High Numerical Aperture Focusing Research Articles

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.

Ultrafast vectorial calculation of tightly focused vortex and non-vortex fields in a meridional plane

It is shown that for vortex and non-vortex vector beams diffracted by the exit pupil of a high numerical aperture (NA) focusing system with axial symmetry, the electromagnetic field near the focus can be represented in a general form involving several one-dimensional (1D) discrete Fourier transforms associated with three orthogonally polarized components of the field. Based on this form, a simple and effective method is proposed for ultrafast calculation of the tightly focused fields in an arbitrary meridional plane using the algorithms of 1D fast Fourier transform or 1D chirp Z transform. To compare the proposed method with the traditional method of direct calculation, three typical examples are given with an emphasis on estimating the time and accuracy of calculating tightly focused vortex and non-vortex electromagnetic fields produced by a high NA aplanatic lens, with linear or radial polarization of the light field at the annular entrance pupil of the lens.

Non-contact optical probe with nanometer resolution and large measurement range based on the astigmatism method

In the measurement field of micro/nano devices, many instruments have a contradiction between high resolution and large measurement range. This paper developed a non-contact optical nanometer probe based on the astigmatism method. This probe employs a high numerical aperture (NA) focusing lens to achieve nanometer resolution of the longitudinal measurement. Meanwhile, a longitudinal scanning measurement method based on two focus error signal (FES) curves is proposed to break the limit of low measurement range caused by high NA value. Therefore, it enables the probe to achieve the nanometer resolution of longitudinal measurement and large measurement ranges. The experiment results show that the longitudinal measurement resolution of the proposed probe is better than 1 nm, and the repeatability error is 17 nm. Combined with the high-precision microstage, the longitudinal range is greater than 15 μm. The proposed probe can be used for large-range longitudinal non-contact measurements with nano-scale measurement requirements.

Magnetization properties of radially polarized Bessel-Gaussian vortex beams with radial phase modulation in a 4π focusing system.

This paper explored the optically induced magnetization properties of radially polarized Bessel-Gaussian vortex beams with radial phase modulation in a 4π high numerical aperture (NA) focusing system, which is based on the vector diffraction theory and the inverse Faraday effect. The results show that in the case of radial modulation parameter L=0, one longitudinal magnetization chain with adjustable length can be obtained by modulating the truncation parameter β. When the radial modulation parameter L=1.3, two magnetization chains can be obtained by modulating the truncation parameter β. By modulating the radial modulation parameter L, two magnetization chains along the optical axis can be generated, each with four dark magnetic traps; meanwhile, the spacing between two magnetization chains can be adjusted. These results may be helpful in high-density all-optical magnetic recording, atom capture, and magnetic resonance microscopy.

High Harmonic Generation near the Low-Frequency Edge of a Plateau under Nonlinear Propagation of 1.24-μm Near-Infrared Femtosecond Laser Radiation in a Dense Argon Jet

High (15–25) harmonic generation in the vacuum ultraviolet spectral range (83–50 nm) has been realized by focused (NA = 0.033) near-infrared femtosecond laser radiation (wavelength λ = 1.24 μm) with a vacuum intensity of ~7.5 × 1014 W/cm2 irradiating a dense gas jet. It has been shown experimentally that the use of such a high-numerical aperture focusing requires high (up to 10 bar) gas jet pressures to optimize phase matching. The use of the dense gas jet results in a noticeable manifestation of nonlinear propagation effects for generating radiation, which affect the generation process through the change in the phase matching conditions. Furthermore, it has been shown that the prechirping of the generating pulse makes it possible to compensate a chirp appearing due to self-phase modulation and to increase the harmonic generation efficiency because of the nonlinear compression of the generating pulse. This approach has allowed 17th (73 nm) harmonic generation with an energy of 2 pJ in a pulse and a generation efficiency of 5.4 × 10–9. The estimates obtained have shown that this radiation can be used for single-pulse maskless photolithography in the extreme ultraviolet range.

Versatile tape-drive target for high-repetition-rate laser-driven proton acceleration

Abstract We present the development and characterization of a high-stability, multi-material, multi-thickness tape-drive target for laser-driven acceleration at repetition rates of up to 100 Hz. The tape surface position was measured to be stable on the sub-micrometre scale, compatible with the high-numerical aperture focusing geometries required to achieve relativistic intensity interactions with the pulse energy available in current multi-Hz and near-future higher repetition-rate lasers ( $>$ kHz). Long-term drift was characterized at 100 Hz demonstrating suitability for operation over extended periods. The target was continuously operated at up to 5 Hz in a recent experiment for 70,000 shots without intervention by the experimental team, with the exception of tape replacement, producing the largest data-set of relativistically intense laser–solid foil measurements to date. This tape drive provides robust targetry for the generation and study of high-repetition-rate ion beams using next-generation high-power laser systems, also enabling wider applications of laser-driven proton sources.

Upper bounds on focusing efficiency.

Upper bounds on the focusing efficiency of aperture fields and lens systems are formulated using integral equation representations of Maxwell's equations and Lagrangian duality. Two forms of focusing efficiency are considered based on lens exit plane fields and optimal polarization currents within lens design regions of prescribed shape and available materials. Bounds are compared against the performance of classical prescriptions of ideal lens aperture fields, hyperbolic lens designs, and lenses produced by inverse design. Results demonstrate that, without regularization, focusing efficiency based solely on lens exit plane fields is unbounded, similar to the problem of unbounded antenna directivity. Additionally, results considering extruded two-dimensional dielectric geometries driven by out-of-plane electric fields for the calculation of bounds and inverse design demonstrate that aperture fields based on time-reversal do not necessarily yield optimal lens focusing efficiency, particularly in the case of near-field (high numerical aperture) focusing.

Versatile focal field design using cascaded artificial neural network

Both forward and inverse design methods have been developed for focal field engineering, which has applications in many areas including super-resolution imaging and optical lithography, high-density optical storage, and particle manipulation. However, a certain method is normally targeted at a unique focal field distribution. Here, we report on a versatile focal field design method based on a cascaded artificial neural network (CANN) for the inverse design of focal field distributions in a high numerical aperture focusing system. The CANN consists of a forward and an inverse artificial neural network. Once trained properly, the CANN can predict modulation phase patterns for multiple focal field distributions. We demonstrate the effectiveness of the CANN by the design of focal field distributions along the optical axis including a uniform optical needle and an anti-point spread function with lengths up to 14 wavelengths and multiple focal spots with controllable intensities as well as those in the focal plane including flat-top and sub-diffraction focal spots.

Ultraviolet metalens and metalens array of focused vortex beams

The solar-blind ultraviolet (UV) wavelength is particularly interesting within the range of 200 nm–300 nm. Here, we propose a focusing metalens, focusing vortex beam (VB) metalens and metalens array that specifically work in the UV band to focus a beam or VB. Firstly, a high numerical aperture (NA) focusing metalens working at a wavelength of 214.2 nm was designed, and the NA reached 0.83. The corresponding conversion efficiency of the unit structure reached as high as 94%, and the full width at half maximum was only 117.2 nm. Metalenses with large NA can act as optical tweezers and can be applied to trap ultracold atoms and molecules. Secondly, a focused VB metalens in the wavelength range of 200 nm–300 nm was also designed, which can convert polarized light into a VB and focus the VB simultaneously. Finally, a metalens array was developed to focus VBs with different topological charges on the same focal plane. This series of UV metalenses could be widely used in UV microscopy, photolithography, photonics communication, etc.

High numerical aperture and large focusing efficiency metalens based on multilayer transmitarray elements

High numerical aperture (NA) metalenses with large focusing efficiency are crucial for various applications in modern optics and photonics, particularly in high resolution imaging, high directivity lasing process and so on. Recent progresses have been achieved in designing high NA metalenses which can surpass conventional ones but mainly in the visible and infrared regimes by using all-dielectric metasurfaces. Here, multilayer phase gradient metallic metasurfaces sandwiched by filling dielectrics are employed to design high NA and large efficiency metalenses in the low spectrums. Benefiting from its high transmission amplitude and the full phase control to the incident waves of the proposed gradient meta-atoms with a double split ring resonator, the designed ultra-thin and small footprint four-layer metalens (5λ × 5λ × 0.23λ, λ is wavelength) demonstrates a high NA in the order of 0.8 and the large focusing efficiency around 40% according to the full-wave simulations and experimental measurements. Furthermore, the influences of the dielectric thickness and the layer number of stacked meta-atoms on the presented high NA metalens are investigated. The results reveal that the NA of proposed metalens can be surprisingly further improved from 0.8 to 0.9 by increasing dielectric thickness and/or the focusing efficiency can be enhanced to above 50% by adding the layer number of the stacked meta-atoms. These findings also imply that our high NA metalens in low spectrum can be compatible to the standard printed circuit board fabrication and also posses of good robustness to the metasurface layer number. The presented work provides new vistas to develop high NA and large efficiency metalens in low microwave or Terahertz (THz) spectrum, where the metallic metasurfaces are commonly used. Besides, it can benefit to the development of various novel metadevices such as miniaturized high-gain lens antenna, compact cloaks and many others in modern microwave engineering and/or THz optics.

Hybrid polarization induced transverse energy flow

Nonzero transverse energy flow, which describes phenomenon in which the energy flux of localized light propagates in a plane perpendicular to the optical axis, has attracted enormous interest recently due to its useful application in micromanipulation. We show that the appearance of transverse energy flow in the focal plane of an aplanatic high numerical aperture focusing system is possible. We demonstrate our approach by specially tailoring the input state of polarization. Calculations reveal that number of transverse energy flow rings is controllable and depend on azimuthal index of the input field, thereby giving rise to tunable manipulating locations in optical trapping.

Tunable focal shift induced by polarization and phase shaping

We propose a simple method to control the move and elongation of focus along the optical axis in a high-numerical aperture focusing system. By introducing the optical degree of freedom of polarization in the radial direction, a tunable focal shift and elongation of focus are achieved simply by tailoring the polarization index and the topological charge of vortex phase, without the need of additional modulations of amplitude or diffractive optical elements. These findings may be of help in the applications like optical micro-manipulation, laser processing, and imaging.

Focus shaping and optical manipulation using highly focused second-order full Poincaré beam.

Generation of vectorial optical fields with arbitrary polarization distribution is of great interest in plenty of applications. In this work, we propose and experimentally demonstrate the generation of a second-order full Poincaré (FP) beam and its application in two-dimensional (2D) flattop beam shaping with spatially variant polarization under a high numerical aperture focusing condition. In addition, the force mechanism of the focal field with 2D flattop beam profile is numerically studied, demonstrating the feasibility to trap a dielectric Rayleigh particle in three-dimensional space. The results show that the additional degree of freedom provided by the FP beam allows one to control the spatial structure of polarization, to engineer the focusing field, and to tailor the optical force exerted on a dielectric Rayleigh particle. The findings reported in the work may find useful applications in laser micromachining, optical trapping, and optical assembly.

Wavefront shaping with disorder-engineered metasurfaces.

Recently, wavefront shaping with disordered media has demonstrated optical manipulation capabilities beyond those of conventional optics, including extended volume, aberration-free focusing and subwavelength focusing. However, translating these capabilities to useful applications has remained challenging as the input-output characteristics of the disordered media (P variables) need to be exhaustively determined via O(P) measurements. Here, we propose a paradigm shift where the disorder is specifically designed so its exact input-output characteristics are known a priori and can be used with only a few alignment steps. We implement this concept with a disorder-engineered metasurface, which exhibits additional unique features for wavefront shaping such as a large optical memory effect range in combination with a wide angular scattering range, excellent stability, and a tailorable angular scattering profile. Using this designed metasurface with wavefront shaping, we demonstrate high numerical aperture (NA > 0.5) focusing and fluorescence imaging with an estimated ~2.2×108 addressable points in an ~8 mm field of view.

Microtube fabrication based on femtosecond Bessel beam and its flexible driving with external magnetic field

Microtube, with simple and uniform geometry, is one of the basic structures in micro/nano field. We present a method for the fabrication of magnetic drivable microtubes, by direct femtosecond laser writing combined with magnetron sputtering with metal layer. Femtosecond laser beam is modulated into Bessel beam with spatial light modulator (SLM), and then Bessel beam is focused with a high numerical aperture objective. Microtubes are fabricated by scanning focused femtosecond Bessel beam in a sample anchored on a three dimension stage. Followed by magnetron sputtering a nickel layer, the microtubes exhibit supermagnetic property and can be flexibly driven by external magnetic field. In this study, the propagation and high numerical aperture focusing properties of femtosecond Bessel beams are investigated. Microtubes, with well controlled diameter, length and distribution are efficiently fabricated. Rapid steering of nickel coated microtubes along specific route in fluid environment with external magnetic field has been realized. The steering of microtubes can be realized in various fluid environments. This method is flexible, controllable and efficient and the fabricated drivable microtubes have a promising applications in noninvasive surgery, targeted drug delivery, bioimaging or biosensing and microenvironment cleaning.

Super-Resolution Far-Field Infrared Imaging by Photothermal Heterodyne Imaging.

Infrared (IR) imaging provides chemical-specific information without the need for exogenous labels. Conventional far-field IR imaging techniques are diffraction limited, which means an effective spatial resolution of >5 μm with currently available optics. In this article, we present a novel far-field IR imaging technique based on photothermal heterodyne imaging (IR-PHI). In our version of IR-PHI, an IR pump laser excites the sample, causing a small temperature rise that is detected by a counterpropagating visible probe beam. Images and spectra of several different types of soft matter systems (polystyrene beads, thin polymer films, and single Escherichia coli bacterial cells) are presented to demonstrate the sensitivity and versatility of the technique. Importantly, the spatial resolution in the IR-PHI measurements is determined by the visible probe beam: a spatial resolution of 0.3 μm was achieved with a 0.53 μm probe wavelength and a high numerical aperture focusing objective. This is the highest spatial resolution reported to date for far-field IR imaging. Analysis of the experiments shows that for polymer beads in a dry environment, the magnitude of the IR-PHI signal is determined by the scattering cross section of the nano-object at the probe wavelength. This is in contrast to conventional PHI experiments in a heat-transfer medium, where the signal scales as the absorption cross section. This different scaling can be understood through the optical theorem. Our analysis also shows that both thermal expansion and changes in the refractive index of the material are important and that these two effects, in general, counteract each other.

Generation of an ultralong pure longitudinal magnetization needle with high axial homogeneity using an azimuthally polarized beam modulated by pure multi-zone plate phase filter

Based on the vector diffraction theory and the inverse Faraday effect in the magneto-optic film, light-induced magnetization distributions, for a high numerical aperture focusing configuration with an azimuthally polarized beam modulated by an optimized pure multi-zone plate phase filter, are investigated. By making use of the compeletely destructive interference of its inter circle with the π phase shift between adjacent sub-annuli, and the capability to extend the constructive interference in the propagating direction through its narrow outer annulus modulated by three misplaced helical phases, an ultralong () magnetization needle with both transverse super-resolution () and uniform axial field strength is achieved in the focal region. The perfect magnetization needle and the accessible method give a guide for ultrahigh density magnetic storage, fabricating magnetic lattices for spin wave operation, as well as atomic trapping.

Tight focusing of radially polarized beams modulated by a fractal conical lens

A novel high numerical aperture (NA) focusing system with a fractal conical lens (FCL) is proposed, and tight focusing of radially polarized beams through the proposed optical system is investigated theoretically and numerically. The influence of several relevant factors, including the FCL’s stage S, objective lens’ NA, and truncation parameter β0, on the targeted beam’s focusing characteristics in the focal region is discussed in detail. It is found that, when a FCL with S≥0 is employed, position of the major focal point would shift from the geometric focal point, and the focused intensity distributions cannot maintain symmetrical about the focus any more, although they present different profiles for various truncation parameters β0. When S≥2, multiple focal points can be generated, i.e., a single major focus and a series of subsidiary foci surrounding it along the optical axis, which form a focal region. These unique focusing characteristics with a FCL are remarkably different from that of without a FCL. The fascinating findings here may be taken advantage of when using radially polarized beams in exploiting new-type optical tweezers and making use of a FCL.

Magnetization shaping generated by tight focusing of azimuthally polarized vortex multi-Gaussian beam.

Combining the vector diffraction theory with the inverse Faraday effect, we have theoretically studied magnetization shaping generated by tight focusing of an azimuthally polarized multi-Gaussian beam superimposed with a helical phase. By selecting optimized parameters of a multi-Gaussian beam and topological charge of a spiral phase plate, not only a super-long and sub-wavelength longitudinal magnetization needle with single/dual channels for a single-lens high numerical aperture focusing system, but also an extra-long and three-dimensional super-resolution longitudinal magnetization chain with single/dual channels for a 4π high numerical aperture focusing system is achieved in the focal region. Furthermore, by continuously changing the phase difference between two counter-propagating beams, these super-long longitudinal magnetization chains with three-dimensional super-resolution can dynamically move along the z-axis. It is expected that these results pave the path for fabricating magnetic lattices for spin wave operation, multiple atoms or magnetic particle trapping and transportation, confocal and magnetic resonance microscopy, as well as multilayer ultrahigh density magnetic storage.

Creating adjustable uniform optical cages through polarization shaping in a low NA optical system.

We propose a method to generate uniform optical cages with adjustable number and position along the optical axis in a low numerical aperture (NA) optical system. The uniform optical cages are the superposition of multiple dark and bright spots, which are of x- and y-polarized electric fields with the neglected axial component obtained, respectively, by focusing a quasi-x-polarized vortex beam with topological charge 1 and a quasi-y-polarized beam. By adjusting the number and position of the dark and bright spots with reversal radiation theory, valuable optical cages with uniformity up to 1, such as multiple optical cages, optical chain, and optical tube, can be realized. Moreover, the influences of the axial field to the quality of optical cages are also investigated. Numerical results show that an effective optical cage with uniformity up to 0.695 can be achieved even with an NA close to 0.75. The generated optical cages may find valuable application in optical trapping of samples with a large scale, which are difficult to be trapped under a high NA focusing condition.