Sub-wavelength sized transversely polarized optical needle with exceptionally suppressed side-lobes

Magneto-optical-like effect in tight focusing of azimuthally polarized sine-Gaussian beams

Magneto-optical effects, which have been known for over a century, are among the most fundamental phenomena in physics and describe changes in the polarization state of light when it interacts with magnetic materials. When a polarized plane wave propagates in or through a homogeneous and isotropic transparent medium, it is generally accepted that its transverse polarization structure remains unchanged. However, we show that a strong radial polarization component can be generated when an azimuthally polarized sine-Gaussian plane wave is tightly focused by a high numerical aperture lens, resulting in a magneto-optical-like effect that does not require external magnetic field or magnetic medium. Calculations show that the intensity structure and polarization distribution of the highly confined electric field strongly depend on the parameters m and φ0 in the sinusoidal term, where m can be used to control the number of the multifocal spots and φ0 can be used to control the position of each focal spot. Finally, we show that this peculiar electric field distribution can be used to realize multiple particles trapping with controllable numbers and locations.

Generation of Subdiffraction Optical Needles by Simultaneously Generating and Focusing Azimuthally Polarized Vortex Beams through Pancharatnam-Berry Metalenses

Needle beams have received widespread attention due to their unique characteristics of high intensity, small focal size, and extended depth of focus (DOF). Here, a single-layer all-dielectric metalens based on Pancharatnam-Berry (PB) was used to efficiently generate and focus an azimuthally polarized vortex beam at the same time. Then, additional phase or amplitude modulation was respectively adopted to work with the metalens to produce optical needles. By decorating the PB metalens with the binary optical element (BOE), an optical needle with full-width-at-half-maximum (FWHM) of 0.47 λ and DOF of 3.42 λ could be obtained. By decorating the PB metalens with an annular aperture, an optical needle with long DOF (16.4 λ) and subdiffraction size (0.46 λ) could be obtained. It is expected that our work has potential applications in super-resolution imaging, photolithography, and particle trapping.

Polarization singularities hidden in a deep subwavelength confined electromagnetic field with angular momentum

Topologies associated with polarization point and line singularities can provide tools for controlling light propagation. By using the Stokes parameter, we demonstrate the emergence of polarization singularities hidden in deep subwavelength confined electromagnetic fields with angular momentum. We show that when the incoming orbital angular momentum is appropriately chosen, highly confined electromagnetic fields with super-diffraction-limited spatial dimensions can be obtained. At the same time, a conversion of orbital to spin angular momentum occurs, leading to a non-trivial topology. Our method provides a platform for developing topological photonics and studying the behavior of polarization singularities under strong focusing.

Sinusoidal-amplitude binary phase mask and its application in achieving an ultra-long optical needle

Optical needle has become a hot research topic in recent years, due to the excellent properties and potential applications. To achieve a sub-diffraction optical needle, there are three common methods including planar diffractive lenses, reflective mirrors or axicons, and high-NA objective lenses with the designed phase or amplitude elements. Here, we propose a new kind of designed phase and amplitude element called the sinusoidal-amplitude binary phase mask (SA-BPM), which modulates the amplitude and phase distributions of the incident vector optical fields (VOFs) simultaneously. Based on Richards-Wolf vector diffraction integral, the corresponding parameters of SA-BPM and the optimal optical needle length are calculated by exhaustive method and genetic algorithm. We further upgrade the SA-BPM by adding a Gaussian function in the amplitude modulation, and design the Gaussian SA-BPM (GSA-BPM). We find that the ultra-long optical needles are achieved with the SA-BPM and GSA-BPM, and the depth of focus of the optical needles are improved by 30%-70% compared with the case of binary phase mask. Such SA-BPM and GSA-BPM we proposed have great potential for manipulation and utilization of the ultra-long optical needles.

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.

Optical needles with arbitrary three-dimensional spin angular momentum

Based on our previous research on optical needles with arbitrary three-dimensional (3D) polarization, we investigate the relationship between the electric field and spin angular momentum (SAM). We have realized optical needles with arbitrary 3D spin-orientation and SAM per photon. To our best knowledge, it is the first time to obtain optical needles whose SAM can be customized on both direction and size. The relative error between the obtained spin and customized spin is always less than 5% even if SAM per photon is very small.

Optimization-free customization of optical tightly focused fields: uniform needles and hotspot chains

An optimization-free method based on an inverse problem of nonlinear equations is employed to design the binary phase diffraction optical element (BPDOE) that could modulate the incident light of a high-numerical-aperture (NA) objective lens so that the axisymmetric focal fields can be customized on demand. For example, a 43λ-long optical longitudinally polarized needle with its lateral size beyond diffraction limit is reported by using a 27-belt BPDOE, where the cost evaluated by the ratio of the belt number of BPDOE to the length of needle is record small compared with other optimization algorithms. Moreover, another longitudinal field with multiple hotspots along the propagation direction of light is also achieved with a 10-belt BPDOE. These achieved focal fields are verified doubly by using a finite-difference time-domain (FDTD) method, indicating the validity of Richards-Wolf vector diffraction theory. This optimization-free approach makes the design of BPDOEs with numerous belts viable to generate the expected focal fields, which might benefit various applications such as optical trapping, super-resolution imaging, and lithography.

Enantioselective optical trapping of chiral nanoparticles using a transverse optical needle field with a transverse spin

Since the fundamental building blocks of life are built of chiral amino acids and chiral sugar, enantiomer separation is of great interest in plenty of chemical syntheses. Light-chiral material interaction leads to a unique chiral optical force, which possesses opposite directions for specimens with different handedness. However, usually the enantioselective sorting is challenging in optical tweezers due to the dominating achiral force. In this work, we propose an optical technique to sort chiral specimens by use of a transverse optical needle field with a transverse spin (TONFTS), which is constructed through reversing the radiation patterns from an array of paired orthogonal electric dipoles located in the focal plane of a 4Pi microscopy and experimentally generated with a home-built vectorial optical field generator. It is demonstrated that the transverse component of the photonic spin gives rise to the chiral optical force perpendicular to the direction of the light's propagation, while the transverse achiral gradient force would be dramatically diminished by the uniform intensity profile of the optical needle field. Consequently, chiral nanoparticles with different handedness would be laterally sorted by the TONFTS and trapped at different locations along the optical needle field, providing a feasible route toward all-optical enantiopure chemical syntheses and enantiomer separations in pharmaceuticals.

Optical needles with arbitrary homogeneous three-dimensional polarization

We propose a new method to generate optical needles by focusing vector beams comprised of radially polarized component and azimuthally polarized vortex components. The radial part can generate longitudinal polarization, while the azimuthal parts can generate left- and right-handed polarization. Hence, an arbitrary 3D polarization can be obtained. To our knowledge, it may be the first time that arbitrarily polarized optical needles whose transverse sizes are under 0.5λ have been achieved. The polarized homogeneity of the needles is beyond 0.97.

Pancharatnam-Berry phase shaping for control of the transverse enhancement of focusing

We show that elongating a tightly focused field in the direction perpendicular to the optical axis is possible. We demonstrate our approach by specially shaping the Pancharatnam-Berry (PB) phase. Moreover, the analytical formulae required to calculate the strength vectors and energy flux of the three-dimensional electromagnetic fields near the focus of an aplanatic optical system are derived using the Richards and Wolf vectorial diffraction methods. Calculations reveal that the transverse enhancement is controllable and depend on the phase index in the PB phase, thereby giving rise to a focus with tunable length and subwavelength width in the focal plane.

Tight focusing properties of a circular partially coherent Gaussian beam

Tight focusing properties of a circular partially coherent Gaussian (CPCG) beam with linear polarization have been studied based on vectorial Debye theory. Expressions for the intensity distribution and degree of coherence near the focus are derived. Numerical calculations are performed to show the intensity distribution and degree of coherence of the CPCG beam in the focal region. It is interesting to find that after focusing the CPCG beam through a high numerical-aperture objective we can obtain a super-length optical needle (>12λ) with homogeneous intensity along the propagation axis and wavelength beam size (∼λ). Moreover, the numerical calculations of coherence illustrate that, in the range of full width at half-maximum of the optical needle, for any two of the parallel electric field components of the optical needle the coherence is close to 1, but for any two of orthometric electric field components the value of coherence is between 0.4 and 0.9. Such a non-diffracting optical needle may have potential applications in atom optical experiments, such as in atom traps and atom switches.

Optimization-free approach for generating sub-diffraction quasi-non-diffracting beams

Sub-diffraction quasi-non-diffracting beams with sub-wavelength transverse size are attractive for applications such as optical nano-manipulation, optical nano-fabrication, optical high-density storage, and optical super-resolution microscopy. In this paper, we proposed an optimization-free design approach and demonstrated the possibility of generating sub-diffraction quasi-non-diffracting beams with sub-wavelength size for different polarizations by a binary-phase Fresnel planar lens. More importantly, the optimization-free method significantly simplifies the design procedure and the generation of sub-diffracting quasi-non-diffracting beams. Utilizing the concept of normalized angular spectrum compression, for wavelength λ₀ = 632.8 nm, a binary-phase Fresnel planar lens was designed and fabricated. The experimental results show that the sub-diffraction transverse size and the non-diffracting propagation distances are 0.40λ₀-0.54λ₀ and 90λ₀, 0.43λ₀-0.54λ₀ and 73λ₀, and 0.34λ₀-0.41λ₀ and 80λ₀ for the generated quasi-non-diffracting beams with circular, longitudinal, and azimuthal polarizations, respectively.

Trapping two types of particles by using a tightly focused radially polarized power-exponent-phase vortex beam

We investigate the intensity of a radially polarized power-exponent-phase vortex (PEPV) beam focused by a high-numerical-aperture objective. A bright focal spot and a focal annulus with a dark core can be generated by changing the phase of the PEPV beam. The possibility of trapping a gold particle with the bright focal spot and trapping an air bubble with the focal annulus is discussed, and the force and trapping stability are calculated. It is shown that a tightly focused radially polarized PEPV beam is applicable to trapping two types of particles.

Synthesis of sub-diffraction quasi-non-diffracting beams by angular spectrum compression

Quasi-non-diffracting beams are attractive for various applications, including optical manipulation, super-resolution microscopes, and materials processing. However, it is a great challenge to design and generate super-long quasi-non-diffracting beams with sub-diffraction and sub-wavelength size. In this paper, a method based on the idea of compressing a normalized angular spectrum is developed, which makes it possible and provides a practical tool for the design of a quasi-non-diffracting beam with super-oscillatory sub-wavelength transverse size. It also presents a clear physical picture of the formation of super-oscillatory quasi-non-diffracting beams. Based on concepts of a local grating and super-oscillation, a lens was designed and fabricated for a working wavelength of λ = 632.8 nm. The validity of the idea of normalized angular spectrum compression was confirmed by both numerical investigations and experimental studies. An optical hollow needle with a length of more than 100λ was experimentally demonstrated, in which an optical hollow needle was observed with a sub-diffraction and sub-wavelength transverse size within a non-diffracting propagation distance of 94λ. Longer non-diffracting propagation distance is expected for a lens with larger radius and shorter effective wavelength.

Theoretical guideline for generation of an ultralong magnetization needle and a super-long conveyed spherical magnetization chain

Considering an azimuthally polarized vortex beam with a Gaussian annulus as an incoming light, light induced magnetization fields for both a single high NA lens and a pair of high NA lenses are investigated theoretically. We deduce analytical formulas for the parameters of a magnetization needle and a magnetization chain when the angular width of the incident beam is far less than its central angular position. Through these analytical formulas, the properties of the magnetization needle and the magnetization chain are very clear and distinct. Compared with parameter optimizing to produce an ultralong magnetization needle with lateral sub-wavelength scale and a super-long spherical magnetization chain with three-dimensional super resolution, the analytical method is direct and has a theoretical guideline. The validity of these formulas is proved, compared to numerical solutions. The present work regarding these super-resolution magnetization patterns is of great value in high density all-optical magnetic recording, atomic trapping as well as confocal and magnetic resonance microscopy.

Planar binary-phase lens for super-oscillatory optical hollow needles

Optical hollow beams are suitable for materials processing, optical micromanipulation, microscopy, and optical lithography. However, conventional optical hollow beams are diffraction-limited. The generation of sub-wavelength optical hollow beams using a high numerical aperture objective lens and pupil filters has been theoretically proposed. Although sub-diffraction hollow spot has been reported, nondiffracting hollow beams of sub-diffraction transverse dimensions have not yet been experimentally demonstrated. Here, a planar lens based on binary-phase modulation is proposed to overcome these constraints. The lens has an ultra-long focal length of 300λ. An azimuthally polarized optical hollow needle is experimentally demonstrated with a super-oscillatory transverse size (less than 0.38λ/NA) of 0.34λ to 0.42λ, where λ is the working wavelength and NA is the lens numerical aperture, and a large depth of focus of 6.5λ. For a sub-diffraction transverse size of 0.34λ to 0.52λ, the nondiffracting propagation distance of the proposed optical hollow needle is greater than 10λ. Numerical simulation also reveals a good penetrability of the proposed optical hollow needle at an air-water interface, where the needle propagates through water with a doubled propagation distance and without loss of its super-oscillatory property. The proposed lens is suitable for nanofabrication, optical nanomanipulation, super-resolution imaging, and nanolithography applications.