Nonstationary optics: tutorial.

Over the past several decades, nonstationary optics has risen as a key enabling technology for a multitude of novel applications. These include areas of research such as micromachining and ultrafast optics, as well as the Nobel awarded research in femtochemistry, optical frequency combs, and attosecond physics. This tutorial aims to present some of the main concepts required to analyze nonstationary fields, with an emphasis on pulsed beams. The work begins from the fundamental building blocks of such fields, and builds up to some of their main properties. The spatiotemporal properties and stability of such fields are discussed in length, and some common measurement schemes are reviewed.

Cross-spectral purity of the Stokes parameters in random nonstationary electromagnetic beams.

We consider cross-spectral purity in random nonstationary electromagnetic beams in terms of the Stokes parameters representing the spectral density and the spectral polarization state. We show that a Stokes parameter being cross-spectrally pure is consistent with the property that the corresponding normalized time-integrated coherence (two-point) Stokes parameter satisfies a certain reduction formula. The current analysis differs from the previous works on cross-spectral purity of nonstationary light beams such that the purity condition is in line with Mandel's original definition. In addition, in contrast to earlier works concerning the cross-spectral purity of the polarization-state Stokes parameters, intensity-normalized coherence Stokes parameters are applied. It is consequently found that in addition to separate spatial and temporal coherence factors the reduction formula contains a third factor that depends exclusively on polarization properties. We further show that cross-spectral purity implies a specific structure for electromagnetic spectral spatial correlations. The results of this work constitute foundational advances in the interference of random nonstationary vectorial light.

Three-dimensional polarization effects in optical tunneling.

We consider the three-dimensional (3D) polarimetric properties of an evanescent optical field excited in the gap of a double-prism system by a random plane wave. The analysis covers the case of frustrated total internal reflection (FTIR), i.e., optical tunneling, and relies on the characteristic decomposition of the 3×3 polarization matrix. We find in particular that, for any incident partially polarized plane wave, the evanescent field inside the gap is necessarily in a nonregular, genuine 3D polarization state. We also show that the 3D polarimetric properties of the field at the second boundary are sensitive to the changes of the gap width and that the relevant effects occur for the smaller widths when the angle of incidence of the plane wave becomes larger. The results of this work uncover new aspects of the polarimetric structure of genuine 3D evanescent fields and may find applications in near-field optics and surface nanophotonics.

Reduction formula for cross-spectral purity of nonstationary light fields.

We examine cross-spectral purity of random, nonstationary (pulsed), scalar light fields with arbitrary spectral bandwidth. In particular, we derive a reduction formula in terms of time-integrated coherence functions, which ensures cross-spectral purity of interfering fields having identical normalized spectra. We further introduce fields that are cross-spectrally pure in either a global or local sense. Our analysis is based on an ideal field superposition realizable with all-reflective wavefront-shearing interferometers. Such devices avoid certain problems related to Young's interferometer, which is the framework customarily employed in assessing cross-spectral purity. We show that any partially coherent beam can be transformed into a locally cross-spectrally pure beam whose cross-spectral density is specular. On the other hand, lack of space-frequency (and space-time) coupling ensures cross-spectral purity in the global sense, i.e., across an entire transverse plane, regardless of the spectral bandwidth or the temporal shape of the pulses.

Fast and reliable technique for spatial coherence measurement with a temporally modulated nonredundant slit array.

We propose a method of measuring the spatial coherence of light by means of a temporally modulated nonredundant slit array implemented on a digital micromirror device. We first formulate the theory of the spatial coherence measurement to incorporate a general case when the observation plane is not necessarily placed in the far field of the slit array. We then demonstrate experimentally that a single measurement determines the spatial coherence for 15 different slit separations accurately, even if background light is unavoidable, under the condition that a nonredundant array of six slits is illuminated evenly. These results clearly show that fast and highly reliable spatial coherence measurement is achievable with the proposed method without any difficulties.

100 years of Emil Wolf: introduction.

The groundbreaking research and ideas introduced by Emil Wolf continue to inspire researchers and motivate ongoing research in the wave properties of light. This special issue commemorates the legacy of Emil Wolf with research in physical optics, with specific focus on those areas where Wolf was active, such as optical coherence theory, inverse problems, singular optics, imaging, and polarization, and the intersection of these fields of study. Here we discuss the life of Emil Wolf and his influence on optical science and the optics community.

Singular-value decomposition and electromagnetic coherence of optical beams.

We investigate the implications of the singular-value decomposition of the cross-spectral density (CSD) matrix to the description of electromagnetic spectral spatial coherence of stationary light beams. We show that in a transverse plane any CSD matrix can be expressed as a mixture of two CSD matrices corresponding to beams which are fully polarized but in general spatially partially coherent. The polarization and coherence structures of these constituent beams are specified, respectively, by the singular vectors and singular values of the full CSD matrix. It follows that vector-beam coherence, including the coherence Stokes parameters and the degree of coherence, can be formulated in terms of only two correlation functions. We further establish two-point analogs of the spectral and characteristic decompositions of the polarization matrix and show that in the case of a Hermitian CSD matrix their composition is specified by the so-called degree of cross-polarization.

Polarization-resolved scintillations in Young's experiment.

The conventional scintillation, or intensity fluctuation, that occurs in random electromagnetic beams is just one member of a broader class of four interconnected, polarization-resolved scintillations. We examine these generalized scintillations, called Stokes scintillations, that occur when two stochastic electromagnetic beams are made to interfere in Young's experiment. We find that the magnitude of the conventional scintillation can be decreased, within certain limits, at the expense of an increase of one or more of the other Stokes scintillations. For certain applications however, it may be beneficial to suppress the latter.

On the inclusion of forest exposure pathways into a stylized lake-farm scenario in a geological repository safety analysis.

Geological disposal of radioactive waste has been recognized as the 'reference solution' to ensure the safety required for the present and future society and environment. To study the possible exposure pathways from groundwater to humans, radioactive transport modelling is used. One of the ecosystems that may play a significant role when assessing the dose conversion factor (i.e. the dose resulting from a nominal release of 1 Bq/year of each radionuclide) for humans is forest. In this paper we have developed a model of a lake-farm system with a forest component. The biosphere system used in this study represents a typical agricultural scenario in Finland, amended with a typical forest. A lake is assumed to form due to post-glacial land uplift. The main features of this future lake have been obtained from our probabilistic shoreline displacement model. Both deterministic calculations and sensitivity analysis were carried out to simulate the model. The deterministic simulation demonstrates the behaviour of the studied radionuclides (36Cl, 135Cs, 129I, 237Np, 90Sr, 99Tc and 238U) and the proportions of different exposure pathways to humans. Particularly for 135Cs and 129I, forest pathways make a notable contribution to the dose conversion factor. The sensitivity analysis was done using two methods: EFAST and Sobol'. With both methods, the parameters related to the farm contribute the most to the variance of the dose conversion factor for humans. The study demonstrates that the exposure pathways related to forest products may make a considerable contribution to the dose conversion factor in a lake-farm-forest system. It is also confirmed that an advanced sensitivity analysis for a radionuclide transport and dose assessment model on such a landscape scale is feasible even with moderate computational efforts.

Probing coherence Stokes parameters of three-component light with nanoscatterers.

We establish a method to determine the spectral coherence Stokes parameters of a random three-component optical field via scattering by two dipolar nanoparticles. We show that measuring the intensity and polarization-state fringes of the scattered far field in three directions allows us to construct all nine coherence Stokes parameters at the dipoles. The method extends current nanoprobe techniques to detection of the spatial coherence of random light with arbitrary three-dimensional polarization structure.

Safety assessments undertaken using the BIOMASS methodology: lessons learnt and methodological enhancements.

The International Atomic Energy Agency has coordinated an international project addressing enhancements of methods for modelling in post-closure safety assessments of solid radioactive waste disposal. The project used earlier published work from the IAEA biosphere modelling and assessment (BIOMASS) project to further develop methods and techniques. The task was supported by a parallel on-going project within the BIOPROTA forum. The output from the project is described in detail in a forthcoming IAEA report. Here an overview of the work is given to provide researchers in the broader fields of radioecology and radioactive waste disposal with a summarised review of the enhanced BIOMASS methodology and the work that has been undertaken during the project. It is hoped that such dissemination will support and promote integrated understanding and coherent treatment of the biosphere component within the overall assessment process. The key activities undertaken in the project were: review and identification of those parts of the original BIOMASS methodology that needed enhancement, discussions on lessons learned from applying the BIOMASS method, using real examples to assess the methodology and its usefulness, and writing of those parts of the methodology that were considered could benefit from refinement or for which new guidance was required to take account of scientific developments. The work has shown that the overall approach in the original BIOMASS methodology has proven sound. However, the enhanced version clarifies the need for an iterative and holistic approach with system understanding central to the approach. Specifically, experience, especially in site-specific contexts, has emphasised that adequate system understanding is essential in underpinning safety assessments for radioactive waste disposal. The integral role of the biosphere within safety assessment is also emphasised in the enhanced methodology.

Poincaré sphere representation of scalar two-beam interference under spatial unitary transformations.

We consider two partially correlated scalar light beams in a spatially unitary interference setup. We introduce a state vector in a Poincaré-sphere-like geometrical configuration that fully specifies such an optical system and its evolution under spatial unitary transformations. We also identify three particular unitary operations together with their geometrical representations that can be optically implemented to realize an arbitrary spatial unitary transformation. Our work forms an advantageous geometrical platform to characterize distinguishability, visibility, degree of coherence, and classical entanglement, as well as their spatial unitary evolutions, in scalar two-beam light interference.

Coherence Switching with Metamaterials.

We demonstrate, theoretically, how the insertion of an enhanced epsilon-near-zero (EENZ) mirror in a laser cavity grants exceptional control over the coherence properties of the emitted light beam. By exploiting the peculiar sensitivity to polarization of EENZ materials, we achieve superior control over the spatial coherence of the emitted laser light, which can be switched at will between nearly incoherent and fully coherent, solely by means of polarization optics. Our EENZ cavity design is expected to be an efficient, compact, reconfigurable, and easily scalable source of light for illumination and speckle contrast imaging, as well as any other application that benefits from controlled spatial coherence.

Spatial coherence measurement via a digital micromirror device based spatiotemporal light modulation.

We propose a method for measuring the spatial coherence of light by means of temporal modulation of a double slit displayed on a digital micromirror device. It is demonstrated theoretically and experimentally that the technique is generally insensitive to background light, and thus its suppression or subtraction is not necessary. Moreover, the visibility of the interference fringe pattern can be enhanced by modulating only either one of the two slits. These favorable features enable one to measure the spatial coherence of even faint light more conveniently and accurately.

Complete coherence of random, nonstationary electromagnetic fields.

Despite a wide range of applications, the coherence theory of random, nonstationary (pulsed or otherwise) electromagnetic fields is far from complete. In this work, we show that full coherence of a nonstationary vectorial field at a pair of spatiospectral points is equivalent to the factorization of the cross-spectral density matrix, and full pointwise coherence over a spatial volume and spectral band leads to a factored cross-spectral density throughout the domain. We further show that in the latter case, the time-domain mutual coherence matrix factors in the spatiotemporal variables, and the field is temporally fully coherent throughout the volume. The results of this work justify that certain expressions of random pulsed electromagnetic beams appearing in the literature can be called coherent-mode representations.

Poincaré sphere of electromagnetic spatial coherence.

We introduce a Poincaré sphere construction for geometrical representation of the state of two-point spatial coherence in random electromagnetic (vectorial) beams. To this end, a novel descriptor of coherence is invoked, which shares some important mathematical properties with the polarization matrix and spans a new type of Stokes parameter space. The coherence Poincaré sphere emerges as a geometric interpretation of this novel formalism, which is developed for uniformly and nonuniformly fully polarized beams. The construction is extended to partially polarized beams as well and is demonstrated with a field having separable spatial coherence and polarization characteristics. At a single point, the coherence Poincaré sphere reduces to the conventional polarization Poincaré sphere for any state of partial polarization.

System understanding as a scientific foundation in radioactive waste disposal, legacy site and decommissioning programmes.

Ongoing national programmes and International forums have in recent decades developed and enhanced methods and strategies in how to address the characterisation of potentially suitable sites for radioactive waste repositories. Siting processes, site selection and site investigation programmes have been conducted for near surface and geological repositories and plans for construction are in progress or have already been implemented. Lessons learned from these national and international programmes are available and results are published. In this paper we synthesise the methods and our lessons learned in how to plan, conduct, and achieve site understanding. Effective site understanding should incorporate a multi-disciplinary and integrated view of geosphere and biosphere information for a site, together with the designed parts of a repository or installation that constitute the total system. We argue that this integrated approach, following a staged program of repository development and adopting a graded approach to assessment at each stage, is to be recommended. The recommendation is supported by the results of international cooperation and progress with national programmes (e.g. the Swedish SKB). Further, we argue that this strategy is valid as a foundation for planning and execution of other types of radioactive waste management programmes such as decommissioning, legacy site management and remediation projects.

Correlated and uncorrelated parts of scalar fields in two-beam optical interferometry.

We show that in the interference of two partially correlated scalar light beams, the fields can be divided into parts that are mutually completely correlated (coherent) and parts that are fully uncorrelated with the correlated parts and with each other. Such correlated and uncorrelated parts cannot, in general, be unambiguously specified, but with a certain additional constraint, the partition becomes unique and can be determined. We demonstrate experimentally that the uncorrelated contribution can be physically isolated with the help of a spatial unitary transformation, such as a nonabsorbing beam splitter. Our findings constitute foundational results on optical two-beam interferometry.