tailieunhanh - Wave Propagation Part 5

Tham khảo tài liệu 'wave propagation part 5', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 132 Wave Propagation violet optical and near infrared. The advantage of this approach is clearly glaring as it provides a good picture of the field in a medium with variation of dielectric constant refractive index and above all the method requires no resolution of a system of equations as it can accommodate multiple layers easily. 2. Theoretical procedure This our method is to find a solution p r of the scalar wave equation V2v r ffl2SoPog r v r 0 1 for arbitrary complex dielectric medium permittivity gp r of homogeneous permeability po starting with Halmitonian. In equation 1 we assume the usual time dependence exp -ifflt for the electromagnetic field v r . Such a scalar field describes for instance the transverse electric modes propagating in thin media deposited on glass slide using solution growth technique Ugwu 2005 . Sref is reference medium gp r is perturbed medium. Fig. 1. Geometry used in the model. The dielectric medium for which we see a solution of the wave equation can be split into two parts reference homogeneous medium gref and a perturbed medium where the film is deposited Sp r The assumption made here regarding the dielectric medium is that it is split into two parts a homogenous reference medium of dielectric constant gref and a perturbation Sp r confined to the reference medium. Hence the dielectric function of the system can be written as gp r gref Agp r 2 Where Agp r Sp r - gref. The assumption here can be fulfilled easily where both reference medium and the perturbation depend on the problem we are investigating. For example if one is studying an optical fiber in vacuum the reference medium is the vacuum and the perturbation describes the fiber. For a ridge wedge wave guide the reference medium is the substrate and the perturbation is the ridge In our own case in this work the reference medium is air and the perturbing medium is thin film deposited on glass slide. Lippman-Schwinger equation is associated with the Hamiltonian H which goes with