Abstract We report creation by photolithography techniques of the phase rotor filter, an optical element whose complex transmittance depends in a linear fashion on azimuth angle. Relationships are given that describe scalar diffraction coherent light filter. The results numerical simulation and experiments discussed.

We deduce and study an analytical expression for Fresnel diffraction of a plane wave by spiral phase plate (SPP) that imparts arbitrary-order singularity on the light field. Estimates optical vortex radius depends singularity’s integer order n (also termed topological charge, or dislocation) have been derived. The near-zero intensity is shown to be proportional ρ2n, where ρ radial coordinate. Also, Gaussian beam SPP with nth-order analyzed. far-field distribution maximal depend number....

We obtain analytical expressions for the complex amplitudes of optical vortices deformed by astigmatic transforms, i.e., passed either through a cylindrical lens or an inclined spherical lens. also similar describing propagation vortex generated when Gaussian beam illuminates spiral phase plate (SPP) elliptic SPP (not inclined). All these with topological charge (TC) n are described n-th order Hermite polynomial argument. It is shown that argument real only on straight line in transverse...

We propose a new, three-parameter family of diffraction-free asymmetric elegant Bessel modes (aB-modes) with an integer and fractional orbital angular momentum (OAM). The aB-modes are described by the nth-order function first kind complex argument. asymmetry degree nonparaxial aB-mode is shown to depend on real parameter c≥0: when c=0, identical conventional radially symmetric mode; increasing c, starts acquire crescent form, getting stretched along vertical axis shifted horizontal for c≫1....

Using the Richards-Wolf formulas for an arbitrary circularly polarized optical vortex with integer topological charge m, we obtain explicit expressions all components of electric and magnetic field strength vectors near focus, as well intensity (energy density) energy flux (components Poynting vector) in focal plane aplanatic system. For m=2, from obtained it follows that axis propagates reversed direction, rotating along a spiral around axis. On itself, is maximal decays rapidly distance...

Based on the Richards-Wolf formalism, we obtain for first time a set of explicit analytical expressions that completely describe light field with double higher-order singularity (phase and polarization), as well distributions its intensity energy flux near focus. A is an optical vortex topological charge m nth-order cylindrical polarization (azimuthal or radial). From theory developed, rather general predictions follow. 1) For any orders n, distribution focus has symmetry order 2(n - 1),...

We theoretically show that optical vortices conserve the integer topological charge (TC) when passing through an arbitrary aperture or shifted from axis of axisymmetric carrier beam. If beam contains a finite number off-axis with same-sign different TC, resulting TC is shown to equal sum all constituent TCs. composed on-axis superposition Laguerre-Gauss modes ( n , 0), equals mode highest TC. positive and negative TCs are in magnitude, “winning” one larger absolute value weight coefficient....

We investigate the spin angular momentum (SAM) of double-index cylindrical vector beams in tight focus. Such a set is generalization conventional since polarization order different for transverse field components. Based on Richards-Wolf theory, we obtain an expression SAM distribution and show that if orders are parity, then Hall effect occurs focus, which there alternating areas with positive negative momentum, despite linear initial field. also analyze orbital spectrum all components...

A new family of paraxial laser beams that form an orthogonal basis is discussed. When propagated in uniform space, these preserve their structure to scale. The intensity distribution profile for such similar the Bessel modes, representing a set alternating bright and dark concentric rings. complex amplitude proportional degenerate (confluent) hypergeometric function, therefore we term (HyG) modes. HyG modes are generated with liquid-crystal microdisplay.

We study elliptical vortex Hermite-Gaussian (vHG) beams, which are described by the complex amplitude proportional to nth-order Hermite polynomial whose argument is a function of real parameter a. At |a|<1, on vertical axis beam cross section, there n isolated optical nulls that produce vortices with topological charge +1(a<0) or -1(a>0). |a|>1, similar vHG beams found horizontal axis. a=0, becomes identical HG mode order (0,n). derive orbital angular momentum (OAM) depends and an...

We propose a three-parameter family of asymmetric Bessel-Gauss (aBG) beams with integer and fractional orbital angular momentum (OAM). The aBG are described by the product Gaussian function nth-order Bessel first kind complex argument, having finite energy. beam's asymmetry degree depends on real parameter c≥0: at c=0, beam is coincident conventional radially symmetric (BG) beam; increasing c, acquires semicrescent shape, then becoming elongated along y axis shifting x for c≫1. In initial...

We introduce a family of asymmetric Laguerre-Gaussian (aLG) laser beams. The beams have been derived via complex-valued shift conventional LG in the Cartesian plane. While propagating uniform medium, first bright ring aLG beam becomes less and energy is redistributed toward peripheral diffraction rings. projection orbital angular momentum (OAM) onto optical axis calculated. OAM shown to grow quadratically with increasing asymmetry parameter beam, which equals ratio waist radius. Conditions...

We show that if a nonzero $E$-field intensity is found in the focus of circularly polarized optical vortex with phase singularity or higher-order azimuthally beam polarization singularity, an energy backflow will occur at center focal plane. Using Richards-Wolf formulas, which describe electromagnetic field near tight aplanatic system containing ideal spherical lens, we prove negative on-axis propagation light occurs when focusing (i) left-hand topological charge $m=2$ (ii) conventional...

We obtain a new solution of the paraxial Helmholtz equation that describes family three-dimensional and two-dimensional form-invariant half-Pearcey beams (HP-beams). HP-beams generalize Pearcey obtained in Ring et al (2012) Opt. Express 20 18955, since these can be considered as sum two first-order HP-beams. Three-dimensional have angular spectra plane waves, which are non-zero at half parabola. For functions HP-beam complex amplitudes, orthogonality properties been revealed. Using spatial...

We considered a generalization of the Laguerre-Gaussian (LG) laser beam family by using complex shift amplitude in Cartesian coordinates. In this case, LG-beams lose their axial symmetry. The normalized orbital angular momentum is sum topological charge and term which square dependence on asymmetry parameter. By optical trapping moving polystyrene microspheres focus asymmetric LG-beam, it proven that velocity increases with increasing parameter constant charge.

We derived exact analytical relationships to describe the complex amplitude of a perfect optical vortex generated by means three different elements, namely, (i) an amplitude-phase element with transmission function proportional Bessel function, (ii) optimal phase equal sign and (iii) spiral axicon. The doughnut intensity was shown be highest when using element. spiral-axicon-aided diffraction ring found twice as wide two other elements. Thus, filter best suited for generating vortex....

The tight focusing of an optical vortex with integer topological charge (TC) and linear polarization was considered. We showed that the longitudinal components spin angular momentum (SAM) (it equal to zero) orbital (OAM) product beam power TC) vectors averaged over cross-section were separately preserved during propagation. This conservation led Hall effects. effect expressed in fact areas different signs SAM component separated from each other. marked by separation regions rotation...

We derive analytical expressions containing a hypergeometric function to describe the Fresnel and Fraunhofer diffraction of plane wave circular ringlike cross section by spiral phase plate (SPP) an arbitrary integer order. Experimental patterns generated SPP fabricated in resist through direct e-beam writing are good agreement with theoretical intensity distribution.

An analytical expression for the diffraction of an elliptic Laguerre-Gaussian (LG) beam is derived and analyzed. We show that a with even singularity order has nonzero axial intensity any degree ellipticity at finite distance z from initial plane, whereas = 0 infinity zero. small singularity, two isolated zeroes appear in Fresnel zone on straight line angle 45 deg or -45 deg, depending whether beam's spin right left. The theoretical conclusions are confirmed by numerical simulation physical...

By decomposing a linearly polarized light field in terms of plane waves, the elliptic intensity distribution across focal spot is shown to be determined by E-vector's longitudinal component. Considering that Poynting vector's projection onto optical axis (power flux) independent component, power flux cross section has circular form. Using near-field scanning microscope (NSOM) with small-aperture metal tip, we show glass zone plate (ZP) having length one wavelength focuses Gaussian beam into...

A relationship for the complex amplitude of generalized paraxial Hermite-Gaussian (HG) beams is deduced. We show that under certain parameters, these transform into familiar HG modes and elegant beams. The orbital angular momentum (OAM) a linear combination two with phase shift π/2, their double indices composed adjacent integer numbers taken in direct inverse order, calculated. modulus OAM shown to be an number modes, always equal unity superposition beams, fractional hybrid Interestingly,...

We theoretically study a Gaussian optical beam with an embedded off-axis vortex. also experimentally generate such asymmetric vortex by using spiral phase plate. It is shown that depending on the shift distance laser has form of crescent, which rotated upon propagation. An analytical expression obtained for orbital angular momentum beam, appears to be fractional. When increases, greater number spirality plate or "fork" hologram, slower decreases. The experimental results are in qualitative...

We generalize the concept of perfect optical vortices, studying elliptic vortices (EPOVs), which also have diameters independent topological charge. A phase-only diffractive element is proposed for efficient generation such EPOV. The intensity EPOV generated by this higher than that approximately an elliptical axicon. obtain exact analytical expressions orbital angular momentum (OAM) density and total OAM These show normalized fractional it exceeds conventional circular vortex, equals It...

Using a FDTD-aided numerical simulation we show that sharp focal spot can be generated by spiral metalens made of amorphous silicon, with unit topological charge and aperture (NA = 1). The intensity is nearly round-shaped when using an incident TE-wave, in the form doughnut for TM-wave. We are first to theoretically experimentally pattern has local regions - located symmetrically or asymmetrically both at center on periphery where energy flux inversely directed. discovered effect used moving...

Using Richards–Wolf formulas, we show analytically that when strongly focusing a circularly polarized axisymmetric non-vortex field (e.g., Gaussian beam or zero-order Bessel–Gaussian beam), spiral energy flow is produced around the sub-wavelength focal spot. This phenomenon can be explained by conversion of spin angular momentum associated with circular polarization state into near-focus orbital momentum, on-axis being strictly zero. It also shown linearly optical vortex topological charge 2...