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Based on a generalization of the Lifshiftz theory, we calculate Casimir forces involving magnetodielectric and possibly anisotropic metamaterials, focusing on the possibility of repulsive forces. It is found that Casimir repulsion decreases with magnetic dissipation, and even a small Drude background in metallic-based metamaterials acts to make attractive a Casimir force that would otherwise be predicted to be repulsive. The sign of the force also depends sensitively on the degree of optical anisotropy of the metamaterial and on the form of the frequency dependency of the magnetic response.

By combining stochastic electrodynamics and the Maxwell-Garnett description for effective media we study the radiative heat transfer between two nanoporous materials. We show that the heat flux can be significantly enhanced by air inclusions, which we explain by: (a) the presence of additional surface waves that give rise to supplementary channels for heat transfer throughout the gap, (b) an increase in the contribution given by the ordinary surface waves at resonance, (c) and the appearance of frustrated modes over a broad spectral range. We generalize the known expression for the nanoscale heat flux for anisotropic metamaterials.

We extend our previous work ͓Phys. Rev. Lett. 100, 183602 ͑2008͔͒ on the generalization of the Casimir-Lifshitz theory to treat anisotropic magnetodielectric media, focusing on the forces between metals and magnetodielectric metamaterials and on the possibility of inferring magnetic effects by measurements of these forces. We present results for metamaterials including structures with uniaxial and biaxial magnetodielectric anisotropies, as well as for structures with isolated metallic or dielectric properties that we describe in terms of filling factors and a Maxwell Garnett approximation. The elimination or reduction of Casimir "stiction" by appropriate engineering of metallic-based metamaterials, or the indirect detection of magnetic contributions, appear from the examples considered to be very challenging, as small background Drude contributions to the permittivity act to enhance attraction over repulsion, as does magnetic dissipation. In dielectric-based metamaterials the magnetic properties of polaritonic crystals, for instance, appear to be too weak for repulsion to overcome attraction. We also discuss Casimir-Polder experiments, that might provide another possibility for the detection of magnetic effects.

We present a theoretical study of near-field heat transfer between two uniaxial anisotropic planar structures. We investigate how the distance and relative orientation (with respect to their optical axes) between the objects affect the heat flux. In particular, we show that by changing the angle between the optical axes it is possible in certain cases to modulate the net heat flux up to 90% at room temperature, and discuss possible applications of such a strong effect. 1Since the prediction by Polder and van Hove [1] that the heat exchange between two media at short separations can be much higher than the blackbody limit, numerous works have been carried out to investigate both theoretically and experimentally the physics involved in this transfer. Experimentally, it was shown [2,3] that the radiative heat flux increases for distances shorter than the thermal wavelength and can vastly exceed the black body limit [4,5]. Moreover, very recent experiments [6,7] were in good quantitative agreement with theoretical predictions. On the theoretical side, we can highlight the studies of the heat flux for layered media [8,9], for photonic crystals [10], metamaterials [11], and porous media [12].In addition, the dependence of the heat transfer on the geometry has attracted much interest and has been investigated in a sphere-plane geometry [13,14], for spheroidal particles above a plane surface [15] and between two spheres or nanoparticles [16][17][18][19][20]. Somewhat more applied studies have attempted to take advantage of the potential of the tremendous increase of the radiative heat flux on the nanoscale for thermal imaging of nanostructured surfaces [21][22][23][24].Finally, the formulation of the heat flux in terms of the scattering matrix [25,26] [33] to modulate heat flux between two materials using an electric ac current as external power source. However, due to the properties of these materials, such modulator works reversibly only during a limited number of cycle which typically oscillate between 10 7 and 10 12 . Moreover, such devices work at two discrete levels of flux, one for each state of the phase changing material.In this Letter, we investigate the near-field heat transfer between two polar/metallic misaligned gratings in the long wavelength limit, where they may be described by effective homogeneous anisotropic permittivities. We show that it is possible to get a strong heat flux modulation without cycle limitation just by rotating the relative position of the grating's 2 optical axes [34]. Our approach combines the standard stochastic electrodynamics [35] and the effective medium theory [36][37][38] for the gratings.A sketch of the geometry considered is depicted in Fig. 1. It shows two semi-infinite host materials of complex permittivity ǫ i (ω) (i = 1, 2) with a one dimensional grating engraved on each. The relative orientation of the two gratings is arbitrary in the (x,y) plane, and we assume that their trenches are sufficiently deep so as to (i) render the substrate below those gratings i...