Transport of localized waves via modes and channels
Chapter 2 in the book "Light localisation and lasing Random and Pseudo-random Photonic Structures" eds by Mher Ghulinyan and Lorenzo Pavesi
cond-mat.dis-nn↗
arXiv subjects
Azriel Z. Genack
Publications and source records attributed to Azriel Z. Genack.
Statistics and control of waves in disordered media
Fundamental concepts in the quasi-one-dimensional geometry of disordered wires and random waveguides in which ideas of scaling and the transmission matrix were first introduced are reviewed. We discuss the use of the transmission matrix to describe the scaling, fluctuations, delay time, density of states, and control of waves propagating through and within disordered systems. Microwave measurements, random matrix theory calculations, and computer simulations are employed to study the statistics of transmission and focusing in single samples and the scaling of the probability distribution of transmission and transmittance in random ensembles. Finally, we explore the disposition of the energy density of transmission eigenchannels inside random media.
cond-mat.dis-nn↗
Getting beneath the surface of opaque media: universal structure of transmission eigenchannels
Because the desire to explore opaque materials is ordinarily frustrated by multiple scattering of waves, attention has focused on the transmission matrix of the wave field. This matrix gives the fullest account of transmission and conductance and enables the control of the transmitted flux; however, it cannot address the fundamental issue of the spatial profile of eigenchannels of the transmission matrix inside the sample. Here we obtain a universal expression for the average disposition of energy of transmission eigenchannels for diffusive waves in terms of auxiliary localization lengths determined by the corresponding transmission eigenvalues. The spatial profile of each eigenchannel is shown to be a solution of a generalized diffusion equation. These results reveal the rich structure of transmission eigenchannels and enable the control of wave propagation and the energy distribution inside random media.
physics.optics↗
Transmission eigenchannels and the densities of states of random media
We show in microwave measurements and computer simulations that the contribution of each eigenchannel of the transmission matrix to the density of states (DOS) is the derivative with angular frequency of a composite phase shift. The accuracy of the measurement of the DOS determined from transmission eigenchannels is confirmed by the agreement with the DOS found from the decomposition of the field into modes. The distribution of the DOS, which underlies the Thouless number, is substantially broadened in the Anderson localization transition. We find a crossover from constant to exponential scaling of fluctuations of the DOS normalized by its average value. These results illuminate the relationships between scattering, stored energy and dynamics in complex media.
physics.optics↗
Phase Singularity Diffusion
We follow the trajectories of phase singularities at nulls of intensity in the speckle pattern of waves transmitted through random media as the frequency of the incident radiation is scanned in microwave experiments and numerical simulations. Phase singularities are observed to diffuse with a linear increase of the square displacement with frequency shift. The product of the diffusion coefficient of phase singularities in the transmitted speckle pattern and the photon diffusion coefficient through the random medium is proportional to the square of the effective sample length. This provides the photon diffusion coefficient and a method for characterizing the motion of dynamic material systems.
cond-mat.dis-nn↗
Microwave conductance in random waveguides in the crossover to Anderson localization and single parameter scaling
The nature of transport of electrons and classical waves in disordered systems depends upon the proximity to the Anderson localization transition between freely diffusing and localized waves. The suppression of average transport and the enhancement of relative fluctuations in conductance in one-dimensional samples with lengths greatly exceeding the localization length, $L\gg ξ$, are related in the single parameter scaling (SPS) theory of localization. However, the difficulty of producing an ensemble of statistically equivalent samples in which the electron wavefunction is temporally coherent has so-far precluded the experimental demonstration of SPS. Here we demonstrate SPS in random multichannel systems for the transmittance $T$ of microwave radiation, which is the analogue of the dimensionless conductance. We show that for $L\sim4ξ$ a single eigenvalue of the transmission matrix (TM) dominates transmission and the distribution of the $\ln T$ is Gaussian with a variance equal to the average of $-\ln T$, as conjectured by SPS. For samples in the crossover to localization, $L\simξ$, we find a one-sided distribution for $\ln T$. This anomalous distribution is explained in terms of a charge model for the eigenvalues of the transmission matrix $τ$ in which the Coulomb interaction between charges mimics the repulsion between the eigenvalues of transmission matrix. We show in the localization limit that the joint distribution of $T$ and the effective number of transmission eigenvalues determines the probability distributions of intensity and total transmission for a single incident channel.
cond-mat.dis-nn↗
Transmission eigenvalues in random media with surface reflection
The impact of surface reflection on the statistics of transmission eigenvalues is a largely unexplored subject of fundamental and practical importance in statistical optics. Here, we develop a first-principles theory and confirm numerically that the distribution of transmission eigenvalues of diffusive waves exhibits a nonanalytic `transition' as the strength of surface reflection at one surface passes through a critical value while that at the other is fixed. Above the critical value, the highest transmission eigenvalue is strictly smaller than unity and decreases with increasing internal reflection. When the input and output surfaces are equally reflective, the highest transmission eigenvalue is unity and the transition disappears irrespective of the strength of surface reflection.
cond-mat.dis-nn↗
Focusing through random media in space and time: a transmission matrix approach
We exploit the evolution in time of the transmission matrix following pulse excitation of a random medium to focus radiation at a selected time delay t' and position r. The temporal profile of a focused microwave pulse is the same as the incident Gaussian pulse. The contrast in space at time t' of the focused wave is determined by the participation number of transmission eigenvalues M' and the size N' of the measured transmission matrix. The initial rise and subsequent decay in contrast observed reflects the distribution of decay rates of the quasi-normal modes within the sample.
cond-mat.dis-nn↗
Transmission statistics and focusing in single disordered samples
We show in microwave experiments and random matrix calculations that in samples with a large number of channels the statistics of transmission for different incident channels relative to the average transmission is determined by a single parameter, the participation number of the eigenvalues of the transmission matrix, M. Its inverse, M-1, is equal to the variance of relative total transmission of the sample, while the contrast in maximal focusing is equal to M. The distribution of relative total transmission changes from Gaussian to negative exponential over the range in which M-1 changes from 0 to 1. This provides a framework for transmission and imaging in single samples.
physics.optics↗
Transport through modes in random media
We show that the field speckle pattern of transmitted microwave radiation can be decomposed into a sum of patterns of the modes of the medium. We find strong correlation between modal field speckle patterns which leads to destructive interference between modes. This allows us to explain complexities of steady state and pulsed transmission of localized waves and to harmonize wave and particle descriptions of diffusion.
cond-mat.dis-nn↗
Transmission eigenvalues and the bare conductance in the crossover to Anderson localization
We measure the field transmission matrix t for microwave radiation propagating through random waveguides in the crossover to Anderson localization. From these measurements, we determine the dimensionless conductance, g, and the individual eigenvalues $τ_n$ of the transmission matrix $tt^\dagger$ whose sum equals g. In diffusive samples, the highest eigenvalue, $τ_1$, is close to unity corresponding to a transmission of nearly 100%, while for localized waves, the average of $τ_1$, is nearly equal to g. We find that the spacing between average values of $\lnτ_n$ is constant and demonstrate that when surface interactions are taken into account it is equal to the inverse of the bare conductance.
cond-mat.dis-nn↗
Universal mesoscopic statistics and the localization of light
We follow the evolution with sample thickness, of intensity statistics for localized light transmitted through layered media in a crossover from one to three dimensions occasioned by transverse disorder. The probability distribution of intensity changes from one dimensional to a mixture of a mesoscopic function of a single parameter, the "statistical conductance," and a distribution of intensity for Gaussian waves. This suggests that the change to a universal statistics beyond 1D is associated with the topological change in the spatial field distribution.
cond-mat.dis-nn↗
Mesoscopic Speckle
We have measured the local and global statistics of singularity velocity, v, and have related these through the spatial correlation function of v. The distribution of v is a mixture of a mesoscopic distribution of global change in the speckle pattern and the distribution for v for Gaussian random fields. When v is normalized by the standard deviation of the fractional intensity change, probability distributions and correlation function of v approach those for random Gaussian fields. These results are directly analogous to the statistics of transmitted intensity normalized by the total transmission and provide a unified framework for understanding statistics of speckle evolution and intensity.
cond-mat.mes-hall↗
Photon delocalization transition in dimensional crossover in layered media
We report a crossover in optical propagation in random layered media from localization towards diffusion as the interaction of the wave with the sample is transformed from one to three-dimensional due to nonuniformity in the layer thickness. The crossover occurs at the point that the lateral spread of the wave equals the transverse coherence length in the transmitted speckle pattern.
cond-mat.mes-hall↗
Extended quasimodes within nominally localized random waveguides
We have measured the spatial and spectral dependence of the microwave field inside an open absorbing waveguide filled with randomly juxtaposed dielectric slabs in the spectral region in which the average level spacing exceeds the typical level width. Whenever lines overlap in the spectrum, the field exhibits multiple peaks within the sample. Only then is substantial energy found beyond the first half of the sample. When the spectrum throughout the sample is decomposed into a sum of Lorentzian lines plus a broad background, their central frequencies and widths are found to be essentially independent of position. Thus, this decomposition provides the electromagnetic quasimodes underlying the extended field in nominally localized samples. When the quasimodes overlap spectrally, they exhibit multiple peaks in space.
cond-mat.dis-nn↗
Twist Defect in Chiral Photonic Structures
We demonstrate that twisting one part of a chiral photonic structure about its helical axis produces a single circularly polarized localized mode that gives rise to an anomalous crossover in propagation. Up to a crossover thickness, this defect results in a peak in transmission and exponential scaling of the linewidth for a circularly polarized wave with the same handedness as structure. Above the crossover, however, the linewidth saturates and the defect mode can be excited only by the oppositely polarized wave, resulting in a peak in reflection instead of transmission.
physics.optics↗
Large Coherence Area Thin-Film Photonic Stop-Band Lasers
We demonstrate that the shift of the stop band position with increasing oblique angle in periodic structures results in a wide transverse exponential field distribution corresponding to strong angular confinement of the radiation. The beam expansion follows an effective diffusive equation depending only upon the spectral mode width. In the presence of gain, the beam cross section is limited only by the size of the gain area. As an example of an active periodic photonic medium, we calculate and measure laser emission from a dye-doped cholesteric liquid crystal film.
physics.optics↗