Lifshitz formula by spectral summation method

Abstract

The Lifshitz formula is derived by making use of the spectral summation method which is a mathematically rigorous simultaneous application of both the mode-by-mode summation technique and scattering formalism. The contributions to the Casimir energy of electromagnetic excitations of different types (surface modes, waveguide modes, and photonic modes) are clearly retraced. A correct transition to imaginary frequencies is accomplished with allowance for all the peculiarities of the frequency equations and pertinent scattering data in the complex $\omega$ plane, including, in particular, the cuts connecting the branch points and complex roots of the frequency equations (quasi-normal modes). The principal novelty of our approach is a special choice of appropriate passes in the contour integrals, which are used for transition to imaginary frequencies. As a result, the long standing problem of cuts in the complex $\omega$ plane is solved completely. Inconsistencies of some previous derivations of the Lifshitz formula are traced briefly. For completeness of the presentation, the necessary mathematical facts are also stated, namely, solution of the Maxwell equations for configurations under consideration, scattering formalism for parallel plane interfaces, determination of the frequency equation roots, and others.

The version published in Phys. Rev. A 86, 052503 (2012); criticism of some previous derivations of the Lifshitz formula is diminished (Introduction) and emphasizing the authors achievements (Conclusion) is moderated

References in corpus (11)

• Theory of surface plasmons and surface-plasmon polaritons
• Guided Modes in Negative Refractive Index Waveguides
• The Casimir effect within scattering theory
• The Casimir force and the quantum theory of lossy optical cavities
• The Role of Surface Plasmons in The Casimir Effect
• Casimir Force on Real Materials - the Slab and Cavity Geometry
• Electromagnetic vacuum energy for two parallel slabs in terms of surface, wave guide and photonic modes
• Casimir Force for Absorbing Media in an Open Quantum System Framework: Scalar Model
• Repulsive Casimir forces and the role of surface modes
• Lifshitz formula for the Casimir force and the Gelfand-Yaglom theorem
• Surface modes and photonic modes in Casimir calculations for a compact cylinder

Cited by in corpus (7)

• The quest for Casimir repulsion between Chern-Simons surfaces
• Derivation of the Lifshitz-Matsubara sum formula for the Casimir pressure between metallic plane mirrors
• Casimir energy for surfaces with constant conductivity
• Vacuum-excited surface plasmon polaritons
• Plasma model and Drude model permittivities in Lifshitz formula
• First-order correction to the Casimir force within an inhomogeneous medium
• On the computation of Casimir stresses in open media and Lifshitz theory