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)