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Front Cover -- Photonics -- Copyright -- Contents -- Preface -- Acknowledgments -- Part I Photonic paths -- 1 Open loop -- 1.1 Introduction -- 1.2 Infinite open loop -- 1.3 Free end semiinfinite open loop -- 1.4 Finite open loop -- 1.4.1 Matrix -- 1.4.2 Determinant -- 1.4.3 State definition -- 1.4.4 State phase shift -- 1.4.5 Eigenvalues and interface eigenvectors -- 1.4.6 Response function -- 1.4.7 Complete eigenfunctions -- 1.4.8 Resonant and forced responses -- 1.4.9 Fixed end open loop -- 1.4.10 Breaking translational invariance -- 1.5 Perspectives -- References -- 2 Closed loop

2.1 Introduction -- 2.2 Closing an open loop -- 2.3 Eigenvalues and eigenfunctions -- 2.4 Response function -- 2.5 Two simultaneous identical responses -- 2.6 Activation of the two states of closed loops -- References -- 3 Path states -- 3.1 Introduction -- 3.2 Path state properties -- 3.3 State theorems -- 3.3.1 State number conservation theorem -- 3.3.2 Confined state theorem -- 3.3.3 Bound in continuum state theorem -- 3.3.4 State activation theorems -- 3.3.4.1 Two state active points -- 3.3.4.2 One state active point and one system deformation point -- 3.3.5 Application to path states

3.4 General eigenfunction rules -- 3.4.1 Rule 1 -- 3.4.2 Rule 2 -- 3.5 Robust zeros and eigenvalues -- 3.5.1 Free end open loop -- 3.5.2 Fixed end open loop -- 3.5.3 Closed loop -- 3.5.3.1 For the first degenerate state -- 3.5.3.2 For the second degenerate state -- 3.5.4 Infinite open loop -- 3.5.4.1 For the first degenerate state -- 3.5.4.2 For the second degenerate state -- 3.6 Path state construction -- 3.7 Some perspectives -- Acknowledgments -- References -- 4 Open loop examples -- 4.1 Introduction -- 4.2 T network -- 4.2.1 Path states by inspection

4.2.2 The interface response inverse matrix -- 4.2.3 All eigenvalues from the state phase shift -- 4.2.4 Complete response function -- 4.2.4.1 x and x' in the same wire L -- 4.2.4.2 x and x' in the same wire L' -- 4.2.4.3 x in the wire L and x' in the wire L' -- 4.2.4.4 x in one wire L and x' in the other wire L -- 4.2.5 All eigenvalues and eigenfunctions from the response function -- 4.2.5.1 The ground state -- 4.2.5.2 For C=0 -- 4.2.5.3 For 2SC'+S'C= 0 -- 4.2.6 A possible application: a path bifurcation -- 4.3 Asymmetric cross -- 4.3.1 Path states by inspection

4.3.2 The interface response inverse matrix -- 4.3.3 All eigenvalues from the state phase shift -- 4.3.4 All eigenvalues and interface space eigenvectors -- 4.3.4.1 The ground state -- 4.3.4.2 For C=0 -- 4.3.4.3 For C'=0 -- 4.3.4.4 For C = C'=0 -- 4.3.4.5 For C = �C'0 -- 4.3.5 The interface response matrix -- 4.3.6 The complete response functions -- 4.3.6.1 When x and x' are in the same wire L -- 4.3.6.2 When x and x' are in the same wire L' -- 4.3.6.3 When x is in the wire L and x' in the other wire L -- 4.3.6.4 When x is in one wire L and x' in one wire L'

4.3.7 All eigenvalues and eigenfunctions from the full response function.