Fibre-Optic Communications.pdf

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Fiber-Optic Communications
Figure 1.5. Reflection coefficient versus the angle of incidence:
a) case where n2 > n1; b) case where n2 < n1
For zero (or low) incidences, the reflection coefficient in power equals:
R = ⎜ρ⎜ 2 ⎛ n1
n ⎞
2
= ⎜
−
⎟
⎜ n1
n ⎟
⎝ + 2 ⎠
giving 4% for the air (n ≈ 1) − glass (n ≈ 1.5) interface.
2
This Fresnel reflection is one of the causes of fiber-optic access and connection
losses, and especially of integrated and optoelectronic optical components, where
the indices are much higher. This is remedied by antireflection layers (dielectric
layer stacking for an index adaptation at the wavelength used).
1.1.7. Total reflection
If n2 < n1, there is total reflection for θi > θlim, angle of limit refraction given by:
sin θlim =
n 2
n 1
n2
where sin θt = sin θlim > 1 and cos θt = ± j 1 sin2θ
i −1
n1
n
n2
2
2
The medium 2 impedance, which is in cos θt or 1/cos θt depending on its
polarization, then becomes completely imaginary.
This is the equivalent of an electric line loaded by reactive impedance. The
reflection coefficient becomes imaginary and is written as: