Wave Propagation in Linear Media | re-examined

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coordinate the functions either returns the sum of incident and reflected wave or the portion of the wave inside the tunnel. The parameter w is the ratio of the carrier frequency of the incident wave and the characteristic frequency of the barrier. For tunnelling, 0
A.2 Solutions for the step potential (*-- Functions independent of the waveform --*) TunCoeff[xi_] := 2 xi/(xi + Sqrt[xi^2-1]); TunOsc[a_,b_,c_,d_,xi_] := Exp[I (a xi^2 + b xi + c Sqrt[xi^2 - 1] + d)]; RefCoeff[xi_] := (xi - Sqrt[xi^2-1])/(xi + Sqrt[xi^2-1]); OutOsc[a_,b_,c_,d_,xi_] := Exp[I (a xi^2 + (b+c) xi + d)]; PhiArg[a_,b_,c_,d_][xi_] := a xi^2 + b xi + c Sqrt[xi^2 - 1] + d; GaussTruncLims[w_,k_,n_,wp_] := {N[Sqrt[w] (1-n/(Pi k) * Sqrt[Log[Sqrt[2 Pi] k/Sqrt[n w Sqrt[2 Pi]]/10^-(wp+1)]]), wp+2], N[Sqrt[w] (1+n/(Pi k) * Sqrt[Log[Sqrt[2 Pi] k/Sqrt[n w Sqrt[2 Pi]]/10^-(wp+1)]]), wp+2]}; (*-- Triangular Shape inside the tunnel --*) TriaConst[w_,k_] := Sqrt[3/w] / (2 k Pi^2); TriaShapePos[w_,xi_] := 1/(1-xi/Sqrt[w])^2; TriaShapeNeg[w_,xi_] := 1/(1+xi/Sqrt[w])^2; TriaTransPos[a_,b_,c_,d_,w_,k_][xi_] := TunCoeff[xi] * TriaShapePos[w,xi] * TunOsc[a,b,c,d,xi]; TriaTransNeg[a_,b_,c_,d_,w_,k_][xi_] := TunCoeff[xi] * TriaShapeNeg[w,xi] * TunOsc[a,b,c,d,xi]; TriaGradTransPos[a_,b_,c_,d_,w_,k_][xi_] := TunCoeff[xi] * TriaShapePos[w,xi] * TunOsc[a,b,c,d,xi] * I Sqrt[xi^2 - 1]; TriaGradTransNeg[a_,b_,c_,d_,w_,k_][xi_] := TunCoeff[xi] * TriaShapeNeg[w,xi] * TunOsc[a,b,c,d,xi] * (-I Sqrt[xi^2 - 1]); TriaEvan[a_,b_,c_,d_,w_,k_][xi_] := TriaTransPos[a,b,c,d,w,k][xi] * (-1 + 2 Exp[I (Pi k/Sqrt[w] xi - Pi k)] - Exp[2 I (Pi k/Sqrt[w] xi - Pi k)]); TriaGradEvan[a_,b_,c_,d_,w_,k_][xi_] := TriaGradTransPos[a,b,c,d,w,k][xi] * (-1 + 2 Exp[I (Pi k/Sqrt[w] xi - Pi k)] - Exp[2 I (Pi k/Sqrt[w] xi - Pi k)]); (*-- Triangular Shape outside the tunnel --*) TriaRefPos[a_,b_,c_,d_,w_,k_][xi_] := RefCoeff[xi] * TriaShapePos[w,xi] * OutOsc[a,b,c,d,xi]; TriaRefNeg[a_,b_,c_,d_,w_,k_][xi_] := RefCoeff[xi] * TriaShapeNeg[w,xi] * OutOsc[a,b,c,d,xi]; TriaRefEvan[a_,b_,c_,d_,w_,k_][xi_] := TriaRefPos[a,b,c,d,w,k][xi] * (-1 + 2 Exp[I (Pi k/Sqrt[w] xi - Pi k)] - Exp[2 I (Pi k/Sqrt[w] xi - Pi k)]); TriaIncPos[a_,b_,c_,d_,w_,k_][xi_] := TriaShapePos[w,xi] * OutOsc[a,b,c,d,xi]; TriaIncNeg[a_,b_,c_,d_,w_,k_][xi_] := TriaShapeNeg[w,xi] * OutOsc[a,b,c,d,xi]; TriaIncEvan[a_,b_,c_,d_,w_,k_][xi_] := TriaIncPos[a,b,c,d,w,k][xi] * (-1 + 2 Exp[I (Pi k/Sqrt[w] xi - Pi k)] - Exp[2 I (Pi k/Sqrt[w] xi - Pi k)]); (*-- Rectangular Shape inside the tunnel --*) RectConst[w_,k_] := I / (Sqrt[w] 2 Pi); RectShapePos[w_,xi_] := 1/(1-xi/Sqrt[w]); RectShapeNeg[w_,xi_] := 1/(1+xi/Sqrt[w]); RectTransPos[a_,b_,c_,d_,w_,k_][xi_] := TunCoeff[xi] * RectShapePos[w,xi] * TunOsc[a,b,c,d,xi]; RectTransNeg[a_,b_,c_,d_,w_,k_][xi_] := TunCoeff[xi] * RectShapeNeg[w,xi] * TunOsc[a,b,c,d,xi]; RectEvan[a_,b_,c_,d_,w_,k_][xi_] := RectTransPos[a,b,c,d,w,k][xi] * (-1 + Exp[I 2 (Pi k/Sqrt[w] xi - Pi k)]); (*-- Rectangular Shape outside the tunnel --*) 223
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DISSERTATION Wave Propagation in Li
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Kurzfassung Seit der Entdeckung des
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Nullum est iam dictum, quod non sit
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Preface Our popular writers and rep
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the quest for superluminality and t
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Contents Part I Wave propagation ph
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7.3.4 PartitionPoints . . . . . . .
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Part I Wave propagation phenomena S
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1.1 Phase and group velocity 1.1 Ph
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1.1 Phase and group velocity ! !c v
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1.2 A few notes on dispersion He co
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1.2 A few notes on dispersion v/c 6
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1.3 Signal velocity dipoles with a
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1.3 Signal velocity The arbitrarine
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1.4 Energy velocity For electromagn
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1.5 Other velocity de nitions For n
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1.5 Other velocity de nitions evide
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2.1 Superluminal wave propagation 2
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2.1 Superluminal wave propagation a
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2.1 Superluminal wave propagation t
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2.2 Quantum mechanical tunnelling e
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2.2 Quantum mechanical tunnelling R
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Chapter 3 Wave propagation in elect
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3.1 Model of a transmission line th
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3.2 Excursion: a delay line section
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3.3 Re ection due to termination mi
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3.4 A simple thought experiment I0
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3.5 A dispersive system: the lossle
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3.6 Inhomogeneous transmission line
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3.7 Turn-on e ects in a lossless pl
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3.8 Turn-on e ects in a wave guide
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3.8 Turn-on e ects in a wave guide
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3.9 A Gaussian pulse in plasma Like
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3.9 A Gaussian pulse in plasma 250
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3.9 A Gaussian pulse in plasma 250
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3.9 A Gaussian pulse in plasma Note
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4.1 The potential step 4.1 The pote
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4.1 The potential step Inside the b
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4.2 Initial wave forms -60 -50 -40
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4.2 Initial wave forms -60 -50 -40
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4.3 Examples of scattering processe
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4.4 The square barrier they have va
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4.4 The square barrier 1 0.8 0.6 0.
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4.5 Tunnelling time de nitions for
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4.5 Tunnelling time de nitions for
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4.6 Examples of tunnelling events P
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4.6 Examples of tunnelling events 2
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4.6 Examples of tunnelling events -
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4.6 Examples of tunnelling events t
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4.6 Examples of tunnelling events P
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4.6 Examples of tunnelling events T
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Interlude Wave functions in graphic
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Wave functions in graphical represe
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Part II Numerical aspects of wave e
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5.1 Univariate numerical quadrature
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5.1 Univariate numerical quadrature
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5.2 Convergence acceleration one, t
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5.2 Convergence acceleration (1) ,1
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6.1 Partitioning the integration in
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6.2 Choosing the rst partition poin
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6.3 How to compute the rst integral
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6.3 How to compute the rst integral
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6.4 Asymptotic partition consuming
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6.4 Asymptotic partition of the int
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6.5 Considerations for a Mathematic
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6.6 Controlling the accuracy of the
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Chapter 7 Mathematica implementatio
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7.1 User interface of the function
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7.3 Implementation of OscInt and re
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Page 221 and 222: 8.4 Test of the package 8.4 Test of
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Page 225 and 226: 8.4 Test of the package 0.4 0.2 -0.
Page 227 and 228: 8.4 Test of the package 8.4.2 Forma
Page 229 and 230: 8.4 Test of the package Out[24]= 0
Page 231 and 232: A.1 Numerical quadrature Asymptotic
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Page 245 and 246: A.3 Solutions for the square barrie
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Page 249 and 250: A.4 Electromagnetic waves function
Page 251 and 252: A.5 Utilities for displaying points
Page 253 and 254: Bibliography Bibliography [1] James
Page 255 and 256: Bibliography [29] Kurt Edmund Oughs
Page 257 and 258: Bibliography [59] Ch. Spielmann, R.
Page 259 and 260: Bibliography [91] C. R. Leavens and
Page 261 and 262: Bibliography [123] T. O. Espelid an
Page 263 and 264: Index Index absorption, 7, 9 accura
Page 265 and 266: Index saddle point integration, 11,
Page 267: Curriculum vitae Dipl.-Ing. Thilo S
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