Fiber Communications Around the Globe. • Fiber optics dominates long-distance
telecommunications. • In-line Erbium-Doped Fiber Amplifiers (EDFA's) make ...
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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