Tight Focusing Research Articles

Polarization Möbius strip at the tight focus of a generalized Poincaré beam

Based on the Richards-Wolf formalism, we investigate tight focusing of a generalized Poincaré beam. Analytical expressions are derived for all components of the electric field strength vector in the focal plane. For superposition of a right-handed circularly polarized plane wave with a left-handed circularly polarized optical vortex with topological charge –1, we obtain expressions for the intensity distribution and the longitudinal component of the spin angular momentum vector at the tight focus. We demonstrate both theoretically and numerically that the initial beam has topological charge –1/2 and, in the center of the focal plane, there is a C-point (a point with circular polarization which makes a C-line along the optical axis) with the singularity index of –1/2 (star), whereas the vector of major axis of the polarization ellipse makes along a certain-radius circle around the optical axis a single-side polarization Möbius stripe of the order –3/2, which has three half-turnovers and one stitching, where two opposite major axis vectors of the polarization ellipse meet.

Mode transformation and dark spot formation of cylindrical vector beams by thin dielectric film

An experimental approach is demonstrated for the mode transformation of cylindrical vector (CV) beams in the far field. This approach is based on the cost-effective fabrication of a thin dielectric film that precisely transforms the single-ring-shaped mode of CV beams into the double-ring-shaped mode with a switchable intensity ratio among the rings. Further, this film also increases the dark core size of the fundamental mode more than two times in a controlled manner, resulting in a dark spot space around the focus in the far field. In contrast to earlier research, our method does not employ tight focusing conditions to generate a dark spot with vector beams, which will be an advantage to the optical trapping of the low-refractive-index particles at more considerable distances from imaging systems.

Optical spin and orbital Hall effects at the tight focus of the superposition of two coaxial cylindrical vector beams with different-parity numbers

We study properties of a light field at the tight focus of the superposition of two different-order cylindrical vector beams (CVBs). In the source plane, this superposition has a polarization singularity index amounting to the half-sum of the numbers of two constituent CVBs, while having neither spin angular momentum (SAM) nor transverse energy flow. We show that if the constituent CVBs have different-parity numbers, in the focal plane there occur areas that have opposite-sign longitudinal SAM projections, alongside areas of opposite-handed energy flows rotating on closed paths (clockwise and anticlockwise). The observed phenomena indicate that longitudinal optical spin/orbital Hall effects occur in the focal plane. It is found that if the two constituent CVBs have the same-parity numbers, in the focal plane the light field is inhomogeneously linearly polarized and the energy flow (Umov-Poytning vector) has just a longitudinal component. It is also shown that in the focal plane, the intensity of the on-axis superposition of two opposite-parity CVBs is defined by the sum of the constituent beams’ intensities, as though the two beams would be orthogonally polarized. Meanwhile, in the source plane, the beams under study are not orthogonally polarized and the relation for the intensity contains an interference term.

Nonlinear to geometric focusing transition: beam self-cleaning and self-focusing critical power

We propose an easy but effective approach to find a transition numerical aperture between the regimes of laser pulse filamentation with nonlinear focusing and with geometric focusing predominance. The suggested method based on the beam profile measurements allows correction of the data provided by spectra measurements. Using a simple semi-analytical model, we study the dependence of the transition numerical aperture on the pulse power and medium nonlinearity. The analysis shows that in condensed media the transition from the nonlinear to geometric focusing regime occurs at much tighter focusing than in air. Moreover, if the medium nonlinear refractive index is high enough, only the nonlinear focusing regime is observed even at numerical apertures close to one, which allows symmetric plasma channel formation.

Tailoring focal plane component intensities of polarization singular fields in a tight focusing system

The scientific community studies tight focusing of radially and azimuthally-polarized vector beams as it is a versatile solution for many applications. We offer a new method to produce tight focusing that ensures a more uniform intensity profile in multiple dimensions, providing a more versatile and stable solution. We manipulate the polarization of the radially and azimuthally polarized vector beams to find an optimal operating point. We examine in detail optical fields whose polarization states lie on the equator of the relevant Poincaré spheres namely, the fundamental Poincaré sphere, the hybrid order Poincaré sphere (HyOPS), and the higher order Poincaré sphere. We find via simulation that the fields falling on these equators have focal plane intensity distributions characterized by a single rotation parameter α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha$$\\end{document} determining the individual state of polarization. The strengths of the component field distributions vary with α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha$$\\end{document} and can be tuned to achieve equal strengths of longitudinal (z) and transverse (x and y) components at the focal plane. Without control of this parameter (e.g., using α=0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha =0$$\\end{document} in radially and α=π\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha =\\pi$$\\end{document} in azimuthally-polarized vector beams) intensity in x and y components are at 20% of the z component. In our solution with α=π/2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha =\\pi /2$$\\end{document}, all components are at 80% of the maximum possible intensity of z. In examining the impact of α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha$$\\end{document} on a tightly focused beam, we also found that a helicity inversion of HyOPS beams causes a rotation of 180 degree in the axial intensity distribution.

Tight focusing of hybridly polarized optical vortex

In this work, using the Richards-Wolf formalism, we consider the sharp focusing of optical vortices with hybrid polarization, which combines the properties of azimuthal and circular polarizations. It is shown that these beams have a number of interesting properties: the intensity in such beams rotates with distance from the focal spot, and the longitudinal component of the spin angular momentum has an asymmetric appearance.

Designed 3D Dumpling‐Shaped Femtosecond Laser Structured Light Field for Nanoscale Sensing

AbstractNanoscale optical sensing plays a crucial role in achieving high‐precision non‐contact distance and displacement measurements. As one of the promising alternatives, structured light can greatly simplify optical sensing systems. In this study, a novel optical phenomenon of a structured beam called the “Dumpling‐shaped Structured Light Field” (DSLF) is revealed, which forms during the focusing of cylindrical lens beams. The 3D DSLF comprises two mutually perpendicular primary and secondary foci, offering unique possibilities in micro/nano processing and sensing applications. A thorough investigation of the DSLF is conducted, revealing a correlation between the secondary foci and the phase status at the objective lens's entrance pupil. The propagation of DSLF under tight focus conditions has been verified and discussed through methods of femtosecond laser two‐photon polymerization and light field analysis. Finally, thanks to the unique 3D intensity distribution of 3D DSLF, the applicability of DSLF in high‐precision position and vibration sensing has been demonstrated. By detecting the horizontal and vertical dimensions of the reflected DSLF, position and vibration sensing is achieved with a Z‐direction accuracy of 10 nm (λ/80). This research contributes to understanding structured light, and offers practical applications in various fields, including micro/nano laser processing, optical imaging, sensing, etc.

Femtosecond Laser Nanomachining of High‐Aspect‐Ratio Channels in Bulk Fused Silica

AbstractThee‐dimensional nano‐structuring of bulk fused silica glass remains a challenging issue due to limitations of traditional fabrication methods. In the present work the fabrication of hollow mm‐length channels is demonstrated in bulk fused silica by femtosecond laser irradiation followed by chemical etching, achieving feature sizes of 300 nm. The tight focusing and threshold energy conditions allow to reveal unexplored fabrication regimes. The robustness and repeatability of the process are demonstrated through the fabrication of fused silica diffraction gratings, made of parallel hollow channels with variable pitches even in the sub‐wavelength regime.

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.

Spin Angular Momentum at the Focus of a Superposition of an Optical Vortex and a Plane Wave with Linear Polarizations

In this paper, tight focusing of a superposition of a vortex laser beam with topological charge n with linear polarization and a plane wave with the same linear polarization directed along the horizontal axis is considered. Using the Richards–Wolf formalism, analytical expressions are obtained for the intensity distribution and longitudinal projection of the spin angular momentum in the focal plane. It is shown that for even and odd numbers n, the intensity and the spin angular momentum have different symmetries: for even n they are symmetric about both Cartesian axes, and for odd n they are symmetric only about the vertical axis. The intensity distribution has n local maxima at the focus, and it is nonzero on the optical axis for any n. The distribution of the longitudinal spin angular momentum (spin density) in the focal plane has (n + 2) subwavelength regions with a positive spin angular momentum and (n + 2) regions with a negative spin angular momentum, the centers of which alternately lie on a circle of a certain radius with a center on the optical axis. This spin distribution with different signs demonstrates the spin Hall effect at the focus. Negative and positive spins are mutually compensated, and the total spin is equal to zero at the focus. We have shown that by changing the topological charge of the optical vortex, it is possible to control the spin Hall effect at the focus, that is, to change the number of regions with spins of different signs.

Fast-speed algorithm to compute tight focusing of laser beams: Effectiveness of circularly polarized vortex beam series as a mathematical basis

Fast-speed algorithm to compute tight focusing of laser beams: Effectiveness of circularly polarized vortex beam series as a mathematical basis

Visualizing cortical blood perfusion after photothrombotic stroke in vivo by needle-shaped beam optical coherence tomography angiography

Optical imaging techniques provide low-cost, non-radiative images with high spatiotemporal resolution, making them advantageous for long-term dynamic observation of blood perfusion in stroke research and other brain studies compared to non-optical methods. However, high-resolution imaging in optical microscopy fundamentally requires a tight optical focus, and thus a limited depth of field (DOF). Consequently, large-scale, non-stitched, high-resolution images of curved surfaces, like brains, are difficult to acquire without z-axis scanning. To overcome this limitation, we developed a needle-shaped beam optical coherence tomography angiography (NB-OCTA) system, and for the first time, achieved a volumetric resolution of less than 8 μm in a non-stitched volume space of 6.4 mm × 4 mm × 620 μm in vivo. This system captures the distribution of blood vessels at 3.4-times larger depths than normal OCTA equipped with a Gaussian beam (GB-OCTA). We then employed NB-OCTA to perform long-term observation of cortical blood perfusion after stroke in vivo, and quantitatively analyzed the vessel area density (VAD) and the diameters of representative vessels in different regions over 10 days, revealing different spatiotemporal dynamics in the acute, sub-acute and chronic phase of post-ischemic revascularization. Benefiting from our NB-OCTA, we revealed that the recovery process is not only the result of spontaneous reperfusion, but also the formation of new vessels. This study provides visual and mechanistic insights into strokes and helps to deepen our understanding of the spontaneous response of brain after stroke.

Tight focusing of the vector optical field with polarization varying along complex curves of the Poincaré sphere.

Different from the scalar optical field with spatially uniform polarization, the vector optical field exhibits inhomogeneous distribution of polarization on the cross section. Manipulating the variation of polarization in a single optical beam is important to acquire a flexible and controllable focused optical field. Previous studies mainly focused on the vector optical field with its polarization varying along a circular trajectory of the Poincaré sphere. Here, we demonstrate the tight focusing behaviors of the vector optical field with the polarization varying along complex curves of the Poincaré sphere, which is generated by the joint modulation of azimuthal phase and amplitude distributions of orthogonally polarized components. The longitudinal polarization component with a multipolar pattern in rotational symmetry can be achieved with similar distribution of the total focused field. The transverse and longitudinal spin angular momentum distributions in the focal space are discussed. Approximately pure transverse spin angular momentum can be constructed and manipulated in the focal space, which provides the possibility to manipulate the 3D spin flux for the applications of nano and spin photonics.

Increasing Efficiency of Ultrafast Laser Writing Via Nonlocality of Light‐Matter Interaction

AbstractIn ultrafast laser writing, and light‐matter interaction in general, it has been widely accepted that the higher the energy density, the stronger material changes occur, unless thermal effects are involved. Here, this belief is challenged by demonstrating that a decreased energy density—achieved through increased scanning speed and without thermal accumulation—surprisingly leads to a more significant modification of silica glass, i.e, a higher increase in the isotropic refractive index or greater birefringence of nanopore‐mediated modification. This counterintuitive phenomenon is attributed to the nonlocality of light‐matter interaction at tight focusing, where the intensity gradient of the light beam and associated diffusion of charge carriers play a critical role in increasing material modification. A tenfold increase in the writing speed of the polarization multiplexed data storage with the potential to achieve MB s‐1 using high transmission nanopore‐based modification.

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.

Tight focusing Lorenz–Gaussian vortex beams modulated by power order space-variant phase

Tight focusing Lorenz–Gaussian vortex beams modulated by power order space-variant phase

Optical Manipulation of Fibroblasts with Femtosecond Pulse and CW Laser

Using tight focusing light, optical tweezers (OT) are tools that can manipulate and capture microscopic particles and biological cells as well as characterize a wide range of micro and nanomaterials. In this paper, we focused on fibroblasts, which are widely used in the biomedical area for a variety of purposes, including promoting human wound healing and preventing the early proliferation of tumor cells. We first built an optical tweezer experimental platform, using an 808 nm continuous-wave laser as the capture light source, to confirm that the device can precisely control the movement of single or multiple particles as well as fibroblasts. Then, a 1030 nm femtosecond laser was employed as the capture light source to study the manipulation of microparticles and fibroblasts at different powers. Lastly, a protracted manipulation protocol was used to prevent the fibroblasts from adhering to the wall. This method can be used to isolate and precisely block adherent growth of fibroblasts in cell populations. This experimental result can be further extended to other biological cells.

Manipulation of optical orbit-induced localized spin angular momentum using the periodic edge dislocation.

Orbit-induced localized spin angular momentum (OILS) has recently garnered significant attention. This paper introduces periodic edge dislocation (PED) into the tight focusing system. The study delves into the tight focusing characteristics of the radially polarized vortex plane beam with PED, demonstrating that PED serves as a straightforward and effective means of manipulating OILS, especially when both the orbital angular momentum and the polarization of the incident beam are fixed. Our findings indicate that the longitudinal OILS reaches its maximum when the difference between the period of PED and the vortex topological charge is equal to 1. Conversely, when the difference is 0, the transverse OILS reaches its maximum, while the longitudinal OILS reaches its minimum. Similar patterns are also observed in linearly polarized vortex beams. This research proposes a simple and practical way to control OILS, contributing to our understanding of optical orbit-spin coupling.

Treatment Planning and Aberration Correction Algorithm for HIFU Ablation of Renal Tumors.

High-intensity focused ultrasound (HIFU) applications for thermal or mechanical ablation of renal tumors often encounter challenges due to significant beam aberration and refraction caused by oblique beam incidence, inhomogeneous tissue layers, and presence of gas and bones within the beam. These losses can be significantly mitigated through sonication geometry planning, patient positioning, and aberration correction using multielement phased arrays. Here, a sonication planning algorithm is introduced, which uses the simulations to select the optimal transducer position and evaluate the effect of aberrations and acoustic field quality at the target region after aberration correction. Optimization of transducer positioning is implemented using a graphical user interface (GUI) to visualize a segmented 3-D computed tomography (CT)-based acoustic model of the body and to select sonication geometry through a combination of manual and automated approaches. An HIFU array (1.5 MHz, 256 elements) and three renal cell carcinoma (RCC) cases with different tumor locations and patient body habitus were considered. After array positioning, the correction of aberrations was performed using a combination of backpropagation from the focus with an ordinary least squares (OLS) optimization of phases at the array elements. The forward propagation was simulated using a combination of the Rayleigh integral and k-space pseudospectral method (k-Wave toolbox). After correction, simulated HIFU fields showed tight focusing and up to threefold higher maximum pressure within the target region. The addition of OLS optimization to the aberration correction method yielded up to 30% higher maximum pressure compared to the conventional backpropagation and up to 250% higher maximum pressure compared to the ray-tracing method, particularly in strongly distorted cases.

Complex far fields and optical singularities due to propagation beyond tight focusing: combined effects of wavefront curvature and aperture diffraction

All optical systems, which involve the collimation of a reflected, transmitted or scattered wave subsequent to tight focusing, are subject to two kinds of deviations. One is the wavefront curvature due to inaccurate focal placement of the interface or scatterer particle under consideration, and the other is the diffraction caused by the finite lens aperture. In the present paper we explore these phenomena in detail by considering a rigorous simulated model and an appropriate experimental setup. We hence demonstrate the complicated intensity profiles and optical singularity characteristics of the observed far field. Then we describe ways to minimize these deviations in a general experiment. But more importantly, our analysis proves that these deviations by themselves are significant optical phenomena of fundamental interest. The observed complex field profiles have similarities to standard diffraction-limited tight focal fields, though our field detection is different from the standard schemes. This indicates the relevance of these complex fields to a larger class of systems involving wavefront curvature and aperture diffraction. The detailed analysis and results of the present paper already serve as core explorations of these optical phenomena; and we also suggest future research directions where these system aspects can be purposefully created and explored further.