Transverse plane

About: Transverse plane is a research topic. Over the lifetime, 17069 publications have been published within this topic receiving 194059 citations. The topic is also known as: axial plane.

Analytical determination of coronal parameters using the period ratio P1/2P2

Abstract: Context. In transverse coronal loop oscillations, two periodicities have been measured simultaneously and are interpreted as the fundamental kink mode (with period P1) and the first harmonic (with period P2). Deviations of the period ratio P1/2P2 from unity provide information about the extent of longitudinal structuring within the loop. Aims. Here we develop an analytical approximation that describes the shift in P1/2P2 in terms of the ratio L/Λc of the length 2L of a coronal loop and the density scale height Λc. Methods. We study the MHD wave equations in a low β plasma using the thin tube approximation. Disturbances are described by a differential equation which may be solved for various equilibrium density profiles, obtaining dispersion relations in terms of Bessel functions. These dispersion relations may be used to obtain analytical approximations to the periods P1 and P2 .W e also present a variational approach to determining the period ratio and show how the WKB method may be used. Results. Analytical approximations to the period ratio P1/2P2 are used to shed light on the magnitude of longitudinal structuring in a loop, leading to a determination of the density scale height. We apply our formula to the observations in Verwichte et al. (2004) and Van Doorsselaere et al. (2007), obtaining the coronal density scale height. Conclusions. Our simple formula and approximate approaches highlight a useful analytical tool for coronal seismology. We demonstrate that P1/2P2 is linked to the density scale height, with no need for estimates of other external parameters. Given the accuracy of current observations, our formula provides a convenient means of determining density scale heights.

Propagation of hybrid transverse magnetic-transverse electric plasmons on magnetically biased graphene sheets

Abstract: The propagation of plasmons on magnetically biased graphene sheets is addressed. The analysis is based on the transverse resonance method extended to handle the graphene conductivity tensor and allows easily accounting for substrate effects. A transcendental equation is obtained for the propagation constant of the resulting hybrid transverse magnetic-transverse electric mode. A closed-form approximate expression for a graphene layer sandwitched between two different media is also provided. Application of the method shows that the presence of a magnetic field leads to extreme field localization, namely, very small guided wavelength, as compared with usual plasmons in graphene or noble metals. The extent of field localization and its frequency can be dynamically controlled by modifying the applied magnetostatic and electrostatic bias field, respectively. These features could enable extreme device miniaturization and enhanced resolution in sensing applications.

Controlling the contribution of the electric field components to the focus of a high-aperture lens using binary phase structures

Abstract: We show that the contribution of the electric field components into the focal region can be controlled using binary phase structures. We discuss differently polarized incident waves, for each case suggesting easily implemented binary phase distributions that ensure a maximum contribution of a definite electric field component on the optical axis. A decrease in the size of the central focal spot produced by a high numerical aperture (NA) focusing system comes as the result of the spatial redistribution of the contribution of different electric field components into the focal region. Using a polarization conversion matrix of a high NA lens and the numerical simulation of the focusing system in Debye’s approximation, we demonstrate benefits of using asymmetric to polar angle ϕ binary phase distributions (such as arg[cos ϕ] or arg[sin 2ϕ]) for generating a subwavelength focal spot in separate electric field components. Additional binary structure variations with respect to the azimuthal angle also make possible controlling the longitudinal distribution of light. In particular, the contribution of the transverse components in the focal plane can be reduced by the use of a simple axicon-like structure that serves to enhance the NA of the lens central part, redirecting the energy from focal plane. As compared with the superimposition of a narrow annular aperture, this approach is more energy efficient, and as compared with the Toraldo filters, it is easier to control when applied to three-dimensional focal shaping.

Front and back instability of a liquid film on a slightly inclined plate

Abstract: We study the transverse instability of a liquid ridge on horizontal and inclined substrates using a film evolution equation based on a long wave approximation. The equation incorporates an additional pressure term—the disjoining pressure—accounting for the effective interaction of the film with the substrate. On a horizontal substrate the dominant instability mode is varicose, but may turn into a zigzag mode on a slightly inclined substrate depending on the inclination angle and the ridge volume. For larger angles or volumes the instabilities at the front and back decouple. The linear stability properties of a one-dimensional transverse ridgelike state are studied in detail, and an energy analysis is used to demonstrate that the disjoining pressure provides the dominant instability mechanism at both the front and the back, while the body force is responsible for the main differences between these two instabilities. An amplitude equation for the time evolution of perturbations with small transverse wave numbers is derived that predicts correctly the linear crossing of the most dangerous eigenvalues at zero wave number in the inclined case, in contrast to the situation on a horizontal substrate.