Design and optimization of tapered structure of near‐field fibre probe based on finite‐difference time‐domain simulation
The finite‐difference time‐domain method was employed to simulate light propagation in tapered near‐field fibre probes with small metal aperture. By conducting large‐volume simulations, including tapered metal‐cladding waveguide and connected optical fibre waveguide, we illustrated the coupling between these guiding modes as well as the electric field distribution in the vicinity of the aperture. The high collection efficiency of a double‐tapered probe was reproduced and was ascribed to the shortening of the cut‐off region and the efficient coupling to the guiding mode of the optical fibre. The dependence of the efficiency on the tapered structure parameters was also examined.
Complex flow and reflection of evanescent waves from a nanometer-sized hole in a cylindrical waveguide.
The results of the theoretical studies on the leakage of the optical radiation through a truncated waveguide with a subwavelength-sized exit hole are reported. We develop a self-consistent approach for the description of the fields behavior by taking into account the transformation of the initial wave into all possible modes, which appear due to the influence of the exit aperture. Our approach allows us to evaluate the amplitude reflection coefficient for the initial evanescent wave and to establish its relationship with the impedance of an infinite waveguide and the impedance of the exit aperture coupling a truncated waveguide with a free space. We determine the complex flow through the exit hole and the transmission coefficient to the far-field zone and express them through the reflection coefficient. Special attention in the work is paid to the evaluation of specific dependencies of the reflection and transmission coefficients on the ratio of the aperture radius to the light wavelength, on the dielectric constants of the waveguide core and the surrounding matter, and on the type of the waveguide mode. It is demonstrated that in the case of a metallic matter at the exit of a waveguide there is a strong resonance enhancement in the amplitude of the reflected wave and in the resulting amplitude of the tangential component of the electric field.
LYAPUNOV-BASED TRANSFER BETWEEN ELLIPTIC KEPLERIAN ORBITS
We present a study of the transfer of satellites between elliptic Keplerian orbits using Lyapunov stability theory specific to this problem. The construction of Lyapunov functions is based on the fact that a non-degenerate Keplerian orbit is uniquely described by its angular momentum and Laplace (- Runge-Lenz) vectors. We suggest a Lyapunov function, which gives a feedback controller such that the target elliptic orbit becomes a locally asymptotically stable periodic orbit in the closed-loop dynamics. We show how to perform a global transfer between two arbitrary elliptic orbits based on the local transfer result. Finally, a second Lyapunov function is presented that works only for circular target orbits.