Теория связанных мод |
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Симметричная |
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+ |
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(U1 U2 ) exp[ikz (neff |
n)] |
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U1 |
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U2 |
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Анти-симметричная |
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(U1 U2 ) exp[ikz (neff |
n)] |
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U1 |
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U2 U2 exp(i ) |
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Для равных амплитуд: |
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(U1 U2 ) exp[ikz (neff |
)] (U1 U2 ) exp[ikz (neff )] |
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z = 0 |
z = π/2kΔn |
z = π/kΔn |
π/kΔn |
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Длина биений |
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2U1 |
2U exp(iπ/2Δn) |
2U exp(iπ/Δn) |
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2 |
1 |
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z
2
Направленный ответвитель
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Beating length π/kβ |
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Symmetric |
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Asymmetric waveguide |
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coupler |
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directional coupler |
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Optical power |
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Optical power |
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Propagation distance |
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Propagation distance |
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3dB direction |
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coupler |
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WG 1 |
WG 2 |
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Cladding |
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10 log10 (0.5) ~ 3.0(dB)
Матричное представление
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b1 |
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b2 |
a2 |
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b |
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Linear |
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2 |
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a1 |
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a1 |
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device |
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b1 |
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a2 |
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In a linear, unidirectional |
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single-mode 4-port device, |
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the complex amplitude of input |
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Cascadability: |
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& output light is correlated by: |
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a1 |
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k11 |
k12 |
b1 |
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a Ktotalb |
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k |
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a |
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k |
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b |
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Ktotal KnKn 1...K1 |
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2 |
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21 |
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22 |
2 |
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a Kb
a1 |
Linear |
Linear |
… |
Linear |
b1 |
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a2 |
device 1 |
device 2 |
device n |
b |
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2 |
Изгиб волновода
Потери на изгибе
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утечка |
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neff x n(x) |
1 |
2x |
; x R |
r |
r1 |
r1 |
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R |
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r |
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1 2 |
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2 kn0 |
При критическом радиусе |
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нечетные
Граничные условия
Guided wave optics |
Quantum mechanics |
• Continuity of wave function
• Continuity of the first order derivative of wave function
Polarization dependent!
TE mode profile
Core |
y |
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Cladding |
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x |
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z |
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Substrate |
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TE mode: Ez = 0, usually Ex >> Ey
TM mode: Hz = 0, usually Ey >> Ex
Ex amplitude |
y |
y |
|
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of TE mode |
z |
x |
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x |
Discontinuity |
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of field due to |
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boundary |
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condition! |
Концентрация поля в материале с низким показателем преломления
(Slot waveguide) |
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|||
y |
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x |
slot |
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z |
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Cladding
Substrate
TE mode profile
Use low index material for:
•Light emission
•Light modulation
•Plasmonic waveguiding
V. Almeida et al., “Guiding and
confining light in void nanostructure,” Opt. Lett. 29, 1209-1211 (2004).