A 3D finite element model for waveguide-based plasmonic sensors

The context of this theoretical and numerical study is the design of efficient plasmonic waveguides for infrared sensing. The device configuration is fully integrated and based on a ridge waveguide upon which metallic... [ view full abstract ]

The context of this theoretical and numerical study is the design of efficient plasmonic waveguides for infrared sensing. The device configuration is fully integrated and based on a ridge waveguide upon which metallic scattering nano-objects will ensure the coupling between the guided modes and superstrate of the device. Chalcogenide glasses are chosen for the main layers due to their high transparencies for infrared wavelengths. Ultimately, the metallic scatterers are planned to be functionalized in order to react to the targeted chemical species. In order to model the response of the resulting 3D guiding structure, we adopt a diffracted field formulation consisting of two sequential steps, the output of first step being the input of the second one. First, we
determine the guided leaky modes for a fixed frequency, corresponding to the 7.7micron wavelength of interest, of the unperturbed 2D waveguide (without the plasmonic nanostructures). This is a ridge waveguide made of chalcogenide layers on a silicon substrate, assumed to be invariant along its propagation axis. We use usual vector FEM method with the Galerkin approach to solve the associated eigenvalue problem. This first step provides both the propagation constants (eigenvalues) and the associated modes profiles (eigenvectors). Second, these  guided modes are used as incident fields for the full 3D problem (i.e. with the metallic nanostructures). The electromagnetic problem to solve for this second step is then a scattering problem. It is finally possible to define a proper energy balance (transmission and reflexion into the ridge guide, absorption taking place into the plasmonic rods, radiation losses) allowing to characterize the efficiency of the device as a plasmonic sensor. 

Our method allows to compute all the required energy-related quantities to investigate quantitatively the behavior of the full structure including the impact of the metal nanoparticles located on the top of the waveguide and to take into account the way it is excited by the selected propagating mode. We provide a studyof the influence of the nano-particle parameters on the output field as well as a study of more complex nano-structuration on top of the ridge waveguide consisting of arrays of metallic particles.