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Bachelard N, Schumer A, Kumar B, Garay C, Arlandis J, Touzani R, Sebbah P. Coalescence of Anderson-localized modes at an exceptional point in 2D random media. OPTICS EXPRESS 2022; 30:18098-18107. [PMID: 36221617 DOI: 10.1364/oe.454493] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/23/2022] [Accepted: 04/09/2022] [Indexed: 06/16/2023]
Abstract
In non-Hermitian settings, the particular position at which two eigenstates coalesce in the complex plane under a variation of a physical parameter is called an exceptional point. An open disordered system is a special class of non-Hermitian system, where the degree of scattering directly controls the confinement of the modes. Herein a non-perturbative theory is proposed which describes the evolution of modes when the permittivity distribution of a 2D open dielectric system is modified, thereby facilitating to steer individual eigenstates to such a non-Hermitian degeneracy. The method is used to predict the position of such an exceptional point between two Anderson-localized states in a disordered scattering medium. We observe that the accuracy of the prediction depends on the number of localized states accounted for. Such an exceptional point is experimentally accessible in practically relevant disordered photonic systems.
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Balasubrahmaniyam M, Mondal S, Mujumdar S. Necklace-State-Mediated Anomalous Enhancement of Transport in Anderson-Localized non-Hermitian Hybrid Systems. PHYSICAL REVIEW LETTERS 2020; 124:123901. [PMID: 32281859 DOI: 10.1103/physrevlett.124.123901] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/19/2019] [Revised: 02/04/2020] [Accepted: 02/21/2020] [Indexed: 06/11/2023]
Abstract
Non-Hermiticity is known to manifest interesting modifications in the transport properties of complex systems. We report an intriguing regime of transport of hybrid quasiparticles in a non-Hermitian setting. We calculate the probability of transport, quantified by the Thouless conductance, of hybrid plasmons under varying degrees of disorder. With increasing disorder, we initially observe an expected decrease in average transmission, followed by an anomalous rise at localizing disorder. The behavior originates from the confluence of hybridization and non-Hermiticity, in which the former realizes the aggregation of eigenvalues migrating under disorder, while the latter enables energy transfer between the eigenmodes. We find that the enhanced transmission is mediated by quasiparticle hopping over various Anderson-localized states within the so-formed necklace states. We note that, in this scenario, all configurations exhibit the formation of necklace states and enhanced transport, unlike the conventionally known behavior of necklace states which only occurs in rare configurations.
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Affiliation(s)
- M Balasubrahmaniyam
- Nano-optics and Mesoscopic Optics Laboratory, Tata Institute of Fundamental Research, 1, Homi Bhabha Road, Mumbai 400 005, India
| | - Sandip Mondal
- Nano-optics and Mesoscopic Optics Laboratory, Tata Institute of Fundamental Research, 1, Homi Bhabha Road, Mumbai 400 005, India
| | - Sushil Mujumdar
- Nano-optics and Mesoscopic Optics Laboratory, Tata Institute of Fundamental Research, 1, Homi Bhabha Road, Mumbai 400 005, India
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3
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Abstract
Diffusion is the result of repeated random scattering. It governs a wide range of phenomena from Brownian motion, to heat flow through window panes, neutron flux in fuel rods, dispersion of light in human tissue, and electronic conduction. It is universally acknowledged that the diffusion approach to describing wave transport fails in translucent samples thinner than the distance between scattering events such as are encountered in meteorology, astronomy, biomedicine, and communications. Here we show in optical measurements and numerical simulations that the scaling of transmission and the intensity profiles of transmission eigenchannels have the same form in translucent as in opaque media. Paradoxically, the similarities in transport across translucent and opaque samples explain the puzzling observations of suppressed optical and ultrasonic delay times relative to predictions of diffusion theory well into the diffusive regime. Despite the universal nature of diffusion, the behavior of light transport in optically thin media has remained unclear. Here the authors show that the description of this behavior in translucent media has the same form as in opaque media, even at length scales far below the mean free path.
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Affiliation(s)
- Zhou Shi
- Department of Physics, Queens College and Graduate Center of the City University of New York, Flushing, NY, 11367, USA.,Chiral Photonics Inc., 26 Chapin Road, Pine Brook, NJ, 07058, USA
| | - Azriel Z Genack
- Department of Physics, Queens College and Graduate Center of the City University of New York, Flushing, NY, 11367, USA.
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4
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Herzig Sheinfux H, Kaminer I, Genack AZ, Segev M. Interplay between evanescence and disorder in deep subwavelength photonic structures. Nat Commun 2016; 7:12927. [PMID: 27708260 PMCID: PMC5059687 DOI: 10.1038/ncomms12927] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/08/2015] [Accepted: 08/17/2016] [Indexed: 11/27/2022] Open
Abstract
Deep subwavelength features are expected to have minimal impact on wave transport. Here we show that in contrast to this common understanding, disorder can have a dramatic effect in a one-dimensional disordered optical system with spatial features a thousand times smaller than the wavelength. We examine a unique regime of Anderson localization where the localization length is shown to scale linearly with the wavelength instead of diverging, because of the role of evanescent waves. In addition, we demonstrate an unusual order of magnitude enhancement of transmission induced due to localization. These results are described for electromagnetic waves, but are directly relevant to other wave systems such as electrons in multi-quantum-well structures. Features much smaller than the wavelength are not expected to have a significant impact on the transport of a wave. Here, the authors show that Anderson localization can dominate light transport in a one-dimensional disordered system, even when the disordered features are a thousand times smaller than the wavelength.
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Affiliation(s)
| | - Ido Kaminer
- Technion, Israel Institute of Technology, Haifa 32000, Israel.,Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Azriel Z Genack
- Physics Department, Queens College and Graduate Center of CUNY, Flushing, New York 11367, USA
| | - Mordechai Segev
- Technion, Israel Institute of Technology, Haifa 32000, Israel
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5
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Shi Z, Davy M, Genack AZ. Statistics and control of waves in disordered media. OPTICS EXPRESS 2015; 23:12293-12320. [PMID: 25969316 DOI: 10.1364/oe.23.012293] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
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.
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Choi SH, Byun KM, Kim YL. Excitation of multiple resonances in 1D Anderson localized systems for efficient light amplification. OPTICS LETTERS 2015; 40:847-850. [PMID: 25723448 DOI: 10.1364/ol.40.000847] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
Excitation of hybridized multiple resonances can be an effective route for coherent light generation in irregular 1D systems larger than the localization length of light. Necklace states are often considered to have nonlocalized states. However, we propose that some hybridized/coupled states can have high-resonant tunneling with spatially extended fields. If strong localization properties are preserved in hybridized resonances, the excitation of such states allows for deposition of the excitation energy deep into the structure and spatial overlap with local gain regions. This result could allow for better utilizing hybridized resonances in biological or natural photonic systems.
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Peña A, Girschik A, Libisch F, Rotter S, Chabanov AA. The single-channel regime of transport through random media. Nat Commun 2014; 5:3488. [PMID: 24663028 PMCID: PMC3973072 DOI: 10.1038/ncomms4488] [Citation(s) in RCA: 41] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/17/2013] [Accepted: 02/21/2014] [Indexed: 11/24/2022] Open
Abstract
The propagation of light through samples with random inhomogeneities can be described by way of transmission eigenchannels, which connect incoming and outgoing external propagating modes. Although the detailed structure of a disordered sample can generally not be fully specified, these transmission eigenchannels can nonetheless be successfully controlled and used for focusing and imaging light through random media. Here we demonstrate that in deeply localized quasi-1D systems, the single dominant transmission eigenchannel is formed by an individual Anderson-localized mode or by a 'necklace state'. In this single-channel regime, the disordered sample can be treated as an effective 1D system with a renormalized localization length, coupled through all the external modes to its surroundings. Using statistical criteria of the single-channel regime and pulsed excitations of the disordered samples allows us to identify long-lived localized modes and short-lived necklace states at long and short time delays, respectively.
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Affiliation(s)
- A. Peña
- Department of Physics and Astronomy, University of Texas at San Antonio, San Antonio, Texas 78249, USA
| | - A. Girschik
- Institute for Theoretical Physics, Vienna University of Technology, A-1040 Vienna, Austria
| | - F. Libisch
- Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - S. Rotter
- Institute for Theoretical Physics, Vienna University of Technology, A-1040 Vienna, Austria
| | - A. A. Chabanov
- Department of Physics and Astronomy, University of Texas at San Antonio, San Antonio, Texas 78249, USA
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8
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Shi Z, Davy M, Wang J, Genack AZ. Focusing through random media in space and time: a transmission matrix approach. OPTICS LETTERS 2013; 38:2714-2716. [PMID: 23903120 DOI: 10.1364/ol.38.002714] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/02/2023]
Abstract
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 of the contrast observed reflect the distribution of decay rates of the quasi-normal modes within the sample.
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Affiliation(s)
- Zhou Shi
- Department of Physics, Queens College of the City University of New York, Flushing, New York 11367, USA.
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9
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Chen L, Jiang X. Characterization of short necklace states in the logarithmic transmission spectra of localized systems. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2013; 25:175901. [PMID: 23567823 DOI: 10.1088/0953-8984/25/17/175901] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/02/2023]
Abstract
High transmission plateaus exist widely in the logarithmic transmission spectra of localized systems. Their physical origins are short chains of coupled localized states embedded inside the localized system, which are dubbed as 'short necklace states'. In this work, we define the essential quantities and then, based on these quantities, we investigate the properties of the short necklace states statistically and quantitatively. Two different approaches are utilized and their results agree very well. In the first approach, the typical plateau-width and the typical order of short necklace states are obtained from the correlation function of the logarithmic transmission. In the second approach, we investigate the statistical distribution of the peak/plateau-width measured in the logarithmic transmission spectra. A novel distribution is found, which can be exactly fitted by the summation of two Gaussian distributions. These two distributions are the results of sharp peaks of localized states and the high plateaus of short necklace states. The center of the second distribution also tells us the typical plateau-width of short necklace states. With increasing system length, the scaling property of the typical plateau-width is very special since it hardly decreases. The methods and quantities defined in this work can be widely used in Anderson localization studies.
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Affiliation(s)
- Liang Chen
- State Key Laboratory of Functional Materials for Informatics, Shanghai Institute of Microsystem and Information Technology, CAS, Shanghai 200050, People's Republic of China
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10
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WANG JING, SHI ZHOU, DAVY MATTHIEU, GENACK AZRIELZ. WAVE PROPAGATION AND LOCALIZATION VIA QUASI-NORMAL MODES AND TRANSMISSION EIGENCHANNELS. ACTA ACUST UNITED AC 2012. [DOI: 10.1142/s2010194512006113] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
Field transmission coefficients for microwave radiation between arrays of points on the incident and output surfaces of random samples are analyzed to yield the underlying quasi-normal modes and transmission eigenchannels of each realization of the sample. The linewidths, central frequencies, and transmitted speckle patterns associated with each of the modes of the medium are found. Modal speckle patterns are found to be strongly correlated leading to destructive interference between modes. This explains distinctive features of transmission spectra and pulsed transmission. An alternate description of wave transport is obtained from the eigenchannels and eigenvalues of the transmission matrix. The maximum transmission eigenvalue, τ1 is near unity for diffusive waves even in turbid samples. For localized waves, τ1 is nearly equal to the dimensionless conductance, which is the sum of all transmission eigenvalues, g = Στn. The spacings between the ensemble averages of successive values of ln τn are constant and equal to the inverse of the bare conductance in accord with predictions by Dorokhov. The effective number of transmission eigenvalues Neff determines the contrast between the peak and background of radiation focused for maximum peak intensity. The connection between the mode and channel approaches is discussed.
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Affiliation(s)
- JING WANG
- Department of Physics, Queens College of the City University of New York, 65-30 Kissena Boulevard Flushing, New York, 11367, United States of America
| | - ZHOU SHI
- Department of Physics, Queens College of the City University of New York, 65-30 Kissena Boulevard, Flushing, New York, 11367, United States of America
| | - MATTHIEU DAVY
- Department of Physics, Queens College of the City University of New York, 65-30 Kissena Boulevard, Flushing, New York, 11367, United States of America
| | - AZRIEL Z. GENACK
- Department of Physics, Queens College of the City University of New York, 65-30 Kissena Boulevard, Flushing, New York, 11367, United States of America
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11
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Labonté L, Vanneste C, Sebbah P. Localized mode hybridization by fine tuning of two-dimensional random media. OPTICS LETTERS 2012; 37:1946-1948. [PMID: 22660082 DOI: 10.1364/ol.37.001946] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
We study numerically the interaction of spatially localized modes in strongly scattering two-dimensional (2D) media. We move eigenvalues in the complex plane by changing gradually the index of a single scatterer. When spatial and spectral overlap is sufficient, localized states couple, and avoided level crossing is observed. We show that local manipulation of the disordered structure can couple several localized states to form an extended chain of hybridized modes crossing the entire sample, thus changing the nature of certain modes from localized to extended in a nominally localized disordered system. We suggest such a chain in 2D random systems is the analog of one-dimensional necklace states, the occasional open channels predicted by Pendry [Physics 1, 20 (2008).] through which the light can sneak through an opaque medium.
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Affiliation(s)
- Laurent Labonté
- Laboratoire de Physique de la Matière Condensée, Université de Nice-Sophia Antipolis-CNRS UMR7336, Parc Valrose, 06108 Nice Cedex 02, France
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12
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Fujii G, Matsumoto T, Takahashi T, Ueta T. Study on transition from photonic-crystal laser to random laser. OPTICS EXPRESS 2012; 20:7300-7315. [PMID: 22453411 DOI: 10.1364/oe.20.007300] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
The dependence of the lasing threshold on the amount of positional disorder in photonic crystal structures is newly studied by means of the finite element method, not of the finite difference time domain method usually used. A two-dimensional model of a photonic crystal consisting of dielectric cylinders arranged on a triangular lattice within a circular region is considered. The cylinders are assumed to be homogeneous and infinitely long. Positional disorder of the cylinders is introduced to the photonic crystals. Optically active medium is introduced to the interspace among the cylinders. The population inversion density of the optically active medium is modeled by the negative imaginary part of dielectric constant. The ratio between radiative power of electromagnetic field without amplification and that with amplification is computed as a function of the frequency and the imaginary part of the dielectric constant, and the threshold of the imaginary part, namely population inversion density for laser action is obtained. These analyses are carried out for various amounts of disorder. The variation of the lasing threshold from photonic-crystal laser to random laser is revealed by systematic computations with numerical method of reliable accuracy for the first time. Moreover, a novel phenomenon, that the lasing threshold have a minimum against the amount of disorder, is found. In order to investigate the properties of the lasing states within the circular system, the distributions of the electric field amplitudes of the states are also calculated.
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Affiliation(s)
- Garuda Fujii
- Department of Mechanical Science and Engineering, Nagoya University, Furo-cho, Chikusa-ku, Nagoya, 464-8603, Japan.
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13
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Rüting F, Huidobro PA, García-Vidal FJ. Emergence of Anderson localization in plasmonic waveguides. OPTICS LETTERS 2011; 36:4341-4343. [PMID: 22089557 DOI: 10.1364/ol.36.004341] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
The propagation of surface plasmon polaritons in dielectric loaded waveguides with randomly placed scatterers is studied using both numerical simulations and a simplified transfer matrix framework. Despite the importance of losses in this system, we find fingerprints of the localized behavior of one-dimensional disordered systems. Furthermore, losses amplify the impact of the necklace states on the transport properties for systems not much larger than the localization length. The system presented here also offers the possibility to use localization effects for engineering purposes by means of deliberately introduced disorder.
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Affiliation(s)
- F Rüting
- Departamento de Física de la Materia Condensada, Universidad Autónoma de Madrid, Madrid, Spain.
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Huang J, Dong B, Zhou L. Nonuniform ensembles of diverse resonances in one-dimensional layered media. OPTICS LETTERS 2011; 36:2477-2479. [PMID: 21725450 DOI: 10.1364/ol.36.002477] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
The transmission spectra perform huge fluctuations even in the mostly suitable one-dimensional localized multilayer system. Fluctuations of layer thicknesses will cause random resonances between light waves and layers. We reveal that the nonuniform ensembles of the resonances are the key for the fluctuations of transmission spectra. The transmission spectra of each stack of layers are numerically calculated through the transfer-matrix method.
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Affiliation(s)
- Junying Huang
- State Key Laboratory of Surface Physics and Department of Physics, Fudan University, Shanghai 200433, China
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15
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Sapienza R, Bondareff P, Pierrat R, Habert B, Carminati R, van Hulst NF. Long-tail statistics of the Purcell factor in disordered media driven by near-field interactions. PHYSICAL REVIEW LETTERS 2011; 106:163902. [PMID: 21599367 DOI: 10.1103/physrevlett.106.163902] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/22/2010] [Revised: 03/23/2011] [Indexed: 05/30/2023]
Abstract
In this Letter, we study the Purcell effect in a 3D disordered dielectric medium through fluorescence decay rates of nanosized light sources. We report distributions of Purcell factor with non-Gaussian long-tailed statistics and an enhancement of up to 8 times the average value. We attribute this large enhancement to strong fluctuations of the local density of states induced by near-field scattering sustained by more than one particle. Our findings go beyond standard diagrammatic and single-scattering models and can be explained only by taking into account the full near-field interaction.
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Affiliation(s)
- R Sapienza
- ICFO-Institut de Ciencies Fotoniques, Mediterranean Technology Park, Castelldefels (Barcelona), Spain.
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16
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Mazoyer S, Lalanne P, Rodier JC, Hugonin JP, Spasenović M, Kuipers L, Beggs DM, Krauss TF. Statistical fluctuations of transmission in slow light photonic-crystal waveguides. OPTICS EXPRESS 2010; 18:14654-14663. [PMID: 20639951 DOI: 10.1364/oe.18.014654] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/29/2023]
Abstract
We report statistical fluctuations for the transmissions of a series of photonic-crystal waveguides (PhCWs) that are supposedly identical and that only differ because of statistical structural fabrication-induced imperfections. For practical PhCW lengths offering tolerable -3dB attenuation with moderate group indices (n(g) approximately 60), the transmission spectra contains very narrow peaks (Q approximately 20,000) that vary from one waveguide to another. The physical origin of the peaks is explained by calculating the actual electromagnetic-field pattern inside the waveguide. The peaks that are observed in an intermediate regime between the ballistic and localization transports are responsible for a smearing of the local density of states, for a rapid broadening of the probability density function of the transmission, and bring a severe constraint on the effective use of slow light for on-chip optical information processing. The experimental results are quantitatively supported by theoretical results obtained with a coupled-Bloch-mode approach that takes into account multiple scattering and localization effects.
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Affiliation(s)
- S Mazoyer
- Laboratoire Charles Fabry de l'Institut d'Optique, CNRS, Univ Paris-Sud, Campus Polytechnique, 91127 Palaiseau cedex, France
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17
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Shadrivov IV, Bliokh KY, Bliokh YP, Freilikher V, Kivshar YS. Bistability of anderson localized States in nonlinear random media. PHYSICAL REVIEW LETTERS 2010; 104:123902. [PMID: 20366536 DOI: 10.1103/physrevlett.104.123902] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/08/2009] [Indexed: 05/29/2023]
Abstract
We study wave transmission through one-dimensional random nonlinear structures and predict a novel effect resulting from an interplay of nonlinearity and disorder. We reveal that, while weak nonlinearity does not change the typical exponentially small transmission in the regime of the Anderson localization, it affects dramatically the disorder-induced localized states excited inside the medium leading to bistable and nonreciprocal resonant transmission. Our numerical modeling shows an excellent agreement with theoretical predictions based on the concept of a high-Q resonator associated with each localized state. This offers a new way for all-optical light control employing statistically homogeneous random media without regular cavities.
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Affiliation(s)
- Ilya V Shadrivov
- Nonlinear Physics Center, Research School of Physics and Engineering, Australian National University, Canberra ACT 0200, Australia
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18
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Lizárraga N, Puente NP, Chaikina EI, Leskova TA, Méndez ER. Single-mode Er-doped fiber random laser with distributed Bragg grating feedback. OPTICS EXPRESS 2009; 17:395-404. [PMID: 19158852 DOI: 10.1364/oe.17.000395] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/27/2023]
Abstract
We report the implementation of a one-dimensional random laser based on an Er/Ge co-doped single-mode fiber with randomly spaced Bragg gratings. The random grating array forms a complex cavity with high quality factor resonances in the range of gain wavelengths centered around 1535.5 nm. The reflection spectra of the grating array and the emission spectra of the laser are investigated for different numbers of gratings. The experimental results are compared qualitatively with numerical simulations of the light propagation in one-dimensional Bragg grating arrays based on a transfer matrix method. The system is pumped at 980 nm and the experimentally observed output radiation presents a typical laser threshold behavior as a function of the pump power. We find that the laser output contains several competing spectral modes.
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Affiliation(s)
- N Lizárraga
- División de Física Aplicada, Centro de Investigación Científica y de Educación Superior de Ensenada, Km. 107 carretera Tijuana-Ensenada, Ensenada, B. C., 22860, México
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19
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Zhang S, Park J, Milner V, Genack AZ. Photon delocalization transition in dimensional crossover in layered media. PHYSICAL REVIEW LETTERS 2008; 101:183901. [PMID: 18999831 DOI: 10.1103/physrevlett.101.183901] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/09/2008] [Revised: 08/28/2008] [Indexed: 05/27/2023]
Abstract
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.
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Affiliation(s)
- Sheng Zhang
- Department of Physics, Queens College, The City University of New York, Flushing, New York 11365, USA
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20
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Bliokh KY, Bliokh YP, Freilikher V, Genack AZ, Sebbah P. Coupling and level repulsion in the localized regime: from isolated to quasiextended modes. PHYSICAL REVIEW LETTERS 2008; 101:133901. [PMID: 18851448 DOI: 10.1103/physrevlett.101.133901] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/04/2008] [Revised: 07/27/2008] [Indexed: 05/13/2023]
Abstract
We study the interaction of Anderson localized states in an open 1D random system by varying the internal structure of the sample. As the frequencies of two states come close, they are transformed into multiply peaked quasiextended modes. Level repulsion is observed experimentally and explained within a model of coupled resonators. The spectral and spatial evolution of the coupled modes is described in terms of the coupling coefficient and Q factors of resonators.
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Affiliation(s)
- K Y Bliokh
- Nonlinear Physics Centre, Research School of Physical Sciences and Engineering, Australian National University, Canberra ACT 0200, Australia
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21
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Ryu JW, Hur G, Kim SW. Quantum localization in open chaotic systems. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 78:037201. [PMID: 18851192 DOI: 10.1103/physreve.78.037201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/05/2008] [Revised: 06/16/2008] [Indexed: 05/26/2023]
Abstract
We study a quasibound state of a delta -kicked rotor with absorbing boundaries focusing on the nature of the dynamical localization in open quantum systems. The localization lengths xi of lossy quasibound states located near the absorbing boundaries decrease as they approach the boundary while the corresponding decay rates Gamma are dramatically enhanced. We find the relation xi approximately Gamma(-1/2) and explain it based upon the finite time diffusion, which can also be applied to a random unitary operator model. We conjecture that this idea is valid for the system exhibiting both the diffusion in classical dynamics and the exponential localization in quantum mechanics.
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Affiliation(s)
- Jung-Wan Ryu
- Department of Physics Education and Department of Physics, Pusan National University, Busan 609-735, Korea
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22
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Laurent D, Legrand O, Sebbah P, Vanneste C, Mortessagne F. Localized modes in a finite-size open disordered microwave cavity. PHYSICAL REVIEW LETTERS 2007; 99:253902. [PMID: 18233521 DOI: 10.1103/physrevlett.99.253902] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/02/2007] [Revised: 10/17/2007] [Indexed: 05/25/2023]
Abstract
We present measurements of the spatial intensity distribution of localized modes in a two-dimensional open microwave cavity randomly filled with cylindrical dielectric scatterers. We show that each of these modes displays a range of localization lengths, and we successfully relate the largest value to the measured leakage rate at the boundary. These results constitute unambiguous signatures of the existence of strongly localized electromagnetic modes in two-dimensional open random media.
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Affiliation(s)
- David Laurent
- Laboratoire de Physique de la Matière Condensée, CNRS UMR 6622, Université de Nice Sophia-Antipolis, 06108 Nice, France
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Aegerter CM, Störzer M, Fiebig S, Bührer W, Maret G. Observation of Anderson localization of light in three dimensions. JOURNAL OF THE OPTICAL SOCIETY OF AMERICA. A, OPTICS, IMAGE SCIENCE, AND VISION 2007; 24:A23-7. [PMID: 17912284 DOI: 10.1364/josaa.24.000a23] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/17/2023]
Abstract
Using time-resolved transmission measurements, we have found indications of Anderson localization of light in bulk three-dimensional systems. The observed deviation from classical diffusion is in good accord with theoretical predictions of localization and cannot be explained by absorption or experimental artifacts such as stratification, fluorescence, or background illumination. Moreover, we show that in our samples the control parameter is given by the mean free path times the wavenumber as required by the Ioffe-Regel criterion. This is in contrast to quasi-one-dimensional systems that were studied with microwaves. There, the control parameter is related to the number of modes inside a waveguide, and deviations from classical diffusion are possible due to a small number of modes.
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Affiliation(s)
- Christof M Aegerter
- Fachbereich Physik, University of Konstanz, Box M621, 78457 Konstanz, Germany.
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Ghulinyan M. Periodic oscillations in transmission decay of anderson localized one-dimensional dielectric systems. PHYSICAL REVIEW LETTERS 2007; 99:063905. [PMID: 17930826 DOI: 10.1103/physrevlett.99.063905] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/09/2007] [Indexed: 05/25/2023]
Abstract
It is well recognized that the transmittance of Anderson localized systems decays exponentially on average with sample size, showing large fluctuations brought up by extremely rare occurrences of necklaces of resonantly coupled states, possessing almost unity transmission. We show here that in a one-dimensional (1D) random photonic system with resonant layers these fluctuations appear to be very regular and have a period defined by the localization length xi of the system. We stress that necklace states are the origin of these well-defined oscillations. We predict that in such a random system efficient transmission channels form regularly each time the increasing sample length fits so-called optimal-order necklaces and demonstrate the phenomenon through numerical experiments. Our results provide new insight into the physics of Anderson localization in random systems with resonant units.
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Affiliation(s)
- Mher Ghulinyan
- Micro-Technology Laboratory, Fondazione Bruno Kessler - irst, via Sommarive 18, I-38050 Povo (Trento), Italy.
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Bliokh KY, Bliokh YP, Freilikher V, Genack AZ, Hu B, Sebbah P. Localized modes in open one-dimensional dissipative random systems. PHYSICAL REVIEW LETTERS 2006; 97:243904. [PMID: 17280287 DOI: 10.1103/physrevlett.97.243904] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/29/2006] [Indexed: 05/13/2023]
Abstract
We consider, both theoretically and experimentally, the excitation and detection of the localized quasimodes (resonances) in an open dissipative 1D random system. We show that, even though the amplitude of transmission drops dramatically so that it cannot be observed in the presence of small losses, resonances are still clearly exhibited in reflection. Surprisingly, small losses essentially improve conditions for the detection of resonances in reflection as compared with the lossless case. An algorithm is proposed and tested to retrieve sample parameters and resonance characteristics inside the random system exclusively from reflection measurements.
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Affiliation(s)
- K Yu Bliokh
- Institute of Radio Astronomy, 4 Krasnoznamyonnaya Street, Kharkov, 61002, Ukraine
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Affiliation(s)
- Ping Sheng
- Department of Physics, The Hong Kong University of Science and Technology, Hong Kong, China.
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Bertolotti J, Galli M, Sapienza R, Ghulinyan M, Gottardo S, Andreani LC, Pavesi L, Wiersma DS. Wave transport in random systems: multiple resonance character of necklace modes and their statistical behavior. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 74:035602. [PMID: 17025699 DOI: 10.1103/physreve.74.035602] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/18/2006] [Indexed: 05/12/2023]
Abstract
We present the experimental observation of multiple resonance transport of light waves, due to necklace states, in disordered one-dimensional systems. Transmission phase measurements allow us to identify these states unambiguously and investigate their statistical properties. A theoretical model is developed to describe the resonance statistics and the frequency dependance of the localization length.
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Affiliation(s)
- J Bertolotti
- European Laboratory for Nonlinear Spectroscopy and INFM-MATIS, via Nello Carrara 1, 50019 Sesto Fiorentino, Florence, Italy
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