Session T53: Focus Session: Wave Propagation in Strongly Scattering Media

Fluctuations in Intensity in disordered media as a New Sub-wavelength Microscopy Tool

The intensity-intensity correlations of waves that propagate coherently through a disordered system are discussed, in the mesoscopic scale. Since many of the properties of those correlations are independent of the transport regime (ballistic, diffusive or localized) they can be discussed using the macroscopic approach of random matrix theory [1]. In that framework we have considered the problem of multiple sources emitting simultaneously in a disoredered medium, and we will show that the correlations and even the intensity fluctuations at a fixed point outside the turbid system can provide useful information about both the relative position of the sources and their coherence. Moreover, the information obtained is relevant at subwavelength lengths, opening the possibility of new applications to fluorescence studies, communications and image processing in turbid environments, complementary to traditional techniques. \\[4pt] [1] G. Cwilich, L. Froufe, J.J. Saenz, Phys Rev E74, 045603 (R) (2006)   

Photon localization in a nematic liquid crystal

The nematic liquid crystal MBBA, due to director fluctuations, is a highly scattering material with low absorption. We previously\footnote{ J. P. McClymer and H.M. Shehadeh, Photon Localization in a Nematic Liquid Crystal, Phys. Rev. A~79, 031802(R)~(2009)} reported that the transmission coefficient for laser light at 633 nm decays exponentially with a decay length of approximately 0.8 mm while the absorption length is over 30 times larger which we interpret as evidence for photon localization. The data does not fit a model of diffusion or diffusion with absorption. We have extended this work by measuring the decay coefficient for incoherent light from 475 to 825 nm. We find that the absorption remains low over this range, with absorption lengths ranging from 8 mm at the blue end of the spectrum to 12 mm in the near IR. The transmission coefficient in the nematic phase shows an exponential decrease with decay constants an order of magnitude smaller than the absorption length, 0.4 mm, in the blue end while increasing to 3 mm in the near IR. The data indicates that photon localization is observed throughout the visible region into the near IR.   

Light Transport in Disordered Media with PT-symmetry

The localization properties of randomly layered optical media with ${\cal PT}$-symmetric refraction index are studied both theoretically and numerically using the transfer-matrix method. The transmission coefficient decays exponentially as a function of the system size, with a rate $\xi_{\gamma}(W)^{-1}=\xi_0(W)^{-1}+\xi_{\gamma}(0)^{-1}$, where $\xi_0(W)$ is the localization length of the equivalent passive disordered system and $\xi_{\gamma}(0)$ is the attenuation/amplification length of the corresponding perfect system with combined gain/loss refraction index profile. While transmission processes are reciprocal to left and right incident waves, one-sided reflection is found.   

New perspectives on waves in random media: Speckle, modes, transmission eigenchannels, and focusing

The understanding of electron localization and conductance fluctuations has been advanced by utilizing notions of speckle, modes, and transmission eigenchannels. These concepts cannot be probed directly for electronic systems but can be explored for classical waves utilizing spectra of field transmission coefficients between arrays of points on the incident and output surfaces of ensembles of random samples. This is illustrated in microwave measurements of transmission through random waveguides in the Anderson localization transition. These experiments supply the link between the statistics of intensity and conductance and show that transmitted wave can be decomposed simultaneously into the underlying quasi-normal modes and transmission eigenchannels of the sample. The power of each of these approaches and the richness of the links between them will be illustrated by examples that reveal new aspects of wave propagation. The delayed onset of transmission following pulse excitation is shown to be the result of destructive interference between highly correlated speckle patterns of neighboring modes, while the falling decay rate at later times reflects the incoherent decay of increasingly prominent long-lived modes. We determine the individual eigenvalues \textit{$\tau $}$_{n}$ of the transmission matrix and achieve nearly complete transmission in opaque diffusive samples. We demonstrate that when reflection at the sample interface is taken into account, the spacing between average values of ln\textit{$\tau $}$_{n}$ is equal to the inverse of the bare conductance, in accord with predictions by Dorokhov [1]. We find that the distribution of total transmission relative to the conductance is determined by the effective number of transmission eigenvalues, $N_{eff} =\left( {\sum\nolimits_{n=1}^N {\tau _n } } \right)^2/\sum\nolimits_{n=1}^N {\tau _n^2 } $, which provides the link between the statistics of intensity and conductance. For diffusive waves, $N_{eff}$ is the inverse of the degree of intensity correlation. The contrast between the peak and background of maximally focused radiation in the transmitted wave, achieved when the incident is phase conjugated relative to the selected focal point, is equal to $(1+N_{eff})$. \\[4pt] [1] O. N. Dorokhov, Solid State Commun. \textbf{51}, 381 (1984).   

Experimental Observation of Brachistochrone Wave Dynamics in PT Symmetric Structures

Mutually coupled modes of a pair of active LRC circuits, one with amplification and another with an equivalent amount of attenuation, provide an experimental realization of a wide class of systems where gain and loss mechanisms break the Hermiticity while preserving parity-time (PT) symmetry. For a value $ \gamma_{ PT} $ of the gain and loss strength parameter the eigenfrequencies undergo a spontaneous phase transition from real to complex values, while the normal modes coalesce, acquiring a definite chirality. A dramatic manifestation of PT symmetry is observed in the brachistochrone wave dynamics. Experimental findings support the theoretical prediction of arbitrarily small energy transfer times between the LRC elements of the circuit. We envision that realization of such design strategies can have applications in telecommunications and metamaterial structures.   

Experimental studies of PT-scattering in arrays of active $LRC$ elements

One of the fundamental tasks in antenna theory is getting an antenna to radiate by removing mismatch losses between the loaded antenna and the transmission line that delivers the power. We will present experimental data suggesting that ${\cal PT}$-symmetric antenna structures, where active elements associated with the real part of impedance ($\pm R$) are involved, can lead to a broadband, reflectionless behavior. The suggested {\it optimal matching} strategy can potentially be superior to the existing one which uses active $LC$ elements in order to balance the reactance. Along these lines, we also envision antenna arrangements with unidirectional ultrafast communication capabilities, where the signal will transfer faster (or slower) between the active elements of the ${\cal PT}$-structure depending on the entrance point of the incident wave.   

Measurement of the Probability Distribution of Optical Transmittance on the Crossover to Anderson localization

We report measurements of spectra of the field transmission matrix $t$ for microwave radiation propagating through waveguide filled with randomly positioned dielectric scattering spheres in the Anderson localization transition. Diagonalizing the matrix product \textit{tt}$^{\dag }$ gives the transmission eigenvalues \textit{$\tau $}$_{n}$, which yields the optical transmittance, $T=\sum\nolimits_{a,b=1}^N {\left| {t_{ba} } \right|^2} =\sum\nolimits_{n=1}^N {\tau _n } $. The ensemble average of the transmittance is equal to the dimensionless conductance, $g=$. We show the probability distribution of transmittance $P(T)$ changes from Gaussian to log-normal as the value of $g$ decreases. The distribution $P(T)$ is analyzed in terms of the underlying transmission eigenvalues \textit{$\tau $}$_{n}$. For random samples with $g\sim $3.9, we found $P(T)$ follows a Gaussian distribution. For $g\sim $0.37, we observe a highly asymmetric distribution for --ln$T. $The sharp drop for high values of $T$ is attributed to the restriction that \textit{$\tau $}$_{n}<$1 and the repulsion between transmission eigenvalues even for localized samples. For $g\sim $0.04, the distribution of transmittance is nearly log-normal. The variance of -ln$T$, \textit{$\sigma $}$^{2}$, scales linearly with $<$-ln$T>$ as predicted by single parameter scaling even for weakly localized waves.   

Mode Statistics in Random Media

The nature of transport through a material is determined by the spectrum of modes or energy levels. We have analyzed the frequency variation of the transmitted microwave field speckle pattern for quasi one-dimensional random samples to obtain the central frequencies, linewidths and speckle patterns of the modes for an ensemble of samples at lengths of two and three times the localization length. The number of modes can be determined unambiguously from the spectrum of the goodness of fit. From these results we obtain the statistics of mode spacings and widths. The distribution of spacings between adjacent modes is close to the Wigner surmise predicted for diffusive waves exhibiting strong level repulsion. However, deviations from the Wigner surmise can be seen in the distribution of spacings beyond nearest modes. A weakening in the rigidity of the modal spectrum is observed as the sample length increases because of reduced level repulsion for more strongly localized waves. In contrast to residual diffusive behavior for level spacing statistics, the distribution of level widths are log-normal as predicted for localized waves.   

A Random Matrix Approach for Understanding Wave Statistics from Wireless Communications to Quantum Dots

Complexity of a wave propagation environment is advantageous from the perspective of wave chaos theory because, in the semiclassical limit, the corresponding ray trajectories of the wave propagation have chaotic dynamical behavior, and a statistical description is most appropriate. Random matrix theory (RMT) successfully describes universal properties of the system. We combine RMT with our random coupling model that includes non-universal effects, such as the radiation impedance of the ports and the effect of short ray trajectories in the system, and we establish a first-principles model for wave statistical properties such as the fading amplitude in wireless communications, the scattering matrix, the impedance matrix, and the thermopower of quantum dots. We also report experimental tests on two ray-chaotic microwave cavities with different degrees of loss. In the high loss regime the results demonstrate that our RMT model agrees with traditional fading models (Rayleigh fading and Rice fading) and provides a more general understanding of the models and a detailed physical basis for their parameters. Moreover, in the low loss regime the RMT approach describes the data better.   

Quantifying Volume Changing Perturbations to a Wave Chaotic System

The Loschmidt Echo and Fidelity decay are used to measure perturbations on a quantum wave chaotic system. We extended these concepts to classical waves to detect perturbations. [1]. In this work, we show that volume changing perturbations to a classical wave chaotic cavity can be quantified with a sub-wavelength sensitivity. This is demonstrated both numerically and experimentally. A wave chaotic quasi-1D star graph model [2], was initially used to show the results. The quantification of electrical-volume changing perturbations to a one cubic meter aluminum box will be demonstrated experimentally; the experimental results are also supported by a finite difference time domain simulation of the box. Finally, the approach to quantify these perturbations will be shown to apply to a generic wave chaotic system by using a time domain version of our Random Coupling Model.   

Nonlinear Time-Reversal in a Wave Chaotic System

Time reversal mirrors are particularly simple to implement in wave chaotic systems and form the basis for a new class of sensors [1-3]. These sensors work by applying the quantum mechanical concepts of Loschmidt echo and fidelity decay to classical waves. The sensors make explicit use of time-reversal invariance and spatial reciprocity in a wave chaotic system to remotely measure the presence of small perturbations to the system. The underlying ray chaos increases the sensitivity to small perturbations throughout the volume explored by the waves. We extend our time-reversal mirror to include a discrete element with a nonlinear dynamical response. The initially injected pulse interacts with the nonlinear element, generating new frequency components originating at the element. By selectively filtering for and applying the time-reversal mirror to the new frequency components, we focus a pulse only onto the element, without knowledge of its location. Furthermore, we demonstrate transmission of arbitrary patterns of pulses to the element, creating a targeted communication channel to the exclusion of 'eavesdroppers' at other locations in the system. [1] Appl. Phys. Lett. 95, 114103 (2009) [2] J. Appl. Phys. 108, 1 (2010) [3] Acta Physica Polonica A 112, 569 (2007)   

Low-Diffracting Modes in Surface Plasmon Metamaterials

Plasmonic structures, with periodic arrays of thin PMMA ridges on metal substrates have been shown experimentally to overcome the diffraction limit. Here we present a theoretical description of this phenomenon. We use mode matching technique to analyze the dynamics of the electromagnetic waves in the periodic systems, taking into account the extended 3D-geometry and the finite thickness of the PMMA ridges. Specifically, we focus on the behavior of plasmonic mode and its non-trivial coupling to the free space waves and to the other guided modes of the system. The eigen states of the periodic system dominated by the surface waves are identified and their dispersion is analyzed via generalization of mode-matching formalism and Bloch-periodic approach. An analytical approximation, adequately describing the behavior of the system is derived and is used to explain the suppression of diffraction in the system.   

Nonsymmorphic Phononic Metamaterials: shaping waves over multiple length scales

The vector nature of the phonon makes rational design of phononic metamaterials challenging, despite potential in unique wave propagation behavior, such as negative refraction and hyper-lensing. While most designs to date focus on the ``meta-atom'' (building block) design, their ``spatial arrangement'' (non-locality) is equally instrumental in dispersion engineering. Here, we present a generalized design framework (DF) for PMM design, utilizing both ``global'' and ``local'' symmetry concepts. We demonstrate, utilizing specific properties of nonsymmorphic plane groups, PMMs possessing i) a low-frequency in-plane complete spectral gap (ICSG) of 102{\%} (CSG of 88{\%}), ii) a set of polychromatic ICSGs totaling over 100{\%} in normalized gap size. Within the same DF, we further integrate broken symmetry states (BSS) (edge states, waveguides, etc) with designed polarization, (de)localization and group velocities. In particular, we demonstrate how these BSS may be utilized to elucidate signatures of complex polarization fields through phonon-structure interactions, leading to interesting applications in elastic-wave imaging, as well as information retrieval by probing polarization states of scattering bodies over multiple scales.