6533b873fe1ef96bd12d5779
RESEARCH PRODUCT
Debye representation of dispersive focused waves
Carlos J. Zapata-rodríguezsubject
PhysicsDiffractionbusiness.industryParaxial approximationComplex systemRotational symmetryAstrophysics::Instrumentation and Methods for AstrophysicsFOS: Physical sciencesPhysics::OpticsAtomic and Molecular Physics and OpticsElectronic Optical and Magnetic MaterialsKirchhoff's diffraction formulasymbols.namesakeOpticssymbolsFresnel numberComputer Vision and Pattern RecognitionbusinessDiffraction gratingDebyeOptics (physics.optics)Physics - Opticsdescription
We report on a matrix-based diffraction integral that evaluates the focal field of any diffraction-limited axisymmetric complex system. This diffraction formula is a generalization of the Debye integral applied to apertured focused beams, which may be accommodated to broadband problems. Longitudinal chromatic aberration may limit the convenience of the Debye formulation and, additionally, spatial boundaries of validity around the focal point are provided. Fresnel number is reformulated in order to guarantee that the focal region is entirely into the region of validity of the Debye approximation when the Fresnel number of the focusing geometry largely exceeds unity. We have applied the matrix-based Debye integral to several examples. Concretely, we present an optical system for beam focusing with strong angular dispersion and free of longitudinal chromatic aberration. This simple formalism leaves an open door for analysis and design of focused beams with arbitrary angular dispersion. Our results are valid for ultrashort pulsed and polychromatic incoherent sources.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2006-09-04 |