Behaviour of Poynting vector for dielectric-metal-dielectric optical waveguides and applications
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Behaviour of Poynting vector for dielectric‑metal‑dielectric optical waveguides and applications Jagneet Kaur Anand1 · Himanshu Kushwah1 Received: 8 May 2020 / Accepted: 29 August 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
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. Keywords Poynting vector · Metal-dielectric waveguides · Plasmonics · Surface-plasmon resonance · Sensors · Evanescently coupled devices
1 Introduction DMD waveguides fall under the broad category of Plasmonic devices, that are currently being studied for their applications as optical sensors and polarisers (Dai et al. 2011; Sharma et al. 2007, 2016; Verma et al. 2015; Nemova and Kashyap 2007). Numerous theoretical, as well as experimental studies, have been reported to propose various configurations of plasmonic sensors and polarisers with improved parameters such as their * Jagneet Kaur Anand [email protected] 1
Department of Electronics, Keshav Mahavidyalaya, University of Delhi, New Delhi, Delhi, India
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sensitivity, resolution, and extinction ratio (Chen and Wang 2000; Chien and Chen 2004; Sharma et al. 2011; Verma et al. 2011; Tabassum and Gupta 2016). To optimize these parameters, many authors have studied the electromagnetics of metals, starting from Maxwell’s equations, with the objective to introduce propagation in waveguides with metal layers which support SP modes at the metal–dielectric interfa
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