By Kenji Kawano, Tsutomu Kitoh
An entire survey of contemporary layout and research concepts for optical waveguidesThis quantity completely info sleek and extensively permitted tools for designing the optical waveguides utilized in telecommunications structures. It deals an easy presentation of the subtle innovations utilized in waveguide research and allows a short take hold of of contemporary numerical tools with effortless arithmetic. The ebook is meant to lead the reader to a finished realizing of optical waveguide research via self-study. This finished presentation includes:* an in depth and exhaustive checklist of mathematical manipulations* specific causes of universal layout equipment: finite point strategy (FEM), finite distinction procedure (FDM), beam propagation approach (BPM), and finite distinction time-domain process (FD-TDM)* motives for numerical suggestions of optical waveguide issues of refined strategies utilized in sleek computer-aided layout (CAD) software program* strategies to Maxwell's equations and the Schrodinger equationThe authors supply very good self-study fabric for practitioners, researchers, and scholars, whereas additionally offering specified mathematical manipulations that may be simply understood via readers who're unexpected with them. advent to Optical Waveguide research offers smooth layout equipment in a entire and easy-to-understand layout.
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Additional info for Introduction to Optical Waveguide Analysis: Solving Maxwells Equations and the Schrodinger Equation
43) by Eq. 42), we get a À tanÀ1 er2 g1 q1 p er1 g2 q1 0; 1; 2; . : 2:46 On the other hand, dividing Eq. 45) by Eq. 44), we get g2 W tan À1 er2 g3 À a q2 p er3 g2 q2 0; 1; 2; . : 2:47 20 ANALYTICAL METHODS Substitution of the variable a in Eq. 46) into Eq. 47) results in the following characteristic equation: À1 g2 W tan er2 g1 À1 er2 g3 tan qp er1 g2 er3 g2 q 0; 1; 2; . : 2:48 Using Eq. 31), we also get g2 W À tan À1 er1 g2 À1 er3 g2 À tan er2 g1 er2 g3 q 1p 2:49 q 0; 1; 2; .
25) by Eq. 24), we get g1 a À tan q1 p g2 À1 q1 0; 1; 2; . : 2:28 On the other hand, dividing Eq. 27) by Eq. 26), we get g3 À a q2 p g2 W tan g2 À1 q2 0; 1; 2; . : 2:29 Substitution of a in Eq. 28) into Eq. 29) results in the following characteristic equation: g1 À1 g3 tan qp g2 W tan g2 g2 À1 q 0; 1; 2; . : 2:30 Or, using tan À1 p À1 x À tan ; x 2 y y 2:31 18 ANALYTICAL METHODS we can rewrite this equation as g2 W À tanÀ1 g2 g À tanÀ1 2 q 1p g1 g3 q 0; 1; 2; .
Applying the rotation formula 1 @Az @Ay @Ar @Az 1 @ 1 @Ar =3A rAy À À r À u z r @y r @r r @y @z @z @r 2:206 for a vector A Ar r Ay u Az z to the Maxwell equations =3E Àjom0 H; 2:207 =3H Àjoe0 er E ÀjoeE; 2:208 we get 1 @Ez jbEy Àjom0 Hr ; r @y 2:209 @Ez Àjom0 Hy ; @r 2:210 1 @ 1 @Er rEy À Àjom0 Hz ; r @r r @y 2:211 1 @Hz jbHy joeEr ; r @y 2:212 ÀjbEr À @Hz ÀjoeEy ; @r 2:213 1 @ 1 @Hr rHy À ÀjoeEz : r @r r @y 2:214 ÀjbHr À 50 ANALYTICAL METHODS Expressing the tangential ®eld components (Er , Ey , Hr , and Hy ) as functions of the longitudinal ®eld components (Ez and Hz ), we get jbEy À jom0 Hr ÀjbEr jom0 Hy joeEr À jbHy 1 @Ez ; r @y 2:215 @Ez ; @r 2:216 1 @Hz ; r @y 2:217 @Hz : @r 2:218 joeEy jbHr À The radial and azimuthal ®eld components are obtained as follows: Equation 2:216 Â b Eq.