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As a classical or quantum system undergoes a cyclic evolution governed by slow change in its parameter space, it acquires a topological phase factor known as the geometric or Berry phase. One popular manifestation of this phenomenon is the Gouy phase which arises when the radius of curvature of the wavefront changes adiabatically in a cyclic manner, for e.g., when focused by a lens. Here, we report on a new manifestation of the Berry phase in 3D structured light which arises when its polarization state adiabatically evolves along the optical path. We show that such a peculiar evolution of angular momentum, which occurs under free space propagation, is accompanied by an accumulated phase shift that elegantly coincides with Berry’s prediction. Unlike the conventional dynamic phase, which accumulates monotonically with propagation, the Berry phase observed here can be engineered on demand, thereby enabling new possibilities; such as spin-dependent spatial frequency shifts, and modified phase matching in resonators and nonlinear interactions. Our findings expand the laws of wave propagation and can be applied in optics and beyond.

In this Letter, we investigate a new class of polarization wave front transformations which exhibit nonconventional far field interference behavior. We show that these can be realized by double-layer metasurfaces, which overcome the intrinsic limitations of single-layer metasurfaces. Holograms that encode four or more distinct patterns in nonorthogonal polarization states are theoretically demonstrated. This Letter clarifies and expands the possibilities enabled by a broad range of technologies which can spatially modulate light's polarization state and, for metasurfaces specifically, rigorously establishes when double-layer metasurfaces are-and are not-required.

Polarization plays a key role in science; hence its versatile manipulation is crucial. Existing polarization optics, however, can only manipulate polarization in a single transverse plane. Here we demonstrate a new class of polarizers and wave plates—based on metasurfaces—that can impart an arbitrarily chosen polarization response along the propagation direction, regardless of the incident polarization. The underlying mechanism relies on transforming an incident waveform into an ensemble of pencil-like beams with different polarization states that beat along the optical axis thereby changing the resulting polarization at will, locally, as light propagates. Remarkably, using form-birefringent metasurfaces in combination with matrix-based holography enables the desired propagation-dependent polarization response to be enacted without a priori knowledge of the incident polarization—a behaviour that would require three polarization-sensitive holograms if implemented otherwise. Our work expands the use of polarization in the design of multifunctional metasurfaces and may find application in tunable structured light, optically switchable devices and versatile light–matter interactions. Using a metasurface that allows shaping of the polarization state of a light beam independently at each point of space along its propagation direction, longitudinally variable polarization optical components are demonstrated, inspiring new directions in structured light, polarization-switchable devices and light–matter interaction.

Metasurfaces are a new class of diffractive optical elements with subwavelength elements whose behavior can be lithographically tailored. By leveraging form birefringence, metasurfaces can serve as multifunctional freespace polarization optics. Metasurface gratings are novel, to the best of our knowledge, polarimetric components that integrate multiple polarization analyzers into a single optical element enabling the realization of compact imaging polarimeters. The promise of metasurfaces as a new polarization building block is contingent on the calibration of metagrating-based optical systems. A prototype metasurface full Stokes imaging polarimeter is compared to a benchtop reference instrument using an established linear Stokes test for 670, 532, and 460 nm gratings. We propose a complementary full Stokes accuracy test and demonstrate it using the 532 nm grating. This work presents methods and practical considerations involved in producing accurate polarization data from a metasurface-based Stokes imaging polarimeter and informs their use in polarimetric systems more generally.

Recent work on beams with light structured along the propagation direction will be presented, where the polarization and the OAM of the beam changed along the propagation direction.

Metasurfaces are arrays of artificially engineered subwavelength nanostructures. Owing to the strong form birefringence of these nanostructures, metasurfaces provide a fascinating platform to realize novel polarization optics. Recently, we proposed a more general design strategy for polarization-dependent metasurfaces using Fourier optics principles applied to the Jones calculus. We use this to design metasurface devices with arbitrarily chosen polarization responses embedded on diffraction orders, such as polarizers, waveplates, and cases that are mixtures of the two. We fabricate these gratings (for operation at visible wavelengths) and test them with Mueller matrix polarimetry, showing agreement with design.

Metasurfaces are arrays of artificially engineered subwavelength nanostructures. Owing to the strong form birefringence of these nanostructures, metasurfaces provide a fascinating platform to realize novel polarization optics. Recently, we propose and implement a general design strategy for polarization-dependent holograms with metasurfaces, using Fourier optics and phase retrieval principles applied to the Jones calculus. We use this to design metasurface holograms with arbitrarily chosen polarization responses. We fabricate these gratings (for operation at visible wavelengths) and test them with Mueller matrix polarimetry, showing agreement with design.

Metasurfaces may be structured with anisotropic constituent elements, leading to form birefringence. In recent years, these devices have enabled a variety of new polarization-dependent optical elements. The most general of these are holograms; a wide variety of polarization-dependent holograms have been demonstrated with metasurfaces, including those that can be switched by an arbitrarily specified basis of (in general) elliptical polarization states. In this presentation, we will thoroughly review work of this nature. In doing so, we will show that the design freedom afforded by form-birefringent metasurfaces to produce polarization-dependent holograms has not been fully exploited: metasurfaces may be used to produce what we dub “Jones matrix holograms”, in which the polarization response is not limited to an orthogonal basis of polarization states. Examples of these are shown.

Vector beams can be structured to change their polarization state and topological charge locally with propagation. We report on the observation of Berry phase factor accompanying these transitions and provide a recipe for engineering it on demand.

We propose a new class of computer generated holograms whose far fields possess designer-specified polarization response. We dub these Jones matrix holograms. We provide a simple procedure for their implementation using form-birefringent metasurfaces. Jones matrix holography generalizes a wide body of past work with a consistent mathematical framework, particularly in the field of metasurfaces, and suggests previously unrealized devices, examples of which are demonstrated here. In particular, we demonstrate holograms whose far-fields implement parallel polarization analysis and custom waveplate-like behavior., 10 pages, 5 figures

Dielectric metasurfaces, which consist of spatially distributed sub-wavelength structures that impart controlled local phase shifts to the exiting light, allow access to modifying the wavefront and achieve desired function of the output beam. By adjusting the sub-wavelength structures’ shape, size, and choice of material, one can locally control the effective refractive index that affects the output light’s phase, amplitude, and dispersion, allowing various degrees of freedom in design parameters. The first generation of metasurfaces consisted of individual lab prototypes that in crucial parts relied on electron beam lithography, which severely restricted scalability. Meanwhile, mask-based methods such as deep UV lithography have been successfully adopted. While such methods open the door to high-throughput fabrication of metasurfaces, they are still limited in their achievable sample dimensions due to size restrictions imposed by wafer-based methods. By using roll-to-roll (R2R) methods, we were able to make large area metasurfaces that could find their use in displays and AR/VR applications, for example. In addition, R2R creates a lower cost method of manufacture for large volumes. In order to utilize R2R methods, there are two important challenges to overcome. First, the pattern must be extended over the large area of a film surface. Second, standard metasurface designs need to be adapted to the material and process constraints of R2R manufacturing. The R2R fabrication route is an extension of large-scale industrial processes that can produce wide format rolls of film.

Polarization, the path along which light’s electric field oscillates, is a key property of electromagnetic radiation. In this work, we motivate a mathematical framework—Matrix Fourier optics—that enables a simple description of light’s interaction with diffractive optics that spatially modify polarization. This formalism generalizes a large body of past work in metasurface polarization optics. We show how Matrix Fourier optics allows for the design of arbitrary polarization-analyzing metasurface gratings. These gratings can be used as the single polarization component in a compact full-Stokes polarization camera. We demonstrate practical, real-time polarization photography with this camera, which may find application in machine vision and remote sensing.

Metasurfaces—subwavelength arrays of phase-shifting elements—present new possibilities for polarization optics and polarimetry. In particular, a periodic, polarization-sensitive metasurface diffraction grating can enable full-Stokes imaging polarimetry with a single polarization-sensitive component. In this work, we show that a suitably-designed metasurface grating can serve as a polarimetric “attachment” to an existing intensity-only imaging system, converting it into one capable of full-Stokes imaging polarimetry. Design rules and tradeoffs governing this adaptation are described and demonstrated using a machine vision imaging system as an example.

Polarization, the path traced by light’s electric field vector, appears in all areas of optics. In recent decades, various technologies have enabled the precise control of light’s polarization state, even on a subwavelength scale, at optical frequencies. In this review, we provide a thorough, high-level review of the fundamentals of polarization optics and detail how the Jones calculus, alongside Fourier optics, can be used to analyze, classify, and compare these optical elements. We provide a review of work in this area across multiple technologies and research areas, including recent developments in optical metasurfaces. This review unifies a large body of work on spatially varying polarization optics and may be of interest to both researchers in optics and designers of optical systems more generally.

Metasurfaces are arrays of sub-wavelength spaced nanostructures, which can be designed to control the many degrees-of-freedom of light on an unprecedented scale. In this work, we design meta-gratings where the diffraction orders can perform general, arbitrarily specified, polarization transformation without any reliance on conventional polarization components, such as waveplates and polarizers. We use matrix Fourier optics to design our devices and introduce a novel approach for their optimization. We implement the designs using form-birefringent metasurfaces and quantify their behavior – retardance and diattenuation. Our work is of importance in applications, such as polarization abberation correction in imaging systems, and in experiments requiring novel and compact polarization detection and control.

We introduce a new class of polarizing elements (analyzers and retarders) that virtually rotate their orientation as a function of the propagation distance, thus expanding the scope of conventional polarization devices into 3D space.

We present compact planar devices that enable light’s spin and orbital angular momenta to evolve, simultaneously, from one state to another along the propagation direction, and report on arbitrary spin-orbit coupling in three dimensional vortices.

Metasurfaces, nanophotonic arrays of subwavelength phase shifting elements, hold promise for the miniaturization of a variety of bulk optical elements. Owing to the flexibility with which their constituent elements may be engineered, metasurfaces allow for point-to-point polarization control on a subwavelength scale. Metasurfaces, then, represent an exciting new platform for polarization optics. A single metasurface may combine many different polarization-dependent functionalities that would ordinarily be spread out over many optical elements. We describe how, through relatively simple optimization methods, a metasurface producing arbitrarily specified polarization states can be designed. This functionality is equivalent to a traditional diffraction grating with individual waveplate optics on each order; here, all the necessary polarization optics can be integrated into a flat, efficient, and ultrathin metasurface optical element. Moreover, such a metasurface can be used in a reverse configuration as a parallel snapshot polarimeter with no need for additional polarization optics. We present a detailed experimental characterization of this device in the visible spectral region and a comparison of the performance of the metasurface to a commercially available rotating waveplate polarimeter. Metasurfaces can enable compact, miniaturized sensors for polarimetry and polarization imaging. We will conclude with a perspective on these possibilities and their implications for remote sensing. Metasurface polarization optics can overcome limitations of previous diffractive/grating based polarimetry schemes are potentially of significant interest to the imaging polarimetry community.

Metasurfaces, nanophotonic arrays of phase shifting elements, hold promise for the miniaturization of a variety of bulk optical elements, most notably lenses and imaging systems. Owing to the flexibility with which their constituent elements may be engineered, metasurfaces allow for point-to-point polarization control on a subwavelength scale. For this reason, metasurfaces represent an exciting new platform for polarization optics as well. I will discuss how this functionality allows for a new perspective on diffractive optics which explicitly acknowledges the vectorial nature of light. This perspective motivates a theory of unitary polarization gratings; I will derive a few key results concerning these gratings. I will discuss and demonstrate how this perspective allows for the design of metasurfaces with new polarization functionalities. I will describe how, through relatively simple optimization methods, a metasurface producing arbitrarily specified polarization states can be designed. This functionality is equivalent to a traditional diffraction grating with individual waveplate optics on each order; here, all the necessary polarization optics can be integrated into a flat, ultrathin optical element. Moreover, such a metasurface can be used in a reverse configuration as a parallel snapshot polarimeter with no need for additional polarization optics. I present a detailed experimental characterization of this device in the visible spectral region and a comparison of the performance of the metasurface to a commercially available rotating waveplate polarimeter. Finally, I will discuss the extension of these concepts to compact polarization imaging systems and will provide a broad outlook on metasurfaces in polarization optics, polarization sensing systems, and polarization instrumentation more generally.

Since the days of Hertz, radio transmitters have evolved from rudimentary circuits emitting around 50 MHz to modern ubiquitous Wi-Fi devices operating at gigahertz radio bands. As wireless data traffic continues to increase, there is a need for new communication technologies capable of high-frequency operation for high-speed data transfer. Here, we give a proof of concept of a compact radio frequency transmitter based on a semiconductor laser frequency comb. In this laser, the beating among the coherent modes oscillating inside the cavity generates a radio frequency current, which couples to the electrodes of the device. We show that redesigning the top contact of the laser allows one to exploit the internal oscillatory current to drive a dipole antenna, which radiates into free space. In addition, direct modulation of the laser current permits encoding a signal in the radiated radio frequency carrier. Working in the opposite direction, the antenna can receive an external radio frequency signal, couple it to the active region, and injection lock the laser. These results pave the way for applications and functionality in optical frequency combs, such as wireless radio communication and wireless synchronization to a reference source.

In polarimetry, that is, a measurement of the four-component polarization Stokes vector, a measurement must either consist of four (or more) sequential intensity measurements, sacrificing time resolution, or contain four separate light paths each with separate polarization optics, increasing bulk, cost, and system complexity. Similar issues present difficulty across polarization optics technology. Metasurfaces, nanophotonic arrays of phase shifting elements, have emerged as a novel platform for polarization optics. These individual phase shifters can be designed with a characteristic anisotropy, and are thus imbued with tunable shape birefringence. A metasurface, then, can function as a subwavelength spaced array of nanoscale waveplates. I will describe how, through relatively simple optimization methods, a metasurface producing arbitrarily specified polarization states (when illuminated with light of a known polarization) can be designed. This functionality is equivalent to a traditional diffraction grating with individual waveplate optics on each order; here, all the necessary polarization optics can be integrated into a flat, ultrathin optical element. Moreover, such a metasurface can be used in a reverse configuration as a parallel snapshot polarimeter with no need for additional polarization optics (save for a single polarizer). I present a detailed experimental characterization of both concepts in the visible spectral region and a comparison of the performance of the metasurface to a commercially available rotating waveplate polarimeter. With no bulk birefringent crystal optics, a parallel, full-polarization state measurement can be made with an integrated, scalable, and inexpensive device. Given its diffractive nature, the design naturally extends to spectropolarimetry and polarization imaging.

A metasurface polarization camera Imaging the polarization of light scattered from an object provides an additional degree of freedom for gaining information from a scene. Conventional polarimeters can be bulky and usually consist of mechanically moving parts (with a polarizer and analyzer setup rotating to reveal the degree of polarization). Rubin et al. designed a metasurface-based full-Stokes compact polarization camera without conventional polarization optics and without moving parts. The results provide a simplified route for polarization imaging. Science , this issue p. eaax1839

Optical elements that couple the spin/orbital angular momentum (SAM/OAM) of light have found a range of applications in classical and quantum optics. The J-plate, which refers to the variable denoting the photon’s total angular momentum (TAM), is a metasurface device that allows converting arbitrary, orthogonal input SAM states into two unique OAM states. Using independent phase control of any orthogonal basis of polarization states, the J-plate permits the conversion of arbitrary polarizations into states with arbitrary OAM. Here, we present a further development: Cascaded J-plates provide for versatile combinations of OAM states on any orthogonal basis of spin states. J-plates operating on different polarization bases and imparting independent values of OAM are designed and experimentally demonstrated to generate multiple OAM channels with different polarization states. The generated OAM states are determined by the superposition of the OAM states of the individual J-plates while the generated SAM states are determined by the polarization basis of the last J-plate. Theoretically, there are maximum of 2^n channels of OAM and n×2^n channels of TAM that can be generated by n such cascaded J-plates. It is also demonstrated that cascaded J-plates may produce complex structured light. Cascading J-plates provides a new way to control the TAM of a laser beam. These results may find application in quantum and classical communication.

The recently discovered ability of the quantum cascade laser to produce a harmonic frequency comb has attracted new interest in these devices for both applications and fundamental laser physics. In this review we present an extensive experimental phenomenology of the harmonic state, including its appearance in mid-infrared and terahertz quantum cascade lasers, studies of its destabilization induced by delayed optical feedback, and the assessment of its frequency comb nature. A theoretical model explaining its origin as due to the mutual interaction of population gratings and population pulsations inside the laser cavity will be described. We explore different approaches to control the spacing of the harmonic state, such as optical injection seeding and variation of the device temperature. Prospective applications of the harmonic state include microwave and terahertz generation, picosecond pulse generation in the mid-infrared, and broadband spectroscopy.

Publisher’s Note: This conference presentation recording, originally published on 14 March 2018, was withdrawn per author request on 22 March, 2018.

Controlling the spacing of self-starting harmonic frequency combs in QCLs by design of fundamental laser parameters is arduous. New ways to shape such combs by means of original electrical, optical and radiofrequency techniques are presented.

From spins to spirals The polarization state of light can be used in imaging applications and optical communications. Light can also be structured into vortices that carry optical angular momentum, which can be used for micromanipulation and enhancing the capacity of optical communication channels. Devlin et al. present a metasurface converter for optical states that transforms polarization states into optical angular momentum states. The coupling between arbitrary spin and optical angular momentum states of light in a compact planar structure may find applications in producing complex structured light fields. Science , this issue p. 896

We present a method allowing for the imposition of two independent and arbitrary phase profiles on any pair of orthogonal states of polarization-linear, circular, or elliptical-relying only on simple, linearly birefringent wave plate elements arranged into metasurfaces. This stands in contrast to previous designs which could only address orthogonal linear, and to a limited extent, circular polarizations. Using this approach, we demonstrate chiral holograms characterized by fully independent far fields for each circular polarization and elliptical polarization beam splitters, both in the visible. This approach significantly expands the scope of metasurface polarization optics.

The article presents the short urban history of Tel Aviv as a case-study for critical readings in urban planning. Focusing on Patrick Geddes’ celebrated plan for the city (1925) and its various interpretations along the years, the main claim made in the article is that when present planners are confronted with a past which does not suit current needs, history is contested, or reinvented entirely. The appreciation of Geddes’ plan over the years always reflected the city's contemporary image and its planners’ attitudes, which initially reflected the pioneering spirits of the city's Zionist creation. The plan was later blamed for the city's deterioration; and finally celebrated again, alongside the city's new found architectural heritage and urban spirit.

This special issue aims to foreground the city within diaspora studies and, in particular, within research on South Asian diasporas. Drawing together papers that focus on cities of diasporic depart...

Whilst the city is a central focus of research on diasporic resettlement, little research has explored the city as a site of diasporic return. This paper explores return visits to Calcutta by members of the Anglo-Indian and Jewish communities who have migrated to London, Toronto and Israel since 1947. In doing so, the paper contributes to broader debates about return visits and migrations as well as the connections between cities, communities and diasporas. Unlike research that focuses on the nation and/or ‘homeland’, the paper explores the city as a destination for diasporic return. In contrast to work that concentrates on particular ethnic groups that become minorities after migration and expect to feel an ethnic ‘affiliation’ on their return, the paper studies two communities that were minorities before migration. Drawing on interviews with Anglo-Indian and Jewish Calcuttans, the paper argues that decisions to return – and not to return – are shaped by ideas about the city as home more than the nation ...

Patrick Geddes worked in Jerusalem between 1919 and 1925. He was originally summoned to the city by the Zionists, in order to plan the Hebrew University of Jerusalem; eventually, he also submitted an overall plan for the city, presented to its British Governor. Geddes’ university plan and many of his other local cultural and educational endeavours were not successful. However, his plan for the city was approved and still dictates its development on many planes. The article discusses Geddes’ overall work in Jerusalem as a product of his imperial world view, as he pictured the re-instatement of a biblical Jerusalem and assigned the homecoming Zionists the ancient role of a regional leader among its neighbouring countries. Geddes’ tools for the study of the environment, such as the survey, and his educational endeavours such as the museum and the exhibition, are discussed as local manifestations of the geographical imperial project. Geddes’ urban theory is discussed as a rigid and a foreign product of western and orientalist nature, which was enforced upon the landscape. Geddes himself is presented as a colonial town planner, one who practiced through an imperial professional and personal network and who had aspired to serve both the British and the Jews over the control of identity and space in contested Palestine. Finally, the article links Geography and Planning through the colonial practice of urban and social transformation.

Optical elements coupling the spin and orbital angular momentum (SAM/OAM) of light have found a range of applications in classical and quantum optics. The J-plate, with J referring to the photon's total angular momentum (TAM), is a metasurface device that imparts two arbitrary OAM states on an arbitrary orthogonal basis of spin states. We demonstrate that when these J-plates are cascaded in series, they can generate several single quantum number beams and versatile superpositions thereof. Moreover, in contrast to previous spin-orbit-converters, the output polarization states of cascaded J-plates are not constrained to be the conjugate of the input states. Cascaded J-plates are also demonstrated to produce vector vortex beams and complex structured light, providing new ways to control TAM states of light.

The constituent elements of metasurfaces may be designed with explicit polarization dependence, making metasurfaces a fascinating platform for new polarization optics. In this work we show that a metasurface grating can be designed to produce arbitrarily specified polarization states on a set of defined diffraction orders given that the polarization of the incident beam is known. We also demonstrate that, when used in a reverse configuration, the same grating may be used as a parallel snapshot polarimeter, requiring a minimum of bulk polarization optics. We demonstrate its use in measuring partially polarized light, and show that it performs favorably in comparison to a commercial polarimeter. This work is of consequence in any application requiring lightweight, compact, and low-cost polarization optics, polarimetry, or polarization imaging.

In standing-wave lasers, spatial hole burning induces a static grating of the population inversion, enabling multimode operation with several independent lasing modes. In the presence of a mode-locking mechanism, these modes may become correlated, giving origin to a frequency comb. Quantum cascade lasers, owing to their ultrafast gain dynamics, are ideally suited to achieve comb operation. Here we experimentally demonstrate that the modes of a quantum cascade laser frequency comb coherently beat to produce time-dependent population inversion gratings, which spatially modulate the current in the device at frequencies equal to the mode separation and its higher harmonics. This phenomenon allows the laser to serve as a phased collection of microwave local oscillators and is utilized to demonstrate quadrature amplitude modulation, a staple of modern communications. These findings may provide for a new class of integrated transmitters, potentially extending from the microwave to the low terahertz band.

This paper analyses the seemingly unified perception of Patrick Geddes, an important member of the Town Planning Movement and a profound founding father of the discipline. A critical reading into the appreciation of Geddes as a planner shows that it nevertheless altered considerably over the years. Identifying four major periods in which ‘Geddes appreciation’ changed considerably, I claim that these periods reflect an agreed periodization of modern urban planning, and that variations in the way Geddes has been appreciated over the years mirror changing notions in planning in general. Tracing changes in the perception of Geddes as a planner further raises questions regarding the history of planning itself: Who tells planning history? How do planners interpret past achievements and failures? What do planners today think about their predecessors, and why does it change along the years? By providing a thorough review of Geddes' planning historiography, I thus present his ongoing investigation as a case study ...

The aim of the paper is to bring together art and the city by linking town planning and the Arts & Crafts movement. This association is evident in the theoretical writing and professional practice of the architect Charles Robert Ashbee (1863–1942), whose work is characterized by a blend of tradition and innovation. Ashbee, a prominent artist, served as a British town planner in Jerusalem, assisting its first governor, Sir Ronald Storrs, in laying out the city and providing services for its inhabitants. In Jerusalem, Ashbee received his only chance to realize his artistic urban Utopia. The paper discusses Ashbee as a town planner and explores his artistic urban ideal, revealing his comprehensive appreciation of the city and its constituent artistic and social traits, and his combination of the modern requirements of a growing city with traditional artistic ideals. This was the basis of Ashbee’s work in Jerusalem and determined many of its results. In many ways, Ashbee’s ideas still guide the development of...

We investigate the nonlinear optical response of a commercial extended-wavelength In$_{0.81}$Ga$_{0.19}$As photodetector. Degenerate two-photon absorption in the mid-infrared range is observed at room temperature using a quantum cascade laser emitting at $\lambda=4.5~\mu$m as the excitation source. From the measured two-photon photocurrent signal we extract a two-photon absorption coefficient $\beta^{(2)} = 0.6 \pm 0.2$ cm/MW, in agreement with the theoretical value obtained from the $E_g^{-3}$ scaling law. Considering the wide spectral range covered by extended-wavelength In$_x$Ga$_{1-x}$As alloys, this result holds promise for new applications based on two-photon absorption for this family of materials at wavelengths between 1.8 and 5.6 $\mu$m.