Further improving the axial resolution is paramount for three-dimensional optical imaging systems. Vortex beams are being widely applied in 3D microscopy techniques. Here we theoretically investigate the ultimate resolution limits using Laguerre-Gauss (LG) beams. Various kinds of superpositions can nowadays be easily prepared by spatial light modulators (SLM). It has been keenly shown that LG beams’ superpositions possess more information than pure LG beams yet do not saturate the ultimate limit with a simple intensity scan. More sophisticated detection schemes based on quantum super-resolution protocols are investigated here to retrieve the discarded information.
Further improving the axial resolution is paramount for three-dimensional optical imaging systems. Vortex beams are being widely applied in 3D microscopy techniques. Here we theoretically investigate the ultimate resolution limits using Laguerre-Gauss (LG) beams. Various kinds of superpositions can nowadays be easily prepared by spatial light modulators (SLM). It has been keenly shown that LG beams’ superpositions possess more information than pure LG beams yet do not saturate the ultimate limit with a simple intensity scan. More sophisticated detection schemes based on quantum super-resolution protocols are investigated here to retrieve the discarded information.
Abstract Improving three-dimensional (3D) localization precision is of paramount importance for super-resolution imaging. By properly engineering the point spread function (PSF), such as utilizing Laguerre–Gaussian (LG) modes and their superposition, the ultimate limits of 3D localization precision can be enhanced. However, achieving these limits is challenging, as it often involves complicated detection strategies and practical limitations. In this work, we rigorously derive the ultimate 3D localization limits of LG modes and their superposition, specifically rotation modes, in the multi-parameter estimation framework. Our findings reveal that a significant portion of the information required for achieving 3D super-localization of LG modes can be obtained through feasible intensity detection. Moreover, the 3D ultimate precision can be achieved when the azimuthal index l is zero. To provide a proof-of-principle demonstration, we develop an iterative maximum likelihood estimation (MLE) algorithm that converges to the 3D position of a point source, considering the pixelation and detector noise. The experimental implementation exhibits an improvement of up to two-fold in lateral localization precision and up to twenty-fold in axial localization precision when using LG modes compared to Gaussian mode. We also showcase the superior axial localization capability of the rotation mode within the near-focus region, effectively overcoming the limitations encountered by single LG modes. Notably, in the presence of realistic aberration, the algorithm robustly achieves the Cramér-Rao lower bound. Our findings provide valuable insights for evaluating and optimizing the achievable 3D localization precision, which will facilitate the advancements in super-resolution microscopy.
The resolution of imaging devices is ultimately limited by the diffraction of light. This limit can be circumvented by exploiting near-field phenomena, non-linearities of the sample or specific illumination schemes, which led to the recent explosion of optical super-resolution techniques. However, it would be desirable to reach the nanoscale in the most general way possible, with far-field linear imaging of uniformly illuminated samples. In the last few years, the answer to that came with the field of quantum-inspired super-resolution (QISR), where quantum metrological techniques were used to find novel measurement schemes that, beyond the conventional direct imaging of light, would achieve higher precisions. Interestingly, these ideas would always in some way or another involve transverse spatial modes of light. This thesis presents our work on the subject, with novel theoretical and experimental results. Firstly, we develop the traditional theory of QISR, with has mostly focused on either the estimation of separation of two point sources or on geometric moments of samples. Then, we introduce our own results on optical imaging of general distributions of point sources, in a step to take QISR from toy examples to real imaging scenarios. Secondly, we apply all the concepts studied on a experimental, proof-of-principle implementation of a QISR scheme dubbed Hermite-Gaussian Microscopy (HGM), which uses heterodyne detection with several Hermite-Gaussian modes as local oscillator in order to reconstruct the object sample and achieve super-resolution. We report the techniques necessary for the manipulation of spatial modes of light, as well as our results, where we demonstrated 2D imaging with twofold resolution enhancement beyond the diffraction limit.
Coherent anti-Stokes Raman scattering is a widely used imaging technique that provides chemical contrast without the need for labels, making it an extremely valuable tool in physics, chemistry, and biology. In this work, we explore its fundamental precision limits by applying tools from quantum information theory. We identify optimal measurement strategies and show that spatial mode demultiplexing–a technique already accessible in current experimental setups–can achieve these quantum limits and, in many situations, improve the sensitivity of conventional intensity measurements. Building on this, we introduce an advanced imaging scheme based on vortex beams, which we predict to enhance the image information in the final quantum state of light and thereby lead to even higher resolution and sensitivity. These findings establish a clear path for enhancing nonlinear imaging techniques using concepts from quantum science, bridging the gap between established microscopy methods and the emerging capabilities of quantum technologies.
Spatially structured light has opened a wide range of opportunities for enhanced imaging as well as optical manipulation and particle confinement. Here, we show that phase-coherent illumination with superpositions of radial Laguerre-Gauss (LG) beams provides improved localization for bright optical tweezer traps, with narrowed radial and axial intensity distributions. Further, the Gouy phase shifts for sums of tightly focused radial LG fields can be exploited for phase-contrast strategies at the wavelength scale. One example developed here is the suppression of interference fringes from reflection near nanodielectric surfaces, with the promise of improved cold-atom delivery and manipulation.
To overcome the limit of diffraction while achieving the superresolution technique, solid immersion lenses are the key optical elements for data storage and nanophotonics applications. Recent demonstrations have shown how different nanostructures (such as elliptical solid immersion lenses) are used in diverse fields of increasing resolution in the presence of a structured Gaussian beam. By applying twisted beams such as angular momentum beams (Laguerre- Gaussian) and spatial higher-order Gaussian beams (Hermite- Gauss), we can attain a sharp near-field focal spot pattern, which is considerably better than the conventional solid immersion lens structure in ~mm scale specifically for imaging beyond diffraction limit. Our computation results present a resolution of ~27 nm under a specific Hermite -Gauss mode illumination on a pyramidal shape nanolens structure. By numerical simulations, tolerance has been confirmed with a slight variation in beam size and geometrical modification to make the model compatible with fabrication errors. This narrow bandwidth intensity distribution can be utilized for scanning the sample with higher resolution, especially in the field of quantum technology.