Generation of singular optical beams from fundamental Gaussian beam using Sagnac interferometer

Abstract

We propose a simple free-space optics recipe for the controlled generation of optical vortex beams with a vortex dipole or a single charge vortex, using an inherently stable Sagnac interferometer. We investigate the role played by the amplitude and phase differences in generating higher-order Gaussian beams from the fundamental Gaussian mode. Our simulation results reveal how important the control of both the amplitude and the phase difference between superposing beams is to achieving optical vortex beams. The creation of a vortex dipole from null interference is unveiled through the introduction of a lateral shear and a radial phase difference between two out-of-phase Gaussian beams. A stable and high quality optical vortex beam, equivalent to the first-order Laguerre–Gaussian beam, is synthesized by coupling lateral shear with linear phase difference, introduced orthogonal to the shear between two out-of-phase Gaussian beams.

Ultrashort vortex from a Gaussian pulse – An achromatic-interferometric approach

“…The evenness in introducing linear phase and lateral shear between the interfering beams ensured that the hinge-point is located at x , y = 0 to generate a high-quality single-charge vortex with excellent propagation stability. The novelty of the work presented is the first of its kind use of the century-old Sagnac interferometer without any modifications or introduction of optical elements such as lenses or prisms inside the interferometer, to generate an achromatic vortex from null-interference of Gaussian beams and is therefore not compromised by the demonstrations in earlier works 25 , 27 . In the proposed scheme of vortex generation using the typical Sagnac interferometer, any dispersion leading to stretching of the pulse, experienced equally by both the counter-propagating beams, does not affect the spatial profile of the generated vortex, as exemplified by the cw studies.…”

“…In years that followed Nye and Berry’s seminal work 10 , 11 , the generation of optical vortex beams, with embedded phase singularity is demonstrated via exciting vortex modes in laser cavity 12 and their generation outside the laser cavity using astigmatic mode converters 13 – 15 , spiral phase plate 16 , computer generated holograms and diffractive optical elements displayed on spatial light modulators 17 , 18 , helical mirrors 19 and more recently using optical fibers 20 , birefringent z-cut uniaxial crystals 21 , q-plates 22 and two-beam interference where the contributions come from both amplitude and phase difference between the superposing optical fields 23 – 27 have demonstrated the sheer diversity of techniques capable of introducing the phase singularity in optical beams. The knowledge that the light beams having phase singularities carries and imparts orbital angular momentum (OAM) 28 – 30 lead to their widespread applications in optical trapping, manipulation of atoms and micro particles, laser ablation and surface structuring 31 – 33 .…”

Phase Singularities to Polarization Singularities

“…Other than wedge plates, local tilts introduced in parts of the wavefront [19,20] can be used for the generation of array of vortices of same charge. Sagnac interferometer can be used for vortex generation [306]. In the array form also, these vortices were generated [307].…”

Observation of Polarization Singularities in a Brewster-Reflected Paraxial Beam

“…Even if standard methods [1,17,19,[45][46][47][48][49][50][51][52][53][54] utilize special optical elements and setups to generate well-refined optical singularities, the singularity-generation itself is a remarkably fundamental phenomenon. We have demonstrated the formation of generic optical singularities due to Brewster-reflection of a post-paraxial beam-field.…”

“…(topological indices respectively +1/2, −1/2, −1/2, +1, +1, −1) [1,6,7,[9][10][11][12][13][14][15][16][17][18][19]. Standard methods of generating vortex beams with embedded polarization singularities [1,17,[45][46][47][48][49][50][51][52][53][54] thus involve, in some form or the other, the inherent inhomogeneous polarization of the considered beam-field [55][56][57][58][59][60][61].…”