arXiv subjects

Jörg B. Götte

Publications and source records attributed to Jörg B. Götte.

16 recordsLinked to original sources

arXiv2026

Beam shifts and eigenpolarisations for the reflection of vortex beams from homogeneous magnetic surfaces

Probing surfaces with optical beams is a powerful technique utilised for material characterisation, and more recently, measuring surface magnetisation with vortex beams has opened new avenues by utilising OAM beams for metrology. In this paper, we focus on extending the theoretical framework of unit order vortex beam reflection to spatially homogeneous magnetic surfaces, and derive expressions for the Goos-Hänchen (GH) and Imbert-Federov (IF) shifts. We calculate closed form expressions for the plane wave eigenpolarisations, polarisations which remain in the same vectorial direction after reflection, for both dielectric and homogeneous magnetic surfaces. These are found by extending the singularimetry formalism for dielectric surfaces, where the position of the phase vortex can be analytically approximated by taking into account the finite beam width, to homogeneous magnetic surfaces. From this we find the eigenpolarisations of the unit order vortex beam for reflection from both dielectric and homogeneous magnetic surfaces. We discuss with relation to the analytical forms of the Jones matrices for GH and IF shifts the additional reflection behaviour observed for homogeneous magnetic surfaces.

physics.optics↗

arXiv2025

Quantised helicity in optical media

We present a new approach to the definition of optical helicity in a medium. Our approach resolves the problem that duality transformations which simultaneously combine $\mathbf{E}$ with $\mathbf{H}$ and $\mathbf{D}$ with $\mathbf{B}$ are incompatible with linear constitutive relations. We find that the helicity density in a medium, as the conserved quantity associated with duality transforms, must contain an explicit contribution associated with the polarisation and magnetisation of the matter, and that it can be expressed naturally in terms of the elementary polarised excitations of the system. In media for which the helicity is conserved, each circular excitation carries a well-defined helicity. However, in a medium for which the helicity is not conserved, we find that the time-varying helicity can be viewed in terms of oscillations between different helicity eigenstates, analogous to neutrino oscillations. Here we explicitly study the helicity in homogeneous and lossless media but we believe that, differently to other choices, this helicity is readily generalisable to media that may be inhomogeneous, lossy, chiral or nonreciprocal.

physics.optics↗

arXiv2024

Rotational properties of two interacting cold polar molecules: linear, symmetric, and asymmetric tops

We examine the potential-energy curves and polarization of the dipole moments of two static polar molecules under the influence of an external dc electric field and their anisotropic dipole-dipole interaction. We model the molecules as quantum rigid rotors to take their rotational degrees of freedom into account and consider a selection of linear, symmetric, and asymmetric top molecules. We provide a comprehensive examination of the energy curves and polarization of the dipoles for varying inter-molecular separation and direction of the electric field and find that the properties of the molecules depend strongly on the field's direction at short separations, showing the importance of accounting for molecular rotation. The latter provides insight into the possible effects of accounting for rotational degrees of freedom in molecular dipolar gases.

quant-ph↗

arXiv2024

Higher order weak values for paths in nested Mach-Zender interferometers

We consider weak values in the Feynman propagator framework, to gain a broader understanding of their interpretation in terms of path integrals. In particular, we examine the phenomenon of seemingly discontinuous paths that particles take in nested Mach-Zender interferometer experiments. We extend on existing path integral approaches for weak values by deriving expressions to model a sequence of weak measurements, and study the probe shifts across the different branches of a weak value interferometer. We apply this to scrutinise two scenarios of interest, one which treats photons as measurement apparatus via their spatial projection operators, and the second treating mirrors as probes.

quant-ph↗

arXiv2022

Quantum phases of bosonic chiral molecules in helicity lattices

We reveal the existence of polarizing quantum phases for the enantiomers of cold, interacting chiral molecules in an optical helicity lattice by means of an extended Bose-Hubbard model. These recently proposed lattices have sites with alternating helicity which exert a discriminatory force on chiral molecules with different handedness. In our study of the phase diagram we find that a strong dipolar repulsion between molecules results in the separation of left and right enantiomers.

cond-mat.quant-gas↗

arXiv2020

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.

physics.optics↗

arXiv2019

Radiative spin polarization in an ultrastrong magnetic field

We calculate the spin flip rates for an electron in a homogeneous magnetic field for low excitations ($N\le 5$). Our results apply for all field strengths including those beyond the critical field strength at which the spin contributes as much to the electron's energy as its rest mass. Existing approximations either assume that the electron is in a sufficiently highly excited state such that its orbit can be assumed to be classical or the magnetic field be weak compared to the critical field. The regime of high magnetic field strength and low excitations is therefore poorly covered by them. By comparing our calculations to different approximations, we find that in the high field, low excitation regime the spin flip rates are lower and the equilibrium spin polarization is less pure then one would get by naively applying existing approximations in this regime.

hep-ph↗

arXiv2019

On the conservation of helicity in a chiral medium

We consider the energy and helicity densities of circularly polarised light within a lossless chiral medium, characterised by the chirality parameter $β$. A form for the helicity density is introduced, valid to first order in $β$, that produces a helicity of $\pm\hbar$ per photon for right and left circular polarisation, respectively. This is in contrast to the result obtained if we use the form of the helicity density employed for linear media. We examine the helicity continuity equation, and show that this modified form of the helicity density is required for consistency with the dual symmetry condition of a chiral medium with a constant value of $ε/μ$. Extending the results to arbitrary order in $β$ establishes an exact relationship between the energy and helicity densities in a chiral medium.

physics.optics↗

arXiv2018

Chiral Rotational Spectroscopy

We introduce chiral rotational spectroscopy: a new technique that enables the determination of the orientated optical activity pseudotensor components $B_{XX}$, $B_{YY}$ and $B_{ZZ}$ of chiral molecules, in a manner that reveals the enantiomeric constitution of a sample and provides an incisive signal even for a racemate. Chiral rotational spectroscopy could find particular use in the analysis of molecules that are chiral solely by virtue of their isotopic constitution and molecules with multiple chiral centres. The principles that underpin chiral rotational spectroscopy could be exploited moreover in the search for molecular chirality in space, which, if found, might add weight to hypotheses that biological homochirality and indeed life itself are of cosmic origin. A basic design for a chiral rotational spectrometer together with a model of its functionality is given. Our proposed technique offers the more familiar polarisability components $α_{XX}$, $α_{YY}$ and $α_{ZZ}$ as by-products, which could see it find use even for achiral molecules.

physics.atm-clus↗

arXiv2017

Nonuniform currents and spins of relativistic electron vortices in a magnetic field

We present a relativistic description of electron vortex beams in a homogeneous magnetic field. Including spin from the beginning reveals that spin-polarized electron vortex beams have a complicated azimuthal current structure, containing small rings of counterrotating current between rings of stronger corotating current. Contrary to many other problems in relativistic quantum mechanics, there exists a set of vortex beams with exactly zero spin-orbit mixing in the highly relativistic and nonparaxial regime. The well defined phase structure of these beams is analogous to simpler scalar vortex beams, owing to the protection by the Zeeman effect. For states that do show spin-orbit mixing, the spin polarization across the beam is nonuniform rendering the spin and orbital degrees of freedom inherently inseparable.

quant-ph↗

arXiv2016

The conditions for the preservation of duality symmetry in a linear medium

Electric magnetic duality symmetry is well understood in vacuum. For light propagating through a medium this symmetry is typically broken. We investigate under what conditions duality transformation is preserved in a linear medium and employ these conditions to generalise the definition of optical helicity to a general linear medium. We will discuss some unique properties duality symmetric media possess, provided they exist and reformulate Maxwell's equation in such a way that they explicitly show the decoupling of opposite helicities. The feasibility of constructing a duality symmetric medium is discussed.

physics.optics↗

arXiv2015

Electromagnetic wave propagation in spatially homogeneous yet smoothly time-varying dielectric media

We explore the propagation and transformation of electromagnetic waves through spatially homogeneous yet smoothly time-dependent media within the framework of classical electrodynamics. By modelling the smooth transition, occurring during a finite period τ, as a phenomenologically realistic and sigmoidal change of the dielectric permittivity, an analytically exact solution to Maxwell's equations is derived for the electric displacement in terms of hypergeometric functions. Using this solution, we show the possibility of amplification and attenuation of waves and associate this with the decrease and increase of the time-dependent permittivity. We demonstrate, moreover, that such an energy exchange between waves and non-stationary media leads to the transformation (or conversion) of frequencies. Our results may pave the way towards controllable light-matter interaction in time-varying structures.

physics.optics↗

arXiv2014

Eigenpolarizations for Giant Transverse Optical Beam Shifts

We show how careful control of the incident polarization of a light beam close to the Brewster angle gives a giant transverse spatial shift on reflection. This resolves the long-standing puzzle of why such beam shifts transverse to the incident plane [Imbert-Fedorov (IF) shifts] tend to be an order of magnitude smaller than the related Goos-Hänchen (GH) shifts in the longitudinal direction, which are largest close to critical incidence. We demonstrate that with the proper initial polarization the transverse displacements can be equally large, which we confirm experimentally near Brewster incidence. In contrast to the established understanding these polarizations are elliptical and angle-dependent. We explain the magnitude of the IF shift by an analogous change of the symmetry properties for the reflection operators as compared to the GH shift.

physics.optics↗

arXiv2013

Limits to superweak amplification of beam shifts

The magnitudes of beam shifts (Goos-Hänchen and Imbert-Fedorov, spatial and angular) are greatly enhanced when a reflected light beam is postselected by an analyzer, by analogy with superweak measurements in quantum theory. Particularly strong enhancements can be expected close to angles at which no light is transmitted for a fixed initial and final polarizations. We derive a formula for the angular and spatial shifts at such angles (which includes the Brewster angle), and we show that their maximum size is limited by higher-order terms from the reflection coefficients occurring in the Artmann shift formula.

physics.optics↗

arXiv2012

Are Fresnel filtering and the angular Goos-Hänchen shift the same?

The law of reflection and Snell's law are among the tenets of geometrical optics. Corrections to these laws in wave optics are respectively known as the angular Goos-Hänchen shift and Fresnel filtering. In this paper we give a positive answer to the question of whether the two effects are common in nature and we study both effects in the more general context of optical beam shifts. We find that both effects are caused by the same principle, but have been defined differently. We identify and discuss the similarities and differences that arise from the different definitions.

physics.optics↗

arXiv2012

Topological aberration of optical vortex beams and singularimetry of dielectric interfaces

The splitting of a high-order optical vortex into a constellation of unit vortices, upon total reflection, is described and analyzed. The vortex constellation generalizes, in a local sense, the familiar longitudinal Goos-Hänchen and transverse Imbert-Federov shifts of the centroid of a reflected optical beam. The centroid shift is related to the centre of the constellation, whose geometry otherwise depends on higher-order terms in an expansion of the reflection matrix. We present an approximation of the field around the constellation of increasing order as an Appell sequence of complex polynomials whose roots are the vortices, and explain the results by an analogy with the theory of optical aberration.

physics.optics↗