dorsal/arxiv
View SchemaAxially symmetric focusing as a cuspoid diffraction catastrophe: Scalar and vector cases and comparison with the theory of Mie
| Authors | Johannes Kofler, Nikita Arnold |
|---|---|
| Categories | |
| ArXiv ID | physics/0606025 |
| URL | https://arxiv.org/abs/physics/0606025 |
| DOI | 10.1103/PhysRevB.73.235401 |
| Journal | Phys. Rev. B 73, 235401 (2006) |
Abstract
An analytical description of arbitrary strongly aberrated axially symmetric focusing is developed. This is done by matching the solution of geometrical optics with a wave pattern which is universal for the underlying ray structure. The corresponding canonical integral is the Bessoid integral, which is a three dimensional generalization of the Pearcey integral that approximates the field near an arbitrary two-dimensional cusp. We first develop the description for scalar fields and then generalize it to the vector case. As a practical example the formalism is applied to the focusing of light by transparent dielectric spheres with a few wavelengths in diameter. The results demonstrate good agreement with the Mie theory down to Mie parameters of about 30. Compact analytical expressions are derived for the intensity on the axis and the position of the diffraction focus both for the general case and for the focusing by microspheres. The high intensity region is narrower than for an ideal lens of the same aperture at the expense of longitudinal localization and has a polarization dependent fine structure, which can be explained quantitatively. The results are relevant for aerosol and colloid science where natural light focusing occurs and can be used in laser micro- and nano-processing of materials.
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"abstract": "An analytical description of arbitrary strongly aberrated axially symmetric\nfocusing is developed. This is done by matching the solution of geometrical\noptics with a wave pattern which is universal for the underlying ray structure.\nThe corresponding canonical integral is the Bessoid integral, which is a three\ndimensional generalization of the Pearcey integral that approximates the field\nnear an arbitrary two-dimensional cusp. We first develop the description for\nscalar fields and then generalize it to the vector case. As a practical example\nthe formalism is applied to the focusing of light by transparent dielectric\nspheres with a few wavelengths in diameter. The results demonstrate good\nagreement with the Mie theory down to Mie parameters of about 30. Compact\nanalytical expressions are derived for the intensity on the axis and the\nposition of the diffraction focus both for the general case and for the\nfocusing by microspheres. The high intensity region is narrower than for an\nideal lens of the same aperture at the expense of longitudinal localization and\nhas a polarization dependent fine structure, which can be explained\nquantitatively. The results are relevant for aerosol and colloid science where\nnatural light focusing occurs and can be used in laser micro- and\nnano-processing of materials.",
"arxiv_id": "physics/0606025",
"authors": [
"Johannes Kofler",
"Nikita Arnold"
],
"categories": [
"physics.optics"
],
"doi": "10.1103/PhysRevB.73.235401",
"journal_ref": "Phys. Rev. B 73, 235401 (2006)",
"title": "Axially symmetric focusing as a cuspoid diffraction catastrophe: Scalar and vector cases and comparison with the theory of Mie",
"url": "https://arxiv.org/abs/physics/0606025"
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