skip to main content
Explore Scholarly Publications and Datasets in the NSF-PAR

This content will become publicly available on February 10, 2023

Title: Wave Excitation and Dynamics in Non-Hermitian Disordered Systems
Dynamic and steady-state aspects of wave propagation are deeply connected in lossless open systems ‎in which the scattering matrix is unitary. There is then an equivalence among the energy excited within ‎the medium through all channels, the Wigner time delay, which is the sum of dwell times in all ‎channels coupled to the medium, and the density of states. But these equivalences fall away in the ‎presence of material loss or gain. In this paper, we use microwave measurements, numerical ‎simulations, and theoretical analysis to discover the changing relationships among fundamental wave ‎properties with loss and gain, and their dependence upon dimensionality and spectral overlap. We ‎begin with the demonstrations that the transmission time in random 1D media is equal to the density ‎of states even in the presence of ultrastrong absorption and that its ensemble average is independent ‎of the strengths of scattering and absorption. In contrast, the Wigner time becomes imaginary in the ‎presence of loss, with real and imaginary parts that fall with absorption. In multichannel media, the ‎transmission time remains equal to the density of states and is independent of the scattering strength ‎in unitary systems but falls with absorption to a degree that increases with more » the strengths of absorption ‎and scattering, and the number of channels coupled to the medium. We show that the relationships ‎between key propagation variables in non-Hermitian systems can be understood in terms of the ‎singularities of the phase of the determinant of the transmission matrix. The poles of the transmission ‎matrix are the same as those of the scattering matrix, but the transmission zeros are fundamentally ‎different. Whereas the zeros of the scattering matrix are the complex conjugates of the poles, the ‎transmission zeros are topological: in unitary systems they occur only singly on the real axis or as ‎conjugate pairs. We follow the evolution and statistics of zeros in the complex plane as random ‎samples are deformed. The sensitivity of the spacing of zeros in the complex plane with deformation ‎of the sample has a square-root singularity at a zero point at which two single zeros and a complex ‎pair interconvert. The transmission time is a sum of Lorentzian functions associated with poles and ‎zeros. The sum over poles is the density of states with an average that is independent of scattering ‎and dissipation. But the sum over zeros changes with loss, gain, scattering strength and the number of ‎channels in ways that make it possible to control ultranarrow spectral features in transmission and ‎transmission time. We show that the field, including the contribution of the still coherent incident ‎wave, is a sum over modal partial fractions with amplitudes that are independent of loss and gain. The ‎energy excited may be expressed in terms of the resonances of the medium and is equal to the dwell ‎time even in the presence of loss or gain.‎ « less
Authors:
; ;
Award ID(s):
2022629
Publication Date:
NSF-PAR ID:
10319445
Journal Name:
Physical review research
Volume:
4
Issue:
1
ISSN:
2643-1564
Sponsoring Org:
National Science Foundation
More Like this
  1. ; ( , Physical review)
    Understanding vanishing transmission in Fano resonances in quantum systems and metamaterials and perfect and ultralow transmission in disordered media has advanced the knowledge 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 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 (TM) in the complex plane of frequency and field decay rate have robust topological properties. In systems without lossmore »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 TM. 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 TM. 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 new possibilities for ultrasensitive detection.« less
  2. ; ; ; ; ( , Nanophotonics)
    Abstract We outline and interpret a recently developed theory of impedance matching or reflectionless excitation of arbitrary finite photonic structures in any dimension. The theory includes both the case of guided wave and free-space excitation. It describes the necessary and sufficient conditions for perfectly reflectionless excitation to be possible and specifies how many physical parameters must be tuned to achieve this. In the absence of geometric symmetries, such as parity and time-reversal, the product of parity and time-reversal, or rotational symmetry, the tuning of at least one structural parameter will be necessary to achieve reflectionless excitation. The theory employs amore »recently identified set of complex frequency solutions of the Maxwell equations as a starting point, which are defined by having zero reflection into a chosen set of input channels, and which are referred to as R-zeros. Tuning is generically necessary in order to move an R-zero to the real frequency axis, where it becomes a physical steady-state impedance-matched solution, which we refer to as a reflectionless scattering mode (RSM). In addition, except in single-channel systems, the RSM corresponds to a particular input wavefront, and any other wavefront will generally not be reflectionless. It is useful to consider the theory as representing a generalization of the concept of critical coupling of a resonator, but it holds in arbitrary dimension, for arbitrary number of channels, and even when resonances are not spectrally isolated. In a structure with parity and time-reversal symmetry (a real dielectric function) or with parity–time symmetry, generically a subset of the R-zeros has real frequencies, and reflectionless states exist at discrete frequencies without tuning. However, they do not exist within every spectral range, as they do in the special case of the Fabry–Pérot or two-mirror resonator, due to a spontaneous symmetry-breaking phenomenon when two RSMs meet. Such symmetry-breaking transitions correspond to a new kind of exceptional point, only recently identified, at which the shape of the reflection and transmission resonance lineshape is flattened. Numerical examples of RSMs are given for one-dimensional multimirror cavities, a two-dimensional multiwaveguide junction, and a multimode waveguide functioning as a perfect mode converter. Two solution methods to find R-zeros and RSMs are discussed. The first one is a straightforward generalization of the complex scaling or perfectly matched layer method and is applicable in a number of important cases; the second one involves a mode-specific boundary matching method that has only recently been demonstrated and can be applied to all geometries for which the theory is valid, including free space and multimode waveguide problems of the type solved here.« less
  3. ( )
    Abstract
    An improved understanding of the optical properties of secondary organic aerosol (SOA) particles is needed to better predict their climate impacts. Here, SOA was produced by reacting 1-methylnaphthalene or longifolene with hydroxyl radicals (OH) under variable ammonia (NH3), nitrogen oxide (NOx), and relative humidity (RH) conditions. In the presence of NH3 and NOx, longifolene-derived aerosols had relatively high single scattering albedo (SSA) values and low absorption coefficients at 375 nm independent of RH, suggesting that the longifolene SOA is mostly scattering. In 1-methylnaphthalene experiments, the resulting SSA and SOA mass absorption coefficient (MACorg) values suggest the formation of light-absorbingMore>>
  4. ; ( , European Journal of Applied Mathematics)
    We investigate the Fano resonance in grating structures using coupled resonators. The grating consists of a perfectly conducting slab with periodically arranged subwavelength slit holes, where inside each period, a pair of slits sit very close to each other. The slit holes act as resonators and are strongly coupled. It is shown rigorously that there exist two groups of resonances corresponding to poles of the scattering problem. One sequence of resonances has imaginary part in the order of ε , where ε is the size of the slit aperture, while the other sequence has imaginary part in the order ofmore »ε 2 . When coupled with the incident wave at resonant frequencies, the narrow-band resonant scattering induced by the latter will interfere with the broader background resonant radiation induced by the former. The interference of these two resonances generates the Fano-type transmission anomaly, which persists in the whole radiation continuum of the grating structure as long as the slit aperture size is small compared to the incident wavelength.« less
  5. ; ; ( , New Journal of Physics)
    Abstract We investigate how the local density of states in a plasmonic cavity changes due to the presence of a distorting quantum emitter. To this end, we use first-order scattering theory involving electromagnetic Green’s function tensors for the bare cavity connecting the positions of the emitter that distorts the density of states and the one that probes it. The confined, quasistatic character of the plasmonic modes enables us to write the density of states as a Lorentzian sum. This way, we identify three different mechanisms behind the asymmetric spectral features emerging due to the emitter distortion: the modification of themore »plasmonic coupling to the probing emitter, the emergence of modal-like quadratic contributions and the absorption by the distorting emitter. We apply our theory to the study of two different systems (nanoparticle-on-mirror and asymmetric bow-tie-like geometries) to show the generality of our approach, whose validity is tested against numerical simulations. Finally, we provide an interpretation of our results in terms of a Hamiltonian model describing the distorted cavity.« less
  • Citation Formats
  • MLA
  • APA
  • Chicago
  • BibTeX
  • Save / Share this Record
  • Send to Email