Tailoring Accelerating Beams in Phase Space

An appropriate design of wavefront will enable light fields propagating along arbitrary trajectories thus forming accelerating beams in free space. Previous ways of designing such accelerating beams mainly rely on caustic methods, which start from diffraction integrals and only deal with two-dimensional fields. Here we introduce a new perspective to construct accelerating beams in phase space by designing the corresponding Wigner distribution function (WDF). We find such a WDF-based method is capable of providing both the initial field distribution and the angular spectrum in need by projecting the WDF into the real space and the Fourier space respectively. Moreover, this approach applies to the construction of both two- and three-dimensional fields, greatly generalizing previous caustic methods. It may therefore open up a new route to construct highly-tailored accelerating beams and facilitate applications ranging from particle manipulation and trapping to optical routing as well as material processing.Comment: 8 pages, 6 figure

Spin-orbit interaction of light induced by transverse spin angular momentum engineering

We report the first demonstration of a direct interaction between the extraordinary transverse spin angular momentum in evanescent waves and the intrinsic orbital angular momentum in optical vortex beams. By tapping the evanescent wave of whispering gallery modes in a micro-ring-based optical vortex emitter and engineering the transverse spin state carried therein, a transverse-spin-to-orbital conversion of angular momentum is predicted in the emitted vortex beams. Numerical and experimental investigations are presented for the proof-of-principle demonstration of this unconventional interplay between the spin and orbital angular momenta, which could provide new possibilities and restrictions on the optical angular momentum manipulation techniques on the sub-wavelength scale. This phenomenon further gives rise to an enhanced spin-direction coupling effect in which waveguide or surface modes are unidirectional excited by incident optical vortex, with the directionality jointly controlled by spin-orbit states. Our results enrich the spin-orbit interaction phenomena by identifying a previously unknown pathway between the polarization and spatial degrees of freedom of light, and can enable a variety of functionalities employing spin and orbital angular momenta of light in applications such as communications and quantum information processing

Efficient computation of the gravitational wave spectrum emitted by eccentric massive black hole binaries in stellar environments

We present a fast and versatile method to calculate the characteristic spectrum $h_c$ of the gravitational wave background (GWB) emitted by a population of eccentric massive black hole binaries (MBHBs). We fit the spectrum of a reference MBHB with a simple analytic function and show that the spectrum of any other MBHB can be derived from this reference spectrum via simple scalings of mass, redshift and frequency. We then apply our calculation to a realistic population of MBHBs evolving via 3-body scattering of stars in galactic nuclei. We demonstrate that our analytic prescription satisfactorily describes the signal in the frequency band relevant to pulsar timing array (PTA) observations. Finally we model the high frequency steepening of the GWB to provide a complete description of the features characterizing the spectrum. For typical stellar distributions observed in massive galaxies, our calculation shows that 3-body scattering alone is unlikely to affect the GWB in the PTA band and a low frequency turnover in the spectrum is caused primarily by high eccentricities.Comment: 12 pages, 9 figures, published in MNRA

No tension between assembly models of supermassive black hole binaries and pulsar observations

Pulsar timing arrays (PTAs) are presently the only means to search for the gravitational wave stochastic background from supermassive black hole binary populations, considered to be within the grasp of current or near future observations. However, the stringent upperlimit set by the Parkes PTA (Shannon et al. 2013, 2015) has been interpreted as excluding at $> 90\%$ confidence the current paradigm of binary assembly through galaxy mergers and hardening via stellar interactions, suggesting evolution is accelerated (by stars and/or gas) or stalled. Using Bayesian hierarchical modelling, we consider implications of this upperlimit for a comprehensive range of astrophysical scenarios, without invoking stalling nor more exotic physical processes. We find they are fully consistent with the upperlimit, but (weak) bounds on population parameters can be inferred. Bayes factors between models vary between $\approx 1.03$ -- $5.81$ and Kullback-Leibler divergences between characteristic amplitude prior and posterior lie between $0.37$ -- $0.85$. Considering prior astrophysical information on galaxy merger rates, recent upwards revisions of the black hole-galaxy bulge mass relation (Kormendy & Ho 2013) are disfavoured at $1.6\sigma$ against lighter models (e.g. Shankar et al. 2016). We also show, if no detection is achieved once sensitivity improves by an order of magnitude, the most optimistic scenario is disfavoured at $3.9\sigma$.Comment: 20 pages, 7 figure

Spiral Transformation for High-Resolution and Efficient Sorting of Optical Vortex Modes

Mode sorting is an essential function for optical multiplexing systems that exploit the orthogonality of the orbital angular momentum mode space. The familiar log-polar optical transformation provides a simple yet efficient approach whose resolution is, however, restricted by a considerable overlap between adjacent modes resulting from the limited excursion of the phase along a complete circle around the optical vortex axis. We propose and experimentally verify a new optical transformation that maps spirals (instead of concentric circles) to parallel lines. As the phase excursion along a spiral in the wave front of an optical vortex is theoretically unlimited, this new optical transformation can separate orbital angular momentum modes with superior resolution while maintaining unity efficiency