Characteristics of Spiral Patterns Formed by Coaxial Interference between Two Vortex Beams with Different Radii of Wavefront Curvatures

Abstract

Spiral pattern is formed for coaxial interference between two vortex beams with different radii of wavefront curvatures and different topological charges (TCs). A theoretical model considering various parameters (such as phase difference, radius of wavefront curvature, and TCs) is established to predict all kinds of interference patterns. An improved Mach-Zehnder interferometer is set up in an experiment to generate different kinds of spiral patterns and verify the theoretical model. The number of spiral lobes is determined by the absolute value of TCs’ difference between two vortex beams, and the twist direction relates to the sign of TCs’ difference and the difference of reciprocals for the radii of wavefront curvature, clockwise for the same sign, and counterclockwise for the opposite signs. The twist direction of the spiral pattern reverses and the lobes direction near the core of the pattern changes obviously when the spherical wave changes from convergence to divergence.

Generation of Perfect Vortex Beams with Complete Control over the Ring Radius and Ring Width

“…The number of spiral lobes in the central zone is the TC value, and its rotation direction is clockwise for the negative sign of TC and vice versa. Unlike the spiral interferogram as observed in the interference of normal vortex beam with a Gaussian with a spherical wavefront[72,73], the spiral interferogram in Figure12(c1-c5) and Figure A1(c1-c4) is faint at the center of the interferogram due to the large dark core of the PVB. The fork wire interferograms shown in Figure 12(d1-d5) and Figure A1(d1-d4) have a fork wire fringe.…”

“…Finally, a CMOS camera (CinCam, CMOS-1202) is used to capture the beam patterns (intensity profiles) of the generated PVB in arm 1 and the interferograms generated by the MZI. The spiral interferograms are generated when two beams with different wavefront curvature radius interfere coaxially [73]. Here, the lens f 4 (focal length of 40 mm) is used to focus the reference Gaussian beam and generate sphere-wave reference light.…”

“…The fork number is equal to the TC value of the PVB, and the fork direction is determined by the sign of the TC [74]. The number of spiral lobes depend on the TC value of the PVB, and the twist direction depends on the ring of the TC [73]. From the above analysis, it can be seen that the value of the ring radius obtained in the experiment can be well fitted by ρ = f (n − 1)γ, while the ring half-width obtained in the experiment can be approximately fitted by ∆ = 2 f λ/πw g rather than ∆ = f λ/πw g .…”

“…The fork number is equal to the TC value of the PVB, and the fork direction is determined by the sign of the TC [74]. The number of spiral lobes depend on the TC value of the PVB, and the twist direction depends on the ring of the TC [73].…”

Generation of structured light beams by dual phase modulation with a single spatial light modulator

“…For verifying the phase distribution of LG beam, the interference between LG beam and a spherical beam tilted at an angle is performed. Off centred fork-shaped interference pattern is achieved when the spherical beam is tilted at a small angle having value less than one radian [43,44]. The mathematical expression of such a tilted spherical beam with a tilt angle of α can be expressed as [45],…”