Controlling optical memory effects in disordered media with coated metamaterials

Tiago J. Arruda, Alexandre S. Martinez, and Felipe A. Pinheiro

Phys. Rev. A 98, 043855 – Published 30 October 2018

Abstract

Most applications of memory effects in disordered optical media, such as the tilt-tilt and shift-shift spatial correlations, have focused on imaging through and inside biological tissues. Here we put forward a metamaterial platform not only to enhance but also to tune memory effects in random media. Specifically, we investigate the shift-shift and tilt-tilt spatial correlations in metamaterials composed of coated spheres and cylinders by means of the radiative transfer equation. Based on the single-scattering phase function, we calculate the translation correlations in anisotropically scattering media with spherical or cylindrical geometries and find a simple relation between them. We show that the Fokker-Planck model can be used with the small-angle approximation to obtain the shift-tilt memory effect with ballistic light contribution. By considering a two-dimensional scattering system, composed of thick dielectric cylinders coated with subwavelength layers of thermally tunable magneto-optical semiconductors, we suggest the possibility of tailoring and controlling the shift-shift and tilt-tilt memory effects in light scattering. In particular, we show that the generalized memory effect can be enhanced by increasing the temperature of the system, and it can be decreased by applying an external magnetic field. Altogether our findings unveil the potential applications that metamaterial systems may have to control externally memory effects in disordered media.

Received 11 August 2018

DOI:https://doi.org/10.1103/PhysRevA.98.043855

Physics Subject Headings (PhySH)

Coatings Light propagation, transmission & absorption Magneto-optical effect Mie scattering Scattering theory

Metamaterials Random & disordered media

Atomic, Molecular & Optical

Authors & Affiliations

Tiago J. Arruda^1,*, Alexandre S. Martinez^2,3, and Felipe A. Pinheiro⁴

¹Instituto de Física de São Carlos, Universidade de São Paulo, 13566-590 São Carlos, SP, Brazil
²Faculdade de Filosofia, Ciências e Letras de Ribeirão Preto, Universidade de São Paulo, 14040-901 Ribeirão Preto, SP, Brazil
³National Institute of Science and Technology in Complex Systems, 22290-180 Rio de Janeiro, RJ, Brazil
⁴Instituto de Física, Universidade Federal do Rio de Janeiro, 21941-972 Rio de Janeiro, RJ, Brazil

^*tiagojarruda@ifsc.usp.br

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Issue

Vol. 98, Iss. 4 — October 2018

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Images

Figure 1
Phase function $p (θ)$ calculated by the rigorous Lorenz-Mie theory for a silica ( $ɛ_{{SiO}_{2}} = 2.25$ ) sphere (a) and a silica cylinder (b) embedded in agarose gel ( $n_{ag} = 1.34$ ). Both sphere and cylinder have radius $R = 0.1 mm$ and are normally irradiated with plane waves at a frequency $ω = 2 π \times 2.4 THz$ $(k R \approx 6.74)$ . The forward-peaked single scattering for this set of parameters allow us to use the small-angle approximation of the radiative transfer equation for small optical thicknesses [39].
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Figure 2
Spatial correlation function $C (Δ r, Δ k)$ as predicated by the radiative transfer (RT) equation and by the Fokker-Planck (FP) equation for silica ( ${SiO}_{2}$ ) monodispersed scatterers in agarose gel normally irradiated with $p$ or $s$ waves. The phase functions are calculated by the rigorous Lorenz-Mie theory for ${SiO}_{2}$ spheres or cylinders with radius $R = 0.1 mm$ ( $k R \approx 6.74$ ) and packing fraction $f = 0.45 %$ , for various slab thicknesses $L$ and $ω = 2 π \times 2.4 THz$ . (a) Comparison between $C^{RT}$ (with the background contribution subtracted) for spheres and $C^{FP}$ for $Δ k = 0$ . Solid lines correspond to $C^{RT}$ ; dashed lines, to $C^{FP}$ . (b) Shift-tilt memory effect for the optimal isoplanatic patch condition $Δ k = 3 k Δ r / 2 L$ . For spheres or cylinders, (c) the shift-shift ( $Δ k = 0$ ) and (d) the shift-tilt ( $Δ k = 3 k Δ r / 2 L$ ) correlations $C^{RT}$ are approximately the same.
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Figure 3
Thick cylinders $(k R ≫ 1)$ irradiated with $p$ waves ( $H_{i} | | \hat{z}$ ) at the presence of an external magnetic field $B = B \hat{z}$ . Scatterers are composed of a dielectric ${SiO}_{2}$ cylinder coated with a subwavelength magneto-optical shell of InSb embedded in agarose gel, with packing fraction $f ≪ 1$ . The InSb cylindrical shell is strongly dependent on the external magnetic field and the temperature $T$ .
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Figure 4
Spatial correlation function $C (Δ r, Δ k)$ for monodispersed ( ${SiO}_{2}$ ) core-shell (InSb) cylinders in agarose gel $(f = 0.45 %)$ normally irradiated with $p$ waves ( $ω = 2 π \times 2.4 THz$ ). The core-shell cylinder has radius $R = 100 μ m (k R \approx 6.74)$ , where the ${SiO}_{2}$ core is coated with a InSb single layer of thickness $d = 1 μ m (k d \approx 0.0674)$ . The phase function is calculated by the rigorous Lorenz-Mie theory. (a) Plot showing the increase in $C$ as a function of the temperature $T$ for slab thickness $L = 9.5 mm$ and $Δ k = 0$ , where the maximum memory effect within the validity of the SAA is found for $T = 315 K$ . (b) Shift-tilt memory effect for the optimal isoplanatic patch condition $Δ k = 3 k Δ r / 2 L$ . Even small correlations for a large slab thickness ( $L = 4 \times 9.5 mm$ ) can be considerably enhanced by increasing $T$ for (c) $Δ k = 0$ and (d) $Δ k = 3 k Δ r / 2 L$ .
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Figure 5
Shift-shift correlation function $C (Δ r, Δ k)$ for monodispersed ( ${SiO}_{2}$ ) core-shell (InSb) cylinders in agarose gel $(f = 0.45 %)$ normally irradiated with $p$ waves ( $ω = 2 π \times 2.4 THz$ ). The core-shell cylinder has radius $R = 100 μ m (k R \approx 6.74)$ , where the ${SiO}_{2}$ core is coated with a InSb single layer of thickness $d = 1 μ m (k d \approx 0.0674)$ . The phase function is calculated by the rigorous Lorenz-Mie theory. The plots show that the maximum correlation achieved for $T = 315 K$ in Fig. 4 can be decreased by the application of an external magnetic field $B = B \hat{z}$ . (a) $L = 9.5 mm$ and $Δ k = 0$ . (b) $L = 9.5 mm$ and $Δ k = 3 k Δ r / 2 L$ . (c) $L = 4 \times 9.5 mm$ and $Δ k = 0$ . (d) $L = 4 \times 9.5 mm$ and $Δ k = 3 k Δ r / 2 L$ .
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