Abstract
Surface plasmon polaritons are non radiative modes which exist at the interface between a dielectric and a metal. They can confine light at sub-wavelength scales. However, their propagation is restricted by the intrinsic losses of the metal which imply a rapid absorption of the mode. The aim of this thesis is the study of the coupling of surface plasmons in metallo-dielectric planar structures. Obtaining the properties of the modes implies the extension of the solutions to the complex plane of propagation constants. The method used consists in determining the poles of the scattering matrix by means of Cauchy's integrals. The first solution to solve the problem of propagation of the surface plasmons consists in coupling these modes to one another. In a symmetric medium, when the thickness of the metallic film becomes thin enough, the coupling between the plasmon modes which exist on each side becomes possible. One of the coupled modes which is created, the so-called long range surface plasmon, has a bigger propagation length than the usual plasmon whereas the other coupled mode, named short range surface plasmon, has a smaller propagation length. We present a configuration which allows the excitation of the long range surface plasmon without the short range mode with a metallic layer deposited on a perfect electric conductor substrate. This excitation can be done in air and allows applications, such as the detection and the characterisation of molecules. Then, we present the coupling between dielectric waveguides, and, in particular, the coupled-mode theory in the case of the transverse magnetic polarisation. We consider also the case of PT symmetric structure. The last part of this work presents the demonstration of the strong coupling regime between a surface plasmon and a guided mode. We demonstrate an increase of the propagation length of the hybrid surface plasmon, which still has the confinement of a surface mode. A linear gain is added in the different layers of the structure. When the gain is added in the layer between both coupled modes allows an enhancement of the propagation lengths of the modes, and more precisely of the hybrid surface plasmon mode, which can propagate at the millimeter scale.