Eigen modes for the problem of anomalous light transmission through subwavelength holes

We show that the wide-spread concept of optical eigen modes in lossless waveguide structures, which assumes the separation on propagating and evanescent modes, fails in the case of metal-dielectric structures, including photonic crystals. In addition to these modes, there is a sequence of new eigen-states with complex values of the propagation constant and non-vanishing circulating energy flow. The whole eigen-problem ceases to be hermitian because of changing sign of the optical dielectric constant. The new anomalous modes are shown to be of prime importance for the description of the anomalous light transmission through subwavelength holes.Comment: 5 pages, 4 figure

Quasi-Homogeneous Backward-Wave Plasmonic Structures: Theory and Accurate Simulation

Backward waves and negative refraction are shown to exist in plasmonic crystals whose lattice cell size is a very small fraction of the vacuum wavelength (less than 1/40th in an illustrative example). Such ``quasi-homogeneity'' is important, in particular, for high-resolution imaging. Real and complex Bloch bands are computed using the recently developed finite-difference calculus of ``Flexible Local Approximation MEthods'' (FLAME) that produces linear eigenproblems, as opposed to quadratic or nonlinear ones typical for other techniques. FLAME dramatically improves the accuracy by incorporating local analytical approximations of the solution into the numerical scheme.Comment: 4 pages, 3 figure

Anderson Localization of Classical Waves in Weakly Scattering Metamaterials

We study the propagation and localization of classical waves in one-dimensional disordered structures composed of alternating layers of left- and right-handed materials (mixed stacks) and compare them to the structures composed of different layers of the same material (homogeneous stacks). For weakly scattering layers, we have developed an effective analytical approach and have calculated the transmission length within a wide region of the input parameters. When both refractive index and layer thickness of a mixed stack are random, the transmission length in the long-wave range of the localized regime exhibits a quadratic power wavelength dependence with the coefficients different for mixed and homogeneous stacks. Moreover, the transmission length of a mixed stack differs from reciprocal of the Lyapunov exponent of the corresponding infinite stack. In both the ballistic regime of a mixed stack and in the near long-wave region of a homogeneous stack, the transmission length of a realization is a strongly fluctuating quantity. In the far long-wave part of the ballistic region, the homogeneous stack becomes effectively uniform and the transmission length fluctuations are weaker. The crossover region from the localization to the ballistic regime is relatively narrow for both mixed and homogeneous stacks. In mixed stacks with only refractive-index disorder, Anderson localization at long wavelengths is substantially suppressed, with the localization length growing with the wavelength much faster than for homogeneous stacks. The crossover region becomes essentially wider and transmission resonances appear only in much longer stacks. All theoretical predictions are in an excellent agreement with the results of numerical simulations.Comment: 19 pages, 16 figures, submitted to PR

Double-heterostructure cavities: from theory to design

We derive a frequency-domain-based approach for radiation (FAR) from double-heterostructure cavity (DHC) modes. We use this to compute the quality factors and radiation patterns of DHC modes. The semi-analytic nature of our method enables us to provide a general relationship between the radiation pattern of the cavity and its geometry. We use this to provide general designs for ultrahigh quality factor DHCs with radiation patterns that are engineered to emit vertically

Defect modes in otherwise perfect photonic crystal and photonic crystal fibres

Many of the applications of photonic crystals and photonic crystal fibres require the periodic structure tohave some type of defect. In photonic crystal fibers a point defect defines the fiber core, whereas in photonic crystals a line defect acts as a waveguide, and point defects act as cavities. The modeling of these defects usually either makes use of periodic boundary conditions, by which the defect is replicated periodically, or models a photonic cyrstal of finite extent. HOwever, some applications, for example the cut-off behaviour of a defect mode where the field extends very widely, require methods that can model a defect in an otherwise infinite and perfectly periodic structure. Here we present such a method. It combines the method of fictitious sources with averaging over the Brillouin zone, and we apply it to study the long wavelength behavior of the fundamental mode of photonic crystal fibers

Modes of Random Lasers

In conventional lasers, the optical cavity that confines the photons also determines essential characteristics of the lasing modes such as wavelength, emission pattern, ... In random lasers, which do not have mirrors or a well-defined cavity, light is confined within the gain medium by means of multiple scattering. The sharp peaks in the emission spectra of semiconductor powders, first observed in 1999, has therefore lead to an intense debate about the nature of the lasing modes in these so-called lasers with resonant feedback. In this paper, we review numerical and theoretical studies aimed at clarifying the nature of the lasing modes in disordered scattering systems with gain. We will discuss in particular the link between random laser modes near threshold (TLM) and the resonances or quasi-bound (QB) states of the passive system without gain. For random lasers in the localized regime, QB states and threshold lasing modes were found to be nearly identical within the scattering medium. These studies were later extended to the case of more lossy systems such as random systems in the diffusive regime where differences between quasi-bound states and lasing modes were measured. Very recently, a theory able to treat lasers with arbitrarily complex and open cavities such as random lasers established that the TLM are better described in terms of the so-called constant-flux states.Comment: Review paper submitted to Advances in Optics and Photonic

Suppression of Anderson localization in disordered metamaterials

We study wave propagation in mixed, 1D disordered stacks of alternating right- and left-handed layers and reveal that the introduction of metamaterials substantially suppresses Anderson localization. At long wavelengths, the localization length in mixed stacks is orders of magnitude larger than for normal structures, proportional to the sixth power of the wavelength, in contrast to the usual quadratic wavelength dependence of normal systems. Suppression of localization is also exemplified in long-wavelength resonances which largely disappear when left-handed materials are introduced

Effects of polarization on the transmission and localization of classical waves in weakly scattering metamaterials

We summarize the results of our comprehensive analytical and numerical studies of the effects of polarization on the Anderson localization of classical waves in one-dimensional random stacks. We consider homogeneous stacks composed entirely of normal materials or metamaterials, and also mixed stacks composed of alternating layers of a normal material and metamaterial. We extend the theoretical study developed earlier for the case of normal incidence [A. A. Asatryan et al, Phys. Rev. B 81, 075124 (2010)] to the case of off-axis incidence. For the general case where both the refractive indices and layer thicknesses are random, we obtain the long-wave and short-wave asymptotics of the localization length over a wide range of incidence angles (including the Brewster ``anomaly'' angle). At the Brewster angle, we show that the long-wave localization length is proportional to the square of the wavelength, as for the case of normal incidence, but with a proportionality coefficient substantially larger than that for normal incidence. In mixed stacks with only refractive-index disorder, we demonstrate that p-polarized waves are strongly localized, while for s-polarization the localization is substantially suppressed, as in the case of normal incidence. In the case of only thickness disorder, we study also the transition from localization to delocalization at the Brewster angle.Comment: 15 pages, 11 figures, accepted for publication in PR

Extraordinary absorption of sound in porous lamella-crystals

We present the design of a structured material supporting complete absorption of sound with a broadband response and functional for any direction of incident radiation. The structure which is fabricated out of porous lamellas is arranged into a low-density crystal and backed by a reflecting support. Experimental measurements show that strong all-angle sound absorption with almost zero reflectance takes place for a frequency range exceeding two octaves. We demonstrate that lowering the crystal filling fraction increases the wave interaction time and is responsible for the enhancement of intrinsic material dissipation, making the system more absorptive with less material.The work was supported by the Spanish Ministry of Science and Innovation and European Union FEDER through project FIS2011-29734-C02-01. J.C. gratefully acknowledges financial support from the Danish Council for Independent Research and a Sapere Aude grant (12-134776). V. R. G. gratefully acknowledges financial support from the ''Contratos Post-Doctorales Campus Excelencia Internacional'' UPV CEI-01-11.Christensen, J.; Romero García, V.; Picó Vila, R.; Cebrecos Ruiz, A.; Garcia De Abajo, FJ.; Mortensen, NA.; Willatzen, M.... (2014). Extraordinary absorption of sound in porous lamella-crystals. Scientific Reports. 4(4674). https://doi.org/10.1038/srep04674S44674Mei, J. et al. Dark acoustic metamaterials as super absorbers for low-frequency sound. Nat. Commun. 3, 756 (2012).Leroy, V., Strybulevych, A., Scanlon, M. G. & Page, J. Transmission of ultrasound through a single layer of bubbles. Eur. Phys. J. E 29, 123 (2009).Leroy, V., Bretagne, A., Fink, M. H. W., Tabeling, P. & Tourin, A. Design and characterization of bubble phononic crystals. Appl. Phys. Lett. 95, 171904 (2009).Thomas, E. L. Applied physics: Bubbly but quiet. Nature 462, 990 (2009).Romero-García, V., Sánchez-Pérez, J. V. & Garcia-Raffi, L. M. Tunable wideband bandstop acoustic filter based on two-dimensional multiphysical phenomena periodic systems. J. Appl. Phys. 110, 014904 (2011).Garcia-Chocano, V. M., Cabrera, S. & Sanchez-Dehesa, J. Broadband sound absorption by lattices of microperforated cylindrical shells. Appl. Phys. Lett. 101, 184101 (2012).Kushwaha, M. S., Halevi, P., Dobrzynski, L. & Djafari-Rouhani, B. Acoustic band structure of periodic elastic composites. Phys. Rev. Lett. 71, 2022 (1993).Vasseur, J. O. et al. Experimental and Theoretical Evidence for the Existence of Absolute Acoustic Band Gaps in Two-Dimensional Solid Phononic Crystals. Phys. Rev. Lett. 86, 3012 (2001).Liu, Z. et al. Locally Resonant Sonic Materials. Science 289, 1734 (2000).Christensen, J., Martin-Moreno, L. & Garcia-Vidal, F. J. All-angle blockage of sound by an acoustic double-fishnet metamaterial. Appl. Phys. Lett. 97, 134106 (2010).Botten, L. C., Craig, M. S., McPhedran, R. C., Adams, J. L. & Andrewartha, J. R. The finitely conducting lamellar diffraction grating. Optica Acta 28, 1087 (1981).McPhedran, R. C., Botten, L. C., Craif, M. S., Neviere, M. & Maystre, D. Lossy lamellar gratings in the quasistatic limit. Optica Acta 29, 289 (1982).Kravets, V. G., Schedin, F. & Grigorenko, A. N. Plasmonic blackbody: Almost complete absorption of light in nanostructured metallic coatings. Phys. Rev. B 78, 205405 (2008).Sondergaard, T. et al. Plasmonic black gold by adiabatic nanofocusing and absorption of light in ultra-sharp convex grooves. Nat. Commun. 3, 969 (2012).Clapham, P. B. & Hurtley, M. C. Reduction of Lens Reflexion by the Moth Eye Principle. Nature Vol. 244, 281 (1973).Garcia-Vidal, F. J., Pitarke, J. M. & Pendry, J. B. Effective Medium Theory of the Optical Properties of Aligned Carbon Nanotubes. Phys. Rev. Lett. 78, 4289 (1997).Yang, Z., Ci, L., Bur, J. A., Lin, S. & Ajayan, P. M. Experimental Observation of an Extremely Dark Material Made By a Low-Density Nanotube Array. Nano Lett. 8, 446 (2008).Garcia-Vidal, F. J. Metamaterials: Towards the dark side. Nat. Photonics 2, 215 (2008).Mizunoa, K. et al. A black body absorber from vertically aligned single-walled carbon nanotubes. Proc. Natl. Acad. Sci. USA 106, 6044 (2009).Lidorkis, E. & Ferrari, A. C. Photonics with Multiwall Carbon Nanotube Arrays. ACS Nano 3, 1238 (2009).Beenakker, C. W. J. & Brouwer, P. W. Distribution of the reflection eigenvalues of a weakly absorbing chaotic cavity. Physica E 9, 463 (2001).Lafarge, D., Lemarinier, P., Allard, J. F. & Tarnow, V. Dynamic compressibility of air in porous structures at audible frequencies. J. Acoust. Soc. Am. 102, 1995 (1997), With the macroscopic parameters: ϕ = 0.94, α∞ = 1, σ = 20000 Nm−4s and Λ = Λ′ = 0.41 μm.García de Abajo, F. J. Colloquium: Light scattering by particle and hole arrays. Rev. Mod. Phys. 79, 1267–1290 (2007)

Experimental Verification of the Quantized Conductance of Photonic Crystal Waveguides

We report experiments that demonstrate the quantization of the conductance of photonic crystal waveguides. To obtain a diffusive wave, we have added all the transmitted channels for all the incident angles. The conductance steps have equal height and a width of one half the wavelength used. Detailed numerical results agree very well with the novel experimental results.Comment: Phys. Rev. B (submitted