Convergence of many-body wavefunction expansions using a plane wave basis: from the homogeneous electron gas to the solid state

Using the finite simulation-cell homogeneous electron gas (HEG) as a model, we investigate the convergence of the correlation energy to the complete basis set (CBS) limit in methods utilising plane-wave wavefunction expansions. Simple analytic and numerical results from second-order M{\o}ller-Plesset theory (MP2) suggest a 1/M decay of the basis-set incompleteness error where M is the number of plane waves used in the calculation, allowing for straightforward extrapolation to the CBS limit. As we shall show, the choice of basis set truncation when constructing many-electron wavefunctions is far from obvious, and here we propose several alternatives based on the momentum transfer vector, which greatly improve the rate of convergence. This is demonstrated for a variety of wavefunction methods, from MP2 to coupled-cluster doubles theory (CCD) and the random-phase approximation plus second-order screened exchange (RPA+SOSEX). Finite basis-set energies are presented for these methods and compared with exact benchmarks. A transformation can map the orbitals of a general solid state system onto the HEG plane wave basis and thereby allow application of these methods to more realistic physical problems.Comment: 15 pages, 9 figure

High resolution structural characterisation of laser-induced defect clusters inside diamond

Laser writing with ultrashort pulses provides a potential route for the manufacture of three-dimensional wires, waveguides and defects within diamond. We present a transmission electron microscopy (TEM) study of the intrinsic structure of the laser modifications and reveal a complex distribution of defects. Electron energy loss spectroscopy (EELS) indicates that the majority of the irradiated region remains as $sp^3$ bonded diamond. Electrically-conductive paths are attributed to the formation of multiple nano-scale, $sp^2$-bonded graphitic wires and a network of strain-relieving micro-cracks

Four-dimensional light shaping: manipulating ultrafast spatio-temporal foci in space and time

Spectral dispersion of ultrashort pulses allows simultaneous focusing of light in both space and time creating so-called spatio-temporal foci. Such space-time coupling may be combined with existing holographic techniques to give a further dimension of control when generating focal light fields. It is shown that a phase-only hologram placed in the pupil plane of an objective and illuminated by a spatially chirped ultrashort pulse can be used to generate three dimensional arrays of spatio-temporally focused spots. Exploiting the pulse front tilt generated at focus when applying simultaneous spatial and temporal focusing (SSTF), it is possible to overlap neighbouring foci in time to create a smooth intensity distribution. The resulting light field displays a high level of axial confinement, with experimental demonstrations given through two-photon microscopy and non-linear laser fabrication of glass

Deflectometry based calibration of a deformable mirror for aberration correction and remote focusing in microscopy

Adaptive optics (AO) techniques enhance the capability of optical microscopy through precise control of wavefront modulations to compensate phase aberrations and improves image quality. However, the aberration correction is often limited due to the lack of dynamic range in existing calibration methods, such as interferometry or Shack-Hartmann (SH) wavefront sensors. Here, we use deflectometry (DF) as a calibration method for a deformable mirror (DM) to extend the available range of aberration correction. We characterised the dynamic range and accuracy of the DF-based calibration of DMs depending on the spatial frequency of the test pattern used in DF. We also demonstrated the capability of large magnitude phase control for remote-focusing over a range larger than was possible with SH sensing

Planar polymer waveguides with a graded-index profile resulting from intermixing of methacrylates in closed microchannels

Graded-index waveguides are known to exhibit lower losses and considerably larger bandwidths compared to step-index waveguides. The present work reports on a new concept for realizing such waveguides on a planar substrate by capillary filling microchannels (cladding) with monomer solution (core). A graded-index profile is obtained by intermi xing between the core and cladding material at the microchannel interface. To this end, various ratios of methyl methacrylate (MMA) and octafluoropentyl methacrylate (OFPMA) were evaluated as starting monomers and the results showed that the polymers P50:50 (50:50 MMA:OFPMA) and P0:100 (100% OFPMA) were suitable to be applied as waveguide core and cladding material respectively. Light guiding in the resulting P50:50/P0:100 waveguides was demonstrated and the refractive-index profile was quantified and compared with that of conventional step-index waveguides. The results for both cases were clearly different and a gradual refractive index transition between the core and cladding was found for the newly developed waveguides. Although the concept has been demonstrated in a research environment, it also has potential for upscaling by employing drop-on-demand dispensing of polymer waveguide material in pre-patterned microchannels, for example in a roll-to-roll environment

Adaptive optics allows STED-FCS measurements in the cytoplasm of living cells

Fluorescence correlation spectroscopy in combination with super-resolution stimulated emission depletion microscopy (STED-FCS) is a powerful tool to investigate molecular diffusion with sub-diffraction resolution. It has been of particular use for investigations of two dimensional systems like cell membranes, but has so far seen very limited applications to studies of three-dimensional diffusion. One reason for this is the extreme sensitivity of the axial (z) STED depletion pattern to optical aberrations. We present here an adaptive optics-based correction method that compensates for these aberrations and allows STED-FCS measurements in the cytoplasm of living cells

A Photonic Topological Mode Bound to a Vortex

Topological photonics sheds light on some of the surprising phenomena seen in condensed matter physics that arise with the appearance of topological invariants. Optical waveguides provide a well-controlled platform to investigate effects that relate to different topological phases of matter, providing insight into phenomena such as topological insulators and superconductors by direct simulation of the states that are protected by the topology of the system. Here, we observe a mode associated with a topological defect in the bulk of a 2D photonic material by introducing a vortex distortion to an hexagonal lattice and analogous to graphene. These observations are made possible by advances in our experimental methods. We were able to manufacture uniform large two-dimensional photonic crystal structures, containing thousands of identical waveguides arranged in two dimensions, and we developed a new method to excite multiples of these waveguides with a well-defined light field. This allows us to probe the detailed spatial features of topological defect modes for the first time. The observed modes lie mid-gap at zero energy and are closely related to Majorana bound states in superconducting vortices. This is the first experimental demonstration of a mode that is a solution to the Dirac equation in the presence of a vortex, as proposed by Jackiw and Rossi