Electromagnetic waves near perfect conductors. I. Multiple scattering expansions. Distribution of modes Export

@article{Balian1977, abstract = {An expansion is established for the Green functions describing electromagnetic waves in the presence of a perfectly conducting boundary. Each term represents a process for which the wave scatters several times on the boundary and propagates freely in between. This multiple scattering expansion reduces to ray optics in the high frequency limit, and thus provides a general framework to study diffraction corrections. It also allows one to evaluate quantities averaged over the spectrum. Some symmetry properties of the expansion are exhibited, in particular, the replacement of magnetic fields by electric fields results in a change of sign at each scattering. Convergence is proven for any smooth boundary in the domain Im k | Re k | of complex wavenumbers k . The continuation of the convergence domain around k = 0 is shown to depend upon the topology of the boundary. The multiple scattering expansion method is applied to determine the distribution of electromagnetic eigenmodes in a conducting cavity. The density of modes ( k ) is analyzed in terms of closed classical rays, bouncing off the walls with mirror reflections. Paths of zero length yield the smooth part of , expanded as + ( k −2 )] where V is the volume of the cavity, and ∫ d α/ R is the integral over the boundary of the mean curvature. Paths of finite length L yield contributions to the density ( k ), of the form Im( a exp ikL ) appearing as regular oscillations in the bunching of eigenmodes. For an analytic boundary, inclusion of complex classical rays renders exact the analysis of the eigenmodes in terms of closed paths. As a consequence, the high temperature expansion for the energy of a small blackbody is obtained.}, author = {Balian, R. and Duplantier, B.}, citeulike-article-id = {4978724}, citeulike-linkout-0 = {http://dx.doi.org/10.1016/0003-4916(77)90334-7}, citeulike-linkout-1 = {http://linkinghub.elsevier.com/retrieve/pii/0003491677903347}, doi = {10.1016/0003-4916(77)90334-7}, issn = {00034916}, journal = {Annals of Physics}, keywords = {conductors, modes, multiple, multipole, perfect, scattering, waves}, month = {April}, number = {2}, pages = {300--335}, posted-at = {2009-06-26 16:27:51}, priority = {2}, title = {Electromagnetic waves near perfect conductors. I. Multiple scattering expansions. Distribution of modes}, url = {http://dx.doi.org/10.1016/0003-4916(77)90334-7}, volume = {104}, year = {1977} }

TY - JOUR ID - Balian1977 L3 - citeulike-article-id:4978724 N2 - An expansion is established for the Green functions describing electromagnetic waves in the presence of a perfectly conducting boundary. Each term represents a process for which the wave scatters several times on the boundary and propagates freely in between. This multiple scattering expansion reduces to ray optics in the high frequency limit, and thus provides a general framework to study diffraction corrections. It also allows one to evaluate quantities averaged over the spectrum. Some symmetry properties of the expansion are exhibited, in particular, the replacement of magnetic fields by electric fields results in a change of sign at each scattering. Convergence is proven for any smooth boundary in the domain Im k | Re k | of complex wavenumbers k . The continuation of the convergence domain around k = 0 is shown to depend upon the topology of the boundary. The multiple scattering expansion method is applied to determine the distribution of electromagnetic eigenmodes in a conducting cavity. The density of modes ( k ) is analyzed in terms of closed classical rays, bouncing off the walls with mirror reflections. Paths of zero length yield the smooth part of , expanded as + ( k −2 )] where V is the volume of the cavity, and ∫ d α/ R is the integral over the boundary of the mean curvature. Paths of finite length L yield contributions to the density ( k ), of the form Im( a exp ikL ) appearing as regular oscillations in the bunching of eigenmodes. For an analytic boundary, inclusion of complex classical rays renders exact the analysis of the eigenmodes in terms of closed paths. As a consequence, the high temperature expansion for the energy of a small blackbody is obtained. IS - 2 JF - Annals of Physics SN - 00034916 EP - 335 TI - Electromagnetic waves near perfect conductors. I. Multiple scattering expansions. Distribution of modes VL - 104 SP - 300 KW - conductors KW - modes KW - multiple KW - multipole KW - perfect KW - scattering KW - waves AU - Balian, R AU - Duplantier, B PY - 1977/04// UR - http://dx.doi.org/10.1016/0003-4916(77)90334-7 ER -