在系统中,系统 关键词： 有限时域差分法 光子晶体 随机激光 辐射特性     

Coupling and level repulsion in the localized regime: from isolated to quasiextended modes

We study the interaction of Anderson localized states in an open 1D random system by varying the internal structure of the sample. As the frequencies of two states come close, they are transformed into multiply peaked quasiextended modes. Level repulsion is observed experimentally and explained within a model of coupled resonators. The spectral and spatial evolution of the coupled modes is described in terms of the coupling coefficient and Q factors of resonators.     

Frequency and amplitude alterations of sound modes in a space-dependent random mass density field

Abstract

We investigate the effect of a space-dependent random mass density field on small amplitude acoustic modes that are settled in a semi-infinite medium of a temperature growing linearly with depth. Using a perturbation method, the dispersion relation is derived in the form of Hill's determinant. Numerical solutions of this equation lead to the following conclusions: (a) a weak random field (with σ_eff?=?0.05) essentially affects long waves which experience attenuation and a frequency reduction; (b) for a stronger random field (with σ_eff?=?0.1), high-order sound modes behave as sound waves as they are attenuated and their frequencies are increased; (c) for a sufficiently strong random field (with σ_eff?=?0.2), mode coupling occurs, as a result of which the dispersive curves cross each other, the sound modes loose their identities, and some modes are amplified. Here σ_eff denotes the effective strength of a random field.     

Are random walks random?

Random walks have been created using the pseudo-random generators in different computer language compilers (BASIC, PASCAL, FORTRAN, C++) using a Pentium processor. All the obtained paths have apparently a random behavior for short walks (2¹⁴ steps). From long random walks (2³³ steps) different periods have been found, the shortest being 2¹⁸ for PASCAL and the longest 2³¹ for FORTRAN and C++, while BASIC had a 2²⁴ steps period. The BASIC, PASCAL and FORTRAN long walks had even (2 or 4) symmetries. The C++ walk systematically roams away from the origin. Using deviations from the mean-distance rule for random walks, d² ∝ N, a more severe criterion is found, e.g. random walks generated by a PASCAL compiler fulfills this criterion to N < 10 000.     

Diffusion: A Layman's approach and its applications to one-dimensional random systems

Diffusion characteristics are reduced to the solution of a simple stationary equation. In classical one-dimensional random systems, time-irreversability (provided, e.g., by a magnetic field) implies L ∝ $\text{l}$nt, L is a diffusion length, t is time, while local space assymetry (provided by random fields) implies L ∝ $\text{l}$n²t; both cases are related to the localized particle distribution.     

Localized modes in orientation-disordered one-dimensional media with uniaxial scatterers

Localized modes in one-dimensional (1D) media with uniaxial scatterers that are assumed to be order in spatial location but disorder in spatial orientation of their optical axis are investigated. Based on the holistic effect model in random laser, I.e., the random laser is due to the interaction of the complex localized modes in active random media with local aperiodic quasi-structure with appropriate pump light, a physical model on this type of random media is found. Its disorder degree is defined by D = no/ne. Then, the typical transmission spectrum through the random media and the light field intensity distribution corresponding to the defect modes in photonic band-gap are calculated numerically by means of the transfer matrix method, and the condition that the localized mode appears is discussed. Results show that the medium disorder plays an important role in determining the lightwave state. The localized state appears when the medium disorder is strong enough, and a new mechanism creating random laser phenomenon is brought forward.     

Singularities in forward scattering through random media

Abstract

We consider a random medium in which scattering is exclusively in the forward direction. Waves are emitted by an object in the medium and Fourier components of the intensity are shown to propagate independently. At small wavevectors the intensity propagates very simply through increasing thickness, z, of medium, as λ ^z , and Fourier components of the object can easily be reconstructed. For wavevectors greater than a critical value, q _c , the intensity changes with z in a more complex fashion making it very difficult to reconstruct the object. They develop a simple model for the singularity and apply it to the reconstruction of an object degraded by passage through a random medium.     

随机激光器中准态腔的阈值与其局域化程度的关系

基于光波在有限随机介质中的局域化理论，利用有限时域差分法数值求解Maxwell方程 组，研究了随机介质中的激光现象，分析了准态模的放大与其 空间局域性的关系. 通过研究二维非增益随机介质中光波的局域化，确定了准态模的空间分 布和频谱特征. 通过引入增益，研究了准态模的放大过程和阈值特性. 结果表明空间局域化 强的准态模在增益介质中被优先放大，且有较低的阈值. 关键词： 随机激光器 准态模 随机介质中的光学特性