Numerical Aperture Research Articles

3D Nano‐Printed Bistable Microlens Actuator for Reconfigurable Micro‐Optical Systems

AbstractThe integration of multiple functional microscopy methods into a single, miniaturized instrument, known as multimodal endomicroscopy, presents significant challenges due to the often conflicting optical requirements of each imaging modality. In this study, the use of 3D nano‐printing based on two‐photon polymerization for the monolithic manufacturing of complete optical MEMS devices is investigated as an enabling platform for multimodal endoscopy. This approach offers unparalleled miniaturization, design flexibility, and alignment precision of micro‐optics and actuators. In particular, the design, fabrication, and characterization of a monolithically 3D nano‐printed bistable microlens actuator are discussed. Bistability allows the microlens to switch between two stable positions, thereby changing the focus distance and numerical aperture. The actuator features two coils with opposing current directions, which create a magnetic field gradient around a polymer micro‐magnet. This configuration allows for robust switching between stable positions with an average axial distance of 168.3 ± 7.3 µm. Experiments conducted to ascertain the optical characterization of the actuator demonstrate its capacity to transition between different optical modes. The beam widths are measured to be in the range of 4.1 ± 0.2 µm in the high‐resolution mode and 11.3 ± 1.1 µm in the extended depth of focus mode.

Ultra-short and highly efficient metamaterial Fresnel lens-assisted taper.

This paper demonstrates the benefits of leveraging free-space optics concepts in the design of certain integrated photonic components, leading to a footprint reduction without compromising on performance. Specifically, we present ultra-short, highly efficient and fabrication-friendly mode-size converters based on metamaterial Fresnel lens-assisted tapers. This is achieved using a parameterized inverse-design approach, where the metamaterial phase shifters are realized using fabrication-friendly Manhattan geometries, by optimizing the width, length, and position of the phase shifters. This approach overcomes the limitations of the conventional method that uses local periodic approximation, which is not suitable for lenses with a short focal length and high numerical aperture. We also extend the free-space concept of compound lenses and demonstrate a doublet-based taper to further reduce the footprint. The devices are fabricated and experimentally characterized in terms of insertion loss and signal integrity at high data transmission rates, exhibiting high performance. For the singlet, it effectively achieves mode-size conversion from 15 μm to 0.5 μm within a 15 μm distance, leading to ×10 length reduction compared to a linear taper. The insertion loss is under 1 dB over the entire C-band. The doublet achieves the same mode-size reduction within a 10 μm distance, leading to ×15 length reduction compared to a linear taper. The insertion loss is near 1 dB over most of the C-band. In both cases, the signal integrity is maintained for up to 50 Gbit/s.

Interfacing high numerical aperture metalenses with thermally expanded core fibers via 3D nanoprinting for advanced meta-fiber operation.

This study introduces a novel meta-fiber design that combines single-mode fibers with thermally expanded cores and nano-printed high numerical aperture metalenses. These advanced meta-fibers feature enlarged mode field diameters, offering improved mechanical stability, reduced environmental sensitivity and simplified metalens design by minimizing wavefront curvature. The concept's validity is confirmed through high numerical aperture metalenses, nanoprinted onto thermally expanded core fibers, demonstrating diffraction-limited focusing up to a numerical aperture of 0.9 in air and water. This innovative approach has potential applications in optical trapping, life science imaging, environmental sensing, and fiber-chip coupling in integrated photonics.

Flexible solid immersion meniscus lens (SIMlens) approach for enhancing biological imaging of cleared samples.

Tissue-clearing techniques have revolutionized the field of biological imaging by rendering biological specimens transparent and enabling inside optical detection. Light-sheet fluorescence microscopy (LSFM) is a powerful tool for three-dimensional imaging of large biological samples. Combining tissue-clearing techniques with LSFM has advanced the efficient 3D visualization of these samples. A crucial challenge with LSFM is the requirement for the objective to operate within the clearing reagent, which can cause aberrations. To address this issue, we introduce a novel, to our knowledge, approach for the flexible design of the solid immersion refractive meniscus lens (SIMlens), facilitating the use of air objectives with cleared samples. Compared to the previous SIMlens, this method not only eliminates aberrations but also offers customized options for enhancing the numerical aperture and working distance of the objective lens, achieving at least a 10% improvement. We have demonstrated the feasibility of this new method using mouse brain samples.

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.

Off-axis reflective microscope objective with a centimeter scale field of view and micron resolution.

Microscope objectives with wide field-of-view (FOV) and high resolution are urgently needed for the frontier research in life sciences. However, traditional transmission microscope objectives typically have a narrow FOV and severe chromatic aberration. A new off-axis reflective microscope objective with a centimeter scale FOV and micron resolution is proposed in this paper. This objective, with its simple structure, can operate over a wide wavelength range. A design method for a wide FOV optical system is presented, which can eliminate the obstruction of the rays and control the intermediate image plane. Using this method, we design a novel off-axis four-mirror microscope objective with a FOV of 10 mm × 1.5 mm and a numerical aperture of 0.33.

Application of the Knife-Edge Technique on Transition Metal Dichalcogenide Monolayers for Resolution Assessment of Nonlinear Microscopy Modalities.

We report application of the knife-edge technique at the sharp edges of WS2 and MoS2 monolayer flakes for lateral and axial resolution assessment in all three modalities of nonlinear laser scanning microscopy: two-photon excited fluorescence (TPEF), second- and third-harmonic generation (SHG, THG) imaging. This technique provides a high signal-to-noise ratio, no photobleaching effect and shows good agreement with standard resolution measurement techniques. Furthermore, we assessed both the lateral resolution in TPEF imaging modality and the axial resolution in SHG and THG imaging modality directly via the full-width at half maximum parameter of the corresponding Gaussian distribution. We comprehensively analyzed the factors influencing the resolution, such as the numerical aperture, the excitation wavelength and the refractive index of the embedding medium for the different imaging modalities. Glycerin was identified as the optimal embedding medium for achieving resolutions closest to the theoretical limit. The proposed use of WS2 and MoS2 monolayer flakes emerged as promising tools for characterization of nonlinear imaging systems.

Rapid inverse design of metasurfaces with an asymmetric transfer function for all-optical image processing using a mode matching model.

Metasurfaces have recently emerged as an ultra-compact solution to perform all-optical image processing, including phase contrast imaging. Most metasurfaces used in imaging processing applications operate over a restricted numerical aperture. This limitation imposes constraints on the discernible features that can be effectively visualized and consequently leads to the appearance of undesirable artifacts. Engineering a metasurface that exhibits an asymmetric linear optical transfer function over a relatively large numerical aperture, while maintaining a strong contrast, has proven to be a challenge. In this study, we present a novel approach to designing relatively high numerical aperture and contrast nonlocal metasurfaces (up to a numerical aperture of around 0.5 and an intensity contrast of approximately 50%) with unit cells consisting of several plasmonic nanorods through the use of a rapid, quasi-analytic mode-matching technique, coupled with an optimization algorithm. The combination of these methods facilitates the rapid conceptualization of nonintuitive arrangements of metallic nanoparticles, specifically tailored to perform phase contrast imaging. These designs hold substantial promise in the development of ultra-compact imaging systems.

Flat lens–based subwavelength focusing and scanning enabled by Fourier translation

Abstract We demonstrate a technique for flexibly controlling subwavelength focusing and scanning, by using the Fourier translation property of a topology-preserved flat lens. The Fourier transform property of the flat lens enables converting an initial phase shift of light into a spatial displacement of its focus. The flat lens used in the technique exhibits a numerical aperture of 0.7, leading to focusing the incident light to a subwavelength scale. Based on the technique, we realize flexible control of the focal positions with arbitrary incident light, including higher-order structured light. Particularly, the presented platform can generate multifocal spots carrying optical angular momentum, with each focal spot independently controlled by the incident phase shift. This technique results in a scanning area of 10 μm × 10 μm, allowing to realize optical scanning imaging with spatial resolution up to 700 nm. This idea is able to achieve even smaller spatial resolution when using higher-numerical-aperture flat lens and can be extended to integrated scenarios with smaller dimension. The presented technique benefits potential applications such as in scanning imaging, optical manipulation, and laser lithography.

Simultaneous Multifocal Plane Fourier Ptychographic Microscopy Utilizing a Standard RGB Camera.

Fourier ptychographic microscopy (FPM) is a computational imaging technology that can acquire high-resolution large-area images for applications ranging from biology to microelectronics. In this study, we utilize multifocal plane imaging to enhance the existing FPM technology. Using an RGB light emitting diode (LED) array to illuminate the sample, raw images are captured using a color camera. Then, exploiting the basic optical principle of wavelength-dependent focal length variation, three focal plane images are extracted from the raw image through simple R, G, and B channel separation. Herein, a single aspherical lens with a numerical aperture (NA) of 0.15 was used as the objective lens, and the illumination NA used for FPM image reconstruction was 0.08. Therefore, simultaneous multifocal plane FPM with a synthetic NA of 0.23 was achieved. The multifocal imaging performance of the enhanced FPM system was then evaluated by inspecting a transparent organic light-emitting diode (OLED) sample. The FPM system was able to simultaneously inspect the individual OLED pixels as well as the surface of the encapsulating glass substrate by separating R, G, and B channel images from the raw image, which was taken in one shot.

Optical torque calculations and measurements for DNA torsional studies

The angular optical trap (AOT) is a powerful instrument for measuring the torsional and rotational properties of a biological molecule. Thus far, AOT studies of DNA torsional mechanics have been carried out using a high numerical aperture oil-immersion objective, which permits strong trapping but inevitably introduces spherical aberrations due to the glass-aqueous interface. However, the impact of these aberrations on torque measurements is not fully understood experimentally, partly due to a lack of theoretical guidance. Here, we present a numerical platform based on the finite element method to calculate forces and torques on a trapped quartz cylinder. We have also developed a new experimental method to accurately determine the shift in the trapping position due to the spherical aberrations by using a DNA molecule as a distance ruler. We found that the calculated and measured focal shift ratios are in good agreement. We further determined how the angular trap stiffness depends on the trap height and the cylinder displacement from the trap center and found full agreement between predictions and measurements. As a further verification of the methodology, we showed that DNA torsional properties, which are intrinsic to DNA, could be determined robustly under different trap heights and cylinder displacements. Thus, this work has laid both a theoretical and experimental framework that can be readily extended to investigate the trapping forces and torques exerted on particles with arbitrary shapes and optical properties.

Manufacturability-based optical design optimization for advanced Kirkpatrick-Baez X-ray focusing mirrors.

The advanced Kirkpatrick-Baez (AKB) mirror setup is an effective and compelling solution to provide stable X-ray nano-focusing for synchrotron radiation or free-electron laser beamlines. We propose an AKB mirror design optimization approach to mitigate the difficulties associated with mirror fabrication by minimizing the total slope ranges of the four curved mirrors while achieving the expected focusing performance. In the optimization, we have considered geometry constraints to ensure the beam acceptance with the required clear aperture, the diffraction-limited focal size with the adequate numerical aperture, and the desired mirror gaps for adjustment and the necessary working distance for the sample stage. Additionally, practical constraints linked to mirror metrology and fabrication, such as mirror length limits and curvature uncertainty in measurement, are taken into account. Furthermore, progressive objective optimization eliminates the need for any initial guess, fully automating the AKB optimization process. This approach facilitates the development of an elegant Wolter-I or Wolter-III type AKB design solution that satisfies these multiple constraints. In cases where constraints cannot be simultaneously satisfied, the optimization results provide valuable insights into areas where trade-offs need to be considered. Simulations with ray tracing and wavefront propagation validate the optimized AKB design showing high tolerance to the beam incident angle.

Femtosecond laser-induced dewetting of sub-10-nm nanostructures on silicon in ambient air

To realize nanoscale manufacturing based on laser direct writing technology, objective lenses with high numerical apertures immersed in water or oil are necessary. The use of liquid medium restricts its application in semiconductors. Achieving nanoscale features on silicon by laser direct writing in a low refractive index medium has been a challenge. In this work, a microsphere assisted femtosecond laser far-field induced dewetting approach is proposed. A reduction in the full-width at half-maximum of the focused light spot is realized by modulating tightly focused light through microspheres and achieving a minimum feature size of 9 nm on silicon in ambient air with energy smaller than the ablation threshold. Theoretical analysis and numerical simulation of laser processing are performed based on a two-temperature model. Furthermore, we explored the potential of femtosecond laser-induced dewetting in nanolithography and demonstrated its ability to achieve an arbitrary structure on silicon. Our work enables laser-based far-field sub-10-nm feature etching on a large-scale, providing a novel avenue for nanoscale silicon manufacturing.

Numerical investigation of various laser–waterjet coupling methods on spot power density distribution

This paper presents a numerical simulation study on the coupling of lasers and waterjets, focusing on the distribution of the spot power density. The analysis utilized a laser wavelength of 532 nm, chosen for its minimal energy attenuation in water. The key conditions for successful coupling were identified, including the necessity for the spot diameter of the laser beam to be smaller than the nozzle diameter of the waterjet fiber, the numerical aperture of the laser beam to be lower than that of the waterjet fiber, and the divergence angle of the laser to be smaller than the critical angle for total internal reflection. Using the ZEMAX simulation software, various coupling cases were explored, revealing that the radial displacement of the waterjet fiber relative to the laser axis has the most significant impact on the output power density, followed by angular deflection, whereas the axial displacement has the minimal effect. This study also investigates the combined effects of different influencing factors on the peak distribution of the output power density, uncovering distinct characteristics resulting from these deviations. Overall, the research findings provide theoretical insights for achieving effective coupling between fine waterjets and lasers as well as for the design of water-guided laser coupling devices.

Full-colour-sorting metalens based on guided mode resonance

Full-colour-sorting metalens using few nanostructured layers have recently generated considerable interest as high-sensitivity colour image sensors because of their reliability and high resolution. Based on the guided mode resonance principle and propagation phase modulation, a full-colour-sorting metalens is designed, which can theoretically obtain any wavelength of light from the incident white light and realize arbitrary wavelength focusing with the same focal length in the visible range. Without the loss of generality, we propose a prototype of such metalens used for sorting blue, green and red light from the visible spectrum commonly used in practical applications. The maximum focussing efficiency is over 50% with a relatively high numerical aperture of 0.7. The proposed full-colour-sorting metalens can be used in many applications, such as colour mixing, colour holography, colour filtering, wavelength division multiplexing and so on.

Ultra-high NA graphene oxide flat lens on a fiber facet with near diffraction-limited focusing

The realization of a high numerical aperture (NA) fiber lens is critical for achieving high imaging resolution in endoscopes, enabling subwavelength operation in optical tweezers and high efficiency coupling between optical fibers and photonic chips. However, it remains challenging with conventional design and fabrication. Here we propose an ultrathin (400 nm) graphene oxide (GO) film lens fabricated in situ on a standard single-mode fiber facet using the femtosecond laser direct writing technique. An extremely high NA of 0.89 is achieved with a near diffraction-limited focal spot (FWHM=0.68λ), which is verified theoretically and experimentally. The diameter of the fabricated fiber GO lens is as small as 12 μm with no beam expansion structure. The proposed fiber GO lens is promising for applications such as super-resolution imaging, compact optical tweezers, medical endoscopes, and on-chip integration.

High‐Speed High‐Resolution Transport of Intensity Diffraction Tomography with Bi‐Plane Parallel Detection

AbstractA novel high‐speed, high‐resolution 3D microscopy technique named BP‐TIDT is presented that quantifies the refractive index (RI) distribution of label‐free, transparent samples. This method combines a bi‐plane detection scheme (BP) with the transport of intensity diffraction tomography (TIDT), effectively circumventing the need for matched illumination conditions under high numerical aperture (NA) objectives, which enables 15 fps volume rates and 326 nm lateral resolution. The effectiveness and accuracy of the proposed approach are validated through high‐resolution imaging of polystyrene microspheres and HepG2 cells. Moreover, the wide‐ranging applicability of BP‐TIDT is demonstrated by investigating subcellular organelle motion, including mitochondria and lipid droplets, as well as the macroscopic apoptosis process in living COS‐7 cells. To the best of current knowledge, this is the first time that high spatial‐temporal resolution dynamic ODT results are obtained in a non‐interferometric and motion‐free manner, highlighting the potential of BP‐TIDT in advancing research on dynamic cellular processes.

Optical maneuvering of photofunctioning hybrid perovskite for future photonics potential application

Hybrid perovskites, known for their multidimensional opto-electronic properties and capability to generate multi-color emission bands, are highly sought after for light-emitting devices due to their liquid crystalline behavior in the solution phase. This behavior enables easier ion mobility, facilitating ion exchange processes. Exploiting the liquid crystalline properties of perovskites, we applied a halogen exchange reaction in the solution phase using tightly focused laser trapping techniques. Our study demonstrates the successful development of high-luminescent bulk single crystals of methylammonium lead halide alloy MAPb(Br/I)3, which exhibit multi-color emission capabilities, underscoring their potential for optoelectronic applications. We fabricated bulk single crystals of MAPbBr3, measuring 20 × 20 μm2, displaying bright green luminescence. Using a tightly focused trapping laser beam (1064 nm, 1 Watt) with a high numerical aperture (0.9, 60X objective lens), we irradiated a specific area of the green luminescent MAPbBr3 single crystal immersed in a 200 μM methylammonium iodide (MAI) solution for 30 min at room temperature. This treatment induced a red emission band at 605 nm at the irradiated location, while surrounding areas retained the original green luminescence. In a parallel experiment, increasing the iodide concentration to 300 μM caused the emission color of a similar-sized crystal to change uniformly from green to red. Photoluminescence spectroscopy and EDS confirmed the halide exchange from MAPbBr3 to MAPbBr2.3I0.7. This method, influenced by laser parameters such as power, wavelength, and aperture, provides new opportunities for multi-color emission patterning and offers significant insights for advancing optoelectronics.

Raman spectroscopic study of concentration dynamics in glycine crystallization achieved by optical trapping

This study investigates concentration dynamics during optical trapping-induced crystallization (OTIC) of glycine using Raman spectroscopy. In-situ Raman spectroscopy demonstrated that tightly focused laser beams induced faster concentration increase and crystal nucleation at higher supersaturation compared to loosely focused beams. Also, by varying numerical aperture (NA) values of the objective lens used, it was revealed that higher NA led to achieving a shorter induction time and higher crystallization probability. Remarkably, optical trapping using objective lenses with higher NA generated stable liquid droplets, inhibiting crystallization until considerably higher supersaturation was realized. These findings elucidate the complex interplay between optical forces, supersaturation, and crystallization dynamics on the mechanism of OTIC and offer a new method for precise control of laser-induced crystallization. We believe that the insights gained by this study pave the way for innovative developments in crystal chemistry and promising advancements in photochemistry.

A Hybrid Lens to Realize Electrical Real‐Time Super‐Resolution Imaging

AbstractReal‐time dynamic super‐resolution focusing technology is crucial for various imaging applications. However, the diffraction limit significantly impedes the achievement of real‐time dynamic super‐resolution imaging. Prior studies within this domain, such as super‐resolution fluorescence imaging and structured illumination microscopy, heavily rely on fluorescent labels and intricate algorithms. This article proposes a novel approach to achieving real‐time dynamic super‐resolution imaging at microwave frequency by integrating the Mikaelian lens derived from conformal transformation optics with the space‐time‐coding metasurface antenna. Real‐time dynamic super‐resolution focusing with a resolution ranging from 0.3λ to 0.4λ is demonstrated at the periphery of the Mikaelian lens with a numerical aperture (NA) of 0.54. The proposed hybrid lens exhibits the capacity to discern features separated by about one‐third of a wavelength with high precision. The work offers a universal solution for achieving dynamic real‐time super‐resolution imaging electrically, which can be extended to terahertz waves, visible light, and other wave fields, such as acoustic and flexural waves.