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16.711 Lecture 6 Transmission Matrix, DWDM

16.711 Lecture 6 Transmission Matrix, DWDM. Last Lecture. Electro-optics effect Refractive index ellipsoid Linear electro-optic effect, Pockels effect EO modulators based on Crystal and polymers Kerr effect and applications Acoustic optical modulators.

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16.711 Lecture 6 Transmission Matrix, DWDM

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  1. 16.711 Lecture 6 Transmission Matrix, DWDM Last Lecture • Electro-optics effect • Refractive index ellipsoid • Linear electro-optic effect, Pockels effect • EO modulators based on Crystal and polymers • Kerr effect and applications • Acoustic optical modulators

  2. 16.711 Lecture 6 Transmission Matrix, DWDM Today • Distribute Bragg Mirrors • Transmission Matrix • Simulation of DBR Mirrors • Fiber Bragg Gratings • AWG • other DWDM Technology

  3. 16.711 Lecture 6 Transmission Matrix, DWDM Distribute Bragg Mirrors: Reflection as a function: • Indices, n1 and n2 • Layer thicknesses • number of mirror pairs Reflection spectrum: • Indices, n1 and n2 • Layer thicknesses • number of mirror pairs Vertical Cavity Surface Emitting Lasers (VCSEL)

  4. 16.711 Lecture 6 Transmission Matrix, DWDM Transmission Matrix Each interface has two parameters: (1) transmission amplitude (2) reflection amplitude Total transmission and reflection of many pairs are the matrix productions Develop one transmission matrix for a single pair then perform matrix productions.

  5. 16.711 Lecture 6 Transmission Matrix, DWDM Transmission Matrix

  6. 16.711 Lecture 6 Transmission Matrix, DWDM Transmission Matrix When B2 = 0: When A1 = 0:

  7. 16.711 Lecture 6 Transmission Matrix, DWDM Transmission Matrix When B2 = 0: When A1 = 0:

  8. 16.711 Lecture 6 Transmission Matrix, DWDM Transmission Matrix

  9. 16.711 Lecture 6 Transmission Matrix, DWDM Matlab simulation and discussion: k = 1; for k =1:N T1(1,1) = exp(-j*b2(k)*L2); T1(1,2) = -r21*exp(j*b2(k)*L2); T1(2,1) = r12*exp(-j*b2(k)*L2); T1(2,2) = (t12*t21-r12*r21)*exp(j*b2(k)*L2); T1 = T1/t21; T2(1,1) = exp(-j*b1(k)*L1); T2(1,2) = -r12*exp(j*b1(k)*L1); T2(2,1) = r21*exp(-j*b1(k)*L1); T2(2,2) = (t12*t21-r12*r21)*exp(j*b1(k)*L1); T2 = T2/t12; T = T1*T2; T10 = T^10; pi = 3.1416; n1 = 3.5; n2 = n1-n1*0.005; r12 = (n1-n2)/(n1+n2); r21 = (n2-n1)/(n1+n2); t12 = 2*(n1*n2)^0.5/(n1+n2); t21 = t12; lamda = 1.295:0.00001:1.305; b1 = 2*pi*n1./(lamda); b2 = 2*pi*n2./(lamda); L1 = 1.3/(4*3.5); L2 = 1.3/(4*3.5*(1-0.005)); N = length(lamda);

  10. 16.711 Lecture 6 Transmission Matrix, DWDM Matlab simulation and discussion: n1 = 3.5, n2 = 2.5 5 v.s. 20 pairs n1 = 3.5, n2 = 3.45 20 pairs

  11. 16.711 Lecture 6 Transmission Matrix, DWDM Matlab simulation and discussion: n1 = 3.5, n2 = 3.495 1000 pairs, read line delta n = 0.001.

  12. 16.711 Lecture 6 Transmission Matrix, DWDM Fiber Bragg Gratings: Laser written index fluctuation, ~ 0.003-0.03 Phase matching condition: Applications: • wavelength stabilizer • band stop filter

  13. 16.711 Lecture 6 Transmission Matrix, DWDM Fiber Bragg Grating Applications: • OADM • Channel cross-talk power penalty • power penalty in dB: • Band with • Extinction ratio

  14. 16.711 Lecture 6 Transmission Matrix, DWDM Chirped Fiber Bragg Grating for dispersion compensation: • Chirped Fiber Bragg Grating: • Diffractive gratings: • Channel cross-talk power penalty • Band with • Extinction ratio

  15. 16.711 Lecture 6 Transmission Matrix, DWDM Array waveguide gratings (AWG): • Principle of AWG , ,

  16. 16.711 Lecture 6 Transmission Matrix, DWDM Array waveguide gratings (AWG): • AWG based Filter • Path band wavelength • Free-spectral range • Bandwidth • Extinction ratio

  17. Output plane 16.711 Lecture 6 Transmission Matrix, DWDM Array waveguide gratings (AWG): • dispersion • AWG based DWDM • wavelength spacing

  18. Output plane 16.711 Lecture 6 Transmission Matrix, DWDM Array waveguide gratings (AWG): • FSR • AWG based DWDM • Number of channel

  19. 16.711 Lecture 6 Transmission Matrix, DWDM Liquid crystal based DWDM

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