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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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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
slide2

16.711 Lecture 6 Transmission Matrix, DWDM

Today

  • Distribute Bragg Mirrors
  • Transmission Matrix
  • Simulation of DBR Mirrors
  • Fiber Bragg Gratings
  • AWG
  • other DWDM Technology
slide3

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)

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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.

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16.711 Lecture 6 Transmission Matrix, DWDM

Transmission Matrix

When B2 = 0:

When A1 = 0:

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16.711 Lecture 6 Transmission Matrix, DWDM

Transmission Matrix

When B2 = 0:

When A1 = 0:

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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);

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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

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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.

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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
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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
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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
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16.711 Lecture 6 Transmission Matrix, DWDM

Array waveguide gratings (AWG):

  • Principle of AWG

,

,

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16.711 Lecture 6 Transmission Matrix, DWDM

Array waveguide gratings (AWG):

  • AWG based Filter
  • Path band wavelength
  • Free-spectral range
  • Bandwidth
  • Extinction ratio
slide17

Output plane

16.711 Lecture 6 Transmission Matrix, DWDM

Array waveguide gratings (AWG):

  • dispersion
  • AWG based DWDM
  • wavelength spacing
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Output plane

16.711 Lecture 6 Transmission Matrix, DWDM

Array waveguide gratings (AWG):

  • FSR
  • AWG based DWDM
  • Number of channel