Vectorial beam shaping

Abstract

An algorithm is reported for the design of a phase-only diffractive optical element (DOE) that reshapes a beam focused using a high numerical aperture (NA) lens. The vector diffraction integrals are used to relate the field distributions in the DOE plane and focal plane. The integrals are evaluated using the chirp-z transform and computed iteratively within the Method of Generalized Projections (MGP) to identify a solution that simultaneously satisfies the beam shaping and DOE constraints. The algorithm is applied to design a DOE that transforms a circularly apodized flat-top beam of wavelength lambda to a square irradiance pattern when focused using a 1.4-NA objective. A DOE profile is identified that generates a 50 lambda x 50 lambda square irradiance pattern having 7% uniformity error and 74.5% diffraction efficiency (fraction of focused power). The diffraction efficiency and uniformity decrease as the size of the focused profile is reduced toward the diffraction limited spot size. These observations can be understood as a manifestation of the uncertainty principle.

Angular spectrum-based wave-propagation method with compact space bandwidth for large propagation distances

“…These methods are fundamental for 3D imaging in holography [1], diffraction tomography [2], the design of optical elements [3], and in other applications [4]. Rigorous nonparaxial wavefield propagation methods are based on the Rayleigh-Sommerfeld (RS) or the angular spectrum (AS) integrals [5], which are efficiently solved using fast Fourier transform (FFT).…”

A novel method for the design of diffractive optical elements based on the Rayleigh–Sommerfeld integral

“…In addition, scalar diffraction theory is used in the proposed method; this method is straightforward to use compared to the rigorous vector diffraction theory [21]. Generally, scalar diffraction theory is valid only when the sampling interval of the DOE is larger than the wavelength of the incident light [22].…”

The Optics of Spatial Coherence Wavelets

“…The improvement of both the setup and the algorithms for calculating the transmissions for the SLM, in order to optimize the SNR and the shape quality, is currently an active field of investigation.. Two main categories of works can be identified in a simplified way: the improvement of the IFTA algorithm (see Fienup, 1982;Liu and Taghizadeh, 2002;Wyrowski, 1990), and the development of alternative techniques for the design of diffractive optical elements (see Jabbour and Kuebler, 2008;Zhao et al, 2004).…”