Since the popularisation of the Internet in the 1990s, the cyberspace has kept evolving. We have created various computer-mediated virtual environments including social networks, video conferencing, virtual 3D worlds (e.g., VR Chat), augmented reality applications (e.g., Pokemon Go), and Non-Fungible Token Games (e.g., Upland). Such virtual environments, albeit non-perpetual and unconnected, have bought us various degrees of digital transformation. The term `metaverse' has been coined to further facilitate the digital transformation in every aspect of our physical lives. At the core of the metaverse stands the vision of an immersive Internet as a gigantic, unified, persistent, and shared realm. While the metaverse may seem futuristic, catalysed by emerging technologies such as Extended Reality, 5G, and Artificial Intelligence, the digital `big bang' of our cyberspace is not far away. This survey paper presents the first effort to offer a comprehensive framework that examines the latest metaverse development under the dimensions of state-of-the-art technologies and metaverse ecosystems, and illustrates the possibility of the digital `big bang'. First, technologies are the enablers that drive the transition from the current Internet to the metaverse. We thus examine eight enabling technologies rigorously - Extended Reality, User Interactivity (Human-Computer Interaction), Artificial Intelligence, Blockchain, Computer Vision, IoT and Robotics, Edge and Cloud computing, and Future Mobile Networks. In terms of applications, the metaverse ecosystem allows human users to live and play within a self-sustaining, persistent, and shared realm. Therefore, we discuss six user-centric factors -- Avatar, Content Creation, Virtual Economy, Social Acceptability, Security and Privacy, and Trust and Accountability. Finally, we propose a concrete research agenda for the development of the metaverse.

All One Needs to Know about Metaverse: A Complete Survey on Technological Singularity, Virtual Ecosystem, and Research Agenda

In the last 10 years, freeform optics has enabled compact and high-performance imaging systems. This article begins with a brief history of freeform optics, focusing on imaging systems, including marketplace emergence. The development of this technology is motivated by the clear opportunity to enable science across a wide range of applications, spanning from extreme ultraviolet lithography to space optics. Next, we define freeform optics and discuss concurrent engineering that brings together design, fabrication, testing, and assembly into one process. We then lay out the foundations of the aberration theory for freeform optics and emerging design methodologies. We describe fabrication methods, emphasizing deterministic computer numerical control grinding, polishing, and diamond machining. Next, we consider mid-spatial frequency errors that inherently result from freeform fabrication techniques. We realize that metrologies of freeform optics are simultaneously sparse in their existence but diverse in their potential. Thus, we focus on metrology techniques demonstrated for the measurement of freeform optics. We conclude this review with an outlook on the future of freeform optics.

Freeform optics for imaging

Highly concentrated optical fiber-based daylighting systems for multi-floor office buildings

Freeform optics constitutes a new technology that is currently driving substantial changes in illumination design. It liberates designers and engineers from restrictions of optical surface geometry, enabling them to achieve compact, lightweight, and efficient illumination systems with excellent optical performance. Freeform optics is currently used widely for both fundamental research and practical applications. This Review focuses on the design of freeform illumination optics, which is a key factor in advancing the development of illumination engineering. The design methods of freeform illumination optics can be divided into two groups: zero-´etendue algorithms based on ideal source assumption and design algorithms for extended light sources. The zero-´etendue algorithms include ray mapping method, Monge–Ampere equation method, and supporting quadric method. The algorithms for extended sources include illumination optimization, feedback design, and simultaneous multiple surfaces method. The characteristics and limitations of these design methods are illustrated and a summary of these methods with future outlooks is also given.

Design of Freeform Illumination Optics

In this work, a new two-dimensional optics design method is proposed that enables the coupling of three ray sets with two lens surfaces. The method is especially important for optical systems designed for wide field of view and with clearly separated optical surfaces. Fermat’s principle is used to deduce a set of functional differential equations fully describing the entire optical system. The presented general analytic solution makes it possible to calculate the lens profiles. Ray tracing results for calculated 15th order Taylor polynomials describing the lens profiles demonstrate excellent imaging performance and the versatility of this new analytic design method.

Analytic design method for optimal imaging: coupling three ray sets using two free-form lens profiles.

We reply to the comments on our paper Perfect Drain for the Maxwell fish eye lens (NJP 13 (2011) 023038) made by Fei Sun. We believe that Sun comments have several mistakes in theoretical concepts and simulation results.

Reply to comment on Perfect drain for the Maxwell fish eye lens

Leonhardt (2009 New J. Phys. 11 093040) demonstrated that the two-dimensional (2D) Maxwell fish eye (MFE) lens can focus perfectly 2D Helmholtz waves of arbitrary frequency; that is, it can transport perfectly an outward (monopole) 2D Helmholtz wave field, generated by a point source, towards a ?perfect point drain? located at the corresponding image point. Moreover, a prototype with ?/5 super-resolution property for one microwave frequency has been manufactured and tested (Ma et al 2010 arXiv:1007.2530v1; Ma et al 2010 New J. Phys. 13 033016). However, neither software simulations nor experimental measurements for a broad band of frequencies have yet been reported. Here, we present steady-state simulations with a non-perfect drain for a device equivalent to the MFE, called the spherical geodesic waveguide (SGW), which predicts up to ?/500 super-resolution close to discrete frequencies. Out of these frequencies, the SGW does not show super-resolution in the analysis carried out.

Super-resolution for a point source better than λ/500 using positive refraction

Multi-chip and large size LEDs dominate the lighting market in developed countries these days. Nevertheless, a general optical design method to create prescribed intensity patterns for this type of extended sources does not exist. We present a design strategy in which the source and the target pattern are described by means of “edge wavefronts” of the system. The goal is then finding an optic coupling these wavefronts, which in the current work is a monolithic part comprising up to three freeform surfaces calculated with the simultaneous multiple surface (SMS) method. The resulting optic fully controls, for the first time, three freeform wavefronts, one more than previous SMS designs. Simulations with extended LEDs demonstrate improved intensity tailoring capabilities, confirming the effectiveness of our method and suggesting that enhanced performance features can be achieved by controlling additional wavefronts.

Compact illumination optic with three freeform surfaces for improved beam control.

The Simultaneous Multiple Surface design method in three dimensions (SMS3D) is applied to the design of free-form V-groove reflectors. The general design problem is how to achieve the coupling of two wavefronts after two reflections at the V-groove, no matter which side of the groove the rays hit first. This paper also explains a design procedure for thin dielectric grooved-reflector substitutes for conventional mirrored surfaces. Some canonical V-groove designs are ray-traced in detail.

Free-form V-groove reflector design with the SMS method in three dimensions.

The Simultaneous Multiple Surface design method in two dimensions (SMS2D) is applied to the design of aspheric V-groove reflectors. The general design problem is to achieve perfect coupling of two wavefronts after two reflections at the groove, no matter which side of the groove the rays hit first. Two types of configurations are identified, and several symmetric and asymmetric design examples are given. Computer simulations with a commercial simulation package are also shown.

Dejan Grabovičkić

Papers

Reply to comment on Perfect drain for the Maxwell fish eye lens

Super-resolution for a point source better than λ/500 using positive refraction

Compact illumination optic with three freeform surfaces for improved beam control.

Free-form V-groove reflector design with the SMS method in three dimensions.

Aspheric V-groove reflector design with the SMS method in two dimensions.