110 research outputs found
Statistics and control of waves in disordered media
No full textFundamental 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.Comment: 28 Pages, 18 Figures (Review
Probing nonorthogonality of eigenfunctions and its impact on transport through open systems
No full textInternational audienc
Selectively exciting quasi-normal modes in open disordered systems
No full textInternational audienceTransmission through disordered samples can be controlled by illuminating a sample with waveforms corresponding to the eigenchannels of the transmission matrix (TM). But can the TM be exploited to selectively excite quasi-normal modes and so control the spatial profile and dwell time inside the medium? We show in microwave and numerical studies that spectra of the TM can be analyzed into modal transmission matrices of rank unity. This makes it possible to enhance the energy within a sample by a factor equal to the number of channels. Limits to modal selectivity arise, however, from correlation in the speckle patterns of neighboring modes. In accord with an effective Hamiltonian model, the degree of modal speckle correlation grows with increasing modal spectral overlap and non-orthogonality of the modes of non-Hermitian systems. This is observed when the coupling of a sample to its surroundings increases, as in the crossover from localized to diffusive waves
FLUCTUATIONS, CORRELATION AND AVERAGE TRANSPORT OF ELECTROMAGNETIC RADIATION IN RANDOM MEDIA
No full textTransmission Zeros with Topological Symmetry in Complex Systems
No full textUnderstanding vanishing transmission in Fano resonances in quantum systems and metamaterials and perfect and ultralow transmission in disordered media, has advanced the understanding and applications of wave interactions. Here we use analytic theory and numerical simulations to understand and control the transmission and transmission time in complex systems by deforming a medium and by adjusting the level of gain or loss. Unlike the zeros of the scattering matrix, the position and motion of the zeros of the determinant of the transmission matrix in the complex plane of frequency and field decay rate have robust topological properties. In systems without loss or gain, the transmission zeros appear either singly on the real axis or as conjugate pairs in the complex plane. As the structure is modified, two single zeros and a complex conjugate pair of zeros may interconvert when they meet at a square root singularity in the rate of change of the distance between the transmission zeros in the complex plane with sample deformation. The transmission time is the spectral derivative of the argument of the determinant of the transmission matrix. It is a sum over Lorentzian functions associated with the resonances of the medium, which is the density of states, and with the zeros of the transmission matrix. Transmission vanishes, and the transmission time diverges as zeros are brought near the real axis. Monitoring the transmission and transmission time when two zeros are close may open up new possibilities for ultrasensitive detection
Steady-state and dynamic aspects of photon localization in quasi-one-dimensional disordered systems
No full textThis item is available only to currently enrolled UTSA students, faculty or staff. To download, navigate to Log In in the top right-hand corner of this screen, then select Log in with my UTSA ID.Anderson Localization is a wave interference phenomenon in which diffusion is absent and spatial localization of waves in multiply scattering media emerges in the presence of disorder. This regime of transport stands in contrast to wave diffusion which may occur in random media with dimensions less than the wave localization length. We have designed and built an experimental setup to study statistical aspects of steady-state and dynamic wave transport in quasi-one dimensional (Q1D) systems for microwave transmission through ensembles of realizations of disorder. We (i) find a breakdown of universal conductance fluctuations in dynamics within diffusive Q1D systems, (ii) introduce statistical criteria of single-channel transport in Q1D systems which can be used to chart the crossover from multi-channel transport in the diffusive regime to single-channel transport in the localized regime, (iii) show that the statistics of transmittance in the single-channel regime can be mapped onto a 1D system with a renormalized localization length, (iv) demonstrate that in the single-channel regime, the dominant eigenchannel is formed by a single localized mode or necklace state, (v) explore the dynamics of single-channel transport, and (vi) investigate whether the formation of optimal-order necklaces may occur in Q1D systems. These results are fundamental to understanding the static and dynamic behavior of waves in random media and can be useful in describing transmitting energy and information transfer through strongly scattering complex systems.Physics and Astronom
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