Compact device for the generation of toroidal spatiotemporal optical vortices.

Due to the unique spatiotemporal coupling characteristics in phase, spatiotemporal optical vortices have attracted extensive attention. Toroidal vortices, as high-dimensional spatiotemporal optical vortices, have become a research hotspot in recent years due to their unique topological structures. In this paper, we propose an asymmetric grating structure for the generation of optical toroidal vortices in a compact way.

Rational number vortex beam multiplier and divider based on an Archimedean spiral mapping.

Orbital angular momentum (OAM), as an extra dimension of light, holds substantial potential in both classical and quantum optical communication systems. In such systems, the ability to arbitrarily convert the OAM of light is of great importance. In this work, we demonstrate an arbitrary rational number of multiplication and division of the OAM of light based on an Archimedean spiral mapping.

Generalized spiral transformation for high-resolution sorting of vortex modes.

We achieve high-resolution sorting of the orbital angular momentum (OAM) of light with two bespoke diffractive optical elements using the generalized spiral transformation. The experimental sorting finesse is 5.3, approximately two times better performance than what has been reported.

Non-spreading Bessel spatiotemporal optical vortices.

Non-spreading nature of Bessel spatiotemporal wavepackets is theoretically and experimentally investigated and orders of magnitude improvement in the spatiotemporal spreading has been demonstrated. The spatiotemporal confinement provided by the Bessel spatiotemporal wavepacket is further exploited to transport transverse orbital angular momentum through embedding spatiotemporal optical vortex into the Bessel spatiotemporal wavepacket, constructing a new type of wavepacket: Bessel spatiotemporal optical vortex. Both numerical and experimental results demonstrate that spatiotemporal vortex structure can be well maintained and confined through much longer propagation.

High-resolution optical orbital angular momentum sorter based on Archimedean spiral mapping.

We propose a generalized spiral transformation scheme that is versatile to incorporate various types of spirals such as the Archimedean spiral and the Fermat spiral. Taking advantage of the equidistant feature, we choose the Archimedean spiral mapping and demonstrate its application in high-resolution optical orbital angular momentum (OAM) mode sorting. Experimental results show 90% efficiency and cross-talk of -8.

Optical vortex fields with an arbitrary orbital angular momentum orientation.

Optical vortex fields with a tilted phase singularity line are associated with a tilted orbital angular momentum (OAM). In this Letter, we propose a method to generate optical vortex fields with arbitrary OAM orientation based on the time-reversal method, vectorial diffraction theory, and a 4Pi optical configuration. The ability to control the 3D OAM orientation may find applications in optical tweezing, light-matter interaction, and spin-orbital coupling.

Photonic orbital angular momentum with controllable orientation.

Vortices are whirling disturbances, commonly found in nature, ranging from tremendously small scales in Bose-Einstein condensations to cosmologically colossal scales in spiral galaxies. An optical vortex, generally associated with a spiral phase, can carry orbital angular momentum (OAM). The optical OAM can either be in the longitudinal direction if the spiral phase twists in the spatial domain or in the transverse direction if the phase rotates in the spatiotemporal domain.

Transversely oriented cylindrically polarized optical fields.

Cylindrical vector (CV) beams have nonuniform polarization vector distribution with a singularity line directed along the optical axis. In this paper, we propose a method to synthesize transversely oriented cylindrically polarized optical fields in the focal region with a singularity line perpendicular to the optical axis. The scheme is based on the time-reversal method, the vectorial diffraction theory, and the 4Pi optical configuration.

Generation of transversely oriented optical polarization Möbius strips.

We report a time-reversal method based on the Richards-Wolf vectorial diffraction theory to generate a prescribed polarization topology on a defined trajectory within areas of relatively high intensity. An example is given to generate transversely oriented optical Möbius strips that wander around an axis perpendicular to the beam propagation direction. A number of sets of dipole antennae are purposefully positioned on a defined trajectory in the y = 0 plane and the radiation fields are collected by one high-NA objective lens.

Subwavelength focusing of a spatio-temporal wave packet with transverse orbital angular momentum.

We report the method of producing a spatio-temporal (ST) wave packet carrying pure transverse orbital angular momentum (OAM) with subwavelength spatial sizes. Due to the lack of temporal focusing, an ST wave packet focused by a high numerical aperture (NA) objective lens experiences a "spatio-temporal astigmatism" effect similar to the focusing action of a cylindrical lens on the transverse profile of optical field. Thus an ST vortex with a spiral phase in the ST domain focused through a high NA objective will be distorted and lose the ST characteristic spiral phase pattern.

Generation of exotic optical polarization Möbius strips.

We report a method of generating exotic optical polarization Möbius strips through tightly focusing an arbitrary vector beam. A heart-shaped Möbius strip, an "8"-shaped twin Möbius strip, and a circular Möbius strip with varying polarization twisting rate are demonstrated. The ability of tailoring three-dimensional optical polarization topologies may spur novel studies of optics and physics and find their applications in sensing, light coupling to nanostructures, light-matter interaction, and metamaterial fabrication.

Laguerre-Gaussian mode expansion for arbitrary optical fields using a subspace projection method.

Laguerre-Gaussian (LG) mode decomposition has found applications in various optics fields. However, numerical LG mode expansion for arbitrary field is still a problem, since the physical dimension of LG modes would vary with three parameters-the beam waist width w, the radial index p, and the azimuthal index m, which make it difficult to determine the optimal value of w and the truncation order on p. Here a general method of LG mode expansion for an arbitrary field is developed.

Diffraction-limited near-spherical focal spot with controllable arbitrary polarization using single objective lens.

We report a time-reversal method based on the Richards-Wolf vectorial diffraction theory to generate a diffraction-limited near-spherical focal spot with arbitrary three-dimensional state of polarization using single objective lens. Three orthogonal dipole antennae are positioned above a flat mirror at a prescribed distance and an aplanatic objective lens is utilized to collect all the radiation fields emitted by the dipole antennae. The optical field in the pupil plane is calculated in a time-reversal manner and the vectorial Debye integral is used to verify the spatial intensity and polarization distributions in the focal region.

Vectorial optical fields: recent advances and future prospects.

Driven by their potential applications, vectorial optical fields with spatially inhomogeneous states of polarization within the cross section have drawn significant attention recently. This work intends to review some of the latest development of this rapidly growing field of optics and offer a general overview of the current status of this field in a few areas. Mathematical descriptions of generalized vectorial optical fields are provided along with several special examples.

High efficiency geometric-phase polarization fan-out grating on silicon.

We report the design, fabrication and characterization of a 1-by-5 geometric-phase polarization fan-out grating for coherent beam combining at 1550 nm. The phase profile of the grating is accurately controlled by the local orientation of the binary subwavelength structure instead of the etching depth and profile empowering the grating to be more tolerant to fabrication errors. Deep-UV interference lithography on silicon offers an inexpensive, highly efficient and high damage threshold solution to fabricating large-area fan-out gratings than electron beam lithography (EBL) and photoalignment liquid crystals.

Tightly focused optical field with controllable photonic spin orientation.

The spin angular momentum of photons offers a robust, scalable and high-bandwidth toolbox for many promising applications based upon spin-controlled manipulations of light. In this work, we develop a method to achieve controllable photonic spin orientation within a diffraction limited optical focal spot produced by a high numerical aperture objective lens. The required pupil field is found analytically through reversing the radiation patterns from two electric dipoles located at the focal point of the lens with orthogonal oscillation directions and quadrature phase.

Tailoring optical orbital angular momentum spectrum with spiral complex field modulation.

We report the generation of prescribed optical orbital angular momentum (OAM) spectrum with spiral complex field modulation. Both symmetric and asymmetric OAM spectrums are generated with a vector beam generator and measured with a hybrid conformal mapper. Three methods for OAM spectrum generation ranging from the pure spiral phase modulation, the spiral amplitude and phase modulation, to the spiral phase and polarization modulation are demonstrated.

Experimental generation of complex optical fields for diffraction limited optical focus with purely transverse spin angular momentum.

We demonstrate a method to generate complex optical fields at the pupil plane of a high numerical aperture (NA) objective lens for the creation of diffraction limited optical focus with purely transverse spin angular momentum. The complex optical fields are analytically deduced through reversing the radiated patterns from two electric dipoles, which are located at the focal point of the high NA lens and oscillate respectively in x- and z- directions with phase difference of π/2. The derived fields can be experimentally created with a vectorial optical field generator.

Precise transverse alignment of spatial light modulator sections for complex optical field generation.

Based on the properties of the dove prism and the Fourier optics approach, the coordinate relationships among four spatial light modulator (SLM) sections in a vectorial optical field generator are derived and experimentally verified. Taking the coordinate system of the first SLM section as a reference, the coordinate displacements between the first section and subsequent sections are determined via employing specially designed four-quadrant patterns, which enable the visualization of the degree of freedom controlled by each SLM section. A complex optical field could be accurately generated through combining the derived coordinate relationships and pre-compensation of the measured coordinate displacements.

Experimental Demonstration of a Highly Efficient Fan-out Polarization Grating.

Highly efficient fan-out elements are crucial in coherent beam combining architectures especially in coupled laser resonators where the beam passes through the fan-out element twice per round trip. Although the theoretical efficiency is usually less than 86%, the Dammann gratings are ubiquitously utilized in a variety of types of coherent beam combining systems due to the facile design and fabrication. In the current paper, we experimentally demonstrate a highly efficient fan-out polarization grating.

Laser beam splitting by polarization encoding.

A scheme is proposed to design a polarization grating that splits an incident linearly polarized beam to an array of linearly polarized beams of identical intensity distribution and various azimuth angles of linear polarization. The grating is equivalent to a wave plate with space-variant azimuth angle and space-variant phase retardation. The linear polarization states of all split beams make the grating suitable for coherent beam combining architectures based on Dammann gratings.

Beam shaping characteristics of an unstable-waveguide hybrid resonator.

The unstable-waveguide hybrid resonator emits a rectangular, simple astigmatic beam with a large number of high-spatial-frequency oscillations in the unstable direction. To equalize the beam quality, in this paper, a beam shaping system with a spatial filter for the hybrid resonator was investigated by numerical simulation and experimental method. The high-frequency components and fundamental mode of the output beam of the hybrid resonator in the unstable direction are separated by a focus lens.