From retrodiction to Bayesian quantum imaging

We employ quantum retrodiction to develop a robust Bayesian algorithm for reconstructing the intensity values of an image from sparse photocount data, while also accounting for detector noise in the form of dark counts. This method yields not only a reconstructed image but also provides the full probability distribution function for the intensity at each pixel. We use simulated as well as real data to illustrate both the applications of the algorithm and the analysis options that are only available when the full probability distribution functions are known. These include calculating Bayesian credible regions for each pixel intensity, allowing an objective assessment of the reliability of the reconstructed image intensity values

Gamma Ray Bursts: Cosmic Rulers for the High-Redshift Universe?

The desire to extend the Hubble Diagram to higher redshifts than the range of current Type Ia Supernovae observations has prompted investigation into spectral correlations in Gamma Ray Bursts, in the hope that standard candle-like properties can be identified. In this paper we discuss the potential of these new `cosmic rulers' and highlight their limitations by investigating the constraints that current data can place on an alternative Cosmological model in the form of Conformal Gravity. By fitting current Type 1a Supernovae and Gamma Ray Burst (GRB) data to the predicted luminosity distance redshift relation of both the standard Concordance Model and Conformal Gravity, we show that currently \emph{neither} model is strongly favoured at high redshift. The scatter in the current GRB data testifies to the further work required if GRBs are to cement their place as effective probes of the cosmological distance scale.Comment: 2 pages, 1 figure (black & white, colour available). To be published in "Phil. Trans. of the Royal Society" as proceedings from Discussion Meeting on Gamma Ray Burst

The azimuthal component of Poynting's vector and the angular momentum of light

The usual description in basic electromagnetic theory of the linear and angular momenta of light is centred upon the identification of Poynting's vector as the linear momentum density and its cross product with position, or azimuthal component, as the angular momentum density. This seemingly reasonable approach brings with it peculiarities, however, in particular with regards to the separation of angular momentum into orbital and spin contributions, which has sometimes been regarded as contrived. In the present paper, we observe that densities are not unique, which leads us to ask whether the usual description is, in fact, the most natural choice. To answer this, we adopt a fundamental rather than heuristic approach by first identifying appropriate symmetries of Maxwell's equations and subsequently applying Noether's theorem to obtain associated conservation laws. We do not arrive at the usual description. Rather, an equally acceptable one in which the relationship between linear and angular momenta is nevertheless more subtle and in which orbital and spin contributions emerge separately and with transparent forms

Optical angular momentum in a rotating frame

It is well established that light carrying orbital angular momentum (OAM) can be used to induce a mechanical torque causing an object to spin. We consider the complementary scenario: will an observer spinning relative to the beam axis measure a change in OAM as a result of their rotational velocity? Remarkably, although a linear Doppler shift changes the linear momentum of a photon, the angular Doppler shift induces no change in the angular momentum. Further, we examine the rotational Doppler shift in frequency imparted to the incident light due to the relative motion of the beam with respect to the observer and consider what must happen to the measured wavelength if the speed of light c is to remain constant. We show specifically that the OAM of the incident beam is not affected by the rotating observer and that the measured wavelength is shifted by a factor equal and opposite to that of the frequency shift induced by the rotational Doppler effect

On lines of constant polarisation in structured light beams

We show that Skyrmion field lines, constructed from the local Stokes parameters, trace out lines of constant optical polarisation

Paraxial Skyrmionic beams

Vector vortex beams possess a topological property that derives both from the spatially varying amplitude of the field and also from its varying polarization. This property arises as a consequence of the inherent Skyrmionic nature of such beams and is quantified by the associated Skyrmion number, which embodies a topological property of the beam. We illustrate this idea for some of the simplest vector beams and discuss the physical significance of the Skyrmion number in this context.Comment: 6 pages, 6 figure

Statistics of photon-subtracted and photon-added states

The subtraction or addition of a prescribed number of photons to a field mode does not, in general, simply shift the probability distribution by the number of subtracted or added photons. Subtraction of a photon from an initial coherent state, for example, leaves the photon statistics unchanged and the same process applied to an initial thermal state increases the mean photon number. We present a detailed analysis of the effects of the initial photon statistics on those of the state from which the photons have been subtracted or to which they have been added. Our approach is based on two closely related moment-generating functions, one that is well established and one that we introduce

A Topological Approach to Characterising Optical Skyrmions

Skyrmions are topologically protected field configurations characterised by a topological index, the skyrmion number. Optical skyrmions are ideally suited to investigate topological structures due to the ease of generating arbitrary light fields, and the freedom from energy constraints encountered by, for example, magnetic skyrmions. Building on our previous work of a topologically defined skyrmion number,1 here we demonstrate the conservation of the skyrmion number of hedgehog skyrmions and bimerons under propagation. We furthermore generate tunable multi-skyrmions from superpositions of oppositely polarised Gaussian and split-vortex beams of different waists, and find that the skyrmion number is conserved as a function of waist scaling. For both cases, the topological definition of the skyrmion number forms an intuitive geometric approach to understanding the underlying topology and to identifying the individual skyrmion structures

Optical Skyrmions

We show that Skyrmions provide a natural language and tool with which to describe and model structured light fields. These fields are characterised by an engineered spatial variation of the optical field amplitude, phase and polarisation. In this short presentation there is scope only for dealing with the simplest (and perhaps most significant) of these namely those that can be designed and propagate within the regime of paraxial optics. Paraxial Skyrmions are most readily defined in terms of the normalised Stokes parameters and as such are properties of the local polarisation at any given point in the structured light beam. They are also topological entities and as such are robust against perturbations. We outline briefly how Skyrmionic beams have been generated to order in the laboratory. Optics gives us access, also, to the Skyrmion field and we present the key properties of this field and show how it provides the natural way to describe the polarisation of structured light beams

Topological approach of characterizing optical skyrmions and multi-skyrmions

The skyrmion number of paraxial optical skyrmions can be defined solely via their polarization singularities and associated winding numbers, using a mathematical derivation that exploits Stokes's theorem. It is demonstrated that this definition provides a robust way to extract the skyrmion number from experimental data, as illustrated for a variety of optical (Néel-type) skyrmions and bimerons and multi-skyrmions. This method generates not only an increase in accuracy, but also provides an intuitive geometrical approach to understanding the topology of such quasi-particles of light and their robustness against smooth transformations