Interaction between spherical dielectric particles and surface integrated waveguides: a semi-analytical complex angle approach

A trend in optical biosensors concerns the development of integrated photonic lab-on-chips to develop compact and portable solutions. These sensors take advantage of the enhanced sensitivity of microstructures and rely on the modulation of light properties such as intensity, phase or wavelength. Detection by evanescent coupling of microparticles selectively trapped at the surface of an optical waveguide is a common solution. Many microparticles can be approximated by spherical objects with a complex refractive index different from the medium one. In this case, Mie theory is well-known for describing how they scatter light coming from a plane wave. Less obvious is the description of the light scattering induced by this microparticles on a light propagated in an integrated waveguide. We propose here a semi-analytical modeling based on a complex angle approach to evaluate the interaction between a surface guided mode and dielectric spheres placed on top of the waveguide. In this approach, time-saving with respect to a 3D simulation, an evanescent incident wave is described as a plane wave that is geometrically rotated by a complex angle. We show how it can be used to evaluate the waveguide losses induced by dielectric microparticles placed close to its surface. We then apply this model to a sensor where polystyrene microbeads are selectively trapped on top of a glass surface waveguide thanks to dielectrophoresis.