Cylindrical Vector Beams Research Articles

Polarization detection for cylindrical vector beams empowered by pixelated metasurfaces

Polarimetry plays an indispensable role in the light–matter interactions. Nevertheless, conventional components developed for polarization measurements suffer from bulky volume and spatial alignment schemes, causing them to reveal limited performance in determining inhomogeneous polarization distributions. Here, we propose a polarization detection scheme based on pixelated all-dielectric metasurfaces using spin-multiplexing coding techniques. The polarization resolving capability of the pixelated metasurface under homogeneous linearly polarized illumination was first evaluated, and the extracted peak coordinates were used to establish an exact functional relationship with the azimuthal angle. Subsequently, the measurement of spatial inhomogeneous polarization was further explored with a focusing matrix assembled from pixelated metasurfaces. The proposed polarization detection strategy can be extended to other spectral bands without discrimination, stimulating potential applications in high-resolution imaging, sensing and data communication.

Cylindrical Vector Beam Holography without Preservation of OAM Modes.

Orbital angular momentum (OAM) multiplexed holograms have attracted a great deal of attention recently due to their physically unbounded set of orthogonal helical modes. However, preserving the OAM property in each pixel hinders fine sampling of the target image in principle and requires a fundamental filtering aperture array in the detector plane. Here, we demonstrate the concept of metasurface-based vectorial holography with cylindrical vector beams (CVBs), whose unlimited polarization orders and unique polarization distributions can be used to boost information storage capacity. Although CVBs are composed of OAM modes, the holographic images do not preserve the OAM modes in our design, enabling fine sampling of the target image in a quasi-continuous way like traditional computer-generated holograms. Moreover, the images can be directly observed by passing them through a polarizer without the need for a fundamental mode filter array. We anticipate that our method may pave the way for high-capacity holographic devices.

Generation of cylindrical vector modes via astigmatic mode conversion.

In this work, we propose and demonstrate experimentally a compact technique for generating cylindrical vector beams based on a Michelson interferometer and a π-astigmatic mode converter. The latter is required to invert the topological charge of higher-order Laguerre-Gauss (LG) beams. Our proposed technique generalizes the use of astigmatic mode conversion, commonly associated only with scalar beams, to vector beams with a non-homogeneous polarization distribution. We anticipate that many applications based on Michelson interferometers will benefit from the unique properties of vector beams.

Optical vectorial-mode parity Hall effect: a case study with cylindrical vector beams

The vectorial optical field (VOF) assumes a pivotal role in light-matter interactions. Beyond its inherent polarization topology, the VOF also encompasses an intrinsic degree of freedom associated with parity (even or odd), corresponding to a pair of degenerate orthogonal modes. However, previous research has not delved into the simultaneous manipulation of both even and odd parities. In this study, we introduce and validate the previously unexplored parity Hall effect for vectorial modes using a metasurface design. Our focus lies on a cylindrical vector beam (CVB) as a representative case. Through the tailored metasurface, we effectively separate two degenerate CVBs with distinct parities in divergent directions, akin to the observed spin states split in the spin Hall effect. Additionally, we provide experimental evidence showcasing the capabilities of this effect in multi-order CVB demultiplexing and parity-demultiplexed CVB-encoded holography. This effect unveils promising opportunities for various applications, including optical communication and imaging.

Comparative analysis of geometric transformation-based sorting systems for fractional vector beams with polarization mutation angle indeterminacy

The Polarization Topological Charge (PTC) is a crucial parameter of a Cylindrical Vector Beam (CVB). Defined as the repetition number of polarization state changes along the azimuth axis, its sign indicates the polarization’s rotation direction. This paper delves into the effects of polarization mutation within Fractional Vector Beams (FVB) with angular uncertainty on PTC sorting systems. We compare three optical geometric coordinate transformation methods: Log-Polar (LP), Beam-Copying (BC), and Spiral Transformation (ST), focusing on their robustness and suitability. Our findings show that the azimuth angle of polarization mutation markedly influences the PTC sorting system’s output, leading to measurable uncertainties. Importantly, these uncertainties are not intrinsic to the FVB, but rather stem from the sorting system itself. Our study concludes that the BC method is optimal for PTC spectra analysis, whereas the ST method with carefully selected parameters is preferable for average PTC analysis.

Transverse Spin Hall Effect and Twisted Polarization Ribbons at the Sharp Focus

Transverse Spin Hall Effect and Twisted Polarization Ribbons at the Sharp Focus

Cross-connection of multiplexed cylindrical vector beams using off-axis spin-decoupled metasurfaces.

Cylindrical vector beam (CVB) multiplexing communication demands effective mode cross-connection techniques to establish communication networks. While methods like polarized grating and coordinate transformation have been developed for (de)multiplexing CVB modes, challenges persist in the cross-connection of these multiplexed mode channels, including multi-mode conversion and inhomogeneous polarization control. Herein, we present an independent off-axis spin-orbit interaction strategy utilizing spin-decoupled metasurfaces. Cross-connection is achieved by encoding conjugated Dammann optical vortex grating phases onto the two orthogonal circularly polarized components of CVBs. Experimental results demonstrate the successful interconversion of four CVB modes (CVB+1 and CVB-2, CVB+2 and CVB-4) using a Si-based metasurface with a polarization conversion efficiency exceeding 85%. This facilitates the cross-connection of 200 Gbit/s quadrature phase-shift keying signals with bit-error-rates below 10-6. Offering advantages such as ultra-compact device size, flexible control of CVB modes, and multi-mode parallel processing, this approach shows promise in advancing the networking capabilities of CVB mode multiplexing communication networks.

Second harmonic of higher-order Poincaré sphere beam with two orthogonal 5%MgO:PPLN crystals

In this work, the second harmonic (SH) of higher-order Poincaré sphere (HOPS) beam was introduced and demonstrated with two orthogonal 5%MgO:PPLN crystals. Based on the quasi-phase-matching technique, the vectorial coupled wave equations were derived to simulate the SH of HOPS beams through the two crystals, including the cylindrical vector beams (CVBs), elliptically polarized CVBs (EPCVBs), and circularly polarized vortex beams. Then, the experimental setup was established to reveal that the SH of CVBs and EPCVBs present the four-lobed structure and still exhibit vector characteristics. Meanwhile, the circularly polarized vortex beams become the linearly polarized vortex beams with double phase topology, confirming the conservation of orbital angular momentum. Moreover, the maximum SH conversion efficiency of CVBs, EPCVBs, and circularly polarized vortex beams can reach 25.3%, 23.4%, and 29.4%, respectively, which may be instructive for promoting the SH generation of vector vortex beams with high efficiency.

Optical Force Effects of Rayleigh Particles by Cylindrical Vector Beams.

High-order cylindrical vector beams possess flexible spatial polarization and exhibit new effects and phenomena that can expand the functionality and enhance the capability of optical systems. However, building a general analytical model for highly focused beams with different polarization orders remains a challenge. Here, we elaborately develop the vector theory of high-order cylindrical vector beams in a high numerical aperture focusing system and achieve the vectorial diffraction integrals for describing the tight focusing field with the space-variant distribution of polarization orders within the framework of Richards-Wolf diffraction theory. The analytical formulae include the exact three Cartesian components of electric and magnetic distributions in the tightly focused region. Additionally, utilizing the analytical formulae, we can achieve the gradient force, scattering force, and curl-spin force exerted on Rayleigh particles trapped by high-order cylindrical vector beams. These results are crucial for improving the design and engineering of the tightly focused field by modulating the polarization orders of high-order cylindrical vector beams, particularly for applications such as optical tweezers and optical manipulation. This theoretical analysis also extends to the calculation of complicated optical vortex vector fields and the design of diffractive optical elements with high diffraction efficiency and resolution.

Full higher-order Poincaré sphere beam mode-locked fiber laser

In this paper, the controlled generation of full higher-order Poincaré sphere (HOPS) beams from a mode-locked fiber laser was introduced and demonstrated. In the cavity, two mirror-placed spatial mode converters, consisted of the vortex waveplate, quarter waveplate and half waveplate, were applied to achieve the mutual conversion of the LP01 mode and HOPS beams. Then, the full HOPS beams mode-locked fiber laser was established to obtain the circularly polarized vortex beams, cylindrical vector beams (CVBs), and elliptically polarized CVBs, with pulse width of 390 ps, repetition frequency of 14.7 MHz, central wavelength of 1043.35 nm and 3 dB bandwidth of 0.53 nm. The results may be potentially important for the generation of full HOPS beam from a mode-locked fiber laser.

Comment on M. Babiker, J. Yuan, K. Koksal, and V. Lembessis, Optics Communications 554, 130185 (2024)

In a recent article Babiker et al. (2024) claim that cylindrical vector beams (CVBs), also referred to as higher-order Poincaré (HOP) beams, possess optical chirality densities which exhibit ‘superchirality’. Here we show that, on the contrary, CVBs possess less optical chirality density than a corresponding circularly polarized scalar vortex beam and that the ‘superchiral’ results are nonphysical. We also identify a number of issues concerning the derivation and general theory presented.

Switchable dual-wavelength mode-locked cylindrical vector beam fiber laser based on unpumped EDF saturable absorber and nonlinear polarization rotation

A switchable single- and dual-wavelength mode-locked pulse laser with cylindrical vector beam (CVB) based on an unpumped EDF saturable absorber and a nonlinear polarization rotation (NPR) hybrid mode-locked mechanism has been proposed and experimentally demonstrated. An unpumped EDF saturable absorber is utilized to generate a mode-locked operation that generates high-order laser pulses. Utilizing a hybrid mode-locked mechanism, the signal-to-noise ratio (SNR) and operating stability of the laser are improved compared to the mode-locked operation with a single unpumped EDF saturable absorber. Through adjusting the polarization controller, single- and dual-wavelength stable mode-locked pulses can be easily realized. The single-wavelength mode-locked pulse operates with central wavelengths of 1550.16 nm and 1549.80 nm, repetition frequencies of 6.33 MHz and 6.35 MHz, corresponding to pulse intervals of 158 ns and 157 ns. Further, the long-period grating (LPFG) is used as a mode converter to achieve pulse output with a purity exceeding 95 % in the TM01 and TE01 modes at different operating wavelengths. The proposed fiber laser with a simple structure has provided a flexible pulsed CVB laser source for laser processing, time division, and mode division multiplexing applications.

Multi-dimensional cylindrical vector beam (de)multiplexing through cascaded wavelength- and polarization-sensitive metasurfaces.

Cylindrical vector beams (CVBs) exhibit great potential for multiplexing communication, owing to their mode orthogonality and compatibility with conventional wavelength multiplexing techniques. However, the practical application of CVB multiplexing communication faces challenges due to the lack of effective spatial polarization manipulation technologies for (de)multiplexing multi-dimensional physical dimensions of CVBs. Herein, we introduce a wavelength- and polarization-sensitive cascaded phase modulation strategy that utilizes multiple coaxial metasurfaces for multi-dimensional modulation of CVBs. By leveraging the spin-dependent phase modulation mechanism, these metasurfaces enable the independent transformation of the two orthogonal polarization components of CVB modes. Combined with the wavelength sensitivity of Fresnel diffraction in progressive phase modulation, this approach establishes a high-dimensional mapping relationship among CVB modes, wavelengths, spatial positions, and Gaussian fundamental modes, thereby facilitating multi-dimensional (de)multiplexing involving CVB modes and wavelengths. As a proof of concept, we theoretically demonstrate a 9-channel multi-dimensional multiplexing system, successfully achieving joint (de)multiplexing of 3 CVB modes (1, 2, and 3) and 3 wavelengths (1550 nm, 1560 nm, and 1570 nm) with a diffraction efficiency exceeding 80%. Additionally, we show the transmission of 16-QAM signals across 9 channels with the bit-error-rates below 10-5. By combining the integrability of metasurfaces with the high-dimensional wavefront manipulation capabilities of multilevel modulation, our strategy can effectively address the diverse demands of different wavelengths and CVB modes in optical communication.

Enhancing the Spin Hall Effect of Cylindrically Polarized Beams.

Two linked gear wheels in a micromachine can be simultaneously rotated in opposite directions by using a laser beam that has in its section areas the spin angular momentum (SAM) of the opposite sign. However, for instance, a cylindrical vector beam has zero SAM in the focus. We alter a cylindrical vector beam so as to generate areas in its focus where the SAM is of opposite signs. The first alteration is adding to the cylindrical vector beam a linearly polarized beam. Thus, we study superposition of two rotationally symmetric beams: those with cylindrical and linear polarization. We obtain an expression for the SAM and prove two of its properties. The first property is that changing superposition coefficients does not change the shape of the SAM density distribution, whereas the intensity changes. The second property is that maximal SAM density is achieved when both beams in the superposition have the same energy. The second perturbation is adding a spatial carrier frequency. We study the SAM density of a cylindrical vector beam with a spatial carrier frequency. Due to periodic modulation, upon propagation in space, such a beam is split into two beams, having left and right elliptic polarization. Thus, in the beam transverse section, areas with the spin of different signs are separated in space, which is a manifestation of the spin Hall effect. We demonstrate that such light beams can be generated by metasurfaces, with the transmittance depending periodically on one coordinate.

Stacked Polarizing Elements for Controlling Parameters of Surface Relief Gratings Written in Photosensitive Materials.

Photosensitive materials are widely used for the direct fabrication of surface relief gratings (SRGs) without the selective etching of the material. It is known that the interferometric approach makes it possible to fabricate SRGs with submicron and even subwavelength periods. However, to change the period of the written SRGs, it is necessary to change the convergence angle, shift a sample, and readjust the interferometric setup. Recently, it was shown that structured laser beams with predetermined, periodically modulated polarization distributions can also be used to fabricate SRGs. A structured laser beam with the desired polarization distribution can be formed with just one polarizing optical element-for example, the so-called depolarizer, a patterned micro-retarder array. The use of such stacked elements makes it possible to directly control the modulation period of the polarization of the generated laser beam. We show that this approach allows one to fabricate SRGs with submicron periods. Moreover, the addition of q-plates, elements effectively used to generate cylindrical vector beams with polarization singularities, allows the efficient formation of fork polarization gratings (FPGs) and the fabrication of higher-order fork-shaped SRGs. Full control of the parameters of the generated FPGs is possible. We demonstrate the formation of FPGs of higher orders (up to 12) by only adding first- and second-order q-plates and half-wave plates to the depolarizers. In this work, we numerically and experimentally study the parameters of various types of SRGs formed using these stacked polarizing elements and show the significant potential of this method for the laser processing of photosensitive materials, which often also serve as polarization sensors.

Cylindrical vector beam multiplexing holography employing spin-decoupled phase modulation metasurface

Abstract Cylindrical vector beams (CVBs) hold considerable promise as high-capacity information carriers for multiplexing holography due to their mode orthogonality. In CVB holography, phase holograms are encoded onto the wave-front of CVBs with different mode orders while preserving their independence during reconstruction. However, a major challenge lies in the limited ability to manipulate the spatial phase and polarization distribution of CVBs independently. To address this challenge, we propose a spin-decoupled phase modulation strategy by leveraging the propagation and geometric phase of composite phase metasurfaces. By exploiting the polarized Poincaré sphere, we show that CVBs can be decomposed into two circularly polarized components with orthogonal polarization states and conjugate phase distributions. This decomposition enables independent control of the phase and polarization distributions of CVBs by modulating the initial phase and phase difference of these two components. Consequently, two holograms with discrete spatial frequency distributions that carry opposite helical phases are encoded to modulate the wave-front of CVBs by the metasurface consisting of Si nanopillars. This allows for us to achieve successful four-channel CVB multiplexing holography. Benefiting from the non-dispersive nature of geometric phase, this metasurface exhibits a broad operating band spanning the entire visible light spectrum (443 nm–633 nm). These suggest that our proposed method offers comprehensive control over the spatial phase and polarization of CVBs, thereby holding significant potential for advancing their application in holography.

Focusing of linearly polarized optical vortex and a Hall effect

Polarization of a higher-order cylindrical vector beam (CVB) is known to be locally linear. The higher the beam order, the larger number of full circles the local linear polarization vector makes around the optical axis. It is also known that the CVB with radially symmetric amplitude has zero spin angular momentum (SAM) and zero orbital angular momentum (OAM) both in the initial plane and in the focal plane (because in both Cartesian components of the vector field, the angular derivative of phase is zero). We show here that near the focal plane of the CVB (i.e. before and beyond the focus), an even number of local subwavelength areas with rotating polarization vectors are generated. In addition, in the neighboring areas, the polarization vectors are rotating in the opposite directions. Thus, the longitudinal components of the SAM vector in such neighboring areas are of different sign. After passing through the focal plane, the rotation direction of the polarization vector at each point of the beam cross-section changes to the opposite one. Such a spatial separation of the left and right rotation of the polarization vectors is a manifestation of the optical spin Hall effect.

Focusing a cylindrical vector beam and the Hall effect

Polarization of a higher-order cylindrical vector beam (CVB) is known to be locally linear. The higher the beam order, the larger number of full circles the local linear polarization vector makes around the optical axis. It is also known that the CVB with radially symmetric amplitude has zero spin angular momentum (SAM) and zero orbital angular momentum (OAM) both in the initial plane and in the focal plane (because in both Cartesian components of the vector field, the angular derivative of phase is zero). We show here that near the focal plane of the CVB (i.e. before and beyond the focus), an even number of local subwavelength areas with rotating polarization vectors are generated. In addition, in the neighboring areas, the polarization vectors are rotating in the opposite directions. Thus, the longitudinal components of the SAM vector in such neighboring areas are of different sign. After passing through the focal plane, the rotation direction of the polarization vector at each point of the beam cross-section changes to the opposite one. Such a spatial separation of the left and right rotation of the polarization vectors is a manifestation of the optical spin Hall effect.

Selective Excitation of Dark Plasmon Modes Using Cylindrical Vector Beams Studied by Microscopic Imaging of Nonlinear Photoluminescence

Selective Excitation of Dark Plasmon Modes Using Cylindrical Vector Beams Studied by Microscopic Imaging of Nonlinear Photoluminescence

Cylindrical vector beam generation from a hybrid multimode Q-switched mode-locked fiber laser

We demonstrate a hybrid multimode Q-switched mode-locked fiber laser capable of delivering cylindrical vector beams (CVBs). The wavelength-tunable Q-switching, conventional mode-locking, Q-switched mode-locking (QML), and CVB generation under QML operation are respectively achieved in this hybrid multimode cavity. The mode-locking mechanism is based on carbon nanotubes as saturable absorber and two interferometric filtering structures, i.e., multimode fiber-single-mode fiber-multimode fiber and multimode fiber-few-mode fiber-multimode fiber. The mode-selective coupler is used as a mode selector converting the fundamental mode to higher-order mode and as an output coupler to obtain CVB. The Q-switched pulses allow for tunable wavelengths in the range of 1028.2 nm to 1038.2 nm, with a frequency of about 50 KHz. The conventional mode-locking is achieved with a repetition frequency of 15.6 MHz and a pulse interval of 66.7 ns. Specifically, the introduction of dual interferometric filtering structures in the cavity results in noteworthy nonlinear effects, facilitating the generation of third-harmonic mode-locking under the single-wavelength QML operation. These experimental findings highlight the promising applications such as mode-division multiplexed optical communication and laser processing.