The Casimir effect within scattering theory

Abstract

We review the theory of the Casimir effect using scattering techniques. After years of theoretical efforts, this formalism is now largely mastered so that the accuracy of theory-experiment comparisons is determined by the level of precision and pertinence of the description of experimental conditions. Due to an imperfect knowledge of the optical properties of real mirrors used in the experiment, the effect of imperfect reflection remains a source of uncertainty in theory-experiment comparisons. For the same reason, the temperature dependence of the Casimir force between dissipative mirrors remains a matter of debate. We also emphasize that real mirrors do not obey exactly the assumption of specular reflection, which is used in nearly all calculations of material and temperature corrections. This difficulty may be solved by using a more general scattering formalism accounting for nonspecular reflection with wavevectors and field polarizations mixed. This general formalism has already been fruitfully used for evaluating the effect of roughness on the Casimir force as well as the lateral Casimir force appearing between corrugated surfaces. The commonly used 'proximity force approximation' turns out to lead to inaccuracies in the description of these two effects.

Thermal Casimir force between nanostructured surfaces

“…The Casimir force per unit area between two parallel plates is given by the Lifshitz formula [12] with specular reflection on the plates described by Fresnel coefficients. The scattering theory generalizes this formula by treating nonspecular reflections from a grating through the use of reflection operators coupling different plane-wave modes [8]. The Casimir force per unit area F p,g (L) between a plane and a grating at finite temperature T , separated by a distance L, is (1) where the prime on the sum means that the term with n = 0 is to be multiplied by a factor 1/2.…”

“…On the basis of this method a scattering approach to the Casimir force in the gratings geometry at zero temperature has been presented in [6]. In this paper we use the scattering approach to Casimir forces [7][8][9] to calculate the Casimir interaction between a plate and a grating at arbitrary temperature. Alternatively, the Casimir force in such geometries can also be calculated using a modal approach [10], which is in principle identical to the method presented in [6] and in this paper.…”

Casimir forces on a silicon micromechanical chip

“…Metamaterials, with their remarkable optical properties, have been considered as candidates for controlling the Casimir force 9,10 , but initial suggestions that the sign of the force in vacuum could be altered by metamaterials turned out to be unrealistic 11 . With regard to the non-trivial dependence of the Casimir force on the shape of the bodies [12][13][14][15] , experiments involving nanostructured surfaces have demonstrated the nonpairwise additive nature of the Casimir force 16,17 . Recent experiments have also measured the corrections to the Casimir force that arise from the presence of thermal fluctuations, in addition to quantum fluctuations 18 .…”

Statistical approach to Casimir-Polder potentials in heterogeneous media

“…Its mean, U (z), and its variance, δU 2 (z), were calculated from an exact treatment of radiation-matter interaction, based on the scattering approach to Casimir forces [36,37] combined with a diagrammatic description of radiation scattering off the disordered medium [38,39]. In the limit z ≫ λ 0 , the following expression for the mean was found [30]:…”