Behaviour of Poynting vector for dielectric-metal-dielectric optical waveguides and applications

Abstract

In this paper, we derive analytical expressions for the spatial evolution of the instantaneous Poynting vector for the transverse magnetic (TM) surface plasmon (SP) modes of a symmetric planar dielectric-metal-dielectric optical waveguide. We discuss the behaviour of the Poynting vector in the metal film due to the optical absorption of electromagnetic waves propagating through the medium to excite the surface plasmons in a resonant manner in the metal film at the interface. This optical absorption of the electromagnetic waves results in a finite propagation length of SP modes. We derive an analytical formula for the penetration depth of the instantaneous Poynting vector in the dielectric cladding regions and show that it is different as compared to the penetration depth of the average Poynting vector. We utilize this analytical formula to calculate the optimum thickness of the affinity layer in a graphene-based surface plasmon resonance (SPR) biosensor and analyze its performance in terms of sensitivity and Figure-of-Merit. We also show that our analytical formula can be used to calculate the optimum thickness of a thin high-index dielectric layer which is added to any conventional SPR based sensor to enhance its sensitivity. The optimum thickness thus calculated correlates closely with the experimental results that have been published previously. The analysis done in this paper can also be utilized in calculating the separation between any two adjacent waveguides/optical films which are coupled together evanescently, such as directional couplers and TE/TM polarisers.