Abstract:
The Laplace operator is considered for waveguides perturbed by a periodic structure consisting of N congruent obstacles spanning the waveguide. Neumann boundary conditions are imposed on the periodic structure, and either Neumann or Dirichlet conditions on the guide walls. It is proven that there are at least N (resp. N-1) trapped modes in the Neumann case (resp. Dirichlet case) under fairly general hypotheses, including the special case where the obstacles consist of line segments placed parallel to the waveguide walls. This work should be viewed as an extension of "Periodic structures on waveguides" by Linton and McIvor.

Abstract:
The attenuation coefficient of 532 nm light in water under different atmospheric conditions was investigated. Measurements were made over a two-year period at the same location and show that the attenuation coefficient is significantly influenced by the atmospheric environment. It is lowest when the atmospheric pressure is high and temperature is low, and is highest when the atmospheric pressure is low and temperature is high. The maximum attenuation coefficient of pure water in these studies was about three times the minimum value. The mechanism of the phenomena is discussed. These results are also important in underwater acoustics.

Abstract:
We present a fundamental and accurate approach to compute the attenuation of electromagnetic waves propagating in rectangular waveguides with finite conductivity walls. The wavenumbers kx and ky in the x and y directions respectively, are obtained as roots of a set of transcendental equations derived by matching the tangential component of the electric field (E) and the magnetic field (H) at the surface of the waveguide walls. The electrical properties of the wall material are determined by the complex permittivity ε, permeability μ, and conductivity σ. We have examined the validity of our model by carrying out measurements on the loss arising from the fundamental TE10 mode near the cutoff frequency. We also found good agreement between our results and those obtained by others including Papadopoulos’ perturbation method across a wide range of frequencies, in particular in the vicinity of cutoff. In the presence of degenerate modes however, our method gives higher losses, which we attribute to the coupling between modes as a result of dispersion.

Abstract:
This paper presents an analytical formula to evaluate even- and odd-mode characteristics of infinitely parallel coplanar waveguides (CPW) with the same dimensions in each CPW, given name as periodic coplanar waveguides (PCPW). The analysis yields a closed-form expression based on the quasi-TEM assumption and conformal mapping transformation. Calculated results show that both the even- and odd-mode characteristic impedances are in good agreements with the results generated by numerical solvers and available experimental data. The results are important especially for highly demand on miniaturization of circuit design to place multiple CPWs in parallel.

Abstract:
Basic diagnostic methods for examining planar optical waveguides, namely the mode spectroscopy for determining the propagation constants of waveguide modes and two methods for measurement of attenuation coefficient of a waveguide or loss in some waveguide components, are presented. A promising advanced method ￠ € ” optical coherence-domain reflectometry ￠ € ” is briefly mentioned.

Abstract:
Light transport in periodic waveguides coupled to a two-level atom is investigated. By using optical Bloch equations and a photonic modal formalism, we derive semi-analytical expressions for the scattering matrix of one atom trapped in a periodic waveguide. The derivation is general, as the expressions hold for any periodic photonic or plasmonic waveguides. It provides a basic building block to study collective effects arising from photon-mediated multi-atom interactions in periodic waveguides.

Abstract:
We study the essential spectra of formally self-adjoint elliptic systems on doubly periodic planar domains perturbed by a semi-infinite periodic row of foreign inclusions. We show that the essential spectrum of the problem consists of the essential spectrum of the purely periodic problem and another component, which is the union of the discrete spectra of model problems in the infinite perturbation strip; these model problems arise by an application of the partial Floquet-Bloch-Gelfand transform.

Abstract:
We consider a periodic strip in the plane and the associated quantum waveguide with Dirichlet boundary conditions. We analyse finite segments of the waveguide consisting of $L$ periodicity cells, equipped with periodic boundary conditions at the ``new'' boundaries. Our main result is that the distance between the first and second eigenvalue of such a finite segment behaves like $L^{-2}$.

Abstract:
We investigate the lasing action in coupled multi-row nanopillar waveguides of periodic or fractal structure using the finite difference time domain (FDTD) method, coupled to the laser rate equations. Such devices exhibit band splitting with distinct and controllable supermode formation. We demonstrate that selective lasing into each of the supermodes is possible. The structure acts as a microlaser with selectable wavelength. Lasing mode selection is achieved by means of coaxial injection seeding with a Gaussian signal of appropriate transverse amplitude and phase profiles. Based on this we propose the concept of switchable lasing as an alternative to conventional laser tuning by means of external cavity control.