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The Casimir effect is a force arising in the macroscopic world as a result of radiation pressure of vacuum fluctuations. It thus plays a key role in the emerging domain of nano-electro-mechanical systems (NEMS). This role is reviewed in the…

We derive the fully retarded energy shift of a neutral atom in two different geometries useful for modelling etched microstructures. First we calculate the energy shift due to a reflecting cylindrical wire, and then we work out the energy…

We develop a diagrammatic representation of the Casimir energy of a multibody configuration. The diagrams represent multiple reflections between the objects and can be organized by a few simple rules. The lowest-order diagrams (or…

The Casimir effect, arising from vacuum quantum fluctuations, plays a fundamental role in the development of modern quantum electrodynamics. In parallel, the field of condensed matter has flourished through the discovery of various…

We discuss recent experimental and theoretical results on the Casimir force between real material bodies made of different materials. Special attention is paid to calculations of the normal Casimir force acting perpendicular to the surface…

The Casimir force between two parallel thick plates, one perfectly dielectric, the other purely magnetic, has been calculated long ago by Boyer [T. H. Boyer, Phys. Rev. A {\bf 9}, 2078 (1974)]. Its most characteristic property is that it is…

We study the Casimir energy due to a quantum real scalar field coupled to two planar, infinite, zero-width, parallel mirrors with non-homogeneous properties. These properties are represented, in the model we use, by scalar functions defined…

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…

We derive an exact solution for the Casimir force between two arbitrary periodic dielectric gratings and illustrate our method by applying it to two nanostructured silicon gratings. We also reproduce the Casimir force gradient measured…

The interaction between a polarizable particle and a reflecting wall is examined. A macroscopic approach is adopted in which the averaged force is computed from the Maxwell stress tensor. The particular case of a perfectly reflecting wall…

The measurement of the Casimir force between a large gold coated sphere and single crystal silicon plate is performed with an atomic force microscope. A rigorous statistical comparison of data with theory is done, without use of the concept…

We derive a general expression for the Casimir energy corresponding to two flat parallel mirrors in d+1 dimensions, described by nonlocal interaction potentials. For a real scalar field, the interaction with the mirrors is implemented by a…

The Casimir effect, the dispersion force attracting neutral objects to each other, may be understood in terms of multiple scattering of light between the interacting bodies. We explore the simple model in which the bodies are assumed to…

We demonstrate theoretically that one can obtain repulsive Casimir forces and stable nanolevitations by using chiral metamaterials. By extending the Lifshitz theory to treat chiral metamaterials, we find that a repulsive force and a minimum…

The Casimir force follows from quantum fluctuations of the electromagnetic field and yields a nonlinear attractive force between closely spaced conductive objects. Measuring the Casimir force in superconducting materials on either side of…

The dielectric sphere has been an important test case for understanding and calculating the vacuum force of a dielectric body onto itself. Here we develop a method for computing this force in homogeneous spheres of arbitrary dielectric…

We study the general form of the Casimir interaction between two flat finite-width, parallel, infinite mirrors, described by their respective vacuum polarization tensors, under the assumption of translation invariance along the directions…

Multiple scattering formulations have been employed for more than 30 years as a method of studying the quantum vacuum or Casimir interactions between distinct bodies. Here we review the method in the simple context of $\delta$-function…

We study the Casimir effect in a system composed of two Weyl semimetals (WSMs) separated by a gap filled with a chiral medium. We calculate the optical response of the material to chiral photons in order to calculate the Casimir force. We…

We propose the experimental scheme and present detailed theory of the optical chopper which functionality is based on the balance between the Casimir and light pressures. The proposed device consists of two atomically thin metallic mirrors…