Guided Propagation Along the Optical Fibercourses/ele885/Pres3-885-fiber.pdf · Guided Propagation...
Transcript of Guided Propagation Along the Optical Fibercourses/ele885/Pres3-885-fiber.pdf · Guided Propagation...
Guided Propagation Along the Optical Fiber
Xavier FernandoRyerson Comm. Lab
The Nature of Light• Quantum Theory – Light consists of
small particles (photons)• Wave Theory – Light travels as a
transverse electromagnetic wave• Ray Theory – Light travels along a
straight line and obeys laws of geometrical optics. Ray theory is valid when the objects are much larger than the wavelength (multimode fibers)
Different Theories
• We will first use ray theory to understand light propagation in multimode fibres
• Then use electromagnetic wave theory to understand propagation in single mode fibres
• Quantum theory is useful to learn photo detection and emission phenomena
Step Index Fiber
• Core and Cladding are glass with appropriate optical properties
• Buffer is plastic for mechanical protection
n1 n2
n1>n2
The Optical Fiber• Fiber optic cable functions as a ”light guide,”
guiding the light from one end to the other end.
• Categories based on propagation:– Single Mode Fiber (SMF)– Multimode Fiber (MMF)
• Categories based on refractive index profile– Step Index Fiber (SIF)– Graded Index Fiber (GIF)
Step Index Fiber
n
y
n2 n1
Cladding
Core z
y
rφ
Fiber axis
The step index optical fiber. The central region, the core, has greater refractiveindex than the outer region, the cladding. The fiber has cylindrical symmetry. Weuse the coordinates r, φ, z to represent any point in the fiber. Cladding isnormally much thicker than shown.
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
Single Mode Step Index Fiber
Protective polymerinc coating
Buffer tube: d = 1mm
Cladding: d = 125 - 150 µm
Core: d = 8 - 10 µmn
r
The cross section of a typical single-mode fiber with a tight buffertube. (d = diameter)
n1
n2
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
Only one propagation mode is allowed in a given wavelength. This is achieved by very small core diameter (8-10 µm)SMF offers highest bit rate, most widely used in telecom
Ray description of different fibers
Refraction and Reflection
Snell’s Law: n1 Sin Φ1 = n2 Sin Φ2
When Φ2 = 90,
Φ1 = Φc is the
Critical Angle
Φc=Sin-1(n2/n1 )
Step Index Multimode Fiber
1
221
22
21 12 n
nn
nn−≈
−=∆
Step Index Multimode Fiber
• Guided light propagation can be explained by ray optics
• When the incident angle is smaller the acceptance angle, light will propagate via TIR
• Large number of modes possible• Each mode travels at a different velocity Modal Dispersion
• Used in short links, mostly with LED sources
Graded Index Multimode Fiber
• Core refractive index gradually changes towards the cladding
• The light ray gradually bends and the TIR happens at different points
• The rays that travel longer distance also travel faster
• Offer less modal dispersion compared to Step Index MMF
n1
n2
21
3
nO
n1
21
3
n
n2
OO' O''
n2
(a) Multimode stepindex fiber. Ray pathsare different so thatrays arrive at differenttimes.
(b) Graded index fiber.Ray paths are differentbut so are the velocitiesalong the paths so thatall the rays arrive at thesame time.
23
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
Step and Graded Index Fibers
Graded Index Fiber
nb
nc
O O'Ray 1
A
B'
B
θAθB
θB' Ray 2
M
θB' c/nb
c/na12
B''na
a
b
c We can visualize a graded indexfiber by imagining a stratifiedmedium with the layers of refractiveindices na > nb > nc ... Consider twoclose rays 1 and 2 launched from Oat the same time but with slightlydifferent launching angles. Ray 1just suffers total internal reflection.Ray 2 becomes refracted at B andreflected at B'.
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
n decreases step by step from one layerto next upper layer; very thin layers.
Continuous decrease in n gives a raypath changing continuously.
TIR TIR
(a) A ray in thinly stratifed medium becomes refracted as it passes from onelayer to the next upper layer with lower n and eventually its angle satisfies TIR(b) In a medium where n decreases continuously the path of the ray bendscontinuously.
(a) (b)
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
Total Internal Reflection
Fiber axis
12
34
5
Skew ray1
3
2
4
5
Fiber axis
1
2
3Meridional ray
1, 3
2
(a) A meridionaray alwayscrosses the fiberaxis.
(b) A skew raydoes not haveto cross thefiber axis. Itzigzags aroundthe fiber axis.
Illustration of the difference between a meridional ray and a skew ray.Numbers represent reflections of the ray.
Along the fiber
Ray path projectedon to a plane normalto fiber axis
Ray path along the fiber
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
Skew Rays
Skew rays circulate around the core and increase the dispersion
Single Mode Fiber
• Only one electromagnetic mode is allowed to propagate No modal dispersion
• Most widely used in long haul high speed links
• For single mode condition, the V-Number (Normalized Frequency) < Cut-off V
cVNAaV <=λ
π )(2
0 2 4 61 3 5V
b
1
0
0.8
0.6
0.4
0.2
LP01
LP11
LP21
LP02
2.405
Normalized propagation constant b vs. V-numberfor a step index fiber for various LP modes.
0
0.5
1
1.5
0 1 2 3V - number
V[d2(Vb)/dV2]
[d2(Vb)/dV2] vs. V-number for a step index fiber (after W.A. Gambling etal., The Radio and Electronics Engineer, 51, 313, 1981)
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
n2
Light
n2
n1
y
E(y)
E(y,z,t) = E(y)cos(ωt – β0z)
m = 0
Field of evanescent wave(exponential decay)
Field of guided wave
The electric field pattern of the lowest mode traveling wave along theguide. This mode has m = 0 and the lowest θ. It is often referred to as theglazing incidence ray. It has the highest phase velocity along the guide.
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
Field Distribution in the SMF
Mode-field Diameter (2W0)
In a Single Mode Fiber,
)/exp()( 20
20 wrErE −=
At r = wo, E(Wo)=Eo/e
Typically Wo > a
Cladding Power Vs Normalized Frequency
Vc = 2.4
Modes
Power in the cladding
Lower order modes have higher power in the cladding larger MFD
y
E(y)
Cladding
Cladding
Core
λ2 > λ1λ1 > λc
ω2 < ω1ω1 < ωcut-off
vg1
y
vg2 > vg1
The electric field of TE0 mode extends more into thecladding as the wavelength increases. As more of the fieldis carried by the cladding, the group velocity increases.© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
Higher the Wavelength More the Evanescent Field
E
r
E01
Core
Cladding
The electric field distribution of the fundamental modein the transverse plane to the fiber axis z. The lightintensity is greatest at the center of the fiber. Intensitypatterns in LP01, LP11 and LP21 modes.
(a) The electric fieldof the fundamentalmode
(b) The intensity inthe fundamentalmode LP01
(c) The intensityin LP11
(d) The intensityin LP21
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
Light Intensity
Fiber Key Parameters
Fiber Key Parameters
Effects of Dispersion and Attenuation
Dispersion for Digital Signals
t0
Emitter
Very shortlight pulses
Input Output
Fiber
PhotodetectorDigital signal
Information Information
t0
~2² τ1/2
T
t
Output IntensityInput Intensity² τ1/2
An optical fiber link for transmitting digital information and the effect ofdispersion in the fiber on the output pulses.
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
Low order modeHigh order mode
Cladding
Core
Light pulse
t0 t
Spread, ∆τ
Broadenedlight pulse
IntensityIntensity
Axial
Schematic illustration of light propagation in a slab dielectric waveguide. Light pulseentering the waveguide breaks up into various modes which then propagate at differentgroup velocities down the guide. At the end of the guide, the modes combine toconstitute the output light pulse which is broader than the input light pulse.
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
Modal Dispersion
Major Dispersions in Fiber• Modal Dispersion: Different modes travel at
different velocities, exist only in multimode fibers
• This was the major problem in first generation systems
• Modal dispersion was alleviated with single mode fiber– Still the problem was not fully solved
Dispersion in SMF• Material Dispersion: Due to the fact different
wavelength travels at different velocities – because refractive index n is a function of
wavelength, – exists in all fibers – function of the source line width
• Waveguide Dispersion: Signal in the cladding travels with a different velocity than the signal in the core, significant in single mode conditions
τt
Spread, ² τ
t0
λ
Spectrum, ² λ
λ1λ2λo
Intensity Intensity Intensity
Cladding
CoreEmitterVery shortlight pulse
vg(λ2)vg(λ1)
Input
Output
All excitation sources are inherently non-monochromatic and emit within aspectrum, ² λ, of wavelengths. Waves in the guide with different free spacewavelengths travel at different group velocities due to the wavelength dependenceof n1. The waves arrive at the end of the fiber at different times and hence result ina broadened output pulse.
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)Group Velocity Dispersion
Modifying GVD
GVD = Material disp. + Waveguide dispersion• Material dispersion depends on the material
properties and difficult to alter• Waveguide dispersion can be altered by
changing the fiber refractive index profile– 1300 nm optimized– Dispersion Shifting (to 1550 nm)– Dispersion Flattening (from 1300 to 1550 nm)
• GVD is also called ‘Chromatic Dispersion’
GVD = CHD = MD + WGD
0
1.2 1.3 1.4 1.5 1.61.1-30
20
30
10
-20
-10
λ (µm)
Dm
Dm + Dw
Dwλ0
Dispersion coefficient (ps km -1 nm-1)
Material dispersion coefficient (Dm) for the core material (taken asSiO2), waveguide dispersion coefficient (Dw) (a = 4.2 µm) and thetotal or chromatic dispersion coefficient Dch (= Dm + Dw) as afunction of free space wavelength, λ.
Zero Dispersion Wavelength
Material and waveguide dispersion coefficients in anoptical fiber with a core SiO2-13.5%GeO2 for a = 2.5to 4 µm.
0
–10
10
20
1.2 1.3 1.4 1.5 1.6–20
λ (µm)
Dm
Dw
SiO2-13.5%GeO2
2.53.03.54.0a (µm)
Dispersion coefficient (ps km-1 nm-1)
Modifying the WGD to shift the zero dispersion wavelength Dispersion Shifted Fiber
20
-10
-20
-30
10
1.1 1.2 1.3 1.4 1.5 1.6 1.7
0
30
λ (µm)
Dm
Dw
Dch = Dm + Dw
λ1
Dispersion coefficient (ps km -1 nm-1)
λ2
n
r
Thin layer of claddingwith a depressed index
Dispersion flattened fiber example. The material dispersion coefficient ( Dm) for thecore material and waveguide dispersion coefficient ( Dw) for the doubly clad fiberresult in a flattened small chromatic dispersion between λ1 and λ2.
Modifying the WGD to flatten GVD Dispersion Flattened Fiber
Different Index Profiles
1300 nm optimized
Dispersion Shifted
Different Index Profiles
Dispersion Flattened
Large area dispersion shifted Large area dispersion flattened
Different waveguide dispersion profiles
Dispersion Shifting/Flattening
Polarization Mode Dispersion
• Due to differently polarized light traveling at slightly different velocity
• Usually small • Significant if all other dispersion
mechanisms are small
Polarizations of fundamental mode
Two polarization states exist in the fundamental mode in a single mode fiber
Polarization Mode Dispersion (PMD)
Each polarization state has a different velocity PMD
Total Dispersion
For Multi Mode Fibers:
For Single Mode Fibers:
Group Velocity Dispersion
If PMD is negligible
Mode-field diameter Vs wavelength
• Note dispersion modified fibers have low MFD (modified WGD)
Disp. & Attenuation Summary
t0
Pi = Input light power
Emitter
OpticalInput
OpticalOutput
Fiber
PhotodetectorSinusoidal signal
Sinusoidal electrical signalt
t0f
1 kHz 1 MHz 1 GHz
Po / Pi
fop
0.10.05
f = Modulation frequency
An optical fiber link for transmitting analog signals and the effect of dispersion in thefiber on the bandwidth, fop.
Po = Output light power
Electrical signal (photocurrent)
fel
10.707
f1 kHz 1 MHz 1 GHz
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)Fiber Optic Link is a Low Pass Filter for Analog Signals
Attenuation Vs Frequency
Attenuation in FiberAttenuation Coefficient
• Silica has lowest attenuation at 1550 nm• Water molecules resonate and give high
attenuation around 1400 nm in standard fibers• Attenuation happens because:
– Absorption (extrinsic and intrinsic)– Scattering losses (Rayleigh, Raman and Brillouin…)– Bending losses (macro and micro bending)
dB/km dB)(dB)0(z
zPP −=α
All Wave Fiber for DWDM
Lowest attenuation occurs at 1550 nm for Silica
Att
enua
tion
char
acte
rist
ics
Escaping wave
θ θ
θ′ < θ
θθ > θc θ′
Microbending
R
Cladding
Core
Field distribution
Sharp bends change the local waveguide geometry that can lead to wavesescaping. The zigzagging ray suddenly finds itself with an incidenceangle θ′ that gives rise to either a transmitted wave, or to a greatercladding penetration; the field reaches the outside medium and some lightenergy is lost.
Bending Loss
Bending-induced attenuation
Bending effects on loss Vs MFD
Micro-bending losses
Fiber Production
Preform feed
Furnace 2000°C
Thicknessmonitoring gauge
Take-up drum
Polymer coater
Ultraviolet light or furnacefor curing
Capstan
Schematic illustration of a fiber drawing tower.© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)