Diffraction Limit Research Articles

Structured light analogy of quantum squeezed states

Quantum optics has advanced our understanding of the nature of light and enabled applications far beyond what is possible with classical light. The unique capabilities of quantum light have inspired the migration of some conceptual ideas to the realm of classical optics, focusing on replicating and exploiting non-trivial quantum states of discrete-variable systems. Here, we further develop this paradigm by building the analogy of quantum squeezed states using classical structured light. We have found that the mechanism of squeezing, responsible for beating the standard quantum limit in quantum optics, allows for overcoming the “standard spatial limit” in classical optics: the light beam can be “squeezed” along one of the transverse directions in real space (at the expense of its enlargement along the orthogonal direction), where its width becomes smaller than that of the corresponding fundamental Gaussian mode. We show that classical squeezing enables nearly sub-diffraction and superoscillatory light focusing, which is also accompanied by the nanoscale phase gradient of the size in the order of λ/100 (λ/1000), demonstrated in the experiment (simulations). Crucially, the squeezing mechanism allows for continuous tuning of both features by varying the squeezing parameter, thus providing distinctive flexibility for optical microscopy and metrology beyond the diffraction limit and suggesting further exploration of classical analogies of quantum effects.

Practical limits to spatial resolution of magnetic imaging with a quantum diamond microscope

Widefield quantum diamond microscopy is a powerful technique for imaging magnetic fields with high sensitivity and spatial resolution. However, current methods to approach the ultimate spatial resolution (<500 nm) are impractical for routine use as they require time-consuming fabrication or transfer techniques to precisely interface the diamond sensor with the sample to be imaged. To address this challenge, we have designed a co-axial sensor holder that enables simple, repeatable sensor–sample interfacing while being compatible with high numerical aperture (NA) optics. With our new design we demonstrate low standoffs <500 nm with a millimeter sized sensor. We also explore the relationship between spatial resolution and NA spanning from 0.13 to 1.3. The spatial resolution shows good agreement with the optical diffraction limit at low NA but deviates at high NA, which is shown to be due to optical aberrations. Future improvements to our design are discussed, which should enable magnetic imaging with <500 nm resolution in an accessible, easy-to-use instrument.

Study of modulation in complex refractive indices induced by ultrafast relativistic electrons using infrared and THz probe pulses.

Objective 
Achieving ultra-precise temporal resolution in ionizing radiation detection is essential, particularly in positron emission tomography, where precise timing enhances signal-to-noise ratios and may enable reconstruction-less imaging. A promising approach involves utilizing ultrafast modulation of the complex refractive index, where sending probe pulses to the detection crystals will result in changes in picoseconds (ps), and thus a sub - 10 ps coincidence time resolution can be realized. Towards this goal, here, we aim to first measure the ps changes in probe pulses using an ionizing radiation source with high time resolution.
Approach 
We used relativistic, ultrafast electrons to induce complex refractive index and use probe pulses in the near-infrared (800 nm) and terahertz (THz, 300 µm) regimes to test the hypothesized wavelength-squared increase in absorption coefficient in the Drude free-carrier absorption model. We measured BGO, ZnSe, BaF2, ZnS, PBG, and PWO with 1 mm thickness to control the deposited energy of the 3 MeV electrons, simulating ionization energy of the 511 keV photons. 
Main results 
Both with the 800 nm and THz probe pulses, transmission decreased across most samples, indicating the free carrier absorption, with an induced signal change of 11% in BaF2, but without the predicted Drude modulation increase. To understand this discrepancy, we simulated ionization tracks and examined the geometry of the free carrier distribution, attributing the mismatch in THz modulations to the sub-wavelength diameter of trajectories, despite the lengths reaching 500 µm to 1 mm. Additionally, thin samples truncated the final segments of the ionization tracks, and the measured initial segments have larger inter-inelastic collision distances due to lower stopping power (dE/dx) for high-energy electrons, exacerbating diffraction-limited resolution. 
Significance
Our work offers insights into ultrafast radiation detection using complex refractive index modulation and highlights critical considerations in sample preparation, probe wavelength, and probe-charge carrier coupling scenarios.

Imaging interorganelle contacts at a glance.

Eukaryotic cells are compartmentalized into membrane-bound organelles that must coordinate their responses to stimuli. One way that organelles communicate is via membrane contact sites (MCSs), sites of close apposition between organelles used for the exchange of ions, lipids and information. In this Cell Science at a Glance article and the accompanying poster, we describe an explosion of new methods that have led to exciting progress in this area and discuss key examples of how these methods have advanced our understanding of MCSs. We discuss how diffraction-limited and super-resolution fluorescence imaging approaches have provided important insight into the biology of interorganelle communication. We also describe how the development of multiple proximity-based methods has enabled the detection of MCSs with high accuracy and precision. Finally, we assess how recent advances in electron microscopy (EM), considered the gold standard for detecting MCSs, have allowed the visualization of MCSs and associated proteins in 3D at ever greater resolution.

Amorphous to Crystalline Transition in Nanoimprinted Sol-Gel Titanium Oxide Metasurfaces.

Crystalline titanium dioxide (TiO2) (anatase and rutile) possesses a higher refractive index than amorphous TiO2 and near-zero absorption in the visible region, making them an ideal material for visible metasurfaces. However, fabrication limitations hinder their implementation into flat optics. In this work, a wafer-scale manufacturing platform is proposed for crystalline TiO2 metasurfaces. Sol-gel TiO2 is developed as a printable material in which its material phase can be precisely controlled to produce amorphous, anatase, or rutile, depending on the crystallization temperature. Therefore, anatase or rutile metalenses can be fabricated on a wafer scale using thermal nanoimprint lithography and sintering process. The high refractive index of the crystalline TiO2 contributes to the enhanced conversion efficiency of the fabricated metalenses. The fabricated metalenses exhibit diffraction-limited focusing and imaging capabilities, comparable to the theoretically ideal lenses.

Spatial resolution limit for a solid immersion lens

The solid immersion (SI) effect is widely used to increase the spatial resolution of optical focusing systems and even overcome the Abbe diffraction limit. Resolution enhancement offered by a SI lens is mostly a function of its geometry and refractive index nSI. While SI lenses are relatively well understood, the scaling of the resolution enhancement by such lenses is still a subject of debate, with some works reporting ≃nSI and ≃nSI2 dependencies for the hemispherical and hyperhemispherical SI lens configurations, respectively. In this paper, we offer a general argument for a resolution limit for SI optics and, then, verify it via the numerical analysis of the hemispherical and hyperhemispherical silicon SI lenses designed for the terahertz (THz) range. In fact, we find that there is no contradiction in the reported resolution enhancements ≃nSI and ≃nSI2; however, they happen in different operation regimes. We then demonstrate that the resolution values reported for the different SI lens arrangements in the visible (VIS), near-, and middle-infrared (NIR and MIR), as well as THz bands obey the derived limit. Our findings will be useful for the further design and applications of SI optics.

Nanoporous Submicron Gold Particles Enable Nanoparticle-Based Localization Optoacoustic Tomography (nanoLOT).

Localization optoacoustic tomography (LOT) has recently emerged as a transformative super-resolution technique breaking through the acoustic diffraction limit in deep-tissue optoacoustic (OA) imaging via individual localization and tracking of particles in the bloodstream. However, strong light absorption in red blood cells has previously restricted per-particle OA detection to relatively large microparticles, ≈5µm in diameter. Herein, it is demonstrated that submicron-sized porous gold nanoparticles, ≈600nm in diameter, can be individually detected for noninvasive super-resolution imaging with LOT. Ultra-high-speed bright-field microscopy revealed that these nanoparticles generate microscopic plasmonic vapor bubbles, significantly enhancing opto-acoustic energy conversion through a nano-to-micro size transformation. Comprehensive in vitro and in vivo tests further demonstrated the biocompatibility and biosafety of the particles. By reducing the detectable particle size by an order of magnitude, nanoLOT enables microangiographic imaging with a significantly reduced risk of embolisms from particle aggregation and opens new avenues to visualize how nanoparticles reach vascular and potentially extravascular targets. The performance of nanoLOT for non-invasive imaging of microvascular networks in the murine brain anticipates new insights into neurovascular coupling mechanisms and longitudinal microcirculatory changes associated with neurodegenerative diseases.

Second harmonic generation based on graphene hyperstructure for higher resolution and performance on top of achieving fundamental wave detection in theory

In this paper, an innovative one-dimensional graphene hyperstructure (GHS) is proposed, allowing for the concurrent detection of multiple physical parameters in both the fundamental and second harmonic generation. The sensing characteristics of GHS pertaining to magnetic field strength (B), incident electromagnetic wave angle (θ), and graphene thickness (dgt) are systematically investigated. Moreover, through the incorporation of second harmonic generation alongside fundamental detection, higher resolution and performance are achieved. The findings indicate an expansion of the measurement range for B, θ, and dgt, from 0.3∼0.5 T, 35∼55°, and 1∼6 layers to 0.3∼1 T, 35∼65°, and 1∼10 layers, providing increased flexibility and adjustability. Additionally, by leveraging nonlinear effects and widening the Fabry-Perot cavity width, this structure effectively enhances the quality factor (Q) from 2.94 × 102 to 1.95 × 105, resulting in a substantial improvement in sensing performance. This development holds tremendous promise in surpassing the diffraction limit and addressing high-Q value sensing requirements. In comparison to conventional detectors, the GHS not only enhances detection efficiency but also harbors the potential for multiple physical quantities detection. This forward-looking research is pivotal in its successful resolution of detector performance limitations, ushering in novel possibilities across diverse domains.

Unpaired data training enables super-resolution confocal microscopy from low-resolution acquisitions.

Supervised deep-learning models have enabled super-resolution imaging in several microscopic imaging modalities, increasing the spatial lateral bandwidth of the original input images beyond the diffraction limit. Despite their success, their practical application poses several challenges in terms of the amount of training data and its quality, requiring the experimental acquisition of large, paired databases to generate an accurate generalized model whose performance remains invariant to unseen data. Cycle-consistent generative adversarial networks (cycleGANs) are unsupervised models for image-to-image translation tasks that are trained on unpaired datasets. This paper introduces a cycleGAN framework specifically designed to increase the lateral resolution limit in confocal microscopy by training a cycleGAN model using low- and high-resolution unpaired confocal images of human glioblastoma cells. Training and testing performances of the cycleGAN model have been assessed by measuring specific metrics such as background standard deviation, peak-to-noise ratio, and a customized frequency content measure. Our cycleGAN model has been evaluated in terms of image fidelity and resolution improvement using a paired dataset, showing superior performance than other reported methods. This work highlights the efficacy and promise of cycleGAN models in tackling super-resolution microscopic imaging without paired training, paving the path for turning home-built low-resolution microscopic systems into low-cost super-resolution instruments by means of unsupervised deep learning.

Germanium metalens for longwave infrared applications

Metalenses represent a paradigm shift in optics, offering unprecedented control over light manipulation. This study focuses on the design optimization of a polarization-insensitive germanium (Ge) metalens operating in the longwave infrared (LWIR) regime. Employing rigorous coupled-wave analysis (RCWA) and finite-difference time-domain (FDTD) simulations, a metalens with 1mm focal length was designed using nanopillars with 3.5µm height and radius ranging from 0.55µm to 1.2µm. Then, the impact of lattice size and numerical aperture (NA) on lens performance was investigated. The results indicate that smaller lattices allow finer phase control and enhanced transmittance stability across the phase profile if significant coupling effects are not verified. As the NA increases, the focal spot size decreases, albeit with diminishing returns towards the diffraction limit. To the best of our knowledge, it is the first work that shows high focal efficiency (~80%) across multiple NA’s for a LWIR metalens with a diameter under 1100µm. The proposed metalens is compatible with complementary metal-oxide-semiconductor (CMOS) technology and supports low-cost manufacturing.

Deep subwavelength topological edge state in a hyperbolic medium.

Topological photonics offers the opportunity to control light propagation in a way that is robust from fabrication disorders and imperfections. However, experimental demonstrations have remained on the order of the vacuum wavelength. Theoretical proposals have shown topological edge states that can propagate robustly while embracing deep subwavelength confinement that defies diffraction limits. Here we show the experimental proof of these deep subwavelength topological edge states by implementing periodic modulation of hyperbolic phonon polaritons within a van der Waals heterostructure composed of isotopically pure hexagonal boron nitride flakes on patterned gold films. The topological edge state is confined in a subdiffraction volume of 0.021 µm3, which is four orders of magnitude smaller than the free-space excitation wavelength volume used to probe the system, while maintaining the resonance quality factor above 100. This finding can be directly extended to and hybridized with other van der Waals materials to broadened operational frequency ranges, streamline integration of diverse polaritonic materials, and compatibility with electronic and excitonic systems.

Fourier Surfaces Reaching Full-Color Diffraction Limits.

Optical Fourier surfaces (OFSs), characterized by sinusoidally profiled diffractive optical elements, can outperform traditional binary-type counterparts by minimizing optical noise through selectively driving diffraction at desired frequencies. While scanning probe lithography (SPL), gray-scale electron beam lithography (EBL), and holographic inscriptions are effective for fabricating OFSs, achieving full-color diffractions at fundamental efficiency limits is challenging. Here, an integrated manufacturing process is presented, validated theoretically and experimentally, for fully transparent OFSs reaching the fundamental limit of diffraction efficiency. Leveraging holographic inscriptions and soft nanoimprinting, this approach effectively addresses challenges in conventional OFS manufacturing, enabling scalable production of noise-free and maximally efficient OFSs with record-high throughput (1010-1012 µm2h-1), surpassing SPL and EBL by 1010 times. Toward this end, a wafer-scale OFSs array is demonstrated consisting of full-color diffractive gratings, color graphics, and microlenses by the one-step nanoimprinting, which is readily compatible with rapid prototyping of OFSs even on curved panels, demanding for transformative optical devices such as augmented and virtual reality displays.

3D Light-Direction Sensor Based on Segmented Concentric Nanorings Combined with Deep Learning.

High-precision, ultra-thin angular detectable imaging upon a single pixel holds significant promise for light-field detection and reconstruction, thereby catalyzing advancements in machine vision and interaction technology. Traditional light-direction angle sensors relying on optical components like gratings and lenses face inherent constraints from diffraction limits in achieving device miniaturization. Recently, angle sensors via coupled double nanowires have demonstrated prowess in attaining high-precision angle perception of incident light at sub-wavelength device scales, which may herald a novel design paradigm for ultra-compact angle sensors. However, the current approach to measuring the three-dimensional (3D) incident light direction is unstable. In this paper, we propose a sensor concept capable of discerning the 3D light-direction based on a segmented concentric nanoring structure that is sensitive to both elevation angle (θ) and azimuth angle (ϕ) at a micrometer device scale and is validated through simulations. Through deep learning (DL) analysis and prediction, our simulations reveal that for angle scanning with a step size of 1°, the device can still achieve a detection range of 0∼360° for ϕ and 45°∼90° for θ, with an average accuracy of 0.19°, and DL can further solve some data aliasing problems to expand the sensing range. Our design broadens the angle sensing dimension based on mutual resonance coupling among nanoring segments, and through waveguide implementation or sensor array arrangements, the detection range can be flexibly adjusted to accommodate diverse application scenarios.

High-efficiency Yb:YAG thin-disk chirped pulse amplifier delivering 884-femtosecond laser with tunable repetition rates and high stability

We experimentally demonstrated a compact, highly efficient, stable, chirped pulse amplification (CPA) thin-disk regenerative system with a tunable repetition rate. The laser head consists of a 9 at. % Yb:YAG thin-disk with a diameter of 8.8 mm and a thickness of 150 μm, is designed for a 48-pump pass configuration. In CPA-based regenerative amplifier configuration, a maximal output power of 85 W at 500 kHz is achieved with a conversion efficiency of 53.1 %. This corresponds to a pulse energy of 170 μJ. To the best of our knowledge, this is the highest conversion efficiency in CPA thin-disk regenerative amplifiers. The pulse width is compressed to 884 fs with a pair of grating, resulting in a peak power of 192 MW. At 85 W, a near diffraction limit beam quality factor M2 of 1.40 is measured, which is essential in precision applications. In addition, remarkable long-term power stability is confirmed with a root-mean-square (RMS) fluctuation of 0.12 % over a 24-hour duration. The reported femtosecond amplifier is believed to be a promising tool for various applications such as extreme manufacturing, terahertz spectroscopy, etc.

Super-resolution acoustic displacement metrology through topological pairs in orbital meta-atoms

The precise measurement of minute displacements using light is a common practice in modern science and technology. The utilization of sound for precision displacement metrology remains scarce due to the diffraction limit of half-wavelength, while it holds crucial applications in some specific scenarios, such as underwater environments, biological tissues, and complex machinery components. Here, we propose an approach to super-resolution acoustic displacement metrology by introducing the concept of topological pairs in orbital meta-atoms, drawing inspiration from the analogy of Cooper pairs observed in spinful electrons. The topological pairs are conjugately formed to create two distinct pathways in mode space that enable robust generation of interference. This allows the realization of acoustic analogue of Malus’s law and thereby enhances the resolution of displacement measurements. By incorporating a spiral twist configuration in orbital meta-atoms, we demonstrate the first acoustic prototype of a physical micrometer tailored for micron-scale displacement metrology. We observe experimentally a displacement resolving power of 1.2 μm at an audible frequency of 3.43 kHz, approximately 1/105 of the sound wavelength of 100 mm. Our work implies a new paradigm for precise displacement metrology within classical wave physics and lays the foundation for diverse acoustic applications.

Expansion in situ genome sequencing links nuclear abnormalities to hotspots of aberrant euchromatin repression.

Microscopy and genomics are both used to characterize cell function, but approaches to connect the two types of information are lacking, particularly at subnuclear resolution. While emerging multiplexed imaging methods can simultaneously localize genomic regions and nuclear proteins, their ability to accurately measure DNA-protein interactions is constrained by the diffraction limit of optical microscopy. Here, we describe expansion in situ genome sequencing (ExIGS), a technology that enables sequencing of genomic DNA and superresolution localization of nuclear proteins in single cells. We applied ExIGS to fibroblast cells derived from an individual with Hutchinson-Gilford progeria syndrome to characterize how variation in nuclear morphology affects spatial chromatin organization. Using this data, we discovered that lamin abnormalities are linked to hotspots of aberrant euchromatin repression that may erode cell identity. Further, we show that lamin abnormalities heterogeneously increase the repressive environment of the nucleus in tissues and aged cells. These results demonstrate that ExIGS may serve as a generalizable platform for connecting nuclear abnormalities to changes in gene regulation across disease contexts.

Achieving Single Cell Acoustic Localisation with Deactivation Super Resolution.

Super-resolution optical microscopy enables optical imaging of cells, molecules and other biological structures beyond the diffraction limit. However, no similar method exists to super-resolve specific cells with ultrasound. Here we introduce Deactivation Super Resolution (DSR), an ultrasound imaging method that uses the acoustic deactivation of genetically encodable contrast agents to super-resolve individual cells with ultrasound as they navigate through structures that cannot be resolved by conventional imaging methods. DSR takes advantage of gas vesicles, which are air-filled sub-micron protein particles that can be expressed in genetically engineered cells to produce ultrasound contrast. Our experimental results show that DSR can distinguish sub-wavelength microstructures that standard B-mode ultrasound images fail to resolve by super- localizing individual mammalian cells. This study provides a proof of concept for the potential of DSR to serve as a super- resolution ultrasound technique for individual cell localization, opening new horizons in the field.

Breaking the diffraction limit for label-free chemical imaging

Breaking the diffraction limit for label-free chemical imaging

Bound States in the Continuum and Long-Range Coupling of Polaritons in Hexagonal Boron Nitride Nanoresonators.

Bound states in the continuum (BICs) garnered significant interest for their potential to create new types of nanophotonic devices. Most prior demonstrations were based on arrays of dielectric resonators, which cannot be miniaturized beyond the diffraction limit, reducing the applicability of BICs for advanced functions. Here, we demonstrate BICs and quasi-BICs based on high-quality factor phonon-polariton resonances in isotopically pure h11BN and how these states can be supported by periodic arrays of nanoresonators with sizes much smaller than the wavelength. We theoretically illustrate how BICs emerge from the band structure of the arrays and verify both numerically and experimentally the presence of these states and enhanced quality factors. Furthermore, we identify and characterize simultaneously quasi-BICs and bright states. Our method can be generalized to create a large number of optical states and to tune their coupling with the environment, paving the way to miniaturized nanophotonic devices with more advanced functions.

Optical microscope with nanometer longitudinal resolution based on a Linnik interferometer

Abstract A widefield microscope based on a Linnik interferometer was designed, constructed, and tested. The phase-shifting and polarized single-shot methods were used to measure interference patterns. Both methods use a low-coherence light-emitting diode as the light source, achieving a resolution of 10 nm in the Z direction and diffraction-limited resolution in the X and Y directions. The single-shot method is vibration-insensitive, allowing for the observation of moving objects. The simplicity and low cost of this instrument make it valuable for a wide range of applications.