Outgoing wave conditions in photonic crystals and transmission properties at interfaces
| dc.contributor.author | Lamacz, Agnes | |
| dc.contributor.author | Schweizer, Ben | |
| dc.date.accessioned | 2015-09-03T11:48:03Z | |
| dc.date.available | 2015-09-03T11:48:03Z | |
| dc.date.issued | 2015-08-31 | |
| dc.description.abstract | We analyze the propagation of waves in unbounded photonic crystals, the waves are described by a Helmholtz equation with x-dependent coefficients. The scattering problem must be completed with a radiation condition at infinity, which was not available for x-dependent coefficients. We develop an outgoing wave condition with the help of a Bloch wave expansion. Our radiation condition admits a (weak) uniqueness result, formulated in terms of the Bloch measure of solutions. We use the new radiation condition to analyze the transmission problem where, at fixed frequency, a wave hits the interface between free space and a photonic crystal. We derive that the vertical wave number of the incident wave is a conserved quantity. Together with the frequency condition for the transmitted wave, this condition leads (for appropriate photonic crystals) to the effect of negative refraction at the interface. | en |
| dc.identifier.uri | http://hdl.handle.net/2003/34215 | |
| dc.identifier.uri | http://dx.doi.org/10.17877/DE290R-16294 | |
| dc.language.iso | en | |
| dc.subject | Helmholtz equation | en |
| dc.subject | radiation | en |
| dc.subject | Bloch analysis | en |
| dc.subject | outgoing wave condition | en |
| dc.subject | photonic crystal | en |
| dc.subject | transmission problem | en |
| dc.subject | negative refraction | en |
| dc.subject.ddc | 610 | |
| dc.title | Outgoing wave conditions in photonic crystals and transmission properties at interfaces | en |
| dc.type | Text | de |
| dc.type.publicationtype | preprint | en |
| dcterms.accessRights | open access |