3-dB Couplers/splitters 50% 50%
WDM Couplers/splitters 1, 980nm 2, 1550nm 1 3 1 + 2 2 1 + 2 2, 1550nm 1, 980nm 1, 980nm 2, 1550nm Insertion loss Port 1 to 3 0.2dB Port 2 to 3 20dB Insertion loss Port 1 to 3 20dB Port 2 to 3 0.3dB
WDM Couplers/splitters 1, 980nm 1 3 2 1 + 2 2, 1550nm 1, 980nm 2, 1550nm Insertion loss Port 3 to 1 0.2dB Port 3 to 2 20dB Insertion loss Port 3 to 1 20dB Port 3 to 2 0.3dB
Mode–coupling theory Recall mode equations TE Mode: Notice: Mode profile E(x, y) doesn’t change with z if no index perturbation. No coupling between different modes if no index perturbation.
Mode–coupling theory index perturbations Generalized propagation equation
perturbation theory, TE mode Mode–coupling equation
discussion of the mode-coupling equation if no index perturbation, A(z) is an constant, goes back to the normal equation. Cn measures how much the index perturbation changes the propagation constant n. If index perturbation doesn’t vary with z, coupling between the mode depends on the .
Couplers/splitters, working principle – optical mode coupling 1 2 3 Un-connected port A1(z) A2(z) z L Without coupling Mode-coupling equations, phase matched case
Couplers/splitters, working principle – optical mode coupling 1 2 3 Un-connected port A1(z) A2(z) z Energy conservation
WDM Couplers/splitters, working principle – optical mode coupling 1 3 A1(z) A2(z) 2 Un-connected port Fused fiber z L A, B, C, D are determined by the initial conditions
Splitter 1 3 For A1(0) = A1, A2(0) =0 A1(z) A2(z) Un-connected port 4
2 to 1 combiner Initially, A1(0), A2(0) A1(0) = A2(0) 1 3 A1(z) A2(z) 2 Un-connected port z = 0 Similarly
2 to 1 combiner Initially, A1(0), A2(0) A1(0) not eq. A2(0) 1 3 A1(z) A2(z) 2 Un-connected port z = 0 Similarly
No coupling between two different wavelengths 1 3 A1(z) WDM coupler 1, 980nm 2, 1550nm A2(z) 2 Un-connected port Fused fiber No coupling between two different wavelengths For 1, 980nm Initially, A1(0, 1), A2(0, 1) =0 z = 0 z = 0
1 3 A1(z) 1, 980nm 2, 1550nm A2(z) 2 Un-connected port For 2, 1550nm Initially, A1(0, 2)=0, A2(0, 2) z = 0
2, 1550nm 1 3 A1(z) 1, 980nm A2(z) 2 Un-connected port For 2, 1550nm Initially, A1(0, 2), A2(0, 2)=0 For 1, 980nm Initially, A1(0, 1)=0, A2(0, 1)
2, 1550nm For 2, 1550nm 1 3 A1(z) 1, 980nm Initially, A1(0, 2), A2(0, 2)=0 Un-connected port A2(z) 4 For 1, 980nm Initially, A1(0, 1), A2(0, 1) = 0
Waveguide gratings A1(z) A2(z)
Waveguide gratings A1(z) A2(z) A, B, C, D are determined by the initial conditions
Waveguide gratings DBR grating A1(z)|z=0 = A1(0) A1(z) Waveguide A2(z) )|z=L = 0 A2(z)
Waveguide gratings A1(z)|z=0 = A1(0) A1(z) A2(z) )|z=L = 0 A2(z)
Ring resonators
Ring resonators P
Ring resonators T
Ring resonators
Ring resonators
Ring resonators n1 = 1; lamda = 1.538:0.0000001:1.539; %in um beta = 2*pi./lamda; R = 10/(2*pi*n1); kapa = 0.005; F = 1/kapa^2; pha = beta*pi*R*n1; t = sqrt(1-kapa^2); P(1,1) = t; P(1,2) = 1; P(2,1) = 1; P(2,2) = t; P = P/kapa; for m = 1:length(lamda) T(1,1) = exp(-j*pha(m)); T(1,2) = 0; T(2,1) = 0; T(2,2) = exp(j*pha(m)); M = P*T*P; Tr(m) = (abs(M(1,2)/M(2,2)))^2; Trr(m) = Tr(m)*(abs(1/M(1,2)))^2; end plot(lamda,Tr); hold on; plot(lamda,Trr,'r'); zoom on; hold off;
Group velocity Recall velocity of a wave
Group velocity Group velocity dispersion