Localized Random Lasing Modes and a New Path for Observing Localization

We demonstrate that a knowledge of the density-of-states and the eigenstates of a random system without gain, in conjunction with the frequency profile of the gain, can accurately predict the mode that will lase first. Its critical pumping rate can be also obtained. It is found that the shape of the wavefunction of the random system remains unchanged as gain is introduced. These results were obtained by the time-independent transfer matrix method and finite-difference-time-domain (FDTD) methods. They can be also analytically understood by generalizing the semi-classical Lamb theory of lasing in random systems. These findings provide a new path for observing the localization of light, such as looking for mobility edge and studying the localized states. %inside the random systems..Comment: Sent to PRL. 3 figure

Field quantization for open optical cavities

We study the quantum properties of the electromagnetic field in optical cavities coupled to an arbitrary number of escape channels. We consider both inhomogeneous dielectric resonators with a scalar dielectric constant $\epsilon({\bf r})$ and cavities defined by mirrors of arbitrary shape. Using the Feshbach projector technique we quantize the field in terms of a set of resonator and bath modes. We rigorously show that the field Hamiltonian reduces to the system--and--bath Hamiltonian of quantum optics. The field dynamics is investigated using the input--output theory of Gardiner and Collet. In the case of strong coupling to the external radiation field we find spectrally overlapping resonator modes. The mode dynamics is coupled due to the damping and noise inflicted by the external field. For wave chaotic resonators the mode dynamics is determined by a non--Hermitean random matrix. Upon including an amplifying medium, our dynamics of open-resonator modes may serve as a starting point for a quantum theory of random lasing.Comment: 16 pages, added references, corrected typo

Local and average fields inside surface-disordered waveguides: Resonances in the one-dimensional Anderson localization regime

We investigate the one-dimensional propagation of waves in the Anderson localization regime, for a single-mode, surface disordered waveguide. We make use of both an analytical formulation and rigorous numerical simulation calculations. The occurrence of anomalously large transmission coefficients for given realizations and/or frequencies is studied, revealing huge field intensity concentration inside the disordered waveguide. The analytically predicted s-like dependence of the average intensity, being in good agreement with the numerical results for moderately long systems, fails to explain the intensity distribution observed deep in the localized regime. The average contribution to the field intensity from the resonances that are above a threshold transmission coefficient $T_{c}$ is a broad distribution with a large maximum at/near mid-waveguide, depending universally (for given $T_{c}$) on the ratio of the length of the disorder segment to the localization length, $L/\xi$. The same universality is observed in the spatial distribution of the intensity inside typical (non-resonant with respect to the transmission coefficient) realizations, presenting a s-like shape similar to that of the total average intensity for $T_{c}$ close to 1, which decays faster the lower is $T_{c}$. Evidence is given of the self-averaging nature of the random quantity $\log[I(x)]/x\simeq -1/\xi$. Higher-order moments of the intensity are also shown.Comment: 9 pages, 9 figure

Propagation inhibition and wave localization in a 2D random liquid medium

Acoustic propagation and scattering in water containing many parallel air-filled cylinders is studied. Two situations are considered and compared: (1) wave propagating through the array of cylinders, imitating a traditional experimental setup, and (2) wave transmitted from a source located inside the ensemble. We show that waves can be blocked from propagation by disorders in the first scenario, but the inhibition does not necessarily imply wave localization. Furthermore, the results reveal the phenomenon of wave localization in a range of frequencies.Comment: Typos in Fiures are correcte

The three-dimensional random field Ising magnet: interfaces, scaling, and the nature of states

The nature of the zero temperature ordering transition in the 3D Gaussian random field Ising magnet is studied numerically, aided by scaling analyses. In the ferromagnetic phase the scaling of the roughness of the domain walls, $w\sim L^\zeta$, is consistent with the theoretical prediction $\zeta = 2/3$. As the randomness is increased through the transition, the probability distribution of the interfacial tension of domain walls scales as for a single second order transition. At the critical point, the fractal dimensions of domain walls and the fractal dimension of the outer surface of spin clusters are investigated: there are at least two distinct physically important fractal dimensions. These dimensions are argued to be related to combinations of the energy scaling exponent, $\theta$, which determines the violation of hyperscaling, the correlation length exponent $\nu$, and the magnetization exponent $\beta$. The value $\beta = 0.017\pm 0.005$ is derived from the magnetization: this estimate is supported by the study of the spin cluster size distribution at criticality. The variation of configurations in the interior of a sample with boundary conditions is consistent with the hypothesis that there is a single transition separating the disordered phase with one ground state from the ordered phase with two ground states. The array of results are shown to be consistent with a scaling picture and a geometric description of the influence of boundary conditions on the spins. The details of the algorithm used and its implementation are also described.Comment: 32 pp., 2 columns, 32 figure

Asymptotic Expansions for Stationary Distributions of Perturbed Semi-Markov Processes

New algorithms for computing of asymptotic expansions for stationary distributions of nonlinearly perturbed semi-Markov processes are presented. The algorithms are based on special techniques of sequential phase space reduction, which can be applied to processes with asymptotically coupled and uncoupled finite phase spaces.Comment: 83 page

Manifestation of photonic band structure in small clusters of spherical particles

We study the formation of the photonic band structure in small clusters of dielectric spheres. The first signs of the band structure, an attribute of an infinite crystal, can appear for clusters of 5 particles. Density of resonant states of a cluster of 32 spheres may exhibit a well defined structure similar to the density of electromagnetic states of the infinite photonic crystal. The resonant mode structure of finite-size aggregates is shown to be insensitive to random displacements of particles off the perfect lattice positions as large as half-radius of the particle. The results were obtained by an efficient numerical method, which relates the density of resonant states to the the scattering coefficients of the electromagnetic scattering problem. Generalized multisphere Mie (GMM) solution was used to obtain scattering matrix elements. These results are important to miniature photonic crystal design as well as understanding of light localization in dense random media.Comment: 4 pages, 2 figure

Signatures of Classical Diffusion in Quantum Fluctuations of 2D Chaotic Systems

We consider a two-dimensional (2D) generalization of the standard kicked-rotor (KR) and show that it is an excellent model for the study of 2D quantum systems with underlying diffusive classical dynamics. First we analyze the distribution of wavefunction intensities and compare them with the predictions derived in the framework of diffusive {\it disordered} samples. Next, we turn the closed system into an open one by constructing a scattering matrix. The distribution of the resonance widths ${\cal P}(\Gamma)$ and Wigner delay times ${\cal P}(\tau_W)$ are investigated. The forms of these distributions are obtained for different symmetry classes and the traces of classical diffusive dynamics are identified. Our theoretical arguments are supported by extensive numerical calculations.Comment: 20 pages; 12 figure

Diffusive and localization behavior of electromagnetic waves in a two-dimensional random medium

In this paper, we discuss the transport phenomena of electromagnetic waves in a two-dimensional random system which is composed of arrays of electrical dipoles, following the model presented earlier by Erdogan, et al. (J. Opt. Soc. Am. B {\bf 10}, 391 (1993)). A set of self-consistent equations is presented, accounting for the multiple scattering in the system, and is then solved numerically. A strong localization regime is discovered in the frequency domain. The transport properties within, near the edge of and nearly outside the localization regime are investigated for different parameters such as filling factor and system size. The results show that within the localization regime, waves are trapped near the transmitting source. Meanwhile, the diffusive waves follow an intuitive but expected picture. That is, they increase with travelling path as more and more random scattering incurs, followed by a saturation, then start to decay exponentially when the travelling path is large enough, signifying the localization effect. For the cases that the frequencies are near the boundary of or outside the localization regime, the results of diffusive waves are compared with the diffusion approximation, showing less encouraging agreement as in other systems (Asatryan, et al., Phys. Rev. E {\bf 67}, 036605 (2003).)Comment: 8 pages 9 figure

Security and Privacy Issues in Wireless Mesh Networks: A Survey

This book chapter identifies various security threats in wireless mesh network (WMN). Keeping in mind the critical requirement of security and user privacy in WMNs, this chapter provides a comprehensive overview of various possible attacks on different layers of the communication protocol stack for WMNs and their corresponding defense mechanisms. First, it identifies the security vulnerabilities in the physical, link, network, transport, application layers. Furthermore, various possible attacks on the key management protocols, user authentication and access control protocols, and user privacy preservation protocols are presented. After enumerating various possible attacks, the chapter provides a detailed discussion on various existing security mechanisms and protocols to defend against and wherever possible prevent the possible attacks. Comparative analyses are also presented on the security schemes with regards to the cryptographic schemes used, key management strategies deployed, use of any trusted third party, computation and communication overhead involved etc. The chapter then presents a brief discussion on various trust management approaches for WMNs since trust and reputation-based schemes are increasingly becoming popular for enforcing security in wireless networks. A number of open problems in security and privacy issues for WMNs are subsequently discussed before the chapter is finally concluded.Comment: 62 pages, 12 figures, 6 tables. This chapter is an extension of the author's previous submission in arXiv submission: arXiv:1102.1226. There are some text overlaps with the previous submissio