Download Principles of light guidance

Principles of light guidance
Early lightguides
Luminous water fountains
with coloured films over
electric light sources built
into the base were used for
early public displays.
These fountains use the
same basic principle of
light guidance as modern
optical fibres. The same
idea is still used today in
fountains, advertising
displays, car dashboards...
Paris Exposition of 1889
Principles of light guidance
How water can guide light
 The water in the jet has a higher
optical density, or refractive
index, than the surrounding air.
 The water-air surface then acts
as a mirror for light propagating
in the water jet.
 Rays of light travel in straight
lines and are reflected back into
the jet when they reach its
outer surface.
 Hence the light rays follow the
jet of water as it curves towards
the ground under gravity.
Tyndall’s* demonstration for the classroom
* or more accurately, “Colladon’s demonstration”
Optical fibres – threads of glass
Human hair
for comparison
Air
Coating
Cladding
50 – 80 m
Typical refractive indices:
Cladding:
ncl = 1.4440
Core
Core:
nco = 1.4512
Light is guided along the core
by Total Internal Reflection
Cladding helps isolate light
~6-10 m
125 m
~250 m
from edge of fibre where
losses and scattering are high
Total Internal Reflection
Rays striking an interface between two dielectrics from the higher
index side are totally internally reflected if the refracted ray angle
calculated from Snell’s Law would otherwise exceed 90˚.
Refractive index = n1
crit
Refracted ray
( < crit)
T otal internal
reflection ( > crit)
Refractive index = n2 (n 2 > n 1 )
n2 sin  crit  n1 sin 1  n1 sin 90  n1
  crit
n 
1 
 sin 1 
n 
 2 
If n1 = 1.470 and n2 =1.475, say, then crit = 85.28˚ within a fibre core
Bound rays vs Refracting Rays
Bound rays zig-zag indefinitely along a fibre or waveguide
Refracting rays decay rapidly as they propagate
Visible laser focused into an optical fibre
This Argon laser excites both leaky modes and bound modes
“Spatial transient” glow due
to leaky modes scattering
from acrylate jacket material
Several Watts @ l = 514nm
Light scatters off the air itself !
Bound modes continue for
many km along the fibre, and
are seen here due to Rayleigh
scattering, the main cause of
attenuation in modern fibres
Rayleigh scattering
is much reduced at
longer infrared
wavelengths
Applying Snell’s Law: Numerical Aperture
Numerical Aperture is defined as NA = n0 sin where  is the cone halfangle for the emerging light rays, and n0 is the external index. In a simple
way, NA characterises the light gathering ability of an optical fibre.

Ray diagram
Knowing the critical angle inside
the fibre helps us calculate , and
hence the NA by successive
applications of Snell’s Law:
NA  n0 sin   nco sin 90   crit   nco coscrit 
 nco 1 sin 2  crit   nco 1 ncl2 nco2   nco2  ncl2
An optical communications link
So, where does this optical fibre fit into the overall picture?
Digitisation of analogue data
Voice is sampled digitally about 8000 times every second, and each sample
needs 8 bits of data to encode it, so a telephone conversation requires
64,000 bits/sec. Quality does not suffer by discrete sampling if it is fast enough.
This is analogous to projecting 25 discrete movie frames per second, which fools
the eye into seeing a continuous picture sequence.
Dispersion - a problem in step profile fibres
Different rays propagate along step profile fibres at different rates - this
is known as multimode dispersion. Pulse distortion is greater for fibres
with many modes, and gets worse as the fibre length increases.
Dispersion in step profile fibres: How bad?
A simple calculation can tell us how much dispersion to expect in a step profile
multimode fibre. Consider a representative segment:
The speed of light in the core is c / ncore.
Hence the transit time through the segment
for the axial ray is
Taxial  L ncore c 
Of course, that’s the fastest possible
time. The slowest is for the critical ray...
The critical ray travels a distance S, where: S sin  crit  L
 S Lncore nclad 

Hence, the transit time for the critical ray is: Tcrit  S ncore c  L ncore cnclad

2

We are interested in the time delay: Tcrit  Taxial  L ncore c nclad  ncore c 
2

Or more particularly, the time delay D T  ncore ncore  nclad 
L
c nclad
per unit length along the fibre:
For typical multimode fibres, ncore ~1.48, nclad ~ 1.46 , so DT/L ~ 67 ns / km by this
calculation. In fact, practical fibres exhibit DT/L ~ 10 - 50 ns / km, due to mode mixing.
Variation on a theme: Graded index fibre
Shortest Path (physically) travels through the highest
index region and is therefore slow.
Longest Path (physically) travels through lower index
some of the time and is faster
With the correct graded index profile, all rays can have
identical transit times, eliminating multimode dispersion !!
Caution: There are still other types of dispersion present !
Chromatic Dispersion
Even if we eliminate all types of
multimode dispersion, pulses of
light having different wavelengths
still travel at different velocities in
silica, so pulse spreading is still
possible if we use a spread of
wavelengths. This is called
Together, Material Dispersion and
Material Dispersion and is
Waveguide Dispersion are termed
responsible for rainbows etc.
Chromatic Dispersion. The pulse
spread is proportional to fibre
In the fundamental mode, the
light spreads out differently into length L and wavelength spread Dl.
the cladding depending on
wavelength. Hence, different
wavelengths have different
‘effective refractive indices’.
This is Waveguide Dispersion.
Transmission through an optical fibre
Telecommunications engineers quantify the transmission of light
through a system using logarithmic units called decibels (dB):
Transmission in dB = 10 log10 (Pout / Pin)
Linear Ratio dB Scale
1
0
2
3
5
7
10
10
GAIN
100
20
Lasers,
1,000
30
amplifiers
10,000
40
etc...
100,000
50
1,000,000
60
Linear Ratio dB Scale
1
0
0.5
-3
0.2
-7
0.1
-10
0.01
-20
0.001
-30
0.0001
-40
0.00001
-50
0.000001
-60
LOSS
Fibres,
passive
components
etc...
The telecommunications windows
Attenuation mechanisms
Several effects lead to loss of light in fibres:
Absorption by impurity ions and
atoms of the pure glass (eg, OH- ion)
Absorption by vibrating
molecular bonds (eg Si - O)
Rayleigh Scattering by inhomogeneities
frozen into the glass structure itself
Each of these effects has a
strong spectral dependence!