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Padé [2,0] Boundary Conditions • [2,2] Padé Equation ⎛1− s ⎞ ⎜ ⎟E ⎝ ∆z ⎠ 2 ⎛ X 0 X ⎞ 0 ⎛ 1+ s ⎞ + 1( x) = −δ ⎜1 ⎟ + − ⎜ ⎟E j 1( x) 2 8 ⎝ ⎠⎝ 2 ⎠ j + • Laplace transform this equation with respect to x in the exterior region. • Requiring that no poles are present in the right-hand plane of the transform yields the desired boundary condition. Faculty of Science - Department of Physics 5/3/2009 D. Yevick - Evolution Operators and Boundary Conditions 32
[2,2] Boundary Condition Results Faculty of Science - Department of Physics 5/3/2009 D. Yevick - Evolution Operators and Boundary Conditions 33
Page 1 and 2: Evolution Operators and Boundary Co
Page 3 and 4: Outline • Fundamental Equations
Page 5 and 6: Scalar Wave Equation • Scalar, Mo
Page 7 and 8: Modal Analysis • Modal Decomposit
Page 9 and 10: Wide-Angle Approximations • Taylo
Page 11 and 12: Continued Fraction Expansion • It
Page 13 and 14: Finite Difference Method • Applyi
Page 15 and 16: Part II - Nonlocal Boundary Conditi
Page 17 and 18: Electrorefraction Modulator Faculty
Page 19 and 20: Improved Boundary Conditions Facult
Page 21 and 22: Transparent Boundaries E E N + 1
Page 23 and 24: Impedance-Matched Layer Attenuation
Page 25 and 26: Continuous Nonlocal Boundary Facult
Page 27 and 28: Gaussian Beam - Continuous N.L. Fac
Page 29 and 30: Exact Nonlocal Boundary Faculty of
Page 31: Padé [1,1] Boundary Conditions •
Page 35 and 36: General Boundary Conditions (2) •
Page 37 and 38: [N,N] Boundary Condition Results Fa
Page 39 and 40: Facet Reflection Coefficient E y
Page 41 and 42: Standard Operator Results Faculty o
Page 43 and 44: Complex Padé Reflection 0.45 0.41
Page 45 and 46: Rotated Padé Reflection 0.4 0.38 R
Page 47 and 48: Transition, Propagation Operator +
Page 49: Conclusions • Procedures now exis

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