The analytical solution is derived, within the Rayleigh–Sommerfeld formulation of diffraction, for the on-axis spectral irradiance of a broadband source after diffracting through a circular symmetric hard aperture. By using this solution, and within the paraxial approximation, we investigate several diffraction-induced effects originated by binary diffractive optical elements made up of a set of annular apertures with equal areas and periodic in the squared radial coordinate. In particular, the ability to focus femtosecond pulses is investigated. In addition, the analysis of the spectral modifier function associated with these elements allows us to simulate spectral shifts at focus positions. Finally, we introduce a relatively simple and low-cost technique to slice the spectrum of a broadband source in order to generate narrow bands or wavelength channels.
© 2007 Optical Society of America
Diffraction and Gratings
Original Manuscript: July 25, 2007
Manuscript Accepted: September 21, 2007
Published: October 25, 2007
Omel Mendoza-Yero, Gladys Mínguez-Vega, Jesús Lancis, and Vicent Climent, "Focusing and spectral characteristics of periodic diffractive optical elements with circular symmetry under femtosecond pulsed illumination," J. Opt. Soc. Am. A 24, 3600-3605 (2007)