The Casimir force for passive mirrors

We show that the Casimir force between mirrors with arbitrary frequency dependent reflectivities obeys bounds due to causality and passivity properties. The force is always smaller than the Casimir force between two perfectly reflecting mirrors. For narrow-band mirrors in particular, the force is found to decrease with the mirrors bandwidth.Comment: 12 pages, 2 figures, LaTe

Composite mirror facets for ground based gamma ray astronomy

Composite mirrors for gamma-ray astronomy have been developed to fulfill the specifications required for the next generation of Cherenkov telescopes represented by CTA (Cherenkov Telescope Array). In addition to the basic requirements on focus and reflection efficiency, the mirrors have to be stiff, lightweight, durable and cost efficient. In this paper, the technology developed to produce such mirrors is described, as well as some tests that have been performed to validate them. It is shown that these mirrors comply with the needs of CTA, making them good candidates for use on a significant part of the array.Comment: 16 pages, 13 figures, accepted to be published on NIM

Conicoid Mirrors

The first order equation relating object and image location for a mirror of arbitrary conic-sectional shape is derived. It is also shown that the parabolic reflecting surface is the only one free of aberration and only in the limiting case of distant sources.Comment: 9 page

Analytical expressions for optimum alignment modes of highly segmented mirrors

The major sources causing deterioration of optical quality in extremely large optical telescopes are misadjustments of the mirrors, deformations of monolithic mirrors, and misalignments of segments in segmented mirrors. For active optics corrections, all three errors, which can partially compensate each other, are measured simultaneously. It is therefore of interest to understand the similarities and differences between the three corresponding types of modes which describe these errors. The first two types are best represented by Zernike polynomials and elastic modes respectively, both of them being continuous and smooth functions. The segment misaligment modes, which are derived by singular value decomposition, are by their nature not smooth and in general discontinuous. However, for mirrors with a large number of segments, the lowest modes become effectively both smooth and continuous. This paper derives analytical expressions for these modes, using differential operators and their adjoints, for the limit case of infinitesimally small segments. For segmented mirrors with approximately 1000 segments, it is shown that these modes agree well with the corresponding lowest singular value decomposition modes. Furthermore, the analytical expressions reveal the nature of the segment misalignment modes and allow for a detailed comparison with the elastic modes of monolithic mirrors. Some mathematical features emerge as identical in the two cases.Comment: 24 pages, 13 figures, accepted for publication in Journal of Modern Optic

Functional approach to quantum friction: effective action and dissipative force

We study the Casimir friction due to the relative, uniform, lateral motion of two parallel semitransparent mirrors coupled to a vacuum real scalar field, $\phi$. We follow a functional approach, whereby nonlocal terms in the action for $\phi$, concentrated on the mirrors' locii, appear after functional integration of the microscopic degrees of freedom. This action for $\phi$, which incorporates the relevant properties of the mirrors, is then used as the starting point for two complementary evaluations: Firstly, we calculate the { in-out} effective action for the system, which develops an imaginary part, hence a non-vanishing probability for the decay (because of friction) of the initial vacuum state. Secondly, we evaluate another observable: the vacuum expectation value of the frictional force, using the { in-in} or Closed Time Path formalism. Explicit results are presented for zero-width mirrors and half-spaces, in a model where the microscopic degrees of freedom at the mirrors are a set of identical quantum harmonic oscillators, linearly coupled to $\phi

Thermodynamical fluctuations and photo-thermal shot noise in gravitational wave antennae

Thermodynamical fluctuations of temperature in mirrors of gravitational wave antennae are transformed through thermal expansion coefficient into additional noise. This source of noise, which may also be interpreted as fluctuations due to thermoelastic damping, may not be neglected and leads to the necessity to reexamine the choice of materials for the mirrors. Additional source of noise are fluctuations of the mirrors' surfaces caused by optical power absorbed in dielectrical reflective layers.Comment: 20 pages, 2 figure