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.
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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
How water can guide light
* or more accurately, “Colladon’s demonstration”
50 – 80 mm
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
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˚.
If n1 = 1.470 and n2 =1.475, say, then qcrit = 85.28˚ within a fibre core
Bound rays zig-zag indefinitely along a fibre or waveguide
Refracting rays decay rapidly as they propagate
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
Numerical Aperture is defined as NA = n0 sinawhere a 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.
Knowing the critical angle inside the fibre helps us calculate a, and hence the NA by successive applications of Snell’s Law:
So, where does this optical fibre fit into the overall picture?
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.
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.
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
Of course, that’s the fastest possible time. The slowest is for the critical ray...
The critical ray travels a distance S, where:
Hence, the transit time for the critical ray is:
We are interested in the time delay:
Or more particularly, the time delay 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.
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 !
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.
Together, Material Dispersion and Waveguide Dispersion are termed Chromatic Dispersion. The pulse spread is proportional to fibre length L and wavelength spread Dl.
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.
Telecommunications engineers quantify the transmission of light through a system using logarithmic units called decibels (dB):
Transmission in dB = 10 log10 (Pout / Pin)
Lasers, amplifiers etc...
Fibres, passive components etc...
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!