Guided Mode Analysis And Optical Field Characteristics Of Nano-Slot Waveguide Structures

The nano-slot optical waveguide is a planar layered microstructural optical waveguide with a transverse size of nanometer dimensions,which contains a core layer of low-index dielectric sandwiched by a high-index material from two sides.It generally operates at a long wavelength（e.g.,near-infrared wavelength）,which is much larger than the transverse size of the whole structure.Its main optical characteristics are:in the gap（slot）of low refractive index between two dielectric layers with high refractive index,electric field enhancement and optical energy confinement can be achieved in there.The structures based on such slot optical waveguide can confine the light field to a scale much smaller than the diffraction lim-it.The characteristics of the confined light field are significantly different from those of the conventional waveguides（micron dimensions）,which capture and concentrate the light in the guiding dielectric regions with high refractive index.This important result different from the concept of the underlying physical mechanism of the traditional waveguides will expand the application scope of optical waveguides.The microstructural slot waveguide and its ana-logues have important research and application value in biomolecular sensing,functional devices and nonlinear effects.The application scaling the micro-structured slot waveguide down to system-on-chip integration has important research significance and application val-ue for miniaturization and compactness of optical components,and optical interconnection and on-chip integration of different types of functional components.Herein,based on classical electromagnetic theory,field function and eigen-relation e-quations of the guided modes for such layered slot waveguides are analytically derived,and the distribution and eigen relation of the the guided mode are calculated and analyzed.Si-multaneously,using Finite-element Method（FEM）,the mode field distribution function of the designed nano-slot waveguide structures are calculated and analyzed.The guided modes of the structures are also discussed,and furthermore,the physical nature underlying the im-portant optical properties（electric field enhancement and optical energy confinement）man-ifested by the structure is revealed.The aim of this paper is to systematically obtain the electromagnetic guided modes types of the nano-slot waveguide,and to provide a complete electromagnetic theoretical basis for further dealing with the design of functional optical components of the nano-slot waveguides（such as waveguide sensor,optical modulation-s,beam splitters,resonators,etc.）and the applications of on-chip optical integration.The main contents of this paper are presented below:Firstly,the guided mode analysis and calculation of the slot waveguide of the basic five-layer dielectric system are carried out.Based on helmholtz equation,optical field functions of TE/TM guided modes of slot the waveguide structure are derived detailedly and religiously.Four basic field types of TE/TM guided modes（cosh/sinh and cos/sin types）are summarized,and the field functions and their eigen relations are discussed as well.For TM guided mode,which is more attracted to researchers,detailed example analysis is carried out.Additionally,guided mode conditions,attenuation factors,optical field confinement and control（power confinement factors）are deduced and calculated.The results will lay a foundation for the further research and application of the nanoscale slot waveguides.Secondly,the optical field properties of pure dielectric slot waveguide are discussed.The threshold conditions of electric field enhancement and energy confinement of cosh-type mode field one of TM guided modes is analyzed primarily,and simultaneously some decid-ed threshold conditions to realize a enhanced field and light energy concentration in the slot are obtained.The significance of exploring threshold conditions is to solve the optimiza-tion problem of field enhancement and energy confinement in the slot when the waveguide structure is designed.The longitudinal components of two cosh/sinh modes are analyzed and discussed,and it is proved that the longitudinal components of guided modes have impor-tant research and application value to the manipulation of light field.In addition,the three-dimensional slot waveguide structure with more valuable applications is modeled and ana-lyzed.Considering that the slot structure can achieve both high field enhancement factor and more compact configuration,the field enhancement evaluation factors of three-dimensional all-dielectric slot waveguide structure are calculated and discussed by a simulation based on the FEM analysis.The results obtained from the theoretical calculation of slot waveguide and related modeling analysis are of great value and significance for the further design of bio-optical sensors,substrate structures based on SERS application,and the theoretical research and application of the extension to light-on-chip.Finally,the optical field characteristics and applications of the slot waveguide based on the surface plasmon polaritons（SPPs）are discussed.For IMIMI-structured（I-Isolator,M-Metal）plasmonic slot waveguide structure composed of double Metal walls,the expres-sions of the field function and eigen-equations,that are the real parts of the transverse field function of symmetric SPP and antisymmetric SPP mode fields,are derived.As a compari-son,the analytical calculation of the field function agrees well with the results of the finite element simulation.And meanwhile,it is also proved that the electric field enhancement and energy confinement can be realized in the narrow slot between the two metal walls due to the coupling of SPPs propagating along the metal surfaces both sides of the slot.In addition,a hybrid waveguide sensor（Si₃N₄）with an auxiliary layer attached outside the metal（Au）walls is proposed and designed.Considering the field evaluation factors and compactness,the hybrid plasmonic slot waveguide sensor can obtain a gaint local field enhancement factor under the most compact designed structure.