Paulo A. Maia Neto

Casimir effect with rough metallic mirrors

We calculate the second-order roughness correction to the Casimir energy for two parallel metallic mirrors. Our results may also be applied to the plane-sphere geometry used in most experiments. The metallic mirrors are described by the plasma model, with arbitrary values for the plasma wavelength, the mirror separation, and the roughness correlation length, with the roughness amplitude remaining the smallest length scale for perturbation theory to hold. From the analysis of the intracavity field fluctuations, we obtain the Casimir energy correction in terms of generalized reflection operators, which account for diffraction and polarization coupling in the scattering by the rough surfaces. We present simple analytical expressions for several limiting cases, as well as numerical results that allow for a reliable calculation of the roughness correction in real experiments. The correction is larger than the result of the proximity force approximation, which is obtained from our theory as a limiting case (very smooth surfaces)

Casimir Interaction between Plane and Spherical Metallic Surfaces

We give an exact series expansion of the Casimir force between plane and spherical metallic surfaces in the nontrivial situation where the sphere radius R, the plane-sphere distance L and the plasma wavelength lambda(P) have arbitrary relative values. We then present numerical evaluation of this expansion for not too small values of L/R. For metallic nanospheres where R, L and lambda(P) have comparable values, we interpret our results in terms of a correlation between the effects of geometry beyond the proximity force approximation and of finite reflectivity due to material properties. We also discuss the interest of our results for the current Casimir experiments which are performed with spheres of large radius R>>L.

Lateral Casimir Force beyond the Proximity-Force Approximation

We argue that the appropriate variable to study a nontrivial geometry dependence of the Casimir force is the lateral component of the Casimir force, which we evaluate between two corrugated metallic plates outside the validity of the proximity-force approximation. The metallic plates are described by the plasma model, with arbitrary values for the plasma wavelength, the plate separation, and the corrugation period, the corrugation amplitude remaining the smallest length scale. Our analysis shows that in realistic experimental situations the proximity-force approximation overestimates the force by up to 30%.

Thermal Casimir effect in the plane-sphere geometry.

The thermal Casimir force between two metallic plates is known to depend on the description of material properties. For large separations the dissipative Drude model leads to a force a factor of 2 smaller than the lossless plasma model. Here we show that the plane-sphere geometry, in which current experiments are performed, decreases this ratio to a factor of 3/2, as revealed by exact numerical and large-distance analytical calculations. For perfect reflectors, we find a repulsive contribution of thermal photons to the force and negative entropy values at intermediate distances.

Casimir energy between a plane and a sphere in electromagnetic vacuum

Laboratoire Kastler Brossel, CNRS, ENS, Universit´e Pierre et Marie Curie case 74,Campus Jussieu, F-75252 Paris Cedex 05, France(Dated: May 23, 2008)The Casimir energy is computed in the geometry of interest for the most precise experiments,a plane and a sphere in electromagnetic vacuum. The scattering formula is developed on adaptedplane-waves and multipole basis, leading to an expression valid for arbitrary relative values of thesphere radius and inter-plate distance. In the limiting case of perfect reflection, the electromagneticresult is found to depart from the commonly used proximity-force approximation (PFA) significantlymore rapidly than expected from scalar computations.

Fluctuations, Dissipation and the Dynamical Casimir Effect

Vacuum fluctuations provide a fundamental source of dissipation for systems coupled to quantum fields by radiation pressure. In the dynamical Casimir effect, accelerating neutral bodies in free space give rise to the emission of real photons while experiencing a damping force which plays the role of a radiation reaction force. Analog models where non-stationary conditions for the electromagnetic field simulate the presence of moving plates are currently under experimental investigation. A dissipative force might also appear in the case of uniform relative motion between two bodies, thus leading to a new kind of friction mechanism without mechanical contact. In this paper, we review recent advances on the dynamical Casimir and non-contact friction effects, highlighting their common physical origin.

Angular momentum of focused beams : Beyond the paraxial approximation

We investigate in detail the focusing of a circularly polarized Laguerre-Gaussian laser beam [

Thermal Casimir effect for Drude metals in the plane-sphere geometry

\ensuremath{\hbar}\ensuremath{\ell}

Dispersive interactions between atoms and nonplanar surfaces

orbital angular momentum per photon;

Casimir torque between corrugated metallic plates

\ensuremath{\sigma}=1(\ensuremath{-}1)