Optical Fibres -Attenuation - UCY · fibres had a high water impurity content, and hence high overtones of the water absorption peak. • In high purity modern fibres (low OH), loss

ECE 455 – Lecture 07 1

Optical Fibres

- Attenuation

• HMY 445

• Lecture 07

• Fall Semester 2016

Stavros IezekielDepartment of Electrical and

Computer Engineering

University of Cyprus

ECE 455 – Lecture 07

LOOKING AT REFRACTIVE INDEX IN A

NEW WAY

2


Silica optical fibre attenuation varies with wavelength, and over time it has

been reduced through improved manufacturing methods. This has influenced

the evolution of the first, second and third generations of optical fibre

communications.


When we looked at group velocity dispersion in Lecture 06, we saw that

refractive index is an optical material parameter that also varies with

wavelength. Is there a connection?

In electromagnetism, you will have seen that Maxwell’s equations can be used

to derive the wave equation, e.g. in free space for one dimension:

2

2

22

2

002

21

t

E

ct

E

z

E xxx

∂∂

=∂∂

=∂∂

εµ

=0µ Permeability

of free space

=0ε Permittivity

of free space

00

1

εµ=c

(1)

(2)


In a material with refractive index n, we have the phase velocity:

n

cv ==

µε1

00εµµε

==∴v

cn

(3)

(4)

We consider that optical materials used for optical fibres are non-magnetic, such that:

0µµµ r=

0εεε r=

=rµ Relative permeability = dimensionless number

=rε Relative permittivity = dimensionless number

1≈rµ

This then gives Maxwell’s relation for the refractive index of a dielectric:

rrn εµ= (5)

(6)

rn ε≈ (7)

You might have seen in ECE 331 that relative permittivity can be a complex number……


[ ])(exp),( 0 kztjEtzE −= ω

)(cos),( 0 kztEtzE −= ω

n

c

kv ==ω

−= zc

ntjEtzE ωexp),( 0

c

nkω=

From Lecture 05, we saw that a monochromatic wave of light can be written as a

travelling wave:

This can also be written as a complex number:

Phase velocity Phase constant

(8)

(9)

(10) (11)

Substituting (11) into (9):

(12)

So far in ECE 455 we have considered the refractive index to be real.


( )

′−⋅

′′−=

′′−′−=

zc

ntjzn

cE

zc

njntjEtzE

ωω

ω

expexp

exp),(

0

0

What would happen if we assumed a complex refractive index?

njnn ′′−′= (13)

Our monochromatic wave now becomes:

(14)

The imaginary part of the refractive

index corresponds to attenuation as

described by Beer’s law in Lecture 03.

0≥′′n

The real part of the refractive index

corresponds to a phase change term

that can also be seen as a delay.


INTERACTION OF LIGHT WITH

DIELECTRIC MATERIALS

8


Returning to slide 3, the question is, why does

the attenuation vs wavelength profile have this

general shape?

To find the answer, we have to consider what

happens to light as it travels through a

dielectric material (like silica glass).

A dielectric is a material in which charges do

not flow like in a conductor. Instead, we have a

collection of dipoles which under an applied

electric field will be slightly distorted.

We define the dipole moment as the vector

with the same direction as the E-field and

magnitude:

+

-

x

Er

qxp =r

qxp = (15)


So the electric field causes a slight displacement of the electron compared to the much

heavier nucleus. This separation between the electron and the positively charged

nucleus will create an electric field that wants to restore things to their original state

when the external field is removed.

This situation is very similar to that of a spring:

xmdt

dxm

dt

xdmF o

2

2

2

2 ωζ ++=

Damping Restoring force

(Hooke’s law)

Newton’s

second law

And so we can use a spring-mass-damper system

to model a dielectric dipole:

(16)


We can use this spring model to analyse how light, in the form of an incident travelling

electric wave will displace a dipole. The sinusoidal displacement takes the form of simple

harmonic motion.

The oscillating dipole will then act like a mini-antenna, radiating its own electric field:

https://phet.colorado.edu/sims/radiating-charge/radiating-charge_el.html


So as the wave propagates through the dielectric material (e.g. glass):

it excites dipole oscillations, which then emit their own light:

We will return to this concept of dipole oscillations in later exercises, in which we obtain

more detail on the nature of the refractive index and its link with attenuation.


PHYSICAL CAUSES OF OPTICAL FIBRE

ATTENUATION

13


Light can interact with matter in different ways:

Once light is coupled into a standard optical fibre, the attenuation is mainly

caused by absorption and scattering.

We will not consider amplification (e.g. erbium-doped fibre) yet, and we will not

look at nonlinear effects like Raman scattering.


Source: C-L Chen, Elements of Optoelectronics & Fiber Optics

Various sources of fibre attenuation


16

• Attenuation is caused by:

– Absorption: depends on material and impurities

• Intrinsic absorption by atoms of fibre material

• Extrinsic absorption by impurity atoms

• Absorption by atomic defects in glass

– Scattering: due to inhomogeneous material

• Rayleigh scattering

• Mie scattering

– Radiation: due to discontinuities, e.g. bending of fibre

• Macrobends and microbends


• Extrinsic absorption is caused by metal (iron,cobalt, copper

and chromium) and hydroxyl (OH) ions. In the early years,

fibres had a high water impurity content, and hence high

overtones of the water absorption peak.

• In high purity modern fibres (low OH), loss due to extrinsic

absorption has been significantly reduced. (This is achieved by

drying the glass in chlorine gas to leach out the water vapour).

• For both OH and metal ions, ion concentrations of one part

per billion or less are needed to minimise losses to acceptable

levels.

Absorption losses: extrinsic


Absorption spectrum for OH in silica


• Intrinsic absorption results from electronic absorption bands

in the UV region and atomic vibration bands in the near

infrared region. It is the loss associated with the pure fibre

material, and therefore sets the lower limit on absorption.

– In other words, loss due to absorption cannot be reduced

below this limit.

• Attenuation caused by intrinsic absorption in the UV and IR

regions is wavelength dependent as follows:

Absorption losses: intrinsic

αUV = AUV exp (λUV / λ)

αIR = AIR exp (-λIR / λ)


Ex

z

-

-

+

+ +

+ +

+ +

-

-

-

-

-

-

Solid material

Ions form a lattice

• Lattice absorption through a crystal structure

– The EM wave (near infrared light) forces ions to vibrate at

the frequency of the wave; some energy is then lost by

being coupled into lattice vibrations (heat).

αIR = AIR exp (-λIR / λ)

http://en.wikipedia.org/wiki/Transparency_and_translucency


• Absorption of ultraviolet light leading to electronic

transitions:

αUV = AUV exp (λUV / λ)


• Scattering mechanisms cause the transfer of some or all of the optical power contained in one propagating mode to be transferred linearly into a different mode. There are two major types of scattering:

– Rayleigh scattering: caused by inhomogeneities of a random nature occuring on a small scale compared with the wavelength of the light.

– Mie scattering: occurs at inhomogeneities where the discontinuity is comparable to the wavelength.

Scattering losses


+

-

Incident wave Through wave

Scattered wave

Dielectric particle

smaller than wavelength

Scattered waveScattered wave

• Rayleigh scattering:

– The EM wave forces dipole oscillations in the dielectric

particle that it encounters. The particle then acts like a dipole

antenna, radiating waves in many directions.


• Rayleigh scattering has a λ-4 dependence, i.e.

αRayleigh = AR λ-4

1.0

1200 1400 1600Wavelength (nm)

Att

enuat

ion (

dB

/km

)

0.1


Intrinsic attenuation for a pure silica fibre


Measured attenuation for ultra-low loss single-

mode silica fibre


Critical bend radius

usually 3 - 4 cm for standard

SM fibre

Radiation losses usually occur at bends in the optical fibre:


Radiation losses also occur at microbends

introduced due to uneven pressures in cabling of fibre:

Keiser


0 2 4 6 8 10 12 14 16 18

Radius of curvature (mm)

10−3

10−2

10−1

1

10

102

αB (m-1) for 10 cm of bend

λ = 633 nm

λ = 790 nmV ≈ 2.08

V ≈ 1.67

Measured microbending loss for a 10 cm fiber bent by different amounts of radius ofcurvature R. Single mode fiber with a core diameter of 3.9 µm, cladding radius 48 µm,∆ = 0.004, NA = 0.11, V ≈ 1.67 and 2.08 (Data extracted and replotted with ∆ correctionfrom, A.J. Harris and P.F. Castle, IEEE J. Light Wave Technology , Vol. LT14, pp. 34-40, 1986; see original article for discussion of peaks in αB vs. R at 790 nm).

© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)


Absorption

in

Infrared

region

Absorption

Atomic

Defects

Extrinsic

(Impurity

atoms, e.g. OH)

Intrinsic

Absorption

Absorption

in

Ultraviolet

region

Attenuation

Scattering

Losses

Mie

Scattering

Rayleigh

Scattering

Radiative

losses/ Bending

losses

Macroscopic

bends

Microscopic

bends

SUMMARY OF ATTENUATION

Documents

Optical Fibres -Attenuation - UCY · fibres had a high water impurity content, and hence high overtones of the water absorption peak. • In high purity modern fibres (low OH), loss