High-efficiency integer multiplier for the orbital angular momentum of light.

The spiral transformation has attracted an increasing interest in switching orbital angular momentum (OAM) modes. However, the efficiency is deteriorated by the inevitable gap between the turns of the spiral strips. In order to overcome the problem, a multiple-ring conformal mapping scheme is proposed for efficient multiplication of the OAM of light. The OAM mode at the input plane is divided into concentric rings, which are mapped to multiple sectors and connected into a ring at the output plane. This point-to-point mapping mechanism can avoid the generation of high-order diffraction, leading to high conversion efficiency. The scheme may underpin the development of optical communication and quantum key distribution in OAM-based systems.

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. Both the simulation and experimental results have demonstrated the effectiveness of this scheme. This work provides a practical method to manipulate the OAM mode space of light that is directly applicable to high-dimensional optical communication systems.

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. These optical elements will be useful for optical communication based on OAM beams and can be easily extended to other fields that use conformal mapping.

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 order spatiotemporal optical vortices can also be better confined in the spatiotemporal domain and prevented from further breaking up, overcoming a potential major obstacle for future applications of spatiotemporal vortex.

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 -8.78 dB that is sufficient to separate adjacent OAM modes. This generalized transformation scheme may also find various applications in optical transformation and can be easily extended to other fields related to conformal mapping.

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. In this article, we demonstrate the intersection of spatiotemporal vortices and spatial vortices in a wave packet. As a result of this intersection, the wave packet hosts a tilted OAM that provides an additional degree of freedom to the applications that harness the OAM of photons.

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. Both transversely oriented radially polarized and azimuthally polarized optical fields are demonstrated. The superposition of transverse cylindrically polarized optical fields leads to a peculiar distribution carrying controllable transverse spin angular momentum (SAM) and transverse orbital angular momentum (OAM) that may find applications in optical tweezing, light-matter interaction, and unidirectional beam propagation excitation.

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. By sending the complex conjugate of the radiation fields in a time-reversed manner, the focal fields are calculated and the optical polarization topology on the trajectory can be tailored to form prescribed Möbius strips. The ability to control optical polarization topologies may find applications in nanofabrication, quantum communication, and light-matter interaction.

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. With the understanding of such an ST astigmatism, the ST wave packet can be pre-conditioned such that an ST vortex carrying OAM with subwavelength transverse sizes can be obtained after strong focusing. This is the first revelation that a tightly focused ST vortex beam with transverse OAM can be realized, paving the way for potential applications including microscopy, optical trapping, laser machining, nonlinear light-matter interactions, and so on. The ST astigmatism effect also offers insights for the focusing and propagation studies of other types of ST wave packets.

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. It is found that the local frequency distribution of the LG function consists of two parts, the quasi-periodic part and the chirped part. The effective space-bandwidth product of the LG function is defined as the product of the spatial width and frequency-domain width of the quasi-periodic part. Then, based on this space-bandwidth product definition, the criteria for determining the beam waist parameter and the truncation order of LG series expansion are given. The scheme is tested for the representation of off-axis Hermite-Gaussian mode, which shows that our method is of high accuracy.

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. The ability to confine the optical power within a subwavelength near-spherical volume with controllable three-dimensional polarization with single objective lens may be exploited in high-resolution imaging, high-density data storage, laser direct writing, lithography, spin-directional coupling, anisotropic particle trapping and manipulation.

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. A time-reversal methodology for the creation of a wide variety of exotic optical focal fields with prescribed characteristics within the focal volume is presented. Recently developed methods for the generation of vectorial optical fields that utilize fiber lasers, digital lasers, vectorial optical field generator, metasurfaces or photoalignment liquid crystals are summarized. The interactions of these vectorial optical fields with various micro- and nano-structures are presented and the prospects of their potential applications are discussed. The connection of vectorial optical fields with higher dimensionality in quantum information is summarized.

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. The calculated pupil fields are experimentally generated with a vectorial optical field generator. The produced photonic spin orientations are quantitatively evaluated by their spin densities according to the tightly focused electric fields calculated by Richard-Wolf vectorial diffraction theory to demonstrate the validity and capability of the proposed technique.

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. The theoretical and experimental diffraction efficiency of the grating is 87% and 85.7% respectively. Such a fan-out grating may find application to high-power beam combining in the infrared regime.

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. The OAM spectrum generation with spiral complex field modulation may find applications in optical trapping and high-speed data communication.

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. Using the Richard-Wolf vectorial diffraction theory, the electric fields within the focal region are calculated to evaluate the intensities and polarization distributions of the tightly focused beams corresponding to both the theoretical and experimentally generated pupil fields and the results clearly demonstrate the validity of the proposed technique.

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. Several typical complex optical fields are experimentally generated to demonstrate the validity of the proposed transverse alignment method.