dorsal/arxiv
View SchemaAn asymptotic form of the reciprocity theorem with applications in x-ray scattering
| Authors | Ariel Caticha |
|---|---|
| Categories | |
| ArXiv ID | physics/0001005 |
| URL | https://arxiv.org/abs/physics/0001005 |
| DOI | 10.1103/PhysRevB.62.3639 |
| Journal | Physical Review B62, 3639 (2000) |
Abstract
The emission of electromagnetic waves from a source within or near a non-trivial medium (with or without boundaries, crystalline or amorphous, with inhomogeneities, absorption and so on) is sometimes studied using the reciprocity principle. This is a variation of the method of Green's functions. If one is only interested in the asymptotic radiation fields the generality of these methods may actually be a shortcoming: obtaining expressions valid for the uninteresting near fields is not just a wasted effort but may be prohibitively difficult. In this work we obtain a modified form the reciprocity principle which gives the asymptotic radiation field directly. The method may be used to obtain the radiation from a prescribed source, and also to study scattering problems. To illustrate the power of the method we study a few pedagogical examples and then, as a more challenging application we tackle two related problems. We calculate the specular reflection of x rays by a rough surface and by a smoothly graded surface taking polarization effects into account. In conventional treatments of reflection x rays are treated as scalar waves, polarization effects are neglected. This is a good approximation at grazing incidence but becomes increasingly questionable for soft x rays and UV at higher incidence angles. PACs: 61.10.Dp, 61.10.Kw, 03.50.De
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"abstract": "The emission of electromagnetic waves from a source within or near a\nnon-trivial medium (with or without boundaries, crystalline or amorphous, with\ninhomogeneities, absorption and so on) is sometimes studied using the\nreciprocity principle. This is a variation of the method of Green\u0027s functions.\nIf one is only interested in the asymptotic radiation fields the generality of\nthese methods may actually be a shortcoming: obtaining expressions valid for\nthe uninteresting near fields is not just a wasted effort but may be\nprohibitively difficult. In this work we obtain a modified form the reciprocity\nprinciple which gives the asymptotic radiation field directly. The method may\nbe used to obtain the radiation from a prescribed source, and also to study\nscattering problems. To illustrate the power of the method we study a few\npedagogical examples and then, as a more challenging application we tackle two\nrelated problems. We calculate the specular reflection of x rays by a rough\nsurface and by a smoothly graded surface taking polarization effects into\naccount. In conventional treatments of reflection x rays are treated as scalar\nwaves, polarization effects are neglected. This is a good approximation at\ngrazing incidence but becomes increasingly questionable for soft x rays and UV\nat higher incidence angles.\n PACs: 61.10.Dp, 61.10.Kw, 03.50.De",
"arxiv_id": "physics/0001005",
"authors": [
"Ariel Caticha"
],
"categories": [
"physics.class-ph",
"cond-mat.mtrl-sci",
"physics.ed-ph",
"physics.gen-ph",
"physics.optics"
],
"doi": "10.1103/PhysRevB.62.3639",
"journal_ref": "Physical Review B62, 3639 (2000)",
"title": "An asymptotic form of the reciprocity theorem with applications in x-ray scattering",
"url": "https://arxiv.org/abs/physics/0001005"
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