Apodized design of diffractive axicons for twisted partially coherent light

Abstract

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. Both the design and modification are demonstrated with annular-aperture axicons generating uniform-intensity axial line segments in partially coherent TGSM illumination.

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

“…The best method for solving Eq. ( 14) is the stationary phase (SP) approximation [17]. Using SP approximation, the stationary point ρ ′ Sp can be obtained as:…”

“…Since the third century, lenses have been the most widely used optical elements for improving vision and enlarging images. Axicon has gained widespread recognition in optics since the mid-1900s [16,17]. Recent investigations into the applications of axicon have yielded successful results in producing diverse focal shapes, such as double focal spots and flattened beams, within the focal region of a circular classical axicon.…”

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].…”

Intensity distribution of the partially coherent Gaussian Schell vortex beam diffracted by classical axicon

“…Axicons are versatile optical devices that produce focal lines instead of focal point generated by lenses [1]. Axicons have attracted increasing attention because of their diversity and utility in generating various significant beam shapes within the focal region [1][2][3][4]. The classical axicon, characterized by an on-axis intensity linearly increasing along the optical axis, has been employed for the creation of non-diffracting Bessel beams [5], as well as for producing diverse focal shapes, such as hollow laser beams [6], double focal spots [4], thin-sheet lights [7], tight focal spot sizes [2], flat-topped beams [8], and three-dimensional dark spots [9].…”