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Anderson localization in metamaterials and other complex media (Review Article)
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10.1063/1.4736617
/content/aip/journal/ltp/38/7/10.1063/1.4736617
http://aip.metastore.ingenta.com/content/aip/journal/ltp/38/7/10.1063/1.4736617
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

(Ref. 43) Two-component multilayered alternative stack.

Image of FIG. 2.
FIG. 2.

(Ref. 44) Transmission length lT vs. λ for an M-stack (thick solid line, direct simulation and calculations based on WSA recurrence relations) and an H-stack (thick dashed line, direct simulation). Asymptotic values of the localization length l: the short-wavelength asymptotic value (thin dotted line), and the long-wavelength asymptotic values (a thin solid line for the M-stack and a thin dashed line for the H-stack).

Image of FIG. 3.
FIG. 3.

(Ref. 44) Transmission lengths lT (solid black line), and the transmission length for a single realization lN (dashed blue line) vs. λ for an M-stack with Q ν = 0.25, Qd  = 0.2, and N = 104 layers. Each separate point corresponds to a particular wavelength with its own realization of a random stack.

Image of FIG. 4.
FIG. 4.

(Ref. 44) Transmission length lT vs. λ for H-stacks of N = 103 (solid line) and 104 (dotted line) layers (numerical simulation and WSA). Long-wave asymptotic values for the ballistic length in the near and far ballistic regions are plotted in thin solid lines.

Image of FIG. 5.
FIG. 5.

(Ref. 44) Transmission lengths lT (solid black line) and the transmission length for a single realization lN (dashed blue line) vs. λ for an H-stack with Q ν = 0.25, Qd  = 0.2, and N = 104 layers. Each separate point corresponds to a particular wavelength with its own realization of a random stack.

Image of FIG. 6.
FIG. 6.

(Ref. 43) Transmittance |T|2 vs. λ for a single realization (Q = 0.25, N = 103). Solid: normal H-stack, dotted: M-stack.

Image of FIG. 7.
FIG. 7.

(Ref. 44) Single realization transmittance |T|2 vs. wavelength λ for RID M-stacks with Q ν = 0.25 and Qd  = 0 for N = 105 layers (solid line) and N = 103 layers (dotted line).

Image of FIG. 8.
FIG. 8.

(Ref. 44) Single realization transmittance |T|2 vs. λ for an M-stack of N = 103 layers with Q ν = 0.25. Solid line corresponds to an M-stack with Qd  = 0.2, and the dashed line – to an M-stack with no thickness disorder, i.e., Qd  = 0.0.

Image of FIG. 9.
FIG. 9.

(Ref. 44) Ratio s vs. wavelength λ for Q ν = 0.25 and stack length N = 103. Solid and dashed curves are for the RID H-stack and H-stack with Qd  = 0.2, respectively. The middle dashed-dotted curve is for an M-stack with Qd  = 0.25, and the bottom dotted line is for a RID M-stack.

Image of FIG. 10.
FIG. 10.

(Ref. 45) Transmission length lT vs. λ for an M-stack in p-polarized light with Q ν = 0.1, Qd  = 0.2, and N = 106, at the Brewster angle θ = 45° (red solid line). The blue dashed line shows results for s-polarization and an H-stack, replotted for comparison.

Image of FIG. 11.
FIG. 11.

(Ref. 45) Transmission length lT vs. λ for an M-stack in s-polarized light with Q ν = 0.1, Qd  = 0.2, and N = 104, and for the supercritical incidence angle θ = 75°. Red solid curve: numerical simulations; blue dash curve: analytical form.

Image of FIG. 12.
FIG. 12.

(Ref. 45) Transmission length lT vs. incidence angle θ for a mixed stack with Q ν = 0.1, Qd  = 0.2, for λ = 0.1 (a), and λ = 1 (b). The top and bottom curves are, respectively, for p- and s-polarizations.

Image of FIG. 13.
FIG. 13.

(Color online) (Ref. 46) Transmission length lT vs. frequency f at normal incidence (θ0 = 0) for a metamaterial stack without absorption (top curve) and in the presence of absorption (bottom curves). Red solid curves display numerical simulations, while blue dashed curves show analytical predictions. Inset: the real (red solid line) and imaginary (green dashed line) part of the metamaterial layer refractive index.

Image of FIG. 14.
FIG. 14.

(Ref. 46) Transmission length lT vs. frequency f for θ0 = 30° for a metamaterial stack: without absorption, p-polarization (top curves), s-polarization (middle curves); in the presence of absorption (bottom curves).

Image of FIG. 15.
FIG. 15.

(Ref. 46) Transmission length lT vs. angle of incidence for a homogenous metamaterial stack at f = 10.7 GHz with permittivity disorder: in the absence of absorption (upper curve) and for p-polarization; middle curve is for s-polarization; and in the presence of absorption and for both polarizations (lower curves).

Image of FIG. 16.
FIG. 16.

(Ref. 43) Characteristic length l ξ vs. wavelength λ for Q = 0.25 and N = 109 layers; the solid line is for the M-stack, while the dashed line is for the corresponding (normal) H-stack.

Image of FIG. 17.
FIG. 17.

(Ref. 45) Transmission length lT vs. λ for an M-stack with Q ν = 0.25, Qd  = 0, and θ = 30° for p-polarized light (cyan dashed dotted curve, N = 106) and s-polarized light (red solid curve, N = 105; green dashed curve, N = 107; blue dotted curve, N = 8·108).

Image of FIG. 18.
FIG. 18.

(Ref. 46) (a) Transmission length lT vs. frequency f for a mixed stack with N = 107 layers (top dotted blue curve), and only dielectric permittivity disorder. The bottom curves on all the panels (a, b, c) are for a stack with N = 107 layers with both permittivity and permeability disorder (the cyan, solid curve displays simulation results, while the dashed, black curve is for the analytical prediction); (b) is the same as (a), but plotted as a function of free space wavelength λ0, while on panel (c) we plot transmission length as a function of the averaged wavelength inside the stack normalized to the thickness of the layer, for N = 107 layers (blue dotted top curve), N = 106 layers (dashed green curve) and for N = 105 layers (red solid curve), respectively.

Image of FIG. 19.
FIG. 19.

(Ref. 52) (a) The phase space trajectory generated using Eq. ((3.45)) for an H-array with N = 104, ϕ = π/15, for zero disorder (solid circle), and for σ2 = 0.003 (scattered points). (b) One trajectory for an M-array with N = 106, ϕ = 2π/5, σ2 = 0.003. (c) ρ(θ) from Eq. ((3.45)) for an H-array (histogram), and Eq. ((3.56)) (horizontal line); (d) ρ(θ) from Eq. ((3.45)) for an M-array (histogram), and Eq. ((3.57)) (solid curve).

Image of FIG. 20.
FIG. 20.

(Ref. 52) (a) Phase space trajectory in new variables ; (b) distribution ρ(Θ) generated by the transformed map with Eqs. ((3.58) and (3.62)), for γ = 0, ϕ = 2π/5, σ2 = 0.02, and N = 107.

Image of FIG. 21.
FIG. 21.

(Ref. 34) A schematic picture of wave transmission and reflection from a random-layered structure consisting of two types of alternating layers “α” (here—a magnetoactive material) and “β” (here—air) with random widths. Magnetization of the medium, wave polarizations, and directions of propagation are shown for the Faraday and Voigt geometries.

Image of FIG. 22.
FIG. 22.

(Ref. 34) Localization decrement κ vs. magnetooptical parameter Q for opposite modes propagating through a two-component random structure in the Faraday geometry (see details in the text). The modes with ς = ±1 correspond to either opposite circular polarizations or propagation directions. Numerical simulations of exact equations (symbols) and the theoretical formula (4.8) (lines).

Image of FIG. 23.
FIG. 23.

(Ref. 34) Transmission spectra of a random magnetooptical sample in the Faraday geometry (see details in the text) for waves with ς = ±1. While the averaged localization decrements are only slightly different (Fig. 22), all individual resonances are shifted significantly as compared with their widths, Eq. (4.10).

Image of FIG. 24.
FIG. 24.

(Ref. 34) Differential transmittance, + −  , for two resonances from Fig. 22 as dependent on the value of magnetooptical parameter Q, cf. Eq. (4.10).

Image of FIG. 25.
FIG. 25.

(Ref. 34) Differential transmittance, + −  , in the vicinity of a single resonance in the Voigt geometry (see Sec. ??? for details) as dependent on the magnetooptical parameter Q.

Image of FIG. 26.
FIG. 26.

(Ref. 47) Transmission coefficient T(θ) for periodic (thin black line) and disordered (bold blue line) graphene.

Image of FIG. 27.
FIG. 27.

(Ref. 47) Spatial distribution of wave function localized inside the sample for θ, marked by red arrow in Fig. 26.

Image of FIG. 28.
FIG. 28.

(Ref. 31) Nonlinear deformations of transmission spectra of two random resonances at different intensities of the incident wave. Numerical simulations of the Eq. (4.17) (curves) and theoretical Eq. (4.18) (symbols) are shown for the case of defocusing nonlinearity, χ > 0. Light-grey stripes indicate three-valued regions for the high-intensity curves, where only two of them (corresponding to the lower and upper branches) are stable.

Image of FIG. 29.
FIG. 29.

(Ref. 31) Stationary and FDTD simulations showing hysteresis loops in the output vs input power dependence for three different resonances. Panel (d) shows deformation of the transmitted Gaussian pulse corresponding to the hysteresis switching on resonance 2.

Image of FIG. 30.
FIG. 30.

(Ref. 31) (a) Nonreciprocal transmission through the nonlinear disordered structure, showing different output powers for identical waves incident from different directions. (b) Corresponding shape of the incident pulse, and pulses transmitted in different directions.

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/content/aip/journal/ltp/38/7/10.1063/1.4736617
2012-07-27
2014-04-19
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Anderson localization in metamaterials and other complex media (Review Article)
http://aip.metastore.ingenta.com/content/aip/journal/ltp/38/7/10.1063/1.4736617
10.1063/1.4736617
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