Conjugate quasilinear Dirichlet and Neumann problems and a posteriori error bounds

Quasilinear Dirichlet and Neumann problems on a rectangle D with boundary D prime are considered. Using these concepts, conjugate problems, that is, a pair of one Dirichlet and one Neumann problem, the minima of the energies of which add to zero, are introduced. From the concept of conjugate problems, two-sided bounds for the energy of the exact solution of any given Dirichlet or Neumann problem are constructed. These two-sided bounds for the energy at the exact solution are in turn used to obtain a posteriori error bounds for the norm of the difference of the approximate and exact solutions of the problem. These bounds do not involve the unknown exact solution and are easily constructed numerically

Operational frequency stability of rubidium and cesium frequency standards

The frequency stabilities under operational conditions of several commercially available rubidium and cesium frequency standards were determined from experimental data for frequency averaging times from 10 to the 7th power s and are presented in table and graph form. For frequency averaging times between 10 to the 5th power and 10 to the 7th power s, the rubidium standards tested have a stability of between 10 to the minus 12th power and 5 x 10 to the minus 12th power, while the cesium standards have a stability of between 2 x 10 to the minus 13th power and 5 x 10 to the minus 13th power

Robust interferometer for the routing of light beams carrying orbital angular momentum

We have developed an interferometer requiring only minimal angular alignment for the routing of beams carrying orbital angular momentum. The Mach–Zehnder interferometer contains a Dove prism in each arm where each has a mirror plane around which the transverse phase profile is inverted. One consequence of the inversions is that the interferometer needs no alignment. Instead the interferometer defines a unique axis about which the input beam must be coupled. Experimental results are presented for the fringe contrast, reaching a maximum value of 93±1%

Efficient sorting of free electron orbital angular momentum

We propose a method for sorting electrons by orbital angular momentum (OAM). Several methods now exist to prepare electron wavefunctions in OAM states, but no technique has been developed for efficient, parallel measurement of pure and mixed electron OAM states. The proposed technique draws inspiration from the recent demonstration of the sorting of OAM through modal transformation. We show that the same transformation can be performed on electrons with electrostatic optical elements. Specifically, we show that a charged needle and an array of electrodes perform the transformation and phase correction necessary to sort OAM states. This device may enable the analysis of the spatial mode distribution of inelastically scattered electrons

A PI3K-mediated negative feedback regulates Drosophila motor neuron excitability

Negative feedback can act as a homeostatic mechanism to maintain neuronal activity at a particular specified value. At the Drosophila neuromuscular junction, a mutation in the type II metabotropic glutamate receptor gene (mGluRA) increased motor neuron excitability by disrupting an autocrine, glutamate-mediated negative feedback. We show that mGluRA mutations increase neuronal excitability by preventing PI3 kinase (PI3K) activation and consequently hyperactivating the transcription factor Foxo. Furthermore, glutamate application increases levels of phospho-Akt, a product of PI3K signaling, within motor nerve terminals in an mGluRA-dependent manner. In humans, PI3K and type II mGluRs are implicated in epilepsy, neurofibromatosis, autism, schizophrenia and other neurological disorders; however, neither the link between type II mGluRs and PI3K, nor the role of Foxo in the control of neuronal excitability, had been previously reported. Our work suggests that some of the deficits in these neurological disorders might result from disruption of glutamate-mediated homeostasis of neuronal excitability

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

Refractive elements for the measurement of the orbital angular momentum of a single photon

We have developed a mode transformer comprising two custom refractive optical elements which convert orbital angular momentum states into transverse momentum states. This transformation allows for an efficient measurement of the orbital angular momentum content of an input light beam. We characterise the channel capacity of the system for 50 input modes, giving a maximum value of 3.46 bits per photon. Using an electron multiplying CCD (EMCCD) camera with a laser source attenuated such that on average there is less than one photon present within the system per measurement period, we demonstrate that the elements are efficient for the use in single photon experiments

Measuring orbital angular momentum superpositions of light by mode transformation

We recently reported on a method for measuring orbital angular momentum (OAM) states of light based on the transformation of helically phased beams to tilted plane waves [Phys. Rev. Lett.105, 153601 (2010)]. Here we consider the performance of such a system for superpositions of OAM states by measuring the modal content of noninteger OAM states and beams produced by a Heaviside phase plate

Why compensating fibre nonlinearity will never meet capacity demands

Current research efforts are focussed on overcoming the apparent limits of communication in single mode optical fibre resulting from distortion due to fibre nonlinearity. It has been experimentally demonstrated that this Kerr nonlinearity limit is not a fundamental limit; thus it is pertinent to review where the fundamental limits of optical communications lie, and direct future research on this basis. This paper details recently presented results. The work herein briefly reviews the intrinsic limits of optical communication over standard single mode optical fibre (SMF), and shows that the empirical limits of silica fibre power handling and transceiver design both introduce a practical upper bound to the capacity of communication using SMF, on the order of 1 Pbit/s. Transmission rates exceeding 1 Pbit/s are shown to be possible, however, with currently available optical fibres, attempts to transmit beyond this rate by simply increasing optical power will lead to an asymptotically zero fractional increase in capacity.Comment: 4 pages, 2 figure