High Numerical Aperture Systems Research Articles

Customizing subwavelength stochastic light fields via structured spatial coherence in a high-NA resonator

Interaction of light in the high-numerical aperture (high-NA) systems is crucial for theoretical advances and applications such as superresolution imaging and optical nanofabrication. High coherence is demanded at this scale for intensity and spin profile sculpturing, since the underlying physics being wave interference. Here we report that, even for low-coherence light, 3D light features in a nanometer range can be generated by employing structured coherence states of the light beam in a high-NA resonator system. The generated structures, e.g., 3D helix intensity and transverse spin texture, can survive in rather incoherent optical fields at nanoscale. We also found that, counterintuitively, despite the substantial decrease in spatial coherence of the light field, the longitudinal electric field component and transverse spin density are instead enhanced. The applications of the observed twisted spectral density and spin structures may range from high-resolution imaging to metrology.

Optical skyrmion and its "zipper-like" topological behavior in an energy flux field.

The optical skyrmion and its topological behavior are analyzed in an energy flux field constructed by an X-type vortex in a high numerical aperture system. The conditions for the formation of a skyrmion structure in this field are discussed, showing that the vortex pattern of the transverse energy flow and the inverse energy flow are crucial for the skyrmions and also are controlled by the phase gradient of the X-type vortex. Notably, the "zipper-like" topological reaction, which is the first, to our knowledge, found in ferromagnetic materials, is observed, and the physical mechanism is also explained by the relation of orbital angular momentum density and Poynting vectors. The results will reach the topological theory and may have applications in optical traps and data storage.

Frequency selective illumination for high aperture coherence scanning interferometry

Abstract Coherence scanning interferometry is a widely used optical topography measurement technique, which can achieve axial resolutions in the sub-nanometer regime. Nevertheless, in the lateral dimension it is inherently diffraction limited and multiple problems arise when approaching this limit. Especially for challenging surface topographies like steep slopes or small grating periods measurement artifacts start to cause massive deviations in the 3D reconstruction of the surface due to the increased influence of noise on increasingly weak signals. In this study we present an illumination approach for Linnik-type CSI, which highlights oblique incident angles of the illuminating light cone in high numerical aperture (0.95) systems. It is demonstrated, that this approach can significantly improve the signal-to-noise ratio for measurements at steep surface slopes and therefore increase the subsequent surface reconstruction.

Manipulation of Energy Flow with X-Type Vortex

In this study, a new method for manipulating energy flow in a 3D vector field is proposed. In this method, an azimuthally-polarized beam with a noncanonical vortex, the X-type vortex, is focused in a high-numerical aperture system. It is found that, instead of the invariance of the energy flow which is characteristic of the traditional vortex (i.e., canonical vortex), both the longitudinal and the transverse energy flows in virtue of the X-type vortex rotate around the beam center as the beam propagates, and this rotational behavior (including the maxima location and the rotational angle) can be adjusted by the anisotropic parameter and the order the X-type vortex. Through defining a complex transverse Poynting field and applying the equivalence principle, the transverse energy flow and its topological reactions are discussed in the focal plane. Our result shows that, by changing the anisotropic parameter of the X-type vortex, rich topological reactions will occur, resulting in various distribution patterns of the energy flow, such as multi vortex-type singularities around the beam center. Our research demonstrates newly-observed features of the X-type vortex and also provides a simple method to manipulate energy flows both along longitudinal and transverse directions, which will be useful in optical manipulations.

Inverse Design of Focused Vector Beams for Mode Excitation in Optical Nanoantennas

We propose a free-space, inverse design of nanostructure's effective mode-matching fields via a backward propagation of tightly focused vector beams to the pupil plane of an aplanatic system of high numerical aperture. First, we study the nanostructure's eigenmodes without considering any excitation fields and then extract the modal near fields in the focal plane. Each modal field is then taken as the desired focal field, the band-limited waves of which are backward propagated to the pupil plane via a reversal of the Richards--Wolf vector diffraction formula. The pupil fields can be designed to be genuinely paraxial by associating the longitudinal electric/magnetic field component with the radial one on the reference sphere. The inversely designed pupil field in turn is propagated forwardly into the focal region to generate the designed focal field, whose distribution over the nanostructure's surface is used to evaluate the overlap between the designed focal field and the modal fields, i.e., the modal expansion coefficients. Studies for a silicon nanodisk monomer, dimer, and tetramer demonstrate the ability of our inverse approach to design the necessary tightly focused vector field that can effectively and exclusively match a certain eigenmode of interest. Compared with the forward beam-shaping method, the inverse design approach tends to yield quantitatively more precise mode-matching field profiles. This work can have a significant impact on optical applications that rely on controllable and tunable mode excitation and light scattering.

Primary aberrations in tightly focused polarized anomalous vortex beams

Based on the Richards Wolf vector diffraction theory, the intensity profiles of the radially and azimuthally polarized anomalous vortex beams focused by a high numerical aperture (NA) lens in the presence of primary aberration are obtained. The effects of the primary aberration coefficient on the intensity distribution, longitudinal field and the quality of the aberrated focused field through calculating the Strehl ratio under various polarized input beams are analyzed. The results show that spherical aberration destroys the rotational symmetry of the focused intensity about the optical axis. Coma will shift the focal spot which gradually presents an obvious comet shape. Astigmatism will elongate the focal spot. Meanwhile, defocus technology on compensating aberrations is studied. The results have potential applications in the design and assembly of high NA systems or overcoming aberrations in the future.

Focal Surface Detection of High Numerical Aperture Objective Lens Based on Differential Astigmatic Method

Defocus detection technology is the key technology in the fields of laser direct writing, optical disc storage, and high-precision lithography, which directly affects the accuracy of line drawing. In this paper, using the principle of astigmatic method, combined with differential technology, a nano-level defocus detection method based on differential astigmatism for the high numerical aperture systems is proposed. Firstly, by establishing a mathematical model, the theoretical analysis and simulation of the defocus detection method based on differential astigmatism are carried out. In addition, the system parameters at the maximum sensitivity of the high numerical aperture defocus detection system is also solved. Secondly, the defocus detection experimental system based on astigmatic method was built for experimental demonstration. Finally, using the objective lens with a numerical aperture of 0.8, the focus error signal curve with a good linear relationship is obtained in this paper. The linear range is 6μm; the system sensitivity can reach 5 nm; the system detection accuracy is 30 nm, and the repeat positioning accuracy can reach 30 nm. The defocus detection method based on the high numerical aperture objective lens has the advantages of large detection range, high detection accuracy and compact system structure, which can be widely used in various new high-precision laser processing fields.

Photonic Wheels and Their Topological Reaction in a Strongly Focused Amplitude Tailored Beam

In this article, we propose a simple method to generate purely transverse spin density in a high numerical aperture system, and it is realized by focusing an amplitude tailored beam with a dipole-like shape. Through our analytical analysis, it is found that in this focused field the purely transverse spin density is not only confined in the focal plane, but also can exist in two mutually perpendicular meridional planes. Especially, the fields with purely transverse spin density are also examined from the view of topology. Two typical topological events which usually happen in traditional two dimensional transverse fields are observed in the meridional plane with purely transverse spin density, and it shows that the ‘photonic wheels’ follow the rule of topological index in their topological reactions. To the best of our knowledge, it is the first time to test the topological behavior of the field with purely transverse spin density. Our finding not only supplies a simple way to generate ‘photonic wheels’ in three planes of the field, but also adds new features to the field containing ‘photonic wheels’.

Strongly Focused Circularly Polarized Optical Vortices Regulated by a Fractal Conical Lens

In this paper, a recently-proposed pure-phase optical element, the fractal conical lens (FCL), is introduced for the regulation of strongly-focused circularly-polarized optical vortices in a high numerical aperture (NA) optical system. Strong focusing characteristics of circularly polarized optical vortices through a high NA system in cases with and without a FCL are investigated comparatively. Moreover, the conversion between spin angular momentum (SAM) and orbital angular momentum (OAM) of the focused optical vortex in the focal vicinity is also analyzed. Results revealed that a FCL of different stage S could significantly regulate the distributions of tight focusing intensity and angular momentum of the circularly polarized optical vortex. The interesting results obtained here may be advantageous when using a FCL to shape vortex beams or utilizing circularly polarized vortex beams to exploit new-type optical tweezers.

Tunable degree of polarization of an unpolarized, partially coherent beam with circular coherence in a high numerical aperture system.

The polarization properties of a strongly focused, unpolarized, partially coherent beam with circular coherence are studied in this Letter. It is found that the degree of polarization (DoP) in the focal plane can be adjusted, not only by the initial coherence and the semi-aperture angle, but also through an annular pupil due to the unusual coherence of the source. Our results show that for an unpolarized, partially coherent incident beam, the field in the focal plane can go from almost an unpolarized state to almost a fully polarized state along a radial distance, although the initial coherence length is very short. Through adjusting the width of the annular pupil, the DoP on average can be significantly reduced or enhanced. Especially for the very narrow annulus, the approximation expression of the DoP is derived, from which the accurate positions of the peak values of the DoP can be easily calculated. Our findings provide an alternative way to tailor the DoP in three-dimensional optical fields.

High focusing efficiency in subdiffraction focusing metalens

Abstract Vector beams with phase modulation in a high numerical aperture system are able to break through the diffraction limit. However, the implementation of such a device requires a combination of several discrete bulky optical elements, increasing its complexity and possibility of the optical loss. Dielectric metalens, an ultrathin and planar nanostructure, has a potential to replace bulky optical elements, but its optimization with full-wave simulations is time-consuming. In this paper, an accurate and efficient theoretical model of planar metalens is developed. Based on this model, a twofold optimization scheme is proposed for optimizing the phase profile of metalenses so as to achieve subdiffraction focusing with high focusing efficiency. Then, a metalens that enables to simultaneously generate radially polarized beam (RPB) and modulate its phase under the incidence of x-polarized light with the wavelength of 532 nm is designed. Full-wave simulations show that the designed metalens of NA = 0.95 can achieve subdiffraction focusing (FWHM = 0.429λ) with high transmission efficiency (77.6%) and focusing efficiency (17.2%). Additionally, superoscillation phenomenon is found, leading to a compromise between the subdiffraction spot and high efficiency. The proposed method may provide an accurate and efficient way to achieve sub-wavelength imaging with the expected performances, which shows a potential application in super-resolution imaging.

Focus optimization at relativistic intensity with high numerical aperture and adaptive optics

Improved focusing of laser beams using high numerical aperture systems is an efficient route to increasing intensities in the ultrafast regime to relativistic levels. We experimentally demonstrate a new method of optimizing the focus of a high-power laser, using second harmonic generation at full intensity in a low-pressure gas to provide a figure of merit for optimizing the shape of a deformable mirror via a genetic algorithm. Nonlinear and thermal aberrations are corrected, and aberrations introduced by filters are avoided. The method is applied to focus a millijoule, short pulse (30 fs), high repetition rate laser system to relativistic intensity in both near IR and mid IR regimes.

Extreme ultraviolet mask roughness effects in high numerical aperture lithography.

Given the reflective nature of extreme ultraviolet lithography and its extremely short operational wavelength, roughness of the optical surfaces is of significant concern. In particular, roughness in the mask multilayer leads to image plane speckle and ultimately patterned line-edge or line-width variability in the imaging process. Here we consider the implications of this effect for future high numerical aperture (NA) systems that are assumed to require anamorphic magnification projection optics. The results show significant anisotropic behavior at high NA as well as a substantial increase in relative patterned line variability in the shadowed direction when comparing 0.55NA to 0.33NA, despite the assumption of an anamorphic magnification system. The shadowed-direction patterned line variability is 2× larger than for unshadowed lines, and the majority of the increase in variability occurs in the low frequency regime.

Transverse Focal Shift in Vortex Beams

The transverse focal shift (TFS) is a phenomenon that the maximum of a focused field does not occur at the geometrical focus, but is moved a short distance transversely in the focal plane. In this paper, the TFS of vortex beams in a high numerical aperture system is investigated. Four typical types of incident vortex beams are selected and the intensity distributions and the vortices behaviors in the focal region are discussed analytically and numerically. It is found that there are three main parameters, the topological charge, the initial positions of the vortices, and the semiaperture angle influencing the TFS in different ways, and the TFS even can be observed when the vortices annihilate in the focal plane. Our results also show that the intensity maximum can move frνom the y-axis, x-axis to the geometrical focus, or move from +y-axis to -y-axis in different cases, which may have implications in optical trapping.

A versatile apparatus for two-dimensional atomtronic quantum simulation.

We report on the implementation of a novel optical setup for generating high-resolution customizable potentials to address ultracold bosonic atoms in two dimensions. Two key features are developed for this purpose. The customizable potential is produced with a direct image of a spatial light modulator, conducted with an in-vacuum imaging system of high numerical aperture. Custom potentials are drawn over an area of 600×400 μm with a resolution of 0.9 μm. The second development is a two-dimensional planar trap for atoms with an aspect ratio of 900 and spatial extent of Rayleigh range 1.6 × 1.6 mm, providing near-ballistic in-planar movement. We characterize the setup and present a brief catalog of experiments to highlight the versatility of the system.

Critical dimension variation caused by wrinkle in extreme ultra-violet pellicle for 3-nm node

Extreme ultraviolet (EUV) pellicles help in the protection of EUV masks from defects, contaminants, and particles during the exposure process. However, a single-stack EUV pellicle can be easily deformed during the exposure process; therefore, multi-stack pellicles have been proposed to minimize the deformation of an EUV pellicle. However, wrinkles can be formed in an EUV pellicle due to extremely thin thickness. In this study, we investigated the impact of these wrinkles on the transmission and critical dimension (CD) variation for the 5- and 3-nm nodes. The 5- and 3-nm nodes can be used by conventional and high numerical aperture (NA) systems, respectively. The variation in the transmission and the allowable local tilt angle of the wrinkle as a function of the wrinkle height and periodicity were calculated. A change in transmission of 2.2% resulted in a 0.2 nm variation in the CD for the anamorphic NA system (3-nm node), whereas a transmission variation of 1.6% caused a 0.2 nm CD variation in the isomorphic NA system (5-nm node).

Automated aberration correction of arbitrary laser modes in high numerical aperture systems.

Controlling the point-spread-function in three-dimensional laser lithography is crucial for fabricating structures with highest definition and resolution. In contrast to microscopy, aberrations have to be physically corrected prior to writing, to create well defined doughnut modes, bottlebeams or multi foci modes. We report on a modified Gerchberg-Saxton algorithm for spatial-light-modulator based automated aberration compensation to optimize arbitrary laser-modes in a high numerical aperture system. Using circularly polarized light for the measurement and first-guess initial conditions for amplitude and phase of the pupil function our scalar approach outperforms recent algorithms with vectorial corrections. Besides laser lithography also applications like optical tweezers and microscopy might benefit from the method presented.

Anisotropic shadow effects with various pattern directions in an anamorphic high numerical aperture system

A high numerical aperture (NA) system with an NA larger than 0.5 is required to make patterns of 1X nm and below, even though extreme ultraviolet lithography uses a 13.5-nm wavelength source. To avoid the reflective efficiency loss and to avoid an increase in the chief ray angle of incident light, use of an anamorphic high-NA system is suggested. The suggested anamorphic NA system has nonisotropic magnification, x-magnification of 4× and y-magnification of 8×, and the mask NA shape is an ellipse due to the nonisotropic magnification distribution. Anamorphic NA systems have a nonconventional shadow effect due to nonisotropic incident angle distribution and magnification. These nonisotropic characteristics lead to the reduction of asymmetric shadow distribution and a reduction of horizontal–vertical bias. As a result, anamorphic NA systems can achieve balanced patterning results regardless of pattern direction and incident direction.

Optical encryption in the axial domain using beams with arbitrary polarization

Recently, a cryptosystem based on the analysis of light in the focal area of a high numerical aperture system has been proposed. A key element in the design of this device is the selection of the polarization of the input beam. In this paper we analyze how polarization influences the performance of the encoded message. In order to avoid attacks and enhance security, the system is assumed to work in photon-counting illumination conditions.

Signal modeling in low coherence interference microscopy on example of rectangular grating.

Besides the illumination wavelength also the numerical aperture (NA) of a microscope objective affects the fringe spacing in interference microscopy. Therefore, at high NA values an effective wavelength should be obtained by calibration. At step height structures both, the effective wavelength and the batwing effect strongly depend on the height-to-wavelength-ratio (HWR). Therefore, changes of the effective wavelength considering temporal and spatial coherence enable us to estimate the batwing effect in measurement results. For high NA systems and broadband illumination two different theoretical approaches for signal modeling are introduced to study the influence of the center wavelength, the temporal, and the spatial coherence of the illuminating light on measurement results of a rectangular grating. In both models diffraction is considered. While the first simulation model (Kirchhoff) is mostly analytical the second one (Richards-Wolf) is primarily numerical. Simulation results of both models show a good agreement with experimental measurement results.