Tellurite And Fluorotellurite Glasses For Active And Passive

2. Literature review; MDO 35
For total internal reflection, there is a limit on the angle, below which incident light will
be trapped in the core and propagate. This is known as the critical angle, θ. Incident light
of angles > θ , and < 90°, will ‘leak’ into the cladding, and may not result in a guided
mode. Equation (2.5) relates the geometry in fig. (2.5) to the numerical aperture, NA, of
the fibre, the sine of θ [35]. ‘Leaky’ modes can result from this condition, and over short
lengths (e.g. 2 m), the NA of the fibre can appear larger than that calculated, due to modes
just outside of θ, propagated in the cladding. If the NA is measured over, say 1 km, the
NA will be close to the calculated value [34].
2
1/
2
⎡ ⎛ ncl
⎞ ⎤
2 2 1/
2
θ = nco
sin = nco
⎢1
− ⎜ ⎥ = ( nco
n )
⎢ n ⎟
(2.5)
co ⎥
NA = sin φ
− cl
⎣ ⎝ ⎠ ⎦
The higher the refractive index contrast (∆n), the closer NA will be to 1, and more light
can be launched into the fibre.
Mode propagation
Note, that NA does not depend on fibre dimensions, only the refractive indices of the core
and clad glasses. However, fibre dimensions, and the refractive index profile of the fibre
will govern the number of modes which will be guided. Large core, thin cladding fibres
with a step index, are known as mulitimode, as incident light can propagate along a
number of paths through the fibre [35]. This type of fibre, can be used for sensing,
imaging, or power delivery, but is inappropriate for telecommunication applications, as a