Effect of Dependent Scattering on Light Absorption in Highly Scattering Random Media

The approximate nature of radiative transfer equation (RTE) leads to a bunch of considerations on the effect of "dependent scattering" in random media, especially particulate media composed of discrete scatterers, in the last a few decades, which usually indicates those deviations RTE (combined with ISA) lead to from experimental and exact numerical results due to electromagnetic wave interference. Here we theoretically and numerically demonstrate the effect of dependent scattering on absorption in disordered media consisting of highly scattering scatterers. By making comparison between the independent scattering approximation-radiative transfer equation (ISA-RTE) and the full-wave coupled dipole method (CDM), we find that deviations between the two methods increase as scatterer density in the media increases. The discrepancy also grows with optical thickness. To quantitatively take dependent scattering effect into account, we develop a theoretical model using quasi-crystalline approximation (QCA) to derive dependent-scattering corrected radiative properties, based on the path-integral diagrammatic technique in multiple scattering theory. The model results in a more reasonable agreement with numerical simulations. The present work has profound implications for the coherent scattering physics in random media with absorption, correctly modeling light absorptance in random media and interpreting the experimental observations in various applications for random media such as solar energy concentration, micro/nanofluids, structural color generation, etc.Comment: 30 pages, 8 figures, submitte

Tuning toroidal dipole resonances in dielectric metamolecules by an additional electric dipolar response

With the rise of artificial magnetism and metamaterials, the toroidal family recently attracts more attention for its unique properties. Here we propose an all-dielectric pentamer metamolecule consisting of nano-cylinders with two toroidal dipolar resonances, whose frequencies, EM distributions and Q factor can be efficiently tuned due to the additional electric dipole mode offered by a central cylinder. To further reveal the underlying coupling effects and formation mechanism of toroidal responses, the multiple scattering theory is adopted. It is found that the first toroidal dipole mode, which can be tuned from 2.21 to 3.55 $\mu$m, is mainly induced by a collective electric dipolar resonance, while the second one, which can be tuned from 1.53 to 1.84 $\mu$m, relies on the cross coupling of both electric and magnetic dipolar responses. The proposed low-loss metamolecule and modes coupling analyses may pave the way for active design of toroidal responses in advanced optical devices.Comment: 14 pages, 9 figure

Low-temperature thermal conductivity of Dy_2Ti_2O_7 and Yb_2Ti_2O_7 single crystals

We study the low-temperature thermal conductivity (\kappa) of Dy_2Ti_2O_7 and Yb_2Ti_2O_7 single crystals in magnetic fields up to 14 T along the [111], [100] and [110] directions. The main experimental findings for Dy_2Ti_2O_7 are: (i) the low-T \kappa(H) isotherms exhibit not only the step-like decreases at the low-field (< 2 T) magnetic transitions but also obvious field dependencies in high fields (> 7 T); (ii) at T \le 0.5 K, the \kappa(H) curves show anisotropic irreversibility in low fields, that is, the \kappa(H) hysteresis locates at the first-order transition with H \parallel [100] and [110], while it locates between two successive transitions with H \parallel [111]; (iii) the \kappa in the hysteresis loops for H \parallel [100] and [110] show an extremely slow relaxation with the time constant of \sim 1000 min. The main experimental findings for Yb_2Ti_2O_7 are: (i) the zero-field \kappa(T) show a kink-like decrease at the first-order transition (\sim 200 mK) with decreasing temperature; (ii) the low-T \kappa(H) isotherms show a decrease in low field and a large enhancement in high fields; (iii) the low-T \kappa(H) curves show a sharp minimum at 0.5 T for H \parallel [110] and [111]. The roles of monopole excitations, field-induced transitions, spin fluctuations and magnetoelastic coupling are discussed.Comment: 15 pages, 11 figures, accepted for publication in Phys. Rev.