OPTICAL COMMUNICATIONS
Free-Space Propagation:
Mars
• Similar to radiowaves (but more absorption by clouds, haze)
• Same expressions: antenna gain, effective area, power received
• Examples: TV controllers, inter-building and interplanetary links
Earth
Guided Wave Propagation:
Evanescence outside
θi > θc
glass fiber
• Optical fibers guide waves
• Rays inside fiber impact wall beyond critical angle
⇒ total reflection and wave trapping
• Little attenuation 0.5 < λ < 2 microns (can go >100 km)
Devices:
•
•
•
•
Detectors:
Sources:
Modulators:
Other:
phototubes, photodiodes, avalanche photodiodes
LED’s, laser diodes, fiber amplifiers, gas lasers
amplitude and frequency, mixers, switches
filters, spectral multiplexers and combiners
L21-1
UNDERSEA OPTICAL FIBER CABLES
Fiber Communications Around the Globe
2.5 Gbp/s WDM
560 Mbp/s
Non-repeated
Other regenerative
5.0 Gbp/s
2.5 Gbp/s
280 Mbp/s
Terrestrial systems – too numerous to depict
Tyco Submarine systems, 2000
2008: undersea about ×1.5, some are dark
Figure by MIT OpenCourseWare.
• Fiber optics dominates long-distance telecommunications
• In-line Erbium-Doped Fiber Amplifiers (EDFA’s) make extremely
wideband transoceanic transmission possible without repeaters
• Without fiber communications there would be no World Wide Web
L21-2
WDM MULTIPLEXED LINK
WAVELENGTH DIVISION MULTIPLEXING (WDM):
• Multiple wavelengths combined onto one fiber
• All wavelengths amplified simultaneously and
independently in each Optical Amplifier (OAMP)
λ1
λ1
λ3
MUX
λ2
OAMP
λn
OAMP
OAMP
passive multiplexing – e.g. prism
DEMUX
~80 km of fiber
λ2
λ3
λn
L21-3
WAVES IN FIBERS
Optical Fiber – Simple Picture:
glass cladding ε1
6 μm
evanescence
E(r)
glass core ε2 = ε1 + Δε
Δε / ε ≅ 0.02
125 μm
• Total internal reflection in the higher ε glass core traps light
• Small Δε ⇒ very shallow reflection angles.
• Only certain angles are allowed: waves must interfere constructively
⇒ modes (characterized by Bessel functions)
• Mode velocity = f(ε’s, core size, mode)
L21-4
OPTICAL WAVEGUIDES
Dielectric slab waveguide example:
x
Waves reflect if θi > θc
Glass/air θc = sin-1(ng-1)
ng ≅ 1.5 ⇒ θc ≅ 41.8°
Slab ε > εo
z
θ > θc
TE or TM
2d
Ey
Cladding/core θc = ~sin-1(0.98)
⇒ θc ≅ 78.5°
x
TE1
TE2
TE3
+d
Slab waveguide fields:
⎧ sink x x ⎫ − jk z z
ˆ o⎨
E = yE
x ≤d
⎬e
TEodd
⎩cosk x x ⎭
ˆ 1e−αx − jk z z for x > d,
E = yE
0
-d
ˆ 1e+αx − jk z z for x < −d
E = ± yE
slab
Boundary conditions for TEn:
E // and ∂E y ∂x continuous
∇ × E = zˆ ∂E y ∂x − xˆ ∂E y ∂z = −∂H ∂t
L21-5
ELECTROMAGNETIC FIELD DISTRIBUTION
Magnetic Field:
H = − ( ∇ × E ) jωμo
Propagation
2d
x
Inside the slab, |x| < d:
H
E
⎛
⎧sink x x ⎫
⎧− cosk x x ⎫ ⎞ − jk z z
ˆ z⎨
ˆ x⎨
H = (Eo ωμo ) ⎜ − xk
⎬ − zjk
⎬⎟ e
cosk
x
sink
x
⎩
⎩
x ⎭
x ⎭⎠
⎝
Outside, x > d:
z
TEodd
ˆ z − zj
ˆ α ) e−αx − jk z z
H = (E1 ωμo ) ( − xk
Matching Boundary Conditions at x = d:
Dispersion relations:
kx2 + kz2 = ω2μoε
inside the slab, |x| < d
-α2 + kz2 = ω2μoεo outside, |x| > d [let μ = μo]
Continuity of E : Eo cosk x d e− jk z z = E1e-αd- jk z z for TE1,3,5...
Continuity of H: ( − jk xEo ωμo ) sink x d e− jk z z = − ( jαE1 ωμo ) e−αd− jk z z
Therefore:
kx tan kxd = α
kx2 + α2 = ω2μo(ε - εo)
(ratio of continuity equations)
(from dispersion equations)
L21-6
DIELECTRIC SLAB WAVEGUIDES TEodd n
Field continuity equations:
kx tan kxd = α
kx2 + α2 = ω2μo(ε - εo)
(ratio of continuity equations)
(from dispersion equations)
Transcendental equation, graphical solution:
tank x d =
ω2μo (ε − εo )
k 2x
−1
x
Increasing ω
half-TE2
mode
0
σ=∞
π/2
3π/2
5π/2
TE1
mode
TE3
mode
TE5
mode
kxd
E(x)
L21-7
FIBER WAVEGUIDE DESIGN
Loss mechanisms:
Rayleigh scattering from random density fluctuations
Loss ∝ f4 (scattering makes sky blue)
Infrared absorption dominates for λ > ~1.6 microns
Minimum total attenuation ≅ 0.2 dB km-1
Fiber structure:
Typical: 10-μm core in 125-μm diameter glass, with 100-μm-thick
plastic protective cladding (bundled in cables)
Manufacturing: solid or hollow preform grown by vapor deposition
of SiO2 and GeO2 (using e.g. Si(Ge)Cl4 + O2 = Si(Ge)O2 + 2Cl2)
Architecture: various – single or multimode, polarization-selective
Attenuation (dB km-1)
10
H2 O
Multimode core
Clad
1
~1.5 THz Infrared
Rayleigh
0.1
1
1.8
λ
Single-mode core
Single polarization cladding
L21-8
MIT OpenCourseWare
http://ocw.mit.edu
6.013 Electromagnetics and Applications
Spring 2009
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