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

Abstract

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. We also show that, at any twist strength in all correlation levels, the images can be evaluated by using the stationary-phase method. The three-dimensional stationary-phase formula of axicon images is derived. Such formula may be used in fast image evaluation, for designing diffractive axicons that perform a uniform axial intensity in a twisted partially coherent field.

Coherence Properties and Intensity Distribution of a Partially Coherent Lorentz–Gauss Beam Emerging from the Axicon

“…is oscillation could be eliminated by reducing the sharpness of the edges by using an amplitude transmission function (apodization) t(ρ ′ ), that is, unity over most of the annularaperture but falls off smoothly to zero near the edges. One favored amplitude transmission function that is used is the super-Gaussian [22]:…”

Partially Coherent Flat-Topped Beam Generated by an Axicon

“…In Equation ( 9), the phase factor exp[jk f (ρ 1 , ρ 2 )] oscillates around zero intensively within the range of the optical frequencies. Applying the stationary phase method in [12,13,38], the integration result of Equation ( 9) can be acquired:…”

“…For a spatially partially coherent light, Friberg et al proposed a method of designing annular-aperture axicons or apodized annular logarithmic axicons to generate a uniform intensity axial line image [10,11]. Shukri et al designed diffractive axicons to produce uniform line images in a twisted Gaussian Schell-model (TGSM) illumination [12,13]. Pu et al generated adjustable partially coherent bottle beams by focusing partially coherent light with an axicon-lens system [14,15].…”