A modified interferometer that introduces position and momentum shifts in mutually orthogonal directions can transform optical modes by raising and lowering radial and azimuthal mode indices. The action of this interferometer can be generalized in the form of a pair of twisting operators, which can be further written in terms of the ladder operators of the 2-dimensional harmonic oscillator. For lower order input modes there is good agreement between theory and experiment, but as the input mode becomes more complex, experimental results start to deviates from first-order theory. This is due to the shifts becoming larger relative to beam structure. We discuss how higher order corrections can be calculated for such cases.
Orbital angular momentum (OAM), one of the most recently discovered degrees of freedom of light beam field has fundamentally revolutionized optical physics and its technological capabilities. Optical beams with OAM have enabled a large variety of applications, including super-resolution imaging, optical trapping, classical and quantum optical communication, and quantum computing, to mention a few. To enable these and several other emerging applications, optical beams with OAM have been generated using a variety of methods and technologies, such as a simple astigmatic lens pair, one-/two-dimensional holographic optical elements, three-dimensional spiral phase plates, optical fibers, and recent entrants such as metasurfaces. All these techniques achieve spatial light modulation and can be implemented with either passive elements or active devices, such as liquid crystal on silicon and digital micromirror devices. Many of these devices and technologies are not only used for the generation of amplitude phase-polarization structured light beams but are also capable of analyzing them. We have attempted to encompass a wide variety of such technologies as well as a few emerging methodologies, broadly categorized into generation and detection protocols. We address the needs of scientists and engineers who desire to generate/detect OAM modes and are looking for the technique (active or passive) best suited for their application.
That a paraxial light beam with spin angular momentum (SAM,σ ) propagating in a helical trajectory leads to the appearance of Rytov-Vladimirsky-Berry (RVB) phase has been a topic of extensive research for the past several decades. Recently, using geometrical optics approximation, it was shown that variations in the beam propagation direction leads to generic parallel transport law – a beam with intrinsic orbital angular momentum (IOAM, l ) behaves topologically similar to polarized beam containing only SAM but of magnitude proportional to the total angular momentum TAM = l ± σ . By considering the interaction of a beam with IOAM, propagating in a non-planar trajectory and hence with extrinsic orbital angular momentum (EOAM), in an inhomogeneous medium we study the parallel transport of fiber mode structure as a manifestation of orbit-orbit interaction. The resulting rotation of the transverse beam structure due to the parallel transport of the LP fiber mode propagating along non-planar ray direction is attributed to the ‘orbital’ Berry phase. The mode transformation is simulated based on the interference of the vector-vortex modes excited in the TMF. The LP mode rotation angle calculated as a function of the beam position at the fiber input is expected to show topological features that can be mapped onto orbital Poincaré sphere.
We revisit the quantum weak measurement (QWM) by sketching the polarisation state dynamics on the Poincaré sphere and the associated geometric phase, which is considered the soul of QWM. Our experimental arrangement comprises a coherent laser beam as a source of pure state, two polarizers corresponding to pre- and post-selection and a tilted wave plate placed in-between them to introduce weak interaction. The pre-selected state is a linearly polarised beam that can be represented as a point on the Poincaré sphere equator and the weak interaction with the wave plate results in a small spread in S3 axis. Now, an orthogonal projection of this state leads two different geodesics on the surface of the sphere through its poles, starting from both sides of the spread to the orthogonal point. The post-selection is made by moving the projection point slightly away from the orthogonal position so that both geodesics shift to the equator which results in a rapid accumulation of geometric phase in the beam crosssection. A gradient in the linear momentum is developed as a consequence which gives amplified shift in the beam position.
Topological structure of monstar in π-symmetric fields with index Ic = +1/2 and three radial lines ending at C-point is an intermediate structure having properties of lemon and star. We experimentally realized monstar pattern in polarization ellipse orientation via three different routes, from lemon pattern using topologically-invariant squeezing and / or rotation transformations. Our results suggest that lemon and monstar can smoothly transform into each other under any or combination of these transformations leading to one interpretation that monstar is an anisotropic lemon.
Spatially varying polarization modulation with polarization singularities are realized using a birefringent wedge pair (BWP), which is due to coherent superposition of orthogonally polarized beams. We studied the degree of polarization, visibility and the degree of local coherence as a function of spatial coherence using Stokes polarimetric technique in and around the identified polarization singular patterns in the beam cross-section. Through these we illustrate the unification of coherence and polarization.
Polarization structured optical beams have half-integer topological structures: star, lemon, monstar in π-symmetric polarization ellipse orientation tensor field and integer-index topological structures: saddle, spiral, node in 2π-symmetric Poynting vector field. Topological approach to study the polarization structured optical beams is carried out and presented here in some detail. These polarization structured light beams are demonstrated to be the best platform to explore the topological interdependencies. The dependence of one type of topological structure on the other is used to control the Poynting vector density distribution and locally enhance the angular momentum density as compared to its constituent beam fields.
Interference of fiber eigen vector modes of different phase and spatial variation of polarization gives rise to
different types of polarization singularities – isolated C-point surrounded by star / lemon type polarization
morphology patterns, a dipole or two C-points of same index – in 2D polarization fields. In this context, fiber
modal decomposition refers to identifying the constituent modes, their relative amplitude and the phase
relationship among them in the fiber output. The size and location of the L-contour and the location of Cpoints
determine the relative amplitude and the orientation of the polarization morphology pattern provides
information regarding the relative phase difference between the constituent vector modes. We use these
aspects of polarization singularity to demonstrate a novel fiber modal decomposition method.
We report here the characteristics of dark hollow beams (DHBs) generated using negative micro-axicons fabricated via
selective chemical etching process in the tip of optical fibers. The DHB output from the etched fibers were further
manipulated to generate single and multiple period optical bottle beams, 0th- and 1st- order Bessel beams and astigmatic
Bessel beams and beams with helical wavefront. Selective excitation of the guided modes in single and multimode
optical fibers with V-numbers ranging from 2.405 - 5.69 are etched to different negative cone dimensions and are used
to generate in a controllable way DHBs and related optical beams. Negative cones are etched in the fiber tips via
selective chemical etching process wherein the different etch rates of the fiber core and cladding dopants and dopant
concentration results in different cone angles and cone depths. Input laser beam guided through the optical fiber diffracts
and refracts at the tip generating beams with one or many bright rings surrounding the dark central spot. By positioning
the DHB in the front focal plane of a bi-convex lens we generate Bessel beams whose characteristics are compared with
that generated using positive cone etched in the fiber tip and bulk axicon. Under certain excitation conditions we also
observe helical wavefront DHBs with phase dislocation embedded in the beam.
We report here the demonstration of rotational Doppler Effect (RDE) and measurement of rotational frequency shifts
(RFS) in single-charge helical-phased cylindrical vector beams directly generated using a two-mode optical fiber. The
vector-vortex beam with a shifted vortex core, generated by propagating the Gaussian laser beam as an offset-skew ray
selectively excites both the fundamental and first low-order waveguide modes simultaneously in the two-mode optical
fiber. Rotation frequency of the output beam around a shifted axis of the beam is measured as a function the analyzer
rotation for changing handedness of the input circular polarization to demonstrate RDE in the directly excited cylindrical
vector-vortex beams. Even small variations in the input launch conditions were found to dramatically alter the stability
of the vortex beams and hence the demonstration of RDE.