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We conduct a numerical investigation into wave propagation and localization in one-dimensional lattices subject to nonlinear disorder, focusing on cases with fixed input conditions. Utilizing a discrete nonlinear Schr\"odinger equation with Kerr-type nonlinearity and a random coefficient, we compute the averages and variances of the transmittance, $T$, and its logarithm, as functions of the system size $L$, while maintaining constant intensity for the incident wave. In cases of purely nonlinear disorder, we observe power-law localization characterized by $\langle T \rangle \propto L^{-\gamma_a}$ and $\langle \ln T \rangle \approx -\gamma_g \ln L$ for sufficiently large $L$. At low input intensities, a transition from exponential to power-law decay in $\langle T \rangle$ occurs as $L$ increases. The exponents $\gamma_a$ and $\gamma_g$ are nearly identical, converging to approximately 0.5 as the strength of the nonlinear disorder, $\beta$, increases. Additionally, the variance of $T$ decays according to a power law with an exponent close to 1, and the variance of $\ln T$ approaches a small constant as $L$ increases. These findings are consistent with an underlying log-normal distribution of $T$ and suggest that wave propagation behavior becomes nearly deterministic as the system size increases. When both linear and nonlinear disorders are present, we observe a transition from power-law to exponential decay in transmittance with increasing $L$ when the strength of linear disorder, $V$, is less than $\beta$. As $V$ increases, the region exhibiting power-law localization diminishes and eventually disappears when $V$ exceeds $\beta$, leading to standard Anderson localization., Comment: 8 pages, 7 figures

Wavetable synthesis generates quasi-periodic waveforms of musical tones by interpolating a list of waveforms called wavetable. As generative models that utilize latent representations offer various methods in waveform generation for musical applications, studies in wavetable generation with invertible architecture have also arisen recently. While they are promising, it is still challenging to generate wavetables with detailed controls in disentangling factors within the latent representation. In response, we present Wavespace, a novel framework for wavetable generation that empowers users with enhanced parameter controls. Our model allows users to apply pre-defined conditions to the output wavetables. We employ a variational autoencoder and completely factorize its latent space to different waveform styles. We also condition the generator with auxiliary timbral and morphological descriptors. This way, users can create unique wavetables by independently manipulating each latent subspace and descriptor parameters. Our framework is efficient enough for practical use; we prototyped an oscillator plug-in as a proof of concept for real-time integration of Wavespace within digital audio workspaces (DAWs).

We theoretically investigate the scaling behavior of the localization length for $s$-polarized electromagnetic waves incident at a critical angle on stratified random media with short-range correlated disorder. By employing the invariant embedding method, extended to waves in correlated random media, and utilizing the Shapiro-Loginov formula of differentiation, we accurately compute the localization length $\xi$ of $s$ waves incident obliquely on stratified random media that exhibit short-range correlated dichotomous randomness in the dielectric permittivity. The random component of the permittivity is characterized by the disorder strength parameter $\sigma^2$ and the disorder correlation length $l_c$. Away from the critical angle, $\xi$ depends on these parameters independently. However, precisely at the critical angle, we discover that for waves with wavenumber $k$, $k\xi$ depends on the single parameter $kl_c\sigma^2$, satisfying a universal equation $k\xi\approx 1.3717\left(kl_c\sigma^2\right)^{-1/3}$ across the entire range of parameter values. Additionally, we find that $\xi$ scales as ${\lambda}^{4/3}$ for the entire range of the wavelength $\lambda$, regardless of the values of $\sigma^2$ and $l_c$. We demonstrate that under sufficiently strong disorder, the scaling behavior of the localization length for all other incident angles converges to that for the critical incidence., Comment: 8 pages, 5 figures

Conventional GAN-based models for talking head generation often suffer from limited quality and unstable training. Recent approaches based on diffusion models aimed to address these limitations and improve fidelity. However, they still face challenges, including extensive sampling times and difficulties in maintaining temporal consistency due to the high stochasticity of diffusion models. To overcome these challenges, we propose a novel motion-disentangled diffusion model for high-quality talking head generation, dubbed MoDiTalker. We introduce the two modules: audio-to-motion (AToM), designed to generate a synchronized lip motion from audio, and motion-to-video (MToV), designed to produce high-quality head video following the generated motion. AToM excels in capturing subtle lip movements by leveraging an audio attention mechanism. In addition, MToV enhances temporal consistency by leveraging an efficient tri-plane representation. Our experiments conducted on standard benchmarks demonstrate that our model achieves superior performance compared to existing models. We also provide comprehensive ablation studies and user study results.

This paper presents ExeGPT, a distributed system designed for constraint-aware LLM inference. ExeGPT finds and runs with an optimal execution schedule to maximize inference throughput while satisfying a given latency constraint. By leveraging the distribution of input and output sequences, it effectively allocates resources and determines optimal execution configurations, including batch sizes and partial tensor parallelism. We also introduce two scheduling strategies based on Round-Robin Allocation and Workload-Aware Allocation policies, suitable for different NLP workloads. We evaluate ExeGPT on six LLM instances of T5, OPT, and GPT-3 and five NLP tasks, each with four distinct latency constraints. Compared to FasterTransformer, ExeGPT achieves up to 15.2x improvements in throughput and 6x improvements in latency. Overall, ExeGPT achieves an average throughput gain of 2.9x across twenty evaluation scenarios. Moreover, when adapting to changing sequence distributions, the cost of adjusting the schedule in ExeGPT is reasonably modest. ExeGPT proves to be an effective solution for optimizing and executing LLM inference for diverse NLP workload and serving conditions., Comment: Accepted to ASPLOS 2024 (summer cycle)

Generating high-quality videos that synthesize desired realistic content is a challenging task due to their intricate high-dimensionality and complexity of videos. Several recent diffusion-based methods have shown comparable performance by compressing videos to a lower-dimensional latent space, using traditional video autoencoder architecture. However, such method that employ standard frame-wise 2D and 3D convolution fail to fully exploit the spatio-temporal nature of videos. To address this issue, we propose a novel hybrid video diffusion model, called HVDM, which can capture spatio-temporal dependencies more effectively. The HVDM is trained by a hybrid video autoencoder which extracts a disentangled representation of the video including: (i) a global context information captured by a 2D projected latent (ii) a local volume information captured by 3D convolutions with wavelet decomposition (iii) a frequency information for improving the video reconstruction. Based on this disentangled representation, our hybrid autoencoder provide a more comprehensive video latent enriching the generated videos with fine structures and details. Experiments on video generation benchamarks (UCF101, SkyTimelapse, and TaiChi) demonstrate that the proposed approach achieves state-of-the-art video generation quality, showing a wide range of video applications (e.g., long video generation, image-to-video, and video dynamics control)., Comment: Project page is available at https://hxngiee.github.io/HVDM/

We investigate the influence of the temporal variations of various medium parameters on the propagation of Dirac-type waves in materials where the quasiparticles are described by a generalized version of the pseudospin-1/2 Dirac equation. Our considerations also include the propagation of electromagnetic waves in metamaterials with the Dirac-type dispersion. We focus on the variations of the scalar and vector potentials, mass, Fermi velocity, and tilt velocity describing the Dirac cone tilt. We derive the scattering coefficients associated with the temporal interfaces and slabs analytically and find that the temporal scattering is caused by the changes of the mass, Fermi velocity, and vector potential, but does not arise from the changes of the scalar potential and tilt velocity. We also explore the conditions under which the temporal Brewster effect and total interband transition occur and calculate the change in total wave energy. We examine bilayer Dirac temporal crystals where parameters switch between two different sets of values periodically and prove that these systems do not have momentum gaps. Finally, we assess the potential for observing these temporal scattering effects in experiments., Comment: 12 pages, 7 figures

We present a numerical study of the transport and localization properties of excitations in one-dimensional lattices with diagonal disordered mosaic modulations. The model is characterized by the modulation period $\kappa$ and the disorder strength $W$. We calculate the disorder averages $\langle T\rangle$, $\langle \ln T\rangle$, and $\langle P\rangle$, where $T$ is the transmittance and $P$ is the participation ratio, as a function of energy $E$ and system size $L$, for different values of $\kappa$ and $W$. For excitations at quasiresonance energies determined by $\kappa$, we find power-law scaling behaviors of the form $\langle T \rangle \propto L^{-\gamma_{a}}$, $\langle \ln T \rangle \approx -\gamma_g \ln L$, and $\langle P \rangle \propto L^{\beta}$, as $L$ increases to a large value. This behavior is in contrast to the exponential localization behavior occurring at all other energies. The appearance of sharp peaks in the participation ratio spectrum at quasiresonance energies provides additional evidence for the existence of an anomalous power-law localization phenomenon. The corresponding eigenstates demonstrate multifractal behavior and exhibit unique node structures. In addition, we investigate the time-dependent wave packet dynamics and calculate the mean square displacement $\langle m^2(t) \rangle$, spatial probability distribution, participation number, and return probability. When the wave packet's initial momentum satisfies the quasiresonance condition, we observe a subdiffusive spreading of the wave packet, characterized by $\langle m^2(t) \rangle\propto t^{\eta}$ where $\eta$ is always less than 1. We also note the occurrence of partial localization at quasiresonance energies, as indicated by the saturation of the participation number and a nonzero value for the return probability at long times., Comment: 22 pages, 11 figures

In this paper, we propose a diffusion-based face swapping framework for the first time, called DiffFace, composed of training ID conditional DDPM, sampling with facial guidance, and a target-preserving blending. In specific, in the training process, the ID conditional DDPM is trained to generate face images with the desired identity. In the sampling process, we use the off-the-shelf facial expert models to make the model transfer source identity while preserving target attributes faithfully. During this process, to preserve the background of the target image and obtain the desired face swapping result, we additionally propose a target-preserving blending strategy. It helps our model to keep the attributes of the target face from noise while transferring the source facial identity. In addition, without any re-training, our model can flexibly apply additional facial guidance and adaptively control the ID-attributes trade-off to achieve the desired results. To the best of our knowledge, this is the first approach that applies the diffusion model in face swapping task. Compared with previous GAN-based approaches, by taking advantage of the diffusion model for the face swapping task, DiffFace achieves better benefits such as training stability, high fidelity, diversity of the samples, and controllability. Extensive experiments show that our DiffFace is comparable or superior to the state-of-the-art methods on several standard face swapping benchmarks., Comment: Project Page: https://hxngiee.github.io/DiffFace

We study theoretically mode conversion and resonant overreflection of magnetohydrodynamic waves in an inhomogeneous plane-stratified plasma in the presence of a nonuniform shear flow, using precise numerical calculations of the reflection and transmission coefficients and the field distributions based on the invariant imbedding method. The cases where the flow velocity and the external magnetic field are directed perpendicularly to the inhomogeneity direction and both the flow velocity and the plasma density vary arbitrarily along it are considered. When there is a shear flow, the wave frequency is modulated locally by the Doppler shift and resonant amplification and overreflection occur where the modulated frequency is negative and its absolute value matches the local Alfv\'en or slow frequency. For many different types of the density and flow velocity profiles, we find that, especially when the parameters are such that the incident waves are totally reflected, there arises a giant overreflection where the reflectance is much larger than 10 in a fairly broad range of the incident angles, the frequency, and the plasma $\beta$ and its maximum attains values larger than $10^5$. In a finite $\beta$ plasma, both incident fast and slow magnetosonic waves are found to cause strong overreflection and there appear multiple positions exhibiting both Alfv\'en and slow resonances inside the plasma. We explain the mechanism of overreflection in terms of the formation of inhomogeneous and open cavities close to the resonances and the strong enhancement of the wave energy due to the occurrence of semi-bound states there. We give discussions of the observational consequences in magnetized terrestrial and solar plasmas., Comment: 17 pages, 15 figures

We present a numerical study of Anderson localization in disordered non-Hermitian lattice models with flat bands. Specifically we consider one-dimensional stub and two-dimensional kagome lattices that have a random scalar potential and a uniform imaginary vector potential and calculate the spectra of the complex energy, the participation ratio, and the winding number as a function of the strength of the imaginary vector potential, $h$. The flat-band states are found to show a double transition from localized to delocalized and back to localized states with $h$, in contrast to the dispersive-band states going through a single delocalization transition. When $h$ is sufficiently small, all flat-band states are localized. As $h$ increases above a certain critical value $h_1$, some pair of flat-band states become delocalized. The participation ratio associated with them increases substantially and their winding numbers become nonzero. As $h$ increases further, more and more flat-band states get delocalized until the fraction of the delocalized states reaches a maximum. For larger $h$ values, a re-entrant localization takes place and, at another critical value $h_2$, all flat-band states return to compact localized states with very small participation ratios and zero winding numbers. This re-entrant localization transition, which is due to the interplay among disorder, non-Hermiticity, and flat band, is a phenomenon occurring in many models having an imaginary vector potential and a flat band simultaneously. We explore the spatial characteristics of the flat-band states by calculating the local density distribution., Comment: 15 pages, 8 figures

We investigate numerically the time evolution of wave packets incident on one-dimensional semi-infinite lattices with mosaic modulated random on-site potentials, which are characterized by the integer-valued modulation period $\kappa$ and the disorder strength $W$. For Gaussian wave packets with the central energy $E_0$ and a small spectral width, we perform extensive numerical calculations of the disorder-averaged time-dependent reflectance, $\langle R(t)\rangle$, for various values of $E_0$, $\kappa$, and $W$. We find that the long-time behavior of $\langle R(t)\rangle$ obeys a power law of the form $t^{-\gamma}$ in all cases. In the presence of the mosaic modulation, $\gamma$ is equal to 2 for almost all values of $E_0$, implying the onset of the Anderson localization, while at a finite number of discrete values of $E_0$ dependent on $\kappa$, $\gamma$ approaches 3/2, implying the onset of the classical diffusion. This phenomenon is independent of the disorder strength and arises in a quasi-resonant manner such that $\gamma$ varies rapidly from 3/2 to 2 in a narrow energy range as $E_0$ varies away from the quasi-resonance values. We deduce a simple analytical formula for the quasi-resonance energies and provide an explanation of the delocalization phenomenon based on the interplay between randomness and band structure and the node structure of the wave functions. We explore the nature of the states at the quasi-resonance energies using a finite-size scaling analysis of the average participation ratio and find that the states are neither extended nor exponentially localized, but ciritical states.., Comment: 12 pages, 9 figures

Mode conversion of transverse electromagnetic waves into longitudinal oscillations and the associated resonant absorption of wave energy in inhomogeneous plasmas is a phenomenon that has been studied extensively in plasma physics. We show that precisely analogous phenomena occur generically in electronic and photonic systems where dispersionless flat bands and dispersive bands coexist in the presence of an inhomogeneous potential or medium parameter. We demonstrate that the systems described by the pseudospin-1 Dirac equation with two dispersive bands and one flat band display mode conversion and resonant absorption in a very similar manner to $p$-polarized electromagnetic waves in an unmagnetized plasma by calculating the mode conversion coefficient explicitly using the invariant imbedding method. We also show that a similar mode conversion process takes place in many other systems with a flat band such as pseudospin-2 Dirac systems, continuum models obtained for one-dimensional stub and sawtooth lattices, and two-dimensional electron systems with a quadratic band and a nearly flat band. We discuss some experimental implications of mode conversion in flat-band materials and metamaterials., Comment: 12 pages, 9 figures

We study theoretically the mode conversion and the resonant absorption of high frequency electromagnetic waves into longitudinal modes in magnetized and stratified plasmas in the case where the external magnetic field is perpendicular to both the directions of inhomogeneity and wave propagation. Mode conversion is shown to occur only when the waves are extraordinary waves. We develop an efficient method for calculating the mode conversion coefficient for arbitrary spatial configurations of the plasma density and the external magnetic field in a numerically exact manner using the invariant imbedding method. We calculate the mode conversion coefficient extensively as a function of the incident angle, the external magnetic field, and the plasma density in the incident region. We show that there is strong asymmetry under the sign change of the incident angle and the external magnetic field and find that the mode conversion coefficient is close to one in certain ranges of the parameter values. We discuss the implications of our results in plasma heating phenomena., Comment: 8 pages, 6 figures

We study theoretically some unique characteristics of surface electromagnetic waves excited at the interface between two different kinds of general bi-isotropic media, which include Tellegen media and chiral media as special cases. We derive an analytical dispersion relation for those waves, using which we deduce eight different conditions under which they are generated between two Tellegen media and between two chiral media independently of the component of the wave vector along the interface. These make it possible to excite the surface waves for all or a wide range of incident angles in attenuated total reflection experiments on multilayer structures. We generalize the concept of a conjugate matched pair to bi-isotropic media and obtain several conditions under which the omnidirectional total transmission, which we call the super-Klein tunneling, occurs through conjugate matched pairs consisting of Tellegen media and of chiral media. We find that these conditions are closely linked to those for the omnidirectional excitation of surface waves. Using the invariant imbedding method, we perform extensive numerical calculations of the absorptance, the transmittance, and the spatial distribution of the electromagnetic fields for circularly-polarized waves incident on bilayer structures and confirm that the results agree perfectly with the analytical predictions., Comment: 16 pages, 20 figures

We study theoretically Anderson localization of two-dimensional massless pseudospin-1 Dirac particles in a random one-dimensional scalar potential. We focus explicitly on the effect of disorder correlations, considering a short-range correlated dichotomous random potential at all strengths of disorder. We also consider a $\delta$-function correlated random potential at weak disorder. Using the invariant imbedding method, we calculate the localization length in a numerically precise way and analyze its dependencies on incident angle, disorder correlation length, disorder strength, energy, wavelength and average potential over a wide range of parameter values. In addition, we derive analytical formulas for the localization length, which are very accurate in the weak and strong disorder regimes. From the Dirac equation, we obtain an expression for the effective wave impedance, using which we explain several conditions for delocalization. We also deduce a condition under which the localization length vanishes. For all cases considered, the localization length depends non-monotonically on the disorder correlation length and diverges as $\theta^{-4}$ as the incident angle $\theta$ goes to zero. As the disorder strength is varied from zero to infinity, we find that there appear three different scaling regimes. As the energy or wavelength is varied from zero to infinity, there appear three or four different scaling regimes with different exponents, depending on the value of the average potential. The crossovers between different scaling regimes are explained in terms of the disorder correlation effect., Comment: 17 pages, 11 figures

We study numerically the effects of short- and long-range correlations on the localization properties of the eigenstates in a one-dimensional disordered lattice characterized by a random non-Hermitian Hamiltonian, where the imaginary part of the on-site potential is random. We calculate participation number versus strengths of disorder and correlation. In the short-ranged case and when the correlation length is sufficiently small, we find that there exists a critical value of the disorder strength, below which enhancement and above which suppression of localization occurs as the correlation length increases. In the region where the correlation length is larger, localization is suppressed in all cases. A similar behavior is obtained for long-range correlations as the disorder strength and the correlation exponent are varied. Unlike in the case of a long-range correlated real random potential, no signature of the localization transition is found in a long-range correlated imaginary random potential. In the region where localization is enhanced in the presence of long-range correlations, we find that the enhancement occurs in the whole energy band, but is strongest near the band center. In addition, we find that the anomalous localization enhancement effect occurs near the band center in the long-range correlated case., Comment: 16 pages, 9 figures

We study the total transmission of quantum particles satisfying the Klein-Gordon equation through a potential barrier based on the classical wave propagation theory. We deduce an analytical expression for the wave impedance for Klein-Gordon particles. From the condition that the impedance is matched throughout the space, we show that super-Klein tunneling, which refers to the omnidirectional total transmission of particles through a potential barrier when the energy of the particle is equal to the half of the barrier potential, should occur in these systems. We also derive a condition for total transmission of Klein-Gordon particles in the presence of both scalar and vector potentials and discuss the influence of weak scattering at the interfaces on super-Klein tunneling. The theoretical predictions are confirmed by explicit numerical calculations of the transmittance based on the invariant imbedding method., Comment: 5 pages, 4 figures

We study Anderson localization of massless Dirac electrons in two dimensions in one-dimensional random scalar and vector potentials theoretically for two different cases, in which the scalar and vector potentials are either uncorrelated or correlated. From the Dirac equation, we deduce the effective wave impedance, using which we derive the condition for total transmission and those for delocalization in our random models analytically. Based on the invariant imbedding theory, we also develop a numerical method to calculate the localization length exactly for arbitrary strengths of disorder. In addition, we derive analytical expressions for the localization length, which are extremely accurate in the weak and strong disorder limits. In the presence of both scalar and vector potentials, the conditions for total transmission and complete delocalization are generalized from the usual Klein tunneling case. We find that the incident angles at which electron waves are either completely transmitted or delocalized can be tuned to arbitrary values. When the strength of scalar potential disorder increases to infinity, the localization length also increases to infinity, both in uncorrelated and correlated cases. The detailed dependencies of the localization length on incident angle, disorder strength and energy are elucidated and the discrepancies with previous studies and some new results are discussed. All the results are explained intuitively using the concept of wave impedance., Comment: 16 pages, 12 figures

We study theoretically the influence of the surface plasmon excitation on the Goos-H\"{a}nchen lateral shift of a $p$-polarized Gaussian beam incident obliquely on a dielectric-metal bilayer in the Otto configuration. We find that the lateral shift depends sensitively on the thickness of the metal layer and the width of the incident beam, as well as on the incident angle. Near the incident angle at which surface plasmons are excited, the lateral shift changes from large negative values to large positive values as the thickness of the metal layer increases through a critical value. For wide incident beams, the maximal forward and backward lateral shifts can be as large as several hundred times of the wavelength. As the width of the incident Gaussian beam decreases, the magnitude of the lateral shift decreases rapidly, but the ratio of the width of the reflected beam to that of the incident beam, which measures the degree of the deformation of the reflected beam profile, increases. In all cases considered, we find that the reflected beam is split into two parts. We also find that the lateral shift of the transmitted beam is always positive and very weak., Comment: 16 pages, 7 figures

We study theoretically the interplay between the surface confined wave modes and the linear and nonlinear gain of the dielectric layer in the Otto configuration. The surface confined wave modes such as surface plasmons or waveguide modes are excited in the dielectric-metal bilayer by obliquely incident $p$ waves. In the purely linear case, we find that the interplay between linear gain and surface confined wave modes can generate a large reflectance peak with its value much greater than 1. As the linear gain parameter increases, the peak appears at smaller incident angles, and the associated modes also change from surface plasmons to waveguide modes. When the nonlinear gain is turned on, the reflectance shows very strong multistability near the incident angles associated with surface confined wave modes. As the nonlinear gain parameter is varied, the reflectance curve undergoes complicated topological changes and sometimes displays separated closed curves. When the nonlinear gain parameter takes an optimally small value, a giant amplification of the reflectance by three orders of magnitude occurs near the incident angle associated with a waveguide mode. We also find that there exists a range of the incident angle where the wave is dissipated rather than amplified even in the presence of gain. We suggest that this can provide the basis for a possible new technology for thermal control in the subwavelength scale., Comment: 11 pages, 6 figures

Anderson localization of $p$-polarized waves and the Brewster anomaly phenomenon, which is the delocalization of $p$-polarized waves at a special incident angle, in randomly-stratified anisotropic media are studied theoretically for two different random models. In the first model, the random parts of the transverse and longitudinal components of the dielectric tensor, between which the longitudinal component is the one in the stratification direction, are assumed to be uncorrelated, while, in the second model, they are proportional to each other. We calculate the localization length in a precise way using the invariant imbedding method. From analytical considerations, we provide an interpretation of the Brewster anomaly as a phenomenon arising when the wave impedance is effectively uniform. Similarly, the ordinary Brewster effect is interpreted as an impedance matching phenomenon. We derive the existence condition for the Brewster anomaly and concise analytical expressions for the localization length, which are accurate in the weak disorder regime. We find that the Brewster anomaly can arise only when disorder is sufficiently weak and only in the second model with a positive ratio of the random parts. The incident angle at which the anomaly occurs depends sensitively on the ratio of the random parts and the average values of the tensor components. In the cases where the critical angle of total reflection exists, the angle at which the anomaly occurs can be either bigger or smaller than the critical angle. When the transverse and longitudinal components are uncorrelated, localization is dominated by the the transverse component at small incident angles. When only the longitudinal component is random, the localization length diverges as $\theta^{-4}$ as the incident angle $\theta$ goes to zero and is also argued to diverge for all $\theta$ in the strong disorder limit., Comment: 15 pages, 4 figures

We study numerically the localization properties of eigenstates in a one-dimensional random lattice described by a non-Hermitian disordered Hamiltonian, where both the disorder and the non-Hermiticity are inserted simultaneously in the on-site potential. We calculate the averaged participation number, the Shannon entropy and the structural entropy as a function of other parameters. We show that, in the presence of an imaginary random potential, all eigenstates are localized in the thermodynamic limit and strong anomalous Anderson localization occurs at the band center. In contrast to the usual localization anomalies where a weaker localization is observed, the localization of the eigenstates near the band center is strongly enhanced in the present non-Hermitian model. This phenomenon is associated with the occurrence of a large number of strongly-localized states with pure imaginary energy eigenvalues., Comment: 14 pages, 6 figures

The interplay between Anderson localization and total internal reflection of electromagnetic waves incident near the critical angle on randomly-stratified dielectric media is investigated theoretically. Using an exact analytical formula for the localization length for the Schr\"odinger equation with a Gaussian $\delta$-correlated random potential in one dimension, we show that when the incident angle is equal to the critical angle, the localization length for an incident $s$ wave of wavelength $\lambda$ is directly proportional to $\lambda^{4/3}$ throughout the entire range of the wavelength, for any value of the disorder strength. This result is different from that of a recent study reporting that the localization length at the critical incident angle for a binary multilayer system with random thickness variations is proportional to $\lambda$ in the large $\lambda$ region. We also discuss the characteristic behaviors of the localization length or the tunneling decay length for all other incident angles. Our results are confirmed by an independent numerical calculation based on the invariant imbedding method., Comment: 12 pages, 3 figures

We study the mode conversion and resonant absorption phenomena occurring in a slab of a stratified anisotropic medium, optical axes of which are tilted with respect to the direction of inhomogeneity, using the invariant imbedding theory of wave propagation. When the tilt angle is zero, mode conversion occurs if the longitudinal component of the permittivity tensor, which is the one in the direction of inhomogeneity in the non-tilted case, varies from positive to negative values within the medium, while the transverse component plays no role. When the tilt angle is nonzero, the wave transmission and absorption show an asymmetry under the sign change of the incident angle in a range of the tilt angle, while the reflection is always symmetric. We calculate the reflectance, the transmittance and the absorptance for several configurations of the permittivity tensor and find that resonant absorption is greatly enhanced when the medium from the incident surface to the resonance region is hyperbolic than when it is elliptic. For certain configurations, the transmittance and absorptance curves display sharp peaks at some incident angles determined by the tilt angle., Comment: 15 pages, 11 figures

We study numerically the transport and localization properties of waves in ordered and disordered ladder-shaped lattices with local $\mathcal{PT}$ symmetry. Using a transfer matrix method, we calculate the transmittance and the reflectance for the individual channels and the Lyapunov exponent for the whole system. In the absence of disorder, we find that when the gain/loss parameter $\rho$ is smaller than the interchain coupling parameter $t_{v}$, the transmittance and the reflectance are periodic functions of the system size, whereas when $\rho$ is larger than $t_{v}$, the transmittance is found to be an exponentially-decaying function while the reflectance attains a saturation value in the thermodynamic limit. For a fixed system size, there appear perfect transmission resonances in each individual channel at several values of the gain/loss strength smaller than $t_{v}$. A singular behavior of the transmittance is also found to appear at various values of $\rho$ for a given system size. When disorder is inserted into the on-site potentials, these behaviors are changed substantially due to the interplay between disorder and the gain/loss effect. When $\rho$ is smaller than $t_{v}$, we find that the presence of locally $\mathcal{PT}$-symmetric potentials suppresses Anderson localization, as compared to the localization in the corresponding Hermitian system. When $\rho$ is larger than $t_{v}$, we find that localization becomes more pronounced at higher gain/loss strengths. We also find that the phenomenon of anomalous localization occurs in disordered locally $\mathcal{PT}$-symmetric systems precisely at the spectral positions $E=0$ and $E=\pm\sqrt{t_{v}^2-\rho^2}$. The anomaly at the band center manifests as a sharp peak contrary to the conventional cases, whereas the anomalies at $E=\pm\sqrt{t_{v}^2-\rho^2}$ manifest as sharp dips., Comment: 10 pages, 11 figures

We investigate numerically the propagation and the Anderson localization of plane waves in a one-dimensional lattice chain, where disorder and saturable nonlinearity are simultaneously present. Using a calculation scheme for solving the stationary discrete nonlinear Schr\"{o}dinger equation in the fixed input case, the disorder-averaged logarithmic transmittance and the localization length are calculated in a numerically precise manner. The localization length is found to be a nonmonotonic function of the incident wave intensity, acquiring a minimum value at a certain finite intensity, due to saturation effects. For low incident intensities where the saturation effect is ineffective, the enhancement of localization due to Kerr-type nonlinearity occurs in a way similar to the case without saturation. For sufficiently high incident intensities, we find that the localization length is an increasing function of the incident wave intensity, which implies that localization is suppressed for stronger input intensities, and ultimately approaches a saturation value. This feature is associated with the fact that the nonlinear system is reduced to an effectively linear one, when either the incident wave intensity or the saturation parameter is sufficiently large. We also find that the nonlinear saturation effect is stronger and more pronounced when the energy of the incident wave is larger., Comment: 15 pages, 5 figures

We study theoretically the characteristics of surface waves excited at the interface between a metal and a general bi-isotropic medium, which includes isotropic chiral media and Tellegen media as special cases. We derive an analytical dispersion relation for surface waves, using which we calculate the effective index and the propagation length numerically. We also calculate the absorptance, the cross-polarized reflectance and the spatial distribution of the electromagnetic fields for plane waves incident on a bilayer system consisting of a metal layer and a bi-isotropic layer in the Kretschmann configuration, using the invariant imbedding method. The results obtained using the invariant imbedding method agree with those obtained from the dispersion relation perfectly. In the case of chiral media, the effective index is an increasing function of the chirality index, whereas in Tellegen media, it is a decreasing function of the Tellegen parameter. The propagation length for surface waves in both cases increase substantially as either the chirality index or the Tellegen parameter increases. In Tellegen media, it diverges to infinity when the effective index goes to zero, whereas in chiral media, it does when the parameters approach the cutoff values where quasi surface waves are excited. We investigate the characteristics of quasi surface waves excited when the chirality index is sufficiently large., Comment: 15 pages, 13 figures

Bi-isotropic media, which include isotropic chiral media and Tellegen media as special cases, are the most general form of linear isotropic media where the electric displacement and the magnetic induction are related to both the electric field and the magnetic intensity. In inhomogeneous bi-isotropic media, electromagnetic waves of two different polarizations are coupled to each other. In this paper, we develop a generalized version of the invariant imbedding method for the study of wave propagation in arbitrarily-inhomogeneous stratified bi-isotropic media, which can be used to solve the coupled wave propagation problem accurately and efficiently. We verify the validity and usefulness of the method by applying it to several examples, including the wave propagation in a uniform chiral slab, the surface wave excitation in a bilayer system made of a layer of Tellegen medium and a metal layer, and the mode conversion of transverse electromagnetic waves into longitudinal plasma oscillations in inhomogeneous Tellegen media. In contrast to the case of ordinary isotropic media, we find that the surface wave excitation and the mode conversion occur for both s and p waves in bi-isotropic media., Comment: 17 pages, 4 figures

It has been found that in the media where the dielectric permittivity $\epsilon$ or the magnetic permeability $\mu$ is near zero and in transition metamaterials where $\epsilon$ or $\mu$ changes from positive to negative values, there occur a strong absorption or amplification of the electromagnetic wave energy in the presence of an infinitesimally small damping or gain and a strong enhancement of the electromagnetic fields. We attribute these phenomena to the mode conversion of transverse electromagnetic waves into longitudinal plasma oscillations and its inverse process. In this paper, we study analogous phenomena occurring in chiral media theoretically using the invariant imbedding method. In uniform isotropic chiral media, right-circularly-polarized and left-circularly-polarized waves are the eigenmodes of propagation with different effective refractive indices $n_+$ and $n_-$, whereas in the chiral media with a nonuniform impedance variation, they are no longer the eigenmodes and are coupled to each other. We find that both in uniform chiral slabs where either $n_+$ or $n_-$ is near zero and in chiral transition metamaterials where $n_+$ or $n_-$ changes from positive to negative values, a strong absorption or amplification of circularly-polarized waves occurs in the presence of an infinitesimally small damping or gain. We present detailed calculations of the mode conversion coefficient, which measures the fraction of the electromagnetic wave energy absorbed into the medium, for various configurations of $\epsilon$ and $\mu$ with an emphasis on the influence of a nonuniform impedance. We propose possible applications of these phenomena to linear and nonlinear optical devices that react selectively to the helicity of the circular polarization., Comment: 10 pages, 5 figures, Optics Express 24, 1794 (2016)

We study theoretically the mode conversion and the associated resonant absorption of p-polarized electromagnetic waves into longitudinal plasma oscillations in cold, unmagnetized and stratified plasmas with periodic spatial density variations. We consider sinusoidal density configurations for which the frequency band where mode conversion occurs is well included within a transmission band of the one-dimensional plasma photonic crystal. We calculate the mode conversion coefficient, which measures the fraction of the electromagnetic wave energy absorbed into the plasma, and the spatial distribution of the magnetic field intensity for various values of the wave frequency and the incident angle using the invariant imbedding theory of mode conversion. We find that the absorption is greatly enhanced over a wide range of frequency and incident angle due to the interplay between the mode conversion and the photonic band structure. The enhancement occurs because for frequencies within a transmission band, the wave reflection is strongly suppressed and the waves penetrate more deeply into the inhomogeneous region, thereby increasing the possibility for them to reach many resonance points where the dielectric permittivity vanishes., Comment: 11 pages, 5 figures