Guided Propagation Along the Optical Fiber
Xavier FernandoRyerson University
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)
Refraction and reflection
Snell’s Law: n1 Sin Φ1 = n2 Sin Φ2
Critical Angle:Sin Φc=n2/n1
Step Index Fiber
Core and Cladding are glass with appropriate optical properties while buffer is plastic for mechanical
protection
n1 n2
n1>n2
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 refractivindex than the outer region, the cladding. The fiber has cylindrical symmetryuse 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)
Meridian Ray Representation
1
22
1
22
21 12 n
nn
nn−≈
−=∆
Total Internal Reflection
Cladding
Coreα < αm ax
AB
θ < θc
A
B
θ > θc
α > αm ax
n0 n1
n2
Lost
Propagates
Maximum acceptance angleαmax is that which just givestotal internal reflection at thecore-cladding interface, i.e.when α = αmax then θ = θc.Rays with α > αmax (e.g. rayB) become refracted andpenetrate the cladding and areventually lost.
Fiber axis
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
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 indefiber by imagining a stratifiedmedium with the layers of refrindices na > nb > nc ... Consider twclose rays 1 and 2 launched froOat the same time but with slighdifferent launching angles. Rayjust suffers total internal reflecRay 2 becomes refracted at B andreflected at B'.
© 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)
Fiber Key Parameters
Comparison of fiber structures
Fiber Key Parameters
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
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 fibeaxis.
(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
Skew rays circulate around the core and increase the dispersion
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
Major Dispersions in Fiber• Modal Dispersion: Different modes travel at
different velocities, exist only in multimodal conditions
• Waveguide Dispersion: Signal in the cladding travel with a different velocity than the signal in the core, significant in single mode conditions
• Material Dispersion: Refractive index n is a function of wavelength, exists in all fibers, function of the source line width
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
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 Fiber
Higher order modes Larger MFDy
E(y)m = 0 m = 1 m = 2
Cladding
Cladding
Core 2an1
n2
n2
The electric field patterns of the first three modes (m = 0, 1, 2)traveling wave along the guide. Notice different extents of fiepenetration into the cladding.© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
Mode-field Diameter (2W0)
In a Single Mode Fiber,
)/exp()( 20
20 wrErE −=
At r = wo, E(Wo)=Eo/e
Typically Wo > a
Power in the cladding
Lower order modes have higher power in the cladding.
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
Mode-field diameter Vs wavelength
E
r
E01
Core
Cladding
The electric field distribution of the fundamental modin 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)
Cladding Power Vs Normalized Frequency
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)
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)Material Dispersion
Material Dispersion
ZeroDispersionWavelength
Modifying Chromatic Dispersion
Chromatic Dispersion = Material dispersion + 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)
Different Index Profiles
1300 nm optimized
Dispersion Shifted
Different Index Profiles
Dispersion Flattened
Large area dispersion shifted Large area dispersion flattened
Different dispersionprofiles
Dispersion Shifting/Flattening
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.
Zero Dispersion Wavelength
0
1.2 1.3 1.4 1.5 1.61.1-30
20
30
10
-20
-10
λ (µ m)
Dm
Dm + D w
D wλ0
Dispersion coefficient (ps km -1 nm -1 )
M ateria l d i sp ersio n co effi c i en t (D m ) fo r th e co re m ateria l (t ak en asS iO 2), w av eg u id e d i sp ersio n co effi c ien t (D w ) (a = 4 .2 µ m ) an d th eto ta l o r ch ro m at ic d i sp ersio n co effi c ien t D ch (= D m + D w ) as afu n ct io n o f free sp ace w av elen g th , λ .
Material and waveguide dispersion coefficients in anoptical fiber with a core SiO 2-13.5%GeO 2 for a = 2.5to 4 µm.
0
–10
10
20
1.2 1.3 1.4 1.5 1.6–20
λ (µm )
D m
D w
SiO 2-13.5% GeO 2
2.53.03.54.0a (µm )
Dispersion coefficient (ps km -1 nm -1)
Total Dispersion
For Single Mode Fibers:
For Multi Mode Fibers:
Group Velocity Dispersion
If PMD is negligible
Dispersion & 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
Power loss in a curved fiber
Power in the evanescent field evaporates first
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)