We propose and experimentally demonstrate a novel interferometric approach to generate arbitrary cylindrical vector beams on the higher order Poincare sphere. Our scheme is implemented by collinear superposition of two orthogonal circular polarizations with opposite topological charges. By modifying the amplitude and phase factors of the two beams, respectively, any desired vector beams on the higher order Poincare sphere with high tunability can be acquired. Our research provides a convenient way to evolve the polarization states in any path on the high order Poincare sphere.
We propose that the full Poincaré beam with any polarization geometries can be pictorially described by the hybrid-order Poincaré sphere whose eigenstates are defined as a fundamental-mode Gaussian beam and a Laguerre-Gauss beam. A robust and efficient Sagnac interferometer is established to generate any desired full Poincaré beam on the hybrid-order Poincaré sphere, via modulating the incident state of polarization. Our research may provide an alternative way for describing the full Poincaré beam and an effective method to manipulate the polarization of light.
In this work, we develop a hybrid-order Poincaré sphere to describe the evolution of polarization states of wave propagation in inhomogeneous anisotropic media. We extend the orbital Poincaré sphere and high-order Poincaré sphere to a more general form. Polarization evolution in inhomogeneous anisotropic media with special geometry can be conveniently described by state evolution along the longitude line on the hybrid-order Poincaré sphere. Similar to that in previously proposed Poincaré spheres, the Berry curvature can be regarded as an effective magnetic field with monopole centered at the o…
The Poincaré sphere is a graphical representation in a three-dimensional space for the polarization of light. Similarly, an optical element with spatially varying birefringence can be represented by a surface on a four-dimensional "Poincaré hypersphere". A projection of this surface onto the traditional Poincaré sphere provides an intuitive geometric description of the polarization transformation performed by the element, as well as the induced geometric phase. We apply this formalism to quantify the effects of birefringence on the image quality of an optical system.
We realize a robust and compact cylindrical vector beam generator which consists of a simple two-element interferometer composed of a beam displacer and a cube beamsplitter. The interferometer operates on the higher-order Poincare sphere transforming a homogeneously polarized vortex into a cylindrical vector (CV) beam. We experimentally demonstrate the transformation of a single vortex beam into all the well-known CV beams and show the operations on the higher-order Poincare sphere according to the control parameters. Our method offers an alternative to the Pancharatnam-Berry phase optical ele…
We present a generalized Poincaré sphere (G sphere) and generalized Stokes parameters (G parameters), as a geometric representation, which unifies the descriptors of a variety of vector fields. Unlike the standard Poincaré sphere, the radial dimension in the G sphere is not used to describe the partially polarized field. The G sphere is constructed by extending the basic Jones vector basis to the general vector basis with the continuously changeable ellipticity (spin angular momentum, SAM) and the higher dimensional orbital angular momentum (OAM). The north and south poles of different spheric…
Classical beams of light with non-uniform polarization patterns (e.g. radially and azimuthally polarized doughnut beams) may exhibit quantum-like features as, for instance, inseparability. We establish an exact correspondence between radially and azimuthally polarized classical modes of the electromagnetic field and the two-qubit quantum Bell states. We demonstrate the existence of a special representation for such classical modes by means of a pair of Poincaré spheres. Points on these spheres are described by Stokes parameters associated with such modes, and their explicit expressions are giv…
In recent time, the optical-analogous skyrmions, topological quasiparticles with sophisticated vectorial structures, have received an increasing amount of interest. Here we propose theortically and experimentally a generalized family of these, the tunable optical skyrmion, unveiling a new mechanism to transform between various skyrmionic topologies, including Néel-, Bloch-, and antiskyrmion types, via simple parametric tuning. In addition, Poincaré-like geometric representation is proposed to visualize the topological evolution of tunable skyrmions, which we termed Skyrme-Poincaré sphere, akin…
We present a simple and convenient method to yield cylindrical vector (CV) beams and realize its polarization evolution on higher-order Poincare sphere based on inhomogeneous birefringent metasurface. By means of local polarization transformation of the metasurface, it is possible to convert a light beam with homogeneous elliptical polarization into a vector beam with any desired polarization distribution. The Stokes parameters of the output light are measured to verify our scheme, which show well agreement with the theoretical prediction. Our method may provide a convenient way to generate CV…
The control of polarization, an essential property of light, is of wide scientific and technological interest. Polarizer is an indispensable optical element for direct polarization generations. Except common linear and circular polarizations, however, arbitrary polarization generation heavily resorts to bulky optical components by cascading linear polarizers and waveplates. Here, we present a general strategy for designing all-in-one full Poincaré sphere polarizers based on perfect arbitrary polarization conversion dichroism, and realize it in a monolayer all-dielectric metasurface. It allows …
In polarization optics unitary and non-unitary operations can be carried out by the Jones matrix. $\mathbf{Z}$ matrix is the $4\times 4$ analogue of the Jones matrix and the Mueller matrix of a nondepolarizing optical medium can be written as $\mathbf{M}=\mathbf{Z}\mathbf{Z}^*$. Jones matrix acts on the two component complex Jones vector, while the $\mathbf{Z}$ matrix acts on the four component real Stokes vector. Polarizer and retarder $\mathbf{Z}$ matrices can be written in compact forms in terms of the components of the position vector on the Poincaré sphere. In this note it is shown that t…
Phase conjugation with stimulated Brillouin scattering can be used to correct wavefront aberrations in high-power laser systems. Here, we consider such process with cylindrical vector lasers beams. By using a vectorial approach and a modal decomposition, we obtain a differential matrix equation that enables the calculation of the structure of Stokes vector eigenmodes and their Brillouin gain. The emphasis is put on the mode with the largest gain, which contributes the most to the Stokes beam. We show that the phase conjugation of orbital angular momentum in cylindrical vector beams is prevente…
The angular momentum state of light can be described by positions on a higher-order Poincaré (HOP) sphere, where superpositions of spin and orbital angular momentum states give rise to laser beams that have found many applications, including optical communication, quantum information processing, microscopy, optical trapping and tweezing and materials processing. Many techniques exist to create such beams but none to date allow their creation at the source. Here we report on a new class of laser that is able to generate all states on the HOP sphere. We exploit geometric phase control with a non…
The connection between Poincaré spheres for polariz-ation and Gaussian beams is explored, focusing on the interpretation of elliptic polarization in terms of the isotropic 2-dimensional harmonic oscillator in Hamiltonian mechanics, its canonical quantization and semiclassical interpretation. This leads to the interpretation of structured Gaussian modes, the Hermite-Gaussian, Laguerre-Gaussian and Generalized Hermite-Laguerre Gaussian modes as eigenfunctions of operators corresponding to the classical constants of motion of the 2-dimensional oscillator, which acquire an extra significance as fa…
A general family of structured Gaussian beams naturally emerges from a consideration of families of rays. These ray families, with the property that their transverse profile is invariant upon propagation (except for cycling of the rays and a global rescaling), have two parameters, the first giving a position on an ellipse naturally represented by a point on the Poincaré sphere (familiar from polarization optics), and the other determining the position of a curve traced out on this Poincaré sphere. This construction naturally accounts for the familiar families of Gaussian beams, including Hermi…
We present an investigation of magneto-optic rotation in both the Faraday and Voigt geometries. We show that more physical insight can be gained in a comparison of the Faraday and Voigt effects by visualising optical rotation trajectories on the Poincare sphere. This insight is applied to design and experimentally demonstrate an improved ultra-narrow optical bandpass filter based on combining optical rotation from two cascaded cells - one in the Faraday geometry and one in the Voigt geometry. Our optical filter has an equivalent noise bandwidth of 0.56 GHz, and a figure-of-merit value of 1.22(…
We propose theoretically and demonstrate experimentally a generation of light pulses whose polarization varies temporally to cover selected areas of the Poincaré sphere with tunable swirling speed and total duration (1 ps and 10 ps respectively in our implementation). The effect relies on the Rabi oscillations of two polarized fields in the strong coupling regime, excited by two counter-polarized and delayed pulses. The interferences of the oscillating fields result in the precession of the Stokes vector of the emitted light while polariton lifetime imbalance results in its drift from a circle…
A Highly flexible and efficient method of generating stable radially and Azimuthally polarized perfect optical vortex beams and all higher-order cylindrical vector vortex beams are proposed and demonstrated. The method is the most convenient implementation of the superposition of two orthogonally circularly polarized optical vortex beams of arbitrary integer topological charges. By simply controlling the relative amplitude and phase between vertical and horizontal polarization component of an input perfect vortex beam on a phase-sensitive Spatial Light Modulator (SLM) and using a common-path i…
We investigate interesting symmetry properties verified by the down-converted beams produced in optical parametric amplification with structured light. We show that the Poincaré sphere symmetry, previously demonstrated for first-order spatial modes, translates to a multiple Poincaré sphere structure for higher orders. Each one of these multiple spheres is associated with a two-dimensional subspace defined by a different value of the orbital angular momentum. Therefore, the symmetry verified by first order modes is reproduced independently in each subspace. This effect can be useful for paralle…
Optical vortex beam of fractional order is generated by the diffraction of a Gaussian beam using computer generated hologram embedded with mixed screw-edge dislocation. Unfolding of the generated fractional vortex beam into eigen-polarization components inside a birefringent crystal results in the conversion of scalar phase singularity to vector polarization singularities in the beam cross-section. The evolution of the singularities of the ellipse field namely C-points (points of undefined major axis) and L-lines (lines of undefined handedness) across the beam quantifies the transformation. Th…
A geometric view of the polarimetric properties of a nondepolarizing medium is presented by means of a pair of vectors in the Poincaré sphere. An alternative representation constituted by a set of vectors contained in the equatorial plane of the Poincaré sphere is also defined and interpreted. The analyses of the magnitudes and relative orientations of the constitutive vectors of such simple representations allow for a classification of nondepolarizing media.
Cylindrical vector beams (CVBs), which possesses polarization distribution of rotational symmetry on the transverse plane, can be developed in many optical technologies. Conventional methods to generate CVBs contain redundant interferometers or need to switch among diverse elements, thus being inconvenient in applications containing multiple CVBs. Here we provide a passive polarization-selective device to substitute interferometers and simplify generation setup. It is accomplished by reversing topological charges of orbital angular momentum based on polarization-selective Gouy phase. In the pr…
An optics-free method is proposed to generate X-ray radiation with spatially variant states of polarization via an afterburner extension to a Free Electron Laser (FEL). Control of the polarization in the transverse plane is obtained through the overlap of different coherent transverse light distributions radiated from a bunched electron beam in two consecutive orthogonally polarised undulators. Different transverse profiles are obtained by emitting at a higher harmonic in one or both of the undulators. This method enables the generation of beams structured in their intensity, phase, and polari…
Non-separable superpositions of polarization and spatial modes in Gaussian beams have shown rich patterns of spatially-variable polarization encoded in the transverse mode of the light, with the potential for many applications. In this work we investigate encoding similar types of superpositions in Bessel beams. We find that analogously to what is observed in Poincaré-Gaussian beams, Poincaré-Bessel beams can be produced by Bessel-mode superpositions. They show polarization patterns with disclinations in the orientation of the polarization ellipse and mappings of the Poincaré sphere onto the t…
Structured-Gaussian beams are shown to be fully and uniquely represented by a collection of points (or constellation) on the surface of the modal Majorana sphere, providing a complete generalization of the modal Poincaré sphere to higher-order modes. The symmetries of this Majorana constellation translate into invariances to astigmatic transformations, giving way to continuous or quantized geometric phases. The experimental amenability of this system is shown by verifying the existence of both these symmetries and geometric phases.
The dynamics of modes and their states of polarizations in multimode fibers as a function of time, space, and wavelength are experimentally and theoretically investigated. The results reveal that the states of polarizations are displaced in Poincare sphere representation when varying the angular orientations of the polarization at the incident light. Such displacements, which complicates the interpretation of the results, are overcome by resorting to modified Poincare spheres representation. With such modification it should be possible to predict the output modes and their state of polarizatio…
The fundamental equation that describes polarization mode dispersion does not have a mathematically correct and convincing proof. This problem stems from the fact that Poincare's sphere, where Stokes vectors are represented, is just a manifold (a representation space) devoid of metric. In this "space" orthogonal vectors are antiparallel and, therefore, it is hard to justify the use of a Euclidean metric. However, if one realizes that in Poincare's sphere only three-dimensional rotations are represented, a Euclidean pseudo-scalar product can be defined and a mathematically correct proof for the…
