Title : Analysis of instantaneous poynting vector for N-Layer Lossy optical waveguides and applications in the evanescently coupled optical devices
Abstract:
Starting with an introduction to the Poynting theorem, we derive analytical expressions for the instantaneous Poynting vector for an N-layer lossy optical waveguide structure consisting of multiple metal-dielectric interfaces. These expressions are compared with the equivalent expressions for the average Poynting vector discussed in many textbooks on optics. Due to the lossy nature of the optical waveguide considered, the propagation constants of the modes excited in the structure are complex-valued. The modes excited are surface plasmons (SP) and transverse magnetic (TM) in nature. These modes have finite penetration depth, which is defined as the distance from any metal- dielectric interface where the electromagnetic energy reduces to 1/e of its value at the interface. These modes have finite propagation length (also called the ‘range’ of the mode) which is defined as the distance traveled by the modes along the direction of propagation when the electromagnetic energy reduces to 1/e of its initial value. We propose new formulae for the penetration depth and the propagation length of the instantaneous Poynting vector. These are shown to be different from the conventional formulae for the penetration depth and the propagation length defined in terms of the average Poynting vector. It is proposed that the study of the instantaneous Poynting vector is important in understanding the functionality of evanescently coupled optical devices, such as the directional couplers, surface plasmon resonance (SPR) based sensors, TE/TM polarizers. We discuss the application of the new formula proposed for the penetration depth of instantaneous Poynting vector in optimizing the design parameters of an SPR sensor to achieve maximum sensitivity. We also plot the evolution of the instantaneous Poynting vector flux lines for a five-layer SPR bi-metallic sensor in prism coupling Kretschmann configuration, displaying the finite propagation length and penetration depth to be consistent with the proposed formulae.
