High Numerical Aperture Focusing Research Articles

Controlling the contribution of the electric field components to the focus of a high-aperture lens using binary phase structures

We show that the contribution of the electric field components into the focal region can be controlled using binary phase structures. We discuss differently polarized incident waves, for each case suggesting easily implemented binary phase distributions that ensure a maximum contribution of a definite electric field component on the optical axis. A decrease in the size of the central focal spot produced by a high numerical aperture (NA) focusing system comes as the result of the spatial redistribution of the contribution of different electric field components into the focal region. Using a polarization conversion matrix of a high NA lens and the numerical simulation of the focusing system in Debye's approximation, we demonstrate benefits of using asymmetric to polar angle ϕ binary phase distributions (such as arg[cos ϕ] or arg[sin 2ϕ]) for generating a subwavelength focal spot in separate electric field components. Additional binary structure variations with respect to the azimuthal angle also make possible controlling the longitudinal distribution of light. In particular, the contribution of the transverse components in the focal plane can be reduced by the use of a simple axicon-like structure that serves to enhance the NA of the lens central part, redirecting the energy from focal plane. As compared with the superimposition of a narrow annular aperture, this approach is more energy efficient, and as compared with the Toraldo filters, it is easier to control when applied to three-dimensional focal shaping.

Transverse superresolution with extended depth of focus using binary phase filters for optical storage system

This paper reports the study of superresolution and extension of depth of focus (DOF) of three-zone binary phase filters (BPFs) under high numerical aperture (NA) focusing. Two three-zone BPFs (BPF1 and BPF2) are specially designed to achieve transverse superresolution and extension of DOF simultaneously for the optical disc system with an objective lens of NA = 0.65. Numerical simulations based on the vectorial diffraction theory indicate that the transverse focal spot size of this system can be as small as that of NA = 0.85 and its DOF is as large as that of NA = 0.6 with acceptable Strehl ratios (> 0.4 for BPF1 and > 0.35 for BPF2) and low side-lobe intensity ratios (< 10%) by using these BPFs. It suggests that the storage capacity of this optical storage system may be improved to the same as that of a system with an objective lens of NA = 0.85. Moreover, the strict requirement of the focusing servo system caused by decreasing wavelength or employing higher NA objective lens can be mitigated. Therefore, these BPFs presented in this paper should be highly interesting for applications of high density optical data storage.

The quadratic phase factor of tightly focused wavefronts

The phase structure is investigated at the focal plane of an aplanatic, high numerical aperture focusing optical system. The tightly focused field is numerically evaluated using combination of the Richards–Wolf approach and the Stratton–Chu diffraction integral. An investigation is performed for both 2D and 3D geometries for a number of different illumination structures, having piecewise quasi-constant phase at the entrance pupil and different polarization states. For the investigated illumination structures, the quadratic phase term of the focused field was found to depend on the structure of the incident illumination contrary to the paraxial case where it depends solely on the optical system parameters.

Analysis of Phase Distribution of Focused Light in High Numerical Aperture Systems

High numerical aperture focusing is becoming increasingly important for nanotechnology related applications. Rigorous, vector evaluation of the focused field, in such cases, is usually performed using the Richards-Wolf method which is based on the Debye approach. The resulting field is known to have a piecewise quasi planar phase. A corresponding result, produced by a Fresnel-Kirchhoff integral for aplanatic optical systems of medium and low numerical apertures, leads to the well known physical fact that a quadratic phase exists when the entrance pupil is not located at the front focal plane. Yet, the amplitudes produced in both ways are in a good agreement. In this work we investigated the difference, presented above, in a 2D system with the help of the Stratton-Chu diffraction integral. The amplitude obtained by the Stratton-Chu integral was quite similar to the classic results while the phase exhibited a quadratic behavior, with the quadratic coefficient depending on the numerical aperture of the optical system. For lower numerical apertures it approached the result obtained by the Fresnel-Kirchhoff integral while for higher numerical apertures it was approaching the Richards-Wolf result. A mathematical expression for the quadratic coefficient was derived and verified for various values of numerical aperture.

回転楕円体プラズマミラーを用いた超高強度レーザーの高開口数集光

回転楕円体プラズマミラーを用いた超高強度レーザーの高開口数集光

Focusing of radially polarized beam with radial cosine phase wavefront

Radially polarized beam has gained much interest recently due to its properties and applications. In this article, the focusing properties of radially polarized beam with radial cosine phase wavefront are investigated theoretically. Results show that when the radially polarized beam with radial cosine wavefront phase is focused, the focal pattern differs considerably with frequency parameter in the cosine function term. In the high numerical aperture focusing system, focal shift occurs, and novel focal patterns evolve considerably, for instance, from only one peak to two or multiple overlapping peaks. In addition, peak intensity ratio of radially polarized component to longitudinal polarized component in the focal region fluctuates smoothly for low-frequency parameter, then drops sharply, and comes back remarkably with increasing frequency parameter. Simultaneously focal shift increases slowly, and then decreases, suddenly, focal shift sign changes that results from focal switch phenomenon, and then fluctuates.

Modeling Nonlinear Plasma Formation for Femtosecond Processing ofTransparent Materials and Biological Cells at High NA Focusing

Ultrashort laser pulses recently found extensive application in micro- and nanostructuring, in refractive surgery of the eye, and in biophotonics. Due to the high laser intensity required to induce optical breakdown, nonlinear plasma formation is generally accompanied by a number of undesired nonlinear side-effects such as self-focusing, filamentation and plasma-defocusing, seriously limiting achievable precision and reproducibility. To reduce pulse energy, enhance precision, and limit nonlinear side effects, applications of ultrashort pulses have recently evolved towards tight focusing using high numerical aperture microscope objectives. However, from the theoretical and numerical point of view, generation of optical breakdown at high numerical aperture focusing was barely studied. To simulate the interaction of ultrashort laser pulses with transparent materials at high NA focusing, a comprehensive numerical model was introduced by the authors in [1], taking into account nonlinear propagation, plasma generation as well as the pulse's interaction with the generated plasma. The multiple rate equation (MRE) model [2] is used to simultaneously calculate the generation of free electrons. Nonparaxial and vectorial diffraction theory provides initial conditions. The theoretical model derived in [1] is applied to numerically study the generation of optical breakdown plasmas, concentrating on parameters usually found in experimental applications of cell surgery. Water is used as a model substance for biological soft tissue and cellular constituents. For focusing conditions of low to moderate numerical aperture (NA < 0.9) generation of optical breakdown is shown to be strongly influenced by plasma defocusing, resulting in spatially distorted breakdown plasmas of expanded size. For focusing conditions of high numerical aperture (NA ≥ 0.9) on the other hand generation of optical breakdown is found to be almost unaffected by distortive side-effects, perfectly suited for material manipulation of highest precision.

Focusing of high polarization order axially-symmetric polarized beams

We study the high numerical aperture focusing properties and typical applications of axially-symmetric polarized beams (ASPBs) with high polarization orders. We calculate the field distribution near focus of an aplanatic system for incident ASPBs with different polarization orders and initial azimuthal angles, and based on the simulation results, we find some unique focusing properties of the beams, such as ever on-axis energy null, strong longitudinal field, and flowerlike intensity distribution at focus. In addition, we can manipulate the three-dimensional (3D) focused field distribution flexibly by use of diffractive optical elements (DOEs), which will give rise to some interesting applications, and we also discuss possible applications and present an example of a 3D optical chain at last.

Polarization distortion effects in polarimetric two-photon microscopy

We present a global analysis of experimental factors affecting polarization responses in two-photon inverted microscopy. The role of reflection optics and high numerical aperture focusing is investigated in two-photon fluorescence, which can be extended to other nonlinear processes. We show that both effects strongly distort polarization responses and can lead to misleading extraction of molecular order information from polarimetric measurements. We describe a model accounting for these effects and develop a calibration technique for the determination of polarization parameters in the sample plane using two-photon fluorescence polarimetry in liquids.

Single-pulse ultrafast-laser machining of high aspect nano-holes at the surface of SiO_2

Use of high numerical aperture focusing with negative longitudinal spherical aberration is shown to enable deep (> microm), high aspect ratio, nano-scale-width holes to be machined into the surface of a fused-silica (SiO(2)) substrate with single pulses from a 200 fs, 4 microJ Ti-Sapphire laser source. The depths of the nano-holes are characterized by use of a non-destructive acetate replication technique and are confirmed by imaging of sectioned samples with a dual focused ion beam/scanning electron microscope.

Laser micro-machining using near-field optics

Solid immersion lenses (SIL) facilitate high numerical aperture (NA) and consequent sub-wavelength diffraction limited focusing in near-field optics based systems. Such systems are in commercial and research use for various applications including near-field scanning optical microscopy, ultra-high-density magneto-optic data storage and near-field nanolithography. Here, we present a novel manufacturing method using SIL-based near-field optics for laser-induced patterning on silicon wafers. The near-field effect of SILs was investigated by using hemispherical lenses made of three different materials (BK7, Sapphire, LaSFN9) to superfocus an incident Q-switched, 532 nm Nd:YAG laser beam transmitted through a focusing objective. This optical arrangement achieved a laser-processed feature resolution near the diffraction limit in air. Results of experiments that were conducted at various processing conditions to investigate the effects of varying incident laser power (with peak pulse power less than 1 W), pulse width, number of pulses and size of SIL on processed feature size and resolution are presented. Experimental results are compared with numerical simulations using the simplified model.

Eigenfunction expansion of the electric fields in the focal region of a high numerical aperture focusing system

The Debye-Wolf electromagnetic diffraction integral is now routinely used to describe focusing by high numerical (NA) lenses. We obtain an eigenfunction expansion of the electric vector field in the focal region in terms of Bessel and generalized prolate spheroidal functions. Our representation has many optimal and desirable properties which offer considerable simplification to the evaluation and analysis of the Debye- Wolf integral. It is potentially also useful in implementing two-dimensional apodization techniques to synthesize electromagnetic field distributions in the focal region of a high NA lenses. Our work is applicable to many areas, such as optical microscopy, optical data storage and lithography.

Inverse scattering for high-resolution interferometric microscopy

We extend the applicability of inverse scattering for optical coherence tomography (OCT) to the case of high numerical aperture focusing optics. We include the effects of tight focusing so that the approach is applicable to any interferometric microscopy method. The applicability to modalities, such as OCT and optical coherence microscopy, enables computed reconstruction of three-dimensional volumes from en face temporal ranging data. Simulations show that the computed structure outside of the focal plane exhibits spatially invariant resolution on par with the resolution achieved at the focal plane.

Tight parabolic dark spot with high numerical aperture focusing with a circular π phase plate

The properties of tight dark focal spot created using a simple circular π phase plate are presented. For focusing elements with low numerical aperture, the focal plane intensity has r4 dependence, while for focusing elements with high numerical aperture, vectorial diffraction effects become important, and the focal plane intensity surprisingly approaches r2 dependence, indicating a much tighter dark spot.

Modelling local defects on the surface of high performance objective lenses

Performances of high quality imaging systems are often affected by surface or glass defects, like scratches, bubbles and other localized disturbances. The goal of the present investigation is the modelling of scratches on the surfaces of lenses and analysing the resulting changes in the diffraction spot quality. High numerical aperture focusing objectives used in optical storage are especially sensitive to this type of defect, since the size of the diffraction spot and the power–density distribution determines the quality of both the written pits and received signal. We used three different methods—based on the simple geometrical optical approximation, ideal diffraction model and point spread function based diffraction—to model local defects and compared the findings from these methods to the measurements. The model includes the DVD objective lens and the disc. Local defects are modelled as special apertures on the surface of the objective lens. From these computations we calculate the intensity distribution in the focal spot and the encircled energy in the Airy disc. A measurement set-up was built, which is capable of measuring the encircled energy in the Airy disc. Comparison of the measurement results to the calculations helps in determining the tolerances of DVD objective lenses to local surface defects as a function of the size of the defects. The practical application of the model will allow us to redefine the quality criteria for the DVD lenses used.

The focus of light—linear polarization breaks the rotational symmetry of the focal spot

We experimentally demonstrate for the first time that a linearly polarized beam is focused to an asymmetric spot when using a high-numerical aperture focusing system. This asymmetry was predicted by Richards and Wolf in 1959 and can only be measured when a polarization-insensitive sensor is placed in the focal region. We used a specially modified photodiode in a knife-edge-type set-up to obtain highly resolved images of the total electric energy density distribution at the focus. The results are in good agreement with the predictions of a vectorial focusing theory.

Cylindrical vector beam focusing through a dielectric interface

Cylindrical vector beams have been proposed and demonstrated for applications ranging from microscopy to high energy physics.In this paper,we analyze the three-dimensional field distributions of radial and azimuthal beams focused near a dielectric interface.We give particular attention to the classic problem of high numerical aperture focusing from an immersion lens to a glass-air interface and find that the use of radially and azimuthally polarized illumination for this type of imaging provides an impressive lateral confinement of the fields over a wide range of interface positions.

Using GaAsP photodiodes to characterize ultrashort pulses under high numerical aperture focusing in microscopy

SummaryWe demonstrate for the first time that the two‐photon response of GaAsP photodiodes can be used to conveniently characterize the spatial and temporal profiles of ultrashort pulses at the focus of a high numerical aperture system.