http://www.wiretechworld.com/the-future-of-optical-fibres/

EE 443/CS 543 Optical Fiber Communications

Dr. Donald EstreichFall Semester

1

Lecture 4

Optical FiberBasics

2

Highlights from Lecture 3 – I

1. Optical fibers have a core region surrounded by a cladding layer, with a jacket layer (or layers) for protection

2. Silica dominates optical fibers for telecommunication applications3. Silica optical fiber attenuation versus wavelength favors 1300 nm and

1550 nm for lowest attenuation per unit length 4. Rayleigh scattering dominates fiber losses below the IR absorption

limit5. OH- absorption peaks must be accounted for in the use of optical

fibers (especially around 1400 nm)6. Optical fiber attenuation is characterized with attenuation coefficient

with the equation

( ) (0) exp( )P z P z= −

3

Highlights from Lecture 3 – II

7. The absorption coefficient exists in two forms: the Napierian p and the decadal , namely we have

8. The attenuation along a fiber is given by the Lambert-Beer law and is calculated from

9. Power referenced to 1 milliwatt is stated in dBm (it is ten times the base-10 logarithm of the ratio of the power stated to 1 milliwatt), and one milliwatt is equivalent to 0 dBm

10. Optics Review: Light is an electromagnetic wave that carries energy and momentum; travels in vacuum at constant speed of c = 3 108

meters/second11. Snell’s law is12. Law of reflection: On a planar surface the incident angle equals the

reflection angle13. In the core of optical fibers we desire to have total internal reflection

to contain the optical signal

( )( ) (0) expP z P z= −

dB/km 4.343 1/kmp =

1 1 2 2sin( ) sin( )n n =

4

Highlights from Lecture 3 – III

14. Angles greater than the critical angle are completely reflected within the core of the optical fiber

15. The index of refraction n is the ratio of the speed of light in vacuum to the speed of light in the medium (so n is the index of refraction of the medium) and n = 1 for vacuum

16. Waves can exhibit both constructive interference and destructive interference (most important property of waves)

17. Fermat’s principle: Light travels between two points along a path that requires the least time compared to all other possible paths

18. Diffraction gratings: A diffraction grating is an optical component with a periodic structure that splits and diffracts light into several beams travelling in different directions

19. Polarization refers to the direction of the electric field of an electromagnetic wave

5

Highlights from Lecture 3 – IV

20. Vertical and horizontal polarized waves are orthogonal and can thus be separated from each other providing two usable channels.

21. Malus’s rule for two differently aligned polarizers (say angularly different by ) the intensity of a light signal passing through both polarizers is given by

22. Brewster’s angle – the angle of incidence where a given polarization is perfectly transmitted without reflection at the Brewster angle.

23. Optical reflection is modified by the evanescent field extending into the cladding of an optical fiber. Its effect is to lengthen the path of a reflected signal (with total internal reflection) in an optical fiber.

22Intensity cos ( ).I

6

Now . . . Continuing With Optical Fibers

https://www.fibersavvy.com/fiber-optic-cable.aspx

7

Optical fibers are generally made of extremely pure optical glass. An optical fiber is a single, hair-fine filament typically drawn from molten silica glass forming both the core and the cladding.

However, they can also be made of less pure glass, glass plus polymers, or polymers (such as "plastic optical fiber“ aka POF) for shorter distance use.

What is silica?

What Are Optical Fibers Made Of?

https://www.wired.com/story/corning-pure-glass-fiber-optic-cable/

8

Silicon Dioxide (Silica) – Crystalline vs. Amorphous

https://www.jagranjosh.com/articles/cbse-class-12th-chemistry-notes-solid-state-1467032622-1

2(SiO )2(SiO )

59% of Earth’sCrust is Silica

Natural cooling Sudden cooling

Glass is both a super-cooled liquid & an amorphous solid.

9

Amorphous Silica Glass Structure

Soda lime window glass

https://www.quora.com/Why-does-aluminium-oxide-have-higher-fracture-toughness-and-hardness-compared-to-glass

10

Fused Silica is Preferred for Optical Components

Fused silica is a high-purity, non-crystalline material manufactured through

oxidation of raw silica in a flame hydrolysis process, whereas fused quartz is

fabricated by the melting of naturally occurring quartz.

Fused silica is a common glass type used in the optics industry to

manufacture optical components such as lenses, windows, mirrors, prisms,

and beam-splitters. Fused silica is often a preferred material for precision

optics due to its (1) consistent and repeatable optical performance.

Additionally, fused silica demonstrates a (2) low thermal expansion

coefficient that provides (3) high thermal stability and resistance to thermal

shocks, which are often critical characteristics in specific applications.

Fused silica also has a (4) high chemical resistance and (5) minimal

fluorescence. There are many types of fused silica, the most common

includes UV grade fused silica and IR grade fused silica.

https://www.edmundoptics.com/resources/application-notes/optics/uv-vs.-ir-grade-fused-silica/

11

Optical Fiber Manufacturing

https://www.techrepublic.com/article/3d-printing-is-helping-create-complex-fiber-optics/

Preform

PullingColumn Preform

12

Making the Preform for Optical Fiber Manufacturing

The glass for the preform is made by a process called modified chemical vapor deposition (MCVD).In MCVD, oxygen is bubbled through solutions of silicon chloride (SiCl4), germanium chloride (GeCl4) and/or other chemicals. The precise mixture governs the various physical and optical properties (index of refraction, coefficient of expansion, melting point, etc.). The gas vapors flow inside a synthetic silica or quartz tube (cladding) in a special rotating lathe. As the lathe turns, a torch is moved up and down the outside of the tube. The extreme heat from the torch causes:

• The silicon and germanium react with oxygen, forming silicon dioxide (SiO2) and germanium dioxide (GeO2).• This silicon dioxide and germanium dioxide deposit on the inside of the tube and fuse together to form a germanium-doped glass.

The lathe turns continuously to make an even coating and consistent blank. The purity of the glass is maintained by using corrosion-resistant plastic in the gas delivery system (valve blocks, pipes, seals) and by precisely controlling the flow and composition of the mixture. The process of making the preform blank is highly automated and takes several hours.

A greater germanium concentration raises the refractive index of the silica.

13

The basic chemical reaction of manufacturing optical glass is:

SiCl4 (gas) + O2 → SiO2 (solid) + 2Cl2 (in the presence of heat)

GeCl4 (gas) + O2 → GeO2 (solid) + 2Cl2 (in the presence of heat)

Varying amounts of germanium are added to increase the fiber’s core refractive index to the desired level.

Chemical Reaction in Modified Chemical Vapor Deposition

https://www.fiberoptics4sale.com/blogs/archive-posts/95051590-optical-fiber-manufacturing

Multimode Germanium-

Doped Step-Index Preformshttps://www.findlight.net/

14https://www.sciencedirect.com/science/article/pii/S2211379718314268

The Preform is Formed Using Modified Chemical Vapor Deposition

Exhaust

Begins with a hollow glass preform about 3 feet with a 1-inch diameter

Approx. 1900 K

“Vitrification”

15

Vertical Drawing in Optical Fiber Manufacturing

http://www.patentsencyclopedia.com/imgfull/20090126408_04

https://www.fibre-systems.com/suppli

er/nextrom

https://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=6832#ad-image-0

https://www.fiberoptics4sale.com/blogs/archive-posts/95052678-what-is-optical-fiber-dispersion

Index of Refraction versus Wavelength for Silica Glass

16

Refractive indexversus wavelengthfor common silica

glass fiber

Wavelength (microns)

Fused Silica

1.4442

1.4470

n = 1.4527

17

Selected Properties of Transparent Fused Silica

https://en.wikipedia.org/wiki/Fused_quartz

• Density: 2.203 g/cm3

• Hardness: 5.3...6.5 (Mohs scale), 8.8 GPa

• Tensile strength: 48.3 MPa

• Compressive strength: > 1.1 GPa

• Bulk modulus: ~37 GPa

• Young's modulus: 71.7 GPa

• Coefficient of thermal expansion: 5.5 10−7/K (average

from 20 °C to 320 °C)

• Thermal conductivity: 1.3 W/(m·K)

• Specific heat capacity: = 45.3 J/(mol·K)

• Softening point: ≈1665 °C

• Annealing point: ≈1140 °C

• Electrical resistivity: >1018 Ω·m

• Dielectric constant: = 3.75 at 20 °C & 1 MHz

• Index of refraction: n = 1.4585 (at = 587.6 nm)

• Change in refractive index with temperature (0 to 700°C)

at 1.28 10−5/K (between 20 to 30 °C)

Early History of Optical Fiber System Development

18

Year Event

1966 Kao & Hackham identify glass impurities as primary cause of optical loss.

1970 Corning breaks the 20 dB/km loss attenuation milestone.

1973 First diode end-pumped fiber laser demonstrated.

1975 First commercial optical fiber link installed by Dorset (UK) police.

1977 First telephone signals using optical fiber in Long Beach, CA (USA)

1978 Single polarization optical fiber demonstrated.

1986 Erbium-doped fiber amplifier (EDFA) pioneered by David Payne (UK).

1995 Output power from optical fiber laser exceeds 10 watts.

1999 Output power from optical fiber laser exceeds 100 watts.

2009 Charles K. Kao awarded Nobel Prize in Physics for contributionsin improving optical fiber characterisitics.

2009 Output power from optical fiber laser exceeds 10 kilowatts.

https://ceramics.onlinelibrary.wiley.com/doi/10.1111/ijag.12239Charles Kao

19

Charles K. Kao Receives 2009 Nobel Prize in Physics – I

Charles Kuen Kao is known as the “father of fiber optic communications” for

his discovery in the 1960s of certain physical properties of glass, which laid

the groundwork for high-speed data communication in the Information Age.

Before Kao's pioneering work, glass fibers were widely believed to be

unsuitable as a conductor of information because of excessively high signal

loss from light scattering. Kao realized that, by carefully purifying the glass,

bundles of thin fibers could be manufactured that would be capable of carrying

huge amounts of information over long distances with minimal signal

attenuation and that such fibers could replace copper wires for

telecommunication.

"for groundbreaking achievements concerning the transmission of light in fibers for optical communication."

https://www.nobelprize.org/prizes/physics/2009/kao/facts/

20

Charles K. Kao Receives 2009 Nobel Prize in Physics– II

https://www.researchgate.net/figure/The-young-scientist-Charles-Kao-doing-an-early-experiment-on-optical-fibers-at-the_fig12_325025838

From Nobel lecture:

“I cannot think of anything that can replace fiber optics.”

“In the next 1000 years, I can’t think of a better system.”

21https://sites.google.com/site/csapgroupc/home/history-of-optical-fibers

Increase in “Bandwidth-Distance Product” Over Four Generations

FirstGeneration

SecondGeneration Third

Generation

FourthGeneration

22

First generation (Graded-index fibers)

- Year implemented: 1980- Bit rate: 45 Mbps- Regenerator spacing: 10 km- Operating wavelength: 850 nm- Semiconductor: GaAs

https://sites.google.com/site/csapgroupc/home/history-of-optical-fibers

First Generation of Optical Fiber Systems

Corning had reduced optical fiber loss to < 10 dB/km and roomtemperature GaAs diode lasers became available. Used siliconphotodiodes as detectors. Fiber became attractive because coaxial cable transmission lines needed regeneration every 1 km.

23

Second generation (Single-mode fibers)

- Year implemented: 1985- Bit rate: 100 Mbps to 1.7 Gbps- Regenerator spacing: 40 km- Operating wavelength: 1310 nm- Semiconductor: InGaAsP (Bandgap Engineering)

https://sites.google.com/site/csapgroupc/home/history-of-optical-fibers

Second Generation of Optical Fiber Systems

Moved from 850 nm to 1310 nm because fiber loss was < 1 dB/kmand chromatic dispersion was very small at 1310 nm window. Second generation required two technology innovations: (a) Bandgap engineering developed InGaAsP for laser source, and(b) Single-mode fiber (SMF) reduced the modal dispersion in

multi-mode fiber. Needed InP photodetectors at 1310 nm.

24

Third generation (Single-mode lasers)

- Year implemented: 1990

- Bit rate: 10 Gbps

- Regenerator spacing: 100 km

- Operating wavelength: 1550 nm

- Distributed Feedback Lasers

https://sites.google.com/site/csapgroupc/home/history-of-optical-fibers

Third Generation of Optical Fiber Systems

Now fiber loss was at 0.3 dB/km, but silica had higher chromaticdispersion (about -17 ps/nm-km). This meant that the spectral linewidth of the laser source had to much narrower leading to single-mode lasers

25

Fourth generation (Optical amplifiers)

- Year implemented: 1996

- Bit rate: 10 Tbps

- Regenerator spacing: > 10,000 km

- Operating wavelength: 1450 nm to 1620 nm

https://sites.google.com/site/csapgroupc/home/history-of-optical-fibers

Fourth Generation of Optical Fiber Systems

Fourth generation lead to the use of wavelength divisionmultiplexing (WDM) and the introduction of optical amplifiers[such as erbium-doped fiber amplifiers (EDFA)]. With fourth generation chromatic dispersion becomes the major limitation.

26

Generation Year Bit Rate Repeater spacing

Operating Wavelength

1st Generation 1980 45 Mbps 10 km 850 nm

2nd Generation 1985 100 Mbps to 1.7 Gbps

40 km 1310 nm

3rd Generation 1990 10 Gbps 100 km 1550 nm

4th Generation(Optical amplifiers &

WDM)

1996 10 Tbps > 10,000 km 1450 nm to1620 nm

Summary of Optical Fiber System Generations

27

https://www.electronicdesign.com/technologies/communications/article/21800130/whats-the-difference-between-optical-and-electrical-

technology-for-100gbits-connectivity-in-future-systems

Data Rate-Distance Products By Technology

10 100

1000

28

Wave Optics (The Wave Equation)

An electromagnetic signal propagating along a transmission line is governed by the wave equation,

( ) ( )

( ) ( ) ( )

2 2 2, , ; ( ) , , ; 0

2 ( / )2

( / )

, , ; , , exp

Solution:

+ =

= = = =

= −

E x y z t n k E x y z t

c nk and f

c n

E x y z t e E x y z j kz t

The solutions are of the form of complex exponentials where thephase of the traveling waves is

( ) ( )exp j kz t kz t − = −

Solution:

29

Complex Exponentials Written In Form of Sinusoids

The relations between complex exponentials and sinusoidal functions

( )

( )

cos( ) sin( )

cos( ) sin( )

j t z

j t z

e t z j t z

e t z j t z

−

− −

= − + −

= − − −

( ) ( )

( ) ( )

cos( )2

sin( )2

j t z j t z

j t z j t z

e et z

e et z

j

− − −

− − −

+− =

−− =

is the propagation constant (can be complex)k is the wave number (2/) ?k or

30

Visualizing the Phase Velocity of a Sinusoidal Wave

Distance (meters)

Time t0 Time t1

( )0 0Signal = Amplitude cos t z −

t1 > t0

A fixed point on the waveform represents a constant value of (t - z)

constantt z − =

The fixed point on the waveform travels at the phase velocity vp

0

0

(constant) 0 pdt dz d vdz

dt

= =− = =

0

0

2

=

z

31

Phase Velocity and Group Velocity

Communication signals are Fourier wave packets of multiple Frequencies [Remember the Fourier series and Fourier integrals].

A single sinusoidal waveform has a phase velocity (point of constant phase) given by

Phase velocity

A wave packet (signal) moves with group velocity

Group velocity

Group velocity is the speed of the waveform’s centroid as the signal propagates – it is equal to the speed of signal’s energy flow.

= = = ,ph

dz

dt kv

= =gr

d d

dk dv

nk =

32

Phase and Group Velocity for Plane Wave (TEM)

kk0

0

= = =

= =

0

0 0

0

phase

group

at k

cv

k nk n

d cv

dk n

The slope of a straight line is a constant.

TransmissionLine

-k Diagram:

33

Some Useful Relationships

Wave propagation constant or wave vector :

2 2 2radians/meter

Frequency :

1/seconds2 2

Wavelength :

2 2meters

o

o

o

k

n nf nk

c c

f

c c kcf

n n

c c

nf n k n

= = = =

= = = =

= = = =

is the wavelength in vacuum.o

=

2( )n

34

https://www.semanticscholar.org/paper/Influence-of-Higher-order-Modes-in-Coaxial-on-of-Petrov-Rozanov/0e7ab9872e20f0eabac699b91bd5be8b3e42c309

First Higher Order TE11 Mode in a Coaxial Cable

Perpendicular cross-section of a coaxial transmission line.

35

https://www.chegg.com/homework-help/questions-and-answers/figure-8-26-textbook-shows-omega-beta-diagram-

rectangular-waveguide-please-draw-similar-pl-q4969726

- k or - Diagram for Coaxial Line

Group velocity

Phase velocity

Dispersive media

For a TEM wave thegroup velocity is equalto the phase velocity.

TEM

= =phv

nk

Modes Coaxial line

= =2; 1or k n

2

2

2

2

36

Cylindrical Waveguide Modes

https://csttutorial.blogspot.com/2016/06/circular-waveguide-we-simulated-and.html

Cutoff frequency TE11

11

C

TE

f

f

TE11

There are no TEM modes in single conductor waveguides or dielectric waveguides.

37

Optical Fiber

Multimode Single-Mode

Step-Index Graded-Index

Optical Fiber Structure Classifications

38

https://www.computerlanguage.com/results.php?definition=modal+dispersion

Single Mode Fiber versus Multimode Fiber

n1 (core) > n2 (cladding}

For SMF the corediameter is typically 8-10 m

core

cladding

39

https://www.pcmag.com/encyclopedia/term/43125/fiber-optics-glossary

Multi-mode Optical Fiber

MMFSingle-mode Optical Fiber

SMF

Representative Cross Section of Optical Fibers

Some representative dimensions

40

Step Index and Graded Index

https://www.thefoa.org/tech/ref/basic/fiber.html

n2

n1

n1

n2

n1 (core) > n2 (cladding}

n2

n1(x)

n

CL

CL

CL

Guiding an Optical Signal in Graded Index Optical Fiber

41

https://circuitglobe.com/graded-index-fiber.html

Ray Transmission in Multimode Graded Index Fiber

z

42

https://netl.doe.gov/sites/default/files/event-proceedings/2017/crosscutting/Posters/2017_Fin

alPoster01_FE0027891_VirginiaTech.PDF

Graded-Index and Step-Index Optical Fiber Cross-Sections

Fluorine-dopinglowers refractiveindex of silica

Germanium-dopingraises refractiveindex of silica

43

https://www.cozlink.com/modules-a272-275-273/article-69294.html

❑ Higher cost optical sources✓ 1310 + nm lasers (1 & 10 Gbps)✓ 1 Gbps with DWDM✓ Precision packaging

❑ Higher cost connectors needed❑ Higher installation cost❑ Higher system cost❑ Lower transmission loss & higher BW❑ Distances to 60 km and beyond

❑ Lower cost optical sources✓ 850 nm & 1310 nm lasers✓ 850 nm lasers (1 & 10 Gbps)✓ Low precision packaging

❑ Lower cost connectors needed❑ Lower installation cost❑ Lower system cost❑ Higher transmission loss & lower BW❑ Distances up to 2 km

Best forWAN, SAN, Data Center and Exchange

Best forLAN, MAN, Access and Campus

Single Mode Fiber versus Multimode Fiber

44

Common Single Mode Fiber & Multimode Fiber Diameters

Core/Cladding Diameters Category Comments

8 m/125 m SMF Long distances & high data rates

50 m/125 m MMF Short distances & moderate data rates

62.5 m/125 m MMF LAN links

100 m/140 m MMF LAN links & short distances

These are not the only diameters for fiber; but are the most common in use.

45

https://www.researchgate.net/figure/2-Acceptance-cone-in-an-optical-fiber-with-uniform-core-index-of-refraction-Adapted_fig9_315690740

Acceptance Angle to an Optical Fiber

Air (n0

= 1)

Numerical Aperature NA = n0sin

n0

< n1

n1

Solid Angle( )2 1 cos −

n2

46

Numerical Aperature NA and Acceptance Angle

Numerical Aperture (NA) is the measure of the ability of an

optical fiber to collect or confine the incident light ray inside it.

Acceptance angle is the maximum angle where can light enter the fiber’s core and can propagate within the fiber.

Numerical aperture is commonly used in microscopy to

describe the acceptance cone of an but in fiber optics where

it describes the range of angles over which incident light is

captured and propagates along the fiber. In photography we

want to know the NA for a lens assembly (related to the amount of light captured by lens).

47

Numerical Aperature of Fiber

Start with Snell’s Law which is

From figure on prior slide,

Thus,

As → critical then when they are equal,

The numerical aperature (NA) is defined as

Let be the relative refractive index difference between core and cladding.

and define it to be

Then

and

= 0 1sin sinn n

= − 2 criticaland

= = − + =2 2 20 1 1sin cos 1 sin because sin cos 1n n n

−2 20 1 2sinn n n

221 2NA n n= −

2 21 2

21

where 12

n n

n

− =

− = + 1 2

1 2 1

1

because 2n n

n n nn

1 2NA nReference: Pages 18 & 19 of Senior, 3rd ed..

48

Example for Acceptance Angle For Multi-Mode Fiber

From: Jeff Hecht, Understanding Fiber Optics, 3rd edition, Chapter 4, Figure 4.2, page 58.

Note refractive index values.

n1

n2

( ) ( )

( )

−

= − = − =

= = =

2 2

1 o

o

sin 1.5 1.485 2.2500 2.2052 0.044

e

8

sin 0.2116

Acc ptance cone is twice ; 2 = 24.44

sin 0.2116 12.22

Air (n0

= 1)

Cladding, n2 = 1.485

Core, n1 = 1.500

49

Numerical Aperature

https://www.sukhamburg.com/effNumAperture.html

https://en.wikipedia.org/wiki/Numerical_aperture

mode field diameter (MFD)

Effective Numerical Aperture NAe²

Beam spreading

In optics, the numerical

aperture (NA) of an optical

system is a dimensionless

number that characterizes

the range of angles over

which the system can

accept or emit light.

Lens

D/2

2

DNA

f

50

In optics, the numerical aperture

(NA) refers to the cone of light that is

made from focusing lens and

describes the light gathering

capability o the lens. Angle is the

half-angle of the cone of light exiting

the lens output.

The f -number of a lens (f /#) is the

focal length of the lens divided by the

diameter of the lens.

Lens

D/2

( ) ( )

( ) ( )

12

2 212

/# sin

Thus,

1

2 2 /#

ff and NA n

D

D DNA

f fD f

= =

= =

+

Equating Numerical Aperature and f-Number

Read as “f over hash symbol”

51

Skew Waves in Optical Fiber Core

https://slideplayer.com/slide/4666113/

Meridional rays pass through core’s central axis.

52

Modes in a Planar Waveguide

Figure 2.8 (page 26) in Senior, 3rd ed.

The component of the phase propagation constant in the z-direction is z = n1k sin

53https://www.slideshare.net/AsifIqbal109/optical-fiber-communication-unit1

54

Three Lower Modes Showing Ray Propagation & Electric Field

Figure 2.9 (page 28) in Senior, 3rd ed.

Integer m denotesnumber of zeros in the transversedirection.

55

https://www.slideshare.net/fiberoptics4sale/multimode-fiber

Multimode Fiber

Single Mode FiberCore: So small that only one

mode is present

Different Modesl = 0, m = 0 l = 1, m = 1 l = 0, m = 2l = 2, m = 1

Step-Index Multimode Fiber Modes

56

https://www.slideshare.net/tossus/waveguiding-in-optical-fibers

Linearly Polarized (LP) Modes

57

LP01 Mode Distribution LP11 Mode Distribution

https://www.newport.com/t/fiber-optic-basics

When light is launched into a fiber, modes are excited to varying degrees depending on

the conditions of the launch — input cone angle, spot size, axial centration, etc. The

distribution of energy among the modes evolves with distance as energy is exchanged

between them. Energy can be coupled from guided to radiation modes by

“perturbations” such as microbending and twisting of the fiber.

LP01 and LP11 Modes in the Core of an Optical Fiber

Examples of pure modes:

58

Mode Scrambling in Multimode Optical Fiber

Fiber

Mode scrambling is an attempt to equalize the power in all modes, simulating a fully filled launch.

https://www.thefoa.org/tech/ref/testing/test/MPD.html

59

https://mystonehavenfontanahoa.com/contact/

60

http://courses.egr.uh.edu/ECE/ECE5358/Class%20Notes/LectSet%202%20-%20Gaussian%20beam%20basic%205358_p.html

Gaussian Beam Divergence With Distance