Depth of focus and intensity distribution of a lensacon illuminated by a partially coherent Gaussian Schell vortex beam.

Using the extended Huygens-Fresnel principle, a cross-spectral density formula was developed for a Gaussian Schell model vortex (PCGSMV) beam diffracted through a lensacon (lens with an axicon). The intensity and depth of focus (DOF) shaped by the lensacon were calculated. Our numerical results show the relationship between the intensity distribution and depth of focus with the beam waist width as well as the spatial correlation of the coherence length.

Angular width and beam quality of a partially coherent standard Laguerre-Gaussian vortex beam in turbulent plasma.

Analytical formulas for the angular width and propagation factor of a partially coherent standard Laguerre-Gaussian (sLG) vortex beam through anisotropic turbulent plasma were derived based on the extended Huygens-Fresnel integral and the second-order moments of the Wigner distribution function. The evolution properties of the angular width and propagation factor of partially coherent sLG vortex beams propagating in anisotropic turbulent plasma were investigated numerically. The numerical results demonstrate the influence of the source and turbulence parameters on the normalized angular width and normalized propagation factor of the partially coherent sLG vortex beams.

Apodized design of diffractive axicons for twisted partially coherent light.

Within the framework of inverse diffractive optics, we present a design for diffractive axicons in twisted, spatially partially coherent fields, in particular twisted Gaussian Schell-model (TGSM) fields. The design is based on the method of stationary phase. A general modification is introduced to the inverse diffractive optics approach for improving the synthesized optical element to produce the desired intensity distribution.

Spatial correlation properties of twisted partially coherent light focused by diffractive axicons.

We investigate the spatial coherence properties of a twisted, partially coherent field in the focal region of diffractive axicons. We demonstrate that the focused field is a combination of an infinite number of weighted, mutually uncorrelated, helical components, whose weights depend on both the coherence width and the twist strength, and the total helicity of the field inverts its handedness depending on the twist handedness and vanishes at the nontwist limit. Depending on the variances of whichever the effective coherence width, the twist strength, the twist handedness of the illumination, or the shape of the axicon phase function, substantive changes will intervene on the distribution of the spatial coherence degree of the focused field.

Influences of twist phenomenon of partially coherent field with uniform-intensity diffractive axicons.

The effects of twist phenomenon (beam rotation) of a partially coherent field are studied on the operation of two classes of uniform-intensity diffractive axicons. A general theory of axicon image formation is developed, discussed, and examined. We show that the intensity of the diffracted field is a multiple Bessel field, and only the energy of the zero-order Bessel field diffracts along the propagation axes.