Damped vacuum states of light
T G Philbin
Abstract and summary · read the original at the source
In one page
Most Casimir calculations only ever ask for one number — the total energy, or the force it produces — and that habit hides the structure underneath. Thomas Philbin of the University of Exeter opens it up. He takes the simplest interesting case, a slab of real material with light running straight through it, and keeps everything the usual shortcuts throw away: the material absorbs, it disperses, and it obeys the Kramers-Kronig relations that any real substance obeys. Then he asks what the vacuum energy is at each separate frequency. The answer is that the slab pushes some frequencies down below their empty-space value and pushes others up. For a gold-like metal, everything below the plasma frequency is damped and everything above it is lifted. Each of those shifts is finite on its own, with no regularisation needed. And the grand total, once regularised the standard way, still comes out positive.
Why it matters hereChapter 2 says the vacuum is a structured medium whose spectrum you can reshape with ordinary matter, and this is that statement made quantitative frequency by frequency rather than lumped into a single force. It also settles a point of language the site cares about: the modes that fall below the free-space level are not holes in nothing, they are ordinary modes sitting below the ambient level, and the total stays positive. Chapter 5 gets the bridge Philbin draws himself — this is the physics of a quantum damped oscillator, the same object nanomechanics works with. Read it beside the same author’s fibre-optical analogue of an event horizon at /library/stm-a5c8b5b2b0.
What it claims
01One-dimensional propagation of quantum light past a block of material can be treated exactly, with full account of dispersion and absorption, by writing macroscopic electromagnetism as a closed system of fields coupled to a reservoir and diagonalising the Hamiltonian — no idealised boundary conditions and no dielectric functions that violate the Kramers-Kronig relations.Section 2, ‘Set-up’; Eqs. 1 to 3; Figure 1
Published and peer-reviewed02The zero-point electric and magnetic field uncertainties outside the block oscillate with distance from its face, yet the energy per unit length outside is exactly the free-space value: the material dependence cancels for modes propagating perpendicular to the boundaries, so the whole change in zero-point energy sits inside the block.Section 3, Eqs. 11 and 12; Section 4, Eq. 22
Published and peer-reviewed03Inside the block, the zero-point energy per unit frequency is damped below the free-space value for some frequencies and raised above it for others — for a Drude model of gold with plasma frequency 8.45 eV and damping 0.047 eV, the energy is suppressed everywhere below the plasma frequency and enhanced above it, for block lengths of both 1 µm and 10 µm.Section 5, ‘Examples’; Eq. 28; Figure 2
Published and peer-reviewed04The change in zero-point energy caused by the block is finite at every single frequency, before and after regularisation; only the sum over all frequencies diverges, so the frequency-resolved result does not depend on the choice of regulariser.Section 4, paragraph following Eq. 24
Published and peer-reviewed05After the standard Casimir regularisation — the same one used to predict measured Casimir forces — the Casimir energy per unit frequency oscillates between positive and negative values, so individual modes sit below the free-space level, while the total Casimir energy comes out positive for every block length and for both metals and non-metallic dielectrics.Section 4, Eqs. 26 and 27; Figures 3 and 5; Section 6, Conclusions
Published and peer-reviewed06Because the quantum theory of macroscopic electromagnetism is a theory of quantum damped harmonic oscillators, the same modifications of zero-point energy should appear in nanomechanical systems, where a single oscillator is coupled to a reservoir instead of the field’s infinite set.Section 1, Introduction; Section 6, Conclusions
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Read it · abstract
Abstract
We consider one-dimensional propagation of quantum light in the presence of a block of material, with a full account of dispersion and absorption. The electromagnetic zero-point energy for some frequencies is damped (suppressed) by the block below the free-space value, while for other frequencies it is increased. We also calculate the regularized (Casimir) zero-point energy at each frequency and find that it too is damped below the free-space value (zero) for some frequencies. The total Casimir energy is positive.
PACS numbers 42.50.Lc, 42.50.Nn, 12.20.-m
(Abstract only — see the rights note above. The complete paper, with the Green functions, the two worked materials and the five figures, is free to read at arxiv.org/abs/1603.00233 and at the publisher. On this site, Philbin’s fibre-optical analogue of an event horizon, made with the same group at St Andrews, is at /library/stm-a5c8b5b2b0.)
The way in
https://doi.org/10.1088/2040-8978/18/9/095201Published as Journal of Optics 18 (2016) 095201 by Thomas G. Philbin of the Physics and Astronomy Department, University of Exeter. The version of record is free to read at IOP, but under the publisher’s own terms rather than a Creative Commons licence, and the author version on arXiv as 1603.00233 — posted 1 March 2016 with a second version on 13 June 2016 — carries the arXiv non-exclusive distribution licence version 1.0, checked on the arXiv abstract page on 2026-09-08. Neither is a Creative Commons licence and no Creative Commons statement appears in the text, so this sheet carries the summary, the claims and the author’s own abstract and sends the reader to the source. The claims below are located against the arXiv version’s numbered sections, equations and figures. Author acknowledgement in the paper: S. A. R. Horsley.
How to cite it
T G Philbin (2016) Damped vacuum states of light. doi:10.1088/2040-8978/18/9/095201
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