Optical Thouless conductance and level-spacing statistics in two-dimensional Anderson localizing systems

Mondal, Sandip; Kumar, Randhir; Kamp, M.; Mujumdar, Sushil

doi:10.1103/physrevb.100.060201

Cited by 22 publications

(8 citation statements)

References 42 publications

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“…For frequencies in the band gaps we find no modes, all positions are phase coherent and there is no propagation. Next, we calculate the Thouless conductance g Th ¼ δν=Δν, which is a fundamental localization parameter [33][34][35]. Thouless argued that in the Anderson localization regime, the dimensionless ratio g Th ¼ δν=Δν falls below unity.…”

mentioning

confidence: 99%

Experimental Tuning of Transport Regimes in Hyperuniform Disordered Photonic Materials

Aubry¹,

Froufe‐Pérez²,

Kuhl³

et al. 2020

Phys. Rev. Lett.

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We present wave transport experiments in hyperuniform disordered arrays of cylinders with high dielectric permittivity. Using microwaves, we show that the same material can display transparency, photon diffusion, Anderson localization, or a full band gap, depending on the frequency ν of the electromagnetic wave. Interestingly, we find a second weaker band gap, which appears to be related to the second peak of the structure factor. Our results emphasize the importance of spatial correlations on different length scales for the formation of photonic band gaps.

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confidence: 99%

Experimental Tuning of Transport Regimes in Hyperuniform Disordered Photonic Materials

Aubry¹,

Froufe‐Pérez²,

Kuhl³

et al. 2020

Phys. Rev. Lett.

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“…In lower dimensional 1D, 2D and quasi-1D geometries, waves may be localized in small enough samples that the level spacing is large enough relative to the leakage and absorption rates that resonances can be discerned in transmission. It is then possible to determine the central frequencies and linewidths of the modes from transmission spectra and to determine 〈𝜌〉 and 〈𝛾 𝑚 〉 for an ensemble of random samples [21,22]. The field absorption rate could be determined from the narrowed linewidth of transmission peaks in samples with reflectors placed over the boundaries.…”

Section: Discussionmentioning

confidence: 99%

Wave excitation and dynamics in non-Hermitian disordered systems

Huang

Kang

Genack

2022

Phys. Rev. Research

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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 the internal field, transmission, transmission time, dwell time, total excited energy, and the density of states in with loss and gain, and their dependence upon dimensionality and spectral overlap. 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 total energy excited is equal to the dwell time. When modes are spectrally isolated, the energy is proportional to the sum of products of the modal contribution to the density of states and the ratio of the linewidth without and with absorption. When modes overlap, however, the total energy is further reduced by loss and enhanced by gain. In 1D, the average transmission time is independent of loss, gain, and scattering strength. In higher dimensions, however, the average transmission time falls with loss, scattering strength and channel number, and increases with gain. It is the sum over Lorentzian functions associated with the zeros as well as the poles of the transmission matrix. This endows transmission zeros with robust topological characteristics: in unitary media, zeros occur either singly on the real axis or as conjugate pairs in the complex frequency plane. The transmission zeros are moved down or up in the complex plane by an amount equal to the internal rate of decay or growth of the field. In weakly absorbing media, the spectrum of the transmission time of the lowest transmission eigenchannel is the sum of Lorentzians due to transmission zeros plus a background due to far-off-resonance poles. As the scattering strength increases, conjugate pairs of zeros are brought to the real axis and converted to two single zeros which are constrained to move on the real axis until they combine and leave the real axis as a conjugate pair. The average density of transmission zeros in the complex plane is found from the fall of the average transmission time with absorption as zeros are swept into the lower half of the complex frequency plane. As a sample is deformed, two single zeros and a conjugate pair of zeros may interconvert on the real axis with a square root singularity in the sensitivity of the spacing between transmission zeros to structural change. Thus, the disposition of poles and zeros in the complex frequency plane provides a framework for understanding and controlling wave propagation in non-Hermitian systems.

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“…Beyond the differences observed between the two waveguide designs, the methodology used here constitutes an important step forward in understanding light transport in photonic-crystal waveguides subject to structural disorder, which in the slow-light regime is governed by the localization length, ξ. While the exponential decay in transmission measurements cannot disentangle backscattering losses from other losses [7], such as absorption or out-of-plane scattering, the spectral properties of the (quasi-)normal modes in an open finite system [34] are better suited to obtain ξ. The Thouless criterion [35] is not directly applicable to the cavities here, which exhibit transmission peaks even in the absence of scattering.…”

Section: Discussionmentioning

confidence: 99%

Observation of slow light in glide-symmetric photonic-crystal waveguides

Patil,

Arregui,

Mechlenborg

et al. 2021

Preprint

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We report optical transmission measurements on suspended silicon photonic-crystal waveguides, where one side of the photonic lattice is shifted by half a period along the waveguide axis. The combination of this glide symmetry and slow light leads to a strongly enhanced chiral light-matter interaction but the interplay between slow light and backscattering has not been investigated experimentally in such waveguides. We build photonic-crystal resonators consisting of glide-symmetric waveguides terminated by reflectors and use transmission measurements as well as evanescent coupling to map out the dispersion relation. We find excellent agreement with theory and measure group indices exceeding 90, implying significant potential for applications in slow-light devices and chiral quantum optics. By measuring resonators of different length, we assess the role of backscattering induced by fabrication imperfections and its intimate connection to the group index.

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Optical Thouless conductance and level-spacing statistics in two-dimensional Anderson localizing systems

Cited by 22 publications

References 42 publications

Experimental Tuning of Transport Regimes in Hyperuniform Disordered Photonic Materials

Experimental Tuning of Transport Regimes in Hyperuniform Disordered Photonic Materials

Wave excitation and dynamics in non-Hermitian disordered systems

Observation of slow light in glide-symmetric photonic-crystal waveguides

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