INTRODUCTION TO OPTICAL WAVEGUIDE ANALYSIS
1 FUNDAMENTAL EQUATIONS 1 1 1 MAXWELL'S EQUATIONS / 1 1 2 WAVE EQUATIONS / 3 1 3 POYNTING VECTORS / 7 1 4 BOUNDARY CONDITIONS FOR ELECTROMAGNETIC FIELDS / 9 PROBLEMS / 10 REFERENCE / 12 2 ANALYTICAL METHODS 13 2 1 METHOD FOR A THREE-LAYER SLAB OPTICAL WAVEGUIDE / 13 2 2 EFFECTIVE INDEX METHOD / 20 2 3 MARCATILI'S METHOD/23 2 4 METHOD FOR AN OPTICAL FIBER / 36 PROBLEMS / 55 REFERENCES / 57 3 FINITE ELEMENT METHODS 59 3 1 VARIATIONAL METHOD / 59 3 2 GALERKIN METHOD / 68 3 3 AREA COORDINATES AND TRIANGULAR ELEMENTS/72 3 4 DERIVATION OF EIGENVALUE MATRIX EQUATIONS/84 3 5 MATRIX ELEMENTS / 89 3 6 PROGRAMMING/105 3 7 BOUNDARY CONDITIONS / 110 PROBLEMS / 113 REFERENCES/115 4 FINITE-DIFFERENCE METHODS 117 4 1 FINITE-DIFFERENCE APPROXIMATIONS/118 4 2 WAVE EQUATIONS / 120 4 3 FINITE-DIFFERENCE EXPRESSIONS OF WAVE EQUATIONS / 127 4 4 PROGRAMMING/150 4 5 BOUNDARY CONDITIONS / 153 4 6 NUMERICAL EXAMPLE / 160 PROBLEMS / 161 REFERENCES/164 5 BEAM PROPAGATION METHODS 165 5 1 FAST FOURIER TRANSFORM BEAM PROPAGATION METHOD / 165 5 2 FINITE-DIFFERENCE BEAM PROPAGATION METHOD / 180 5 3 WIDE-ANGLE ANALYSIS USING PADÉ APPROXIMANT OPERATORS/204 5 4 THREE-DIMENSIONAL SEMIVECTORIAL ANALYSIS/216 5 5 THREE-DIMENSIONAL FULLY VECTORIAL ANALYSIS / 222 PROBLEMS / 227 REFERENCES/230 6 FINITE-DIFFERENCE TIME-DOMAIN METHOD 233 6 1 DISCRETIZATION OF ELECTROMAGNETIC FIELDS / 233 6 2 STABILITY CONDITION / 239 6 3 ABSORBING BOUNDARY CONDITIONS/241 PROBLEMS / 245 REFERENCES/249 7 SCHRÖDINGER EQUATION 251 7 1 TIME-DEPENDENT STATE / 251 7 2 FINITE-DIFFERENCE ANALYSIS OF TIME-INDEPENDENT STATE / 253 7 3 FINITE-ELEMENT ANALYSIS OF TIME-INDEPENDENT STATE / 254 REFERENCES/263