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

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.

How water can guide light

Principles of light guidance

Tyndall’s* demonstration for the classroom

* or more accurately, “Colladon’s demonstration”

Optical fibres – threads of glass

CoatingCladdingAirCore~6-10 μm125 μm~250 μm

Typical refractive indices:

Cladding: ncl = 1.4440

Core: nco = 1.4512

Light is guided along the core

by Total Internal Reflection

Cladding helps isolate light

from edge of fibre where

losses and scattering are high

Human hairfor comparison

50 – 80 μm

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˚.θcritRefractive index = n2 Refractive index = n1 (n2 > n1)Refracted ray (θ < θcrit) Total internal reflection (θ > θcrit)

n2 sinθcrit = n1 sinθ1 = n1 sin90o =n1 ∴ θcrit = sin−1 n1

n2

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟

If n1 = 1.470 and n2 =1.475, say, then θcrit = 85.28˚ within a fibre core

Bound rays vs Refracting Rays

Bound rays zig-zag indefinitely along a fibre or waveguideθ > θcritCladdingCore

θ < θcritCladdingCore

Refracting rays decay rapidly as they propagate

Visible laser focused into an optical fibre

This Argon laser excites both leaky modes and bound modes

Several Watts @ = 514nm

Light scatters off the air itself !

“Spatial transient” glow due to leaky modes scattering from acrylate jacket material

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

α

Numerical Aperture is defined as NA = n0 sinα where α is the cone half-angle 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.

NA =n0 sinα =ncosin90o −θcrit( ) =ncocosθcrit( )

=nco 1−sin2 θcrit( ) =nco 1−ncl2 nco

2( ) = nco2 −ncl

2

Ray diagram

Knowing the critical angle inside the fibre helps us calculate α, and hence the NA by successive applications of Snell’s Law:

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 critical ray travels a distance S, where:

Taxial=L ncore c( )

Ssinθcrit =L ⇒ S=L ncore nclad( )

Tcrit −Taxial= L ncore2 cnclad( )− ncore c( )[ ]We are interested in the time delay:

For typical multimode fibres, ncore ~1.48, nclad ~ 1.46 , so T/L ~ 67 ns / km by this calculation. In fact, practical fibres exhibit T/L ~ 10 - 50 ns / km, due to mode mixing.

Hence, the transit time for the critical ray is:

Or more particularly, the time delay per unit length along the fibre:

Tcrit =S ncore c( ) =L ncore2 cnclad( )

ΔTL

=ncore ncore−nclad( )

c nclad

The speed of light in the core is c / ncore. Hence the transit time through the segment for the axial ray is

Of course, that’s the fastest possible time. The slowest is for the critical ray...

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 Material Dispersion and is responsible for rainbows etc.

In the fundamental mode, the light spreads out differently into the cladding depending on wavelength. Hence, different wavelengths have different ‘effective refractive indices’. This is Waveguide Dispersion.

Together, Material Dispersion and Waveguide Dispersion are termed Chromatic Dispersion. The pulse spread is proportional to fibre length L and wavelength spread .

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)

PinPoutoptical component

Linear Ratio dB Scale Linear Ratio dB Scale1 0 1 02 3 0.5 -35 7 0.2 -7

10 10 0.1 -10100 20 0.01 -20

1,000 30 0.001 -3010,000 40 0.0001 -40

100,000 50 0.00001 -501,000,000 60 0.000001 -60

GAIN LOSSLasers, amplifiers etc...

Fibres, passive components etc...

The telecommunications windows

Spectral Attenuation of a silica fibre

0.1

1

10

100

700 800 900 1000 1100 1200 1300 1400 1500 1600 1700

Wavelength (nm)

0.2

0.5Rayleigh Scattering Limit

IR Absorption 'edge'

OH- ion (impurity) absorption peaks

UV Absorption tail

1st 'window' 2nd window 3rd window

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!