By Kenji Kawano, Tsutomu Kitoh
A whole survey of contemporary layout and research suggestions for optical waveguidesThis quantity completely information glossy and broadly authorised tools for designing the optical waveguides utilized in telecommunications platforms. It bargains a simple presentation of the subtle recommendations utilized in waveguide research and permits a short take hold of of contemporary numerical equipment with effortless arithmetic. The publication is meant to steer the reader to a complete realizing of optical waveguide research via self-study. This complete presentation includes:* an intensive and exhaustive checklist of mathematical manipulations* targeted motives of universal layout tools: finite aspect approach (FEM), finite distinction procedure (FDM), beam propagation technique (BPM), and finite distinction time-domain procedure (FD-TDM)* motives for numerical strategies of optical waveguide issues of subtle strategies utilized in smooth computer-aided layout (CAD) software program* recommendations to Maxwell's equations and the Schrodinger equationThe authors offer very good self-study fabric for practitioners, researchers, and scholars, whereas additionally providing specified mathematical manipulations that may be simply understood via readers who're surprising with them. creation to Optical Waveguide research offers glossy layout tools in a finished and easy-to-understand layout.
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Extra resources for Introduction to Optical Waveguide Analysis: Solving Maxwell's Equation and the Schrodinger Equation
119), equal at x = —a, we get And setting the magnetic field components Hz of regions 1 and 5, obtained by substituting Eqs. 127) into Eq. 121), equal at* = -a, we get Dividing Eq. 140) by Eq. 139), we get 36 ANALYTICAL METHODS And substituting Eqs. 97) into this equation, we get Therefore Here, adding Eq. 138) to Eq. 141), we get Or, since &o w i,2 ^ ky f°r most cases, we get The propagation constant ft (or the effective index « eff ) is obtained in just the same way as for the E^q mode. 134) corresponds to the characteristic equation of the TM mode for a three-layer slab optical waveguide parallel to the x axis.
47) results in the following characteristic equation: Using Eq. 32) for the TE mode and Eqs. 49) for the TM mode, one discovers that the characteristic equations for the TM mode contain the ratio of the relative permittivities of adjacent media. 2 EFFECTIVE INDEX METHOD Here, we discuss the effective index method, which allows us to analyze two-dimensional (2D) optical waveguide structures by simply repeating the slab optical waveguide analyses. 2 shows an example of a 2D optical waveguide and illustrates the concept of the effective index method.
3 shows a cross-sectional view of a buried optical waveguide. The core has a refractive index « l 5 width 2a, and height 2b. It is surrounded by cladding that has a refractive index n2. In Marcatili's method, it is assumed that the electric fields and magnetic fields are confined to the core and do not exist in the four hatched regions shown in Fig. 3. Thus, the continuity conditions for the electric fields and the magnetic fields are imposed only at the interfaces of regions of 1 and 2, 1 and 3, 1 and 4, and 1 and 5.