Topological light field: from singular to skyrmionic optics and beyond

Light field (LF) imaging has gained significant attention due to its recent success in microscopy, 3-dimensional (3D) displaying and rendering, augmented and virtual reality usage. Postprocessing of LF enables us to extract more information from a scene compared to traditional cameras. However, the use of LF is still a research novelty because of the current limitations in capturing high-resolution LF in all of its four dimensions. While researchers are actively improving methods of capturing high-resolution LF's, using simulation, it is possible to explore a high-quality captured LF's properties. The immediate concerns following the LF capture are its storage and processing time. A rich LF occupies a large chunk of memory ---order of multiple gigabytes per LF---. Also, most feature extraction techniques associated with LF postprocessing involve multi-dimensional integration that requires access to the whole LF and is usually time-consuming. Recent advancements in computer processing units made it possible to simulate realistic images using physical-based rendering software. In this work, at first, a transformation function is proposed for building a camera array (CA) to capture the same portion of LF from a scene that a standard plenoptic camera (SPC) can acquire. Using this transformation, LF simulation with similar properties as a plenoptic camera will become trivial in any rendering software. Artificial intelligence (AI) and machine learning (ML) algorithms ---when deployed on the new generation of GPUs--- are faster than ever. It is possible to generate and train large networks with millions of trainable parameters to learn very complex features. Here, residual convolutional neural network (RCNN) structures are employed to build complex networks for compression and feature extraction from an LF. By combining state-of-the-art image compression and RCNN, I have created a compression pipeline. The proposed pipeline's bit per pixel (bpp) ratio is 0.0047 on average. I show that with a 1% compression time cost and 18x speedup for decompression, our methods reconstructed LFs have better structural similarity index metric (SSIM) and comparable peak signal-to-noise ratio (PSNR) compared to the state-of-the-art video compression techniques used to compress LFs. In the end, using RCNN, I created a network called RefNet, for extracting a group of 16 refocused images from a raw LF. The training parameters of the 16 LFs are set to (\alpha=0.125, 0.250, 0.375, ..., 2.0) for training. I show that RefNet is 134x faster than the state-of-the-art refocusing technique. The RefNet is also superior in color prediction compared to the state-of-the-art

In this paper, an aberration correction method for an extended target is proposed to solve the problem of the lenslet-based plenoptic camera not imaging clearly under the influence of aberrations. We propose a light field manipulation method to improve performance of the light field imaging system. The principle of this method is that the sub-aperture images extracted from the raw light field image are offset when the light field imaging system is affected by aberrations, and the symmetrical arrangement of the sub-aperture image array is destroyed. By repairing the symmetrical arrangement of the sub-aperture image array, the influence of phase aberrations on the imaging system can be eliminated, and the resolution of the plenoptic camera can be improved. We use an image correlation algorithm to process the sub-aperture images of the plenoptic camera, calculate and compensate each sub-aperture image's displacement caused by aberrations, and restore the symmetrical arrangement of the sub-aperture image array; then, a corrected high-resolution refocused image can be generated. In particular, this method uses only the raw light field information obtained by the plenoptic camera in a single exposure, without adding other hardware devices. Furthermore, it takes the extended target itself as the reference image, so the ideal position need not be calibrated in advance. Also, the parallax information of the sub-aperture images is retained, and the method is simple and easy to use. Numerical simulation and experimental results show that the technology proposed in this paper can work well for high-resolution imaging of a plenoptic camera with phase aberrations. This method can be potentially applied to analyze lens aberration, media-induced image distortion such as water turbulence in underwater imaging, and atmospheric turbulence in remote imaging. It may have important application prospects in the fields of astronomical object detection, remote sensing, etc.

Structured light refers to light fields that are specially customized by manipulating their properties across multiple physical dimensions, demonstrating immense potential in applications such as optical communications, precision measurement, advanced imaging, and quantum information. Structured light lasers, capable of directly generating light fields with complex spatial distributions, polarization states, and topological structures, provide efficient and versatile tools for light field manipulation and its applications. Unlike structured light generation techniques that rely on external modulation, structured light lasers achieve compact and high-quality structured light output through direct intracavity control, significantly enhancing system integration and efficiency. This review summarizes the latest research progress in structured light lasers, exploring their fundamental principles, design methodologies, and applications. It introduces the basic concepts of structured light, including typical structured beams such as vortex beams, vector beams, and propagation-invariant beams, as well as more complex topological and quantum structures like optical skyrmions, non-separable states, and ray-wave duality. The review elaborates on the categories of high-dimensional structured light lasers, covering design schemes such as on-cavity structures and intracavity geometries, and provides insight into different architectures ranging from free-space and fiber-based systems to integrated devices. We also discuss the broad applications and future prospects of structured light lasers, highlighting the challenges and opportunities in this rapidly evolving field. This review aims to serve as a resource for researchers who seek to design and develop structured light lasers, as well as for those looking to harness their potential to drive innovation in photonic techniques.

Singular stress field induced two-dimensional topological polar structures in SrTiO3: Topological number manipulation via loading modes

Liquid crystal spatial light modulators for precise dynamic manipulation of coherent light fields, used in diffractive optoelectronic optical data processing systems, are considered. This paper presents the results of a study of the temporal dynamics of the HoloEye PLUTO-2 VIS-016 liquid crystal spatial light modulator for analysis of light fields rate modulation. Experiments using binary phase computer generated holograms and binary focusing phase diffractive optical elements were conducted. Based on experimental data, the time characteristics of the modulator response were determined. It was found that when the rise time of the diffraction efficiency was 146 ms after the hologram displaying onto the SLM, and when switching to a new hologram, the decay time was 97 ms. These results allowed the dynamic generation of an alternating holograms at a refresh rate of 2 Hz with an interference level of –16 dB. Increasing the frequency of fringe pattern updates increases the level of interframe noise in the generated holograms, and when updated at the specification frequency, the generated distributions cannot be separated. Determining the actual frame rate based on the rise and decay times of the diffraction efficiency makes it possible to correctly calculate the minimum operating time of an information optical system containing a liquid crystal spatial light modulator.

The manipulation of solid states using intense infrared or terahertz light fields is a pivotal area in contemporary ultrafast photonics research. While conventional circular polarization has been well explored, the potential of counterrotating bicircular light remains widely underexplored, despite growing interest in theory. In the mid-infrared or multi-terahertz region, experimental challenges lie in difficulties in stabilizing the relative phase between two-color lights and the lack of available polarization elements. Here, we successfully generated phase-stable counterrotating bicircular light pulses in the 14–39 THz frequency range circumventing the above problems. Employing spectral broadening, polarization pulse shaping with a spatial light modulator, and intra-pulse difference frequency generation leveraging a distinctive angular-momentum selection rule within the nonlinear crystal, we achieved direct conversion from near-infrared pulses into the designed counterrotating bicircular multi-terahertz pulses. Use of the spatial light modulator enables programmable control over the shape, orientation, rotational symmetry, and helicity of the bicircular light field trajectory. This advancement provides a novel pathway for the programmable manipulation of light fields, and marks a significant step toward understanding and harnessing the impact of tailored light fields on matter, particularly in the context of topological semimetals.

Conventional iterative algorithms based on 2D Fourier transform, such as Gerchberg‐Saxton, are typically employed to generate customizable 2D light field distributions in the focal plane through holographic phase modulation, enabling efficient two‐photon polymerization processing. However, extending this approach to achieve true 3D light field configurations necessitates the superposition of spherical wavefront phases or the use of 2D FT, which introduces critical limitations (e.g., low overall consistency and interlayer crosstalk). These inherent constraints fundamentally compromise the precision and reproducibility of TPP microfabrication. To overcome these challenges, we propose a 3D holographic algorithm with experimentally validated capabilities for volumetric light‐field modulation, achieving consistency exceeding 90% across all spatial dimensions. The impacts of k ‐domain sampling and iterative weighting on light field consistency are systematically analyzed, and modulation consistency is optimized through selective sampling and intensity compensation. This work demonstrates the first implementation of 3D multi‐foci in TPP processing, simultaneously achieving true volumetric parallelization beyond 2D planar constraints. As a proof‐of‐concept demonstration, 3D spiral array structures are fabricated rapidly and their circular dichroism responses are verified. Our method establishes a pioneering framework for next‐generation rapid micro/nanofabrication through volumetric light field manipulation.

Manipulation of light fields at will is a long-sought goal in the optics community. In this regard, holography, a technology that can modulate an arbitrary light wavefront including not only its intensity but also the phase information in a spatial domain, was invented 60 years ago [1]. Traditional holography has been extensively studied by the information optics community and has made tremendous progress in the past years, leading to many practical applications such as holographic storage [2], interferometry [3], lithography [4], and three-dimensional (3D) displays [5].

Contents: Introduction. §1: Computable rings and modules. §2: Ideal membership relation. §3: Effective structured domains. §4: Completion of a local ring as a domain. §5: The recursive completion. Epilogue. References.Introduction. Completion is an important general mathematical device. Often, but not always, a completion takes the following form. Let A be a topological algebraic structure whose topology is derived from a metric. For A, a topological algebra  and an embedding i: A →  are constructed such that  is a complete metric space in which A is densely embedded by i. The long list of structures for which such completions exist begins with Cantor's construction of the real number field and includes objects like the p-adic integers, Baire space, and Boolean algebras. In Bourbaki [6] a careful and thorough account of completions for arbitrary topological groups and fields is given, for which it is important to note that the topological structures need not be metrizable, but must possess a uniformity.The effectiveness of the completion process of a computable structure A cannot be readily studied using the tools of computable algebra, simply because the resulting structure  is almost invariably uncountable. However, in particular cases, it has been possible to define and study the substructure Ak of computable elements of Â; this has been done for the structures mentioned above, starting with the field of recursive real numbers.In this paper we analyse the effectivity of the completion of a local ring R. We do this using structured Scott-Ershov domains. Our study may be considered as a prototype containing methods applicable to a broad class of completions, including all the examples mentioned above, except for the real number field, which needs a generalisation of the domain concept.A Scott-Ershov domain D formalises how a set Dt of possibly “infinite” elements, called total elements, is constructed from a set Dc of “finite” elements, called compact elements. This is achieved by means of an approximation ordering which determines a topology on D and, in particular, on Dt. Our methodology is to associate to a given topological algebra A a structured domain D(A) such that the total elements D(A)t form a topological algebra topologically isomorphic to A. In such circumstances A is said to be domain definable by D(A). The theory of computability for domains is now applied to study the effectivity of the topological algebra A.

The existence or not of Landau poles is one of the oldest open questions in non-asymptotic quantum field theories. We investigate the Landau pole issue in two condensed matter systems whose long-wavelength physics is described by appropriate quantum field theories: the critical quantum magnet and Dirac fermions in graphene with long-range Coulomb interactions. The critical quantum magnet provides a classic example of a quantum phase transition, and it is well described by the $\phi^4$ theory. We find that the irrelevant but symmetry-allowed couplings, such as the $\phi^6$ potential, can significantly change the fate of the Landau pole in the $\phi^4$ theory. We obtain the coupled beta functions of a $\phi^4 + \phi^6$ potential at both small and large orders. Already from the 1-loop calculation, the Landau pole is replaced by an ultraviolet fixed point. A Lipatov analysis at large orders reveals that the inclusion of a $\phi^6$ term also has important repercussions for the high-order expansion of the beta functions. We also investigate the role of the Landau pole in 2+1 dimensional Dirac fermions with Coulomb interactions, e.g., graphene. Both the weak-coupling perturbation theory up to 2 loops and a low-order large-N calculation show the absence of a Landau pole. Furthermore, we calculate the asymptotic expansion coefficients of the beta function. We find that the asymptotic coefficient is bounded by that of a $\phi^4$ theory, so graphene is free from Landau poles if the $\phi^4$ theory does not manifest a Landau pole. We briefly discuss possible experiments that could potentially probe the existence of a Landau pole in these systems. Studying Landau poles in suitable condensed matter systems is of considerable fundamental importance since the relevant Landau pole energy scales in particle physics, whether it is quantum electrodynamics or Higgs physics, are completely unattainable.

We propose a new scenario for early cosmology, where inflationary de Sitter phase dynamically occurs. The effect emerges as a result of dynamics of the topologically nontrivial sectors in expanding universe. Technically the effect can be described in terms of the auxiliary fields which effectively describe the dynamics of the topological sectors in a gauge theory. Inflaton in this framework is an auxiliary topological non-propagating field with no canonical kinetic term, similar to known topologically ordered phases in condensed matter systems. We explain many deep questions in this framework using the so-called weakly coupled "deformed QCD" toy model.While this theory is weakly coupled gauge theory, it preserves all the crucial elements of strongly interacting gauge theory, including confinement, nontrivial $\theta$ dependence, degeneracy of the topological sectors, etc. We discuss a specific realization of these ideas using a scaled up version of QCD, coined as \qcd, with the scale M_{PL}\gg \Lbar\gg \sqrt[3]{M_{EW}^2M_{PL}}\sim 10^8 {\mathrm{GeV}}. If no other fields are present in the system de Sitter phase will be the final destination of evolution of the universe. If other interactions are present in the system, the inflationary de Sitter phase lasts for a finite period of time. The inflation starts from the thermal equilibrium state long after the \qcd -confinement phase transition at temperature T_{i}\sim \Lbar\sqrt{\frac{\Lbar}{M_{PL}}}. The end of inflation is triggered by the coupling with gauge bosons from the Standard Model. The corresponding interaction is unambiguously fixed by the triangle anomaly. Number of e-folds in the \qcd-inflation framework is determined by the gauge coupling constant at the moment of inflation, and estimated as N_{\rm inf}\sim \alpha_s^{-2}\sim 10^2.

The higher-order Hermite–Gaussian (HG) modes exhibit complex spatial distributions and find a wide range of applications in fields such as quantum information processing, optical communications, and precision measurements. In recent years, the advancement of deep learning has emerged as an effective approach for generating higher-order HG modes. However, the traditional data-driven deep learning method necessitates a substantial amount of labeled data for training, entails a lengthy data acquisition process, and imposes stringent requirements on system stability. In practical applications, these methods are confronted with challenges such as the high cost of data labeling. This paper proposes a method that integrates a physical model with deep learning. By utilizing only a single intensity distribution of the target optical field and incorporating the physical model, the training of the neural network can be accomplished, thereby eliminating the dependency of traditional data-driven deep learning methods on large datasets. Experimental results demonstrate that, compared with the traditional data-driven deep learning method, the method proposed in this paper yields a smaller root mean squared error between the generated higher-order HG modes. The quality of the generated modes is higher, while the training time of the neural network is shorter, indicating greater efficiency. By incorporating the physical model into deep learning, this approach overcomes the limitations of traditional deep learning methods, offering a novel solution for applying deep learning in light field manipulation, quantum physics, and other related fields.

Photonic Radial Modes: Progress in Light Field Manipulation and Quantum Information Applications

After years of development, holography has become an essential tool of modern optics for many applications. Among them, holographic encryption and dynamic display are the two most typical applications. So far, however, only 2D targets or 2D images of 3D targets can be encrypted with holographic technology. The 3D multiplexing holographic technology of 3D multi‐targets has not yet been realized and holographic encryption of 3D multi‐targets is still a blank. Here, the conception of 3D orbital angular momentum (OAM) multiplexing holography is proposed, and holographic encryption of 3D multi‐targets is realized for the first time. This breaks the restriction that only 2D images can be encrypted in traditional holographic encryption. Furthermore, the results also show that the 3D OAM holography can be used in the dynamic display for 3D multi‐targets. In the experiment, the metasurface is used for taking its high‐resolution advantage in light field manipulation, and verify the feasibility of 3D OAM multiplexing holographic technology, holographic encryption of 3D multi‐targets, and holographic dynamic display of 3D targets. The work creates a precedent for the 3D multiplexing holography, encryption, and dynamic display technology of 3D multi‐targets, which brings real 3D life closer to humankind.

The inertial measurement system based on the SERF effect utilizes the rotation of the inertia-sensitive space with longitudinally hyperpolarized nuclear spin, possessing the potential for ultra-high sensitivity measurement, and has become an important development direction for the high-sensitivity miniaturized inertial navigation systems. The polarization distribution uniformity in the atomic spin ensemble significantly influences the scale factor error and bias stability of the SERF inertial measurement system. This paper analyses the factors affecting the longitudinal and transverse polarization distribution in the atomic spin coupled ensemble of the SERF inertial measurement system. To address the issue of non-uniform polarization rate distribution in the electron spin-nuclear spin coupled ensemble, a Bloch differential equation model is established. Using light field manipulation techniques, three-dimensional polarization rate distribution of the atomic spin ensemble under Gaussian, flat-top, and hollow beam pumping are simulated. Relevant simulation parameters are optimized, with over 80% of the normalized nuclear spin polarization rate considered as the uniform region. Under hollow beam pumping, the transverse nuclear spin polarization uniformity is improved by 88.3% compared to Gaussian beams and by 20.9% compared to flat-top beams, providing a theoretical basis for further enhancing the polarization uniformity in the atomic spin coupled ensemble.