Diffraction by a Strip

The problem of diffraction by an infinite strip or slit has been the subject of several investigations. There are at least two "exact" methods for attacking this problem. One of these is the integral equation method, the other the Fourier-Lamé method. The integral equation obtained for this problem cannot be solved in closed form; expansion of the solution in powers of the ratio (strip width/wavelength) leads to useful formulas for low frequencies. In the Fourier-Lamé method the wave equation is separated in coordinates of the elliptic cylinder, the solution appears as an infinite series of Mathieu functions, and the usefulness of the result is limited by the convergence of these infinite series, and by the available tabulation of Mathieu functions. The variational technique developed by Levine and Schwinger avoids some of the difficulties of the above-mentioned methods and, at least in principle, is capable of furnishing good approximations for all frequency-ranges. The scattered field may be represented as the effect of the current induced in the strip, and it has been proved by Levine and Schwinger that it is possible to represent the amplitude of the far-zone scattered field in terms of the induced current in a form which is stationary with respect to small variations of the current about the true current. Substitution, in this representation, of a rough approximation for the current may give a remarkably good approximation of the far-zone scattered field amplitude. In this note we assume a normally incident field polarized parallel to the generators of the strip. As a rough approximation, we take a uniform density of the current induced in the strip. Since the incident magnetic field is constant over the strip, Fock's theory may be cited in support of the uniformity of the current distribution, except near the edges where the behaviour of the field indicates an infinite current density. A more detailed analysis of the current, by Moullin and Phillips, is available but was not used here. Once the (approximate) amplitude of the far-zone field has been obtained, the scattering cross-section may be found by the application of the scattering theorem which relates this cross-section to the imaginary part of the amplitude of the far-zone scattered field along the central line of the umbral region. In spite of the crude approximation adopted for the induced current, the scattering cross-section shows a fair agreement with other available results

Dynamical Theory of Artificial Optical Magnetism Produced by Rings of Plasmonic Nanoparticles

We present a detailed analytical theory for the plasmonic nanoring configuration first proposed in [A. Alu, A. Salandrino, N. Engheta, Opt. Expr. 14, 1557 (2006)], which is shown to provide negative magnetic permeability and negative index of refraction at infrared and optical frequencies. We show analytically how the nanoring configuration may provide superior performance when compared to some other solutions for optical negative index materials, offering a more 'pure' magnetic response at these high frequencies, which is necessary for lowering the effects of radiation losses and absorption. Sensitivity to losses and the bandwidth of operation of this magnetic inclusion are also investigated in details and compared with other available setups.Comment: 34 pages, 3 figure

Reverse Doppler effect in backward spin waves scattered on acoustic waves

We report on the observation of reverse Doppler effect in backward spin waves reflected off of surface acoustic waves. The spin waves are excited in a yttrium iron garnet (YIG) film. Simultaneously, acoustic waves are also generated. The strain induced by the acoustic waves in the magnetostrictive YIG film results in the periodic modulation of the magnetic anisotropy in the film. Thus, in effect, a travelling Bragg grating for the spin waves is produced. The backward spin waves reflecting off of this grating exhibit a reverse Doppler shift: shifting down rather than up in frequency when reflecting off of an approaching acoustic wave. Similarly, the spin waves are shifted up in frequency when reflecting from receding acoustic waves.Comment: 4 pages, 3 figure

Controlling Light Through Optical Disordered Media : Transmission Matrix Approach

We experimentally measure the monochromatic transmission matrix (TM) of an optical multiple scattering medium using a spatial light modulator together with a phase-shifting interferometry measurement method. The TM contains all information needed to shape the scattered output field at will or to detect an image through the medium. We confront theory and experiment for these applications and we study the effect of noise on the reconstruction method. We also extracted from the TM informations about the statistical properties of the medium and the light transport whitin it. In particular, we are able to isolate the contributions of the Memory Effect (ME) and measure its attenuation length

Power Flow Structures in Two Dimensional Electromagnetic Fields

Qualitative behaviour of time average power flow in electromagnetic fields can be studied by observing the critical points of the Poynting vector field, S. In order to analyze the behaviour of the flow lines of a plane Poynting vector field in the neighbourhood of a critical point, the S field is expanded in a Taylor series. Using this expansion, critical points can be classified according to their order and degeneracy. A formula for the index of rotation of the S field at a critical point is derived. The behaviour of the transverse electric or magnetic field component in the neighbourhood of the critical point is also studied. Lowest order critical points are always nondegenerate and they have interesting properties with regards to polarization and energy distribution. Examples involving linearly polarized system of interfering plane and/or cylindrical waves are given to show the critical points. The behaviour of flow lines is illustrated in these examples

Diffraction by a Strip

The problem of diffraction by an infinite strip or slit has been the subject of several investigations. There are at least two "exact" methods for attacking this problem. One of these is the integral equation method, the other the Fourier-Lamé method. The integral equation obtained for this problem cannot be solved in closed form; expansion of the solution in powers of the ratio (strip width/wavelength) leads to useful formulas for low frequencies. In the Fourier-Lamé method the wave equation is separated in coordinates of the elliptic cylinder, the solution appears as an infinite series of Mathieu functions, and the usefulness of the result is limited by the convergence of these infinite series, and by the available tabulation of Mathieu functions. The variational technique developed by Levine and Schwinger avoids some of the difficulties of the above-mentioned methods and, at least in principle, is capable of furnishing good approximations for all frequency-ranges. The scattered field may be represented as the effect of the current induced in the strip, and it has been proved by Levine and Schwinger that it is possible to represent the amplitude of the far-zone scattered field in terms of the induced current in a form which is stationary with respect to small variations of the current about the true current. Substitution, in this representation, of a rough approximation for the current may give a remarkably good approximation of the far-zone scattered field amplitude. In this note we assume a normally incident field polarized parallel to the generators of the strip. As a rough approximation, we take a uniform density of the current induced in the strip. Since the incident magnetic field is constant over the strip, Fock's theory may be cited in support of the uniformity of the current distribution, except near the edges where the behaviour of the field indicates an infinite current density. A more detailed analysis of the current, by Moullin and Phillips, is available but was not used here. Once the (approximate) amplitude of the far-zone field has been obtained, the scattering cross-section may be found by the application of the scattering theorem which relates this cross-section to the imaginary part of the amplitude of the far-zone scattered field along the central line of the umbral region. In spite of the crude approximation adopted for the induced current, the scattering cross-section shows a fair agreement with other available results

Postnatal β2 adrenergic treatment improves insulin sensitivity in lambs with IUGR but not persistent defects in pancreatic islets or skeletal muscle

Placental insufficiency causes intrauterine growth restriction (IUGR) and disturbances in glucose homeostasis with associated β adrenergic receptor (ADRβ) desensitization. Our objectives were to measure insulin-sensitive glucose metabolism in neonatal lambs with IUGR and to determine whether daily treatment with ADRβ2 agonist and ADRβ1/β3 antagonists for 1 month normalizes their glucose metabolism. Growth, glucose-stimulated insulin secretion (GSIS) and glucose utilization rates (GURs) were measured in control lambs, IUGR lambs and IUGR lambs treated with adrenergic receptor modifiers: clenbuterol atenolol and SR59230A (IUGR-AR). In IUGR lambs, islet insulin content and GSIS were less than in controls; however, insulin sensitivity and whole-bodyGUR were not different from controls.Of importance, ADRβ2 stimulation with β1/β3 inhibition increases both insulin sensitivity and whole-body glucose utilization in IUGR lambs. In IUGR and IUGR-AR lambs, hindlimb GURs were greater but fractional glucose oxidation rates and ex vivo skeletal muscle glucose oxidation rates were lower than controls. Glucose transporter 4 (GLUT4) was lower in IUGR and IUGR-AR skeletal muscle than in controls but GLUT1 was greater in IUGR-AR. ADRβ2, insulin receptor, glycogen content and citrate synthase activity were similar among groups. In IUGR and IUGR-AR lambs heart rates were greater, which was independent of cardiac ADRβ1 activation. We conclude that targeted ADRβ2 stimulation improved whole-body insulin sensitivity but minimally affected defects in GSIS and skeletal muscle glucose oxidation. We show that risk factors for developing diabetes are independent of postnatal catch-up growth in IUGR lambs as early as 1 month of age and are inherent to the islets and myocytes