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

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16.711 Lecture 6 Transmission Matrix, DWDM
Today

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

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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
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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
Transmission Matrix
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16.711 Lecture 6 Transmission Matrix, DWDM
Matlab simulation and discussion
k 1 for k 1N T1(1,1) exp(-jb2(k)L2)
T1(1,2) -r21exp(jb2(k)L2) T1(2,1)
r12exp(-jb2(k)L2) T1(2,2)
(t12t21-r12r21)exp(jb2(k)L2) T1
T1/t21 T2(1,1) exp(-jb1(k)L1) T2(1,2)
-r12exp(jb1(k)L1) T2(2,1)
r21exp(-jb1(k)L1) T2(2,2)
(t12t21-r12r21)exp(jb1(k)L1) T2
T2/t12 T T1T2 T10 T10
pi 3.1416 n1 3.5 n2 n1-n10.005 r12
(n1-n2)/(n1n2) r21 (n2-n1)/(n1n2) t12
2(n1n2)0.5/(n1n2) t21 t12 lamda
1.2950.000011.305 b1 2pin1./(lamda) b2
2pin2./(lamda) L1 1.3/(43.5) L2
1.3/(43.5(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

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16.711 Lecture 6 Transmission Matrix, DWDM
Array waveguide gratings (AWG)

• dispersion

• AWG based DWDM

• wavelength spacing

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16.711 Lecture 6 Transmission Matrix, DWDM
Array waveguide gratings (AWG)

• FSR

• AWG based DWDM

• Number of channel

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16.711 Lecture 6 Transmission Matrix, DWDM
Liquid crystal based DWDM