Upload
others
View
11
Download
0
Embed Size (px)
Citation preview
Coupled-Mode Theory
Integrated Optics Prof. Elias N. Glytsis
School of Electrical & Computer Engineering National Technical University of Athens
17/12/2020
Coupled-Mode Theory
Prof. Elias N. Glytsis, School of ECE, NTUA 2
Waveguide Modes (m-th and n-th):
Guided Modes
Radiation Modes
Orthogonality Conditions
Prof. Elias N. Glytsis, School of ECE, NTUA 3
Perturbation along the Waveguide
Transverse Field Expansion for the Perturbed Waveguide
D. L. Lee, Electromagnetic Prnciples of Integrated Optics, John Wiley & Sons, 1986
Prof. Elias N. Glytsis, School of ECE, NTUA 4
Perturbation along the Waveguide
Neglect Radiation Modes (for problems that light remains mostly guided)
D. L. Lee, Electromagnetic Prnciples of Integrated Optics, John Wiley & Sons, 1986
Prof. Elias N. Glytsis, School of ECE, NTUA 5
Lorentz Reciprocity Theorem
D. L. Lee, Electromagnetic Prnciples of Integrated Optics, John Wiley & Sons, 1986
Prof. Elias N. Glytsis, School of ECE, NTUA 6
Lorentz Reciprocity Theorem
Prof. Elias N. Glytsis, School of ECE, NTUA 7
Coupled-Mode Equations
Usually all modes (guided) are normalized to unit power Pm = 1W Usually perturbation is small (ε/ε’ ≈ 1)
Prof. Elias N. Glytsis, School of ECE, NTUA 8
Application of Coupled-Mode Equations to two-coupled waveguides
Two waveguides (A and B) in proximity The presence of each consists a perturbation to its neighbor
Prof. Elias N. Glytsis, School of ECE, NTUA 9
Application of Coupled-Mode Equations to two-coupled waveguides
Waveguide B consists a perturbation for waveguide A
Assume that both waveguides A and B are single (guided)-mode waveguides.
Prof. Elias N. Glytsis, School of ECE, NTUA 10
Application of Coupled-Mode Equations to two-coupled waveguides
Assume that: (approximate orthogonality condition)
Prof. Elias N. Glytsis, School of ECE, NTUA 11
Application of Coupled-Mode Equations to two-coupled waveguides
Coupling Coefficients
However:
Prof. Elias N. Glytsis, School of ECE, NTUA 12
Application of Coupled-Mode Equations to two-coupled waveguides
Prof. Elias N. Glytsis, School of ECE, NTUA 13
Application of Coupled-Mode Equations to two-coupled planar waveguides (directional coupler)
Prof. Elias N. Glytsis, School of ECE, NTUA 14
Application of Coupled-Mode Equations to two-coupled planar waveguides (directional coupler)
Assume solutions of the form:
Prof. Elias N. Glytsis, School of ECE, NTUA 15
Application of Coupled-Mode Equations to two-coupled planar waveguides (directional coupler)
Assume power transfer from B to A:
Waveguide Powers:
Prof. Elias N. Glytsis, School of ECE, NTUA 16
Application of Coupled-Mode Equations to two-coupled planar waveguides (directional coupler)
Prof. Elias N. Glytsis, School of ECE, NTUA 17
Application of Coupled-Mode Equations to two-coupled planar waveguides (directional coupler)
Prof. Elias N. Glytsis, School of ECE, NTUA 18
Supermode Analysis of Directional Coupler
Prof. Elias N. Glytsis, School of ECE, NTUA 19
Supermode Analysis of Directional Coupler
Assume TE modes:
z = 0
Prof. Elias N. Glytsis, School of ECE, NTUA 20
Supermode Analysis of Directional Coupler
z = 0 z = z0
Prof. Elias N. Glytsis, School of ECE, NTUA 21
Supermode Analysis of Directional Coupler
z = L