Page 25 - Fiber Bragg Gratings

6 Chapter 1 Introduction

and stress in the glass, thereby altering the refractive index. The thermal
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6
expansion of boron-silica glass is ~4 X 10"~ °C , several times that of
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1
silica (7 X 10~ °C~ ) [31]. Boron-doped silica glass is generally free of
defects, with a much reduced melting temperature. Boron being a lighter
atom, the vibrational contribution to the absorption loss extends deeper
into the short wavelength region and increases the absorption loss in the
1500-nm window. Boron with germanium doping has been shown to be
excellent for photosensitivity [29].

1.3 Origins of the refractive index of glass

The refractive index n of a dielectric may be expressed as the summation
of the contribution of i oscillators of strength f t each, as [32]

where e and m are the charge and mass of the electron, respectively, (t) t is
the resonance frequency, and Fj is a damping constant of the ith oscillator.
Therefore, refractive index is a complex quantity, in which the real part
contributes to the phase velocity of light (the propagation constant), while
the sign of the imaginary part gives rise to either loss or gain. In silica
optical fibers, far away from the resonances of the deep UV wavelength
region, which contribute to the background refractive index, the loss is
negligible at telecommunications wavelengths. However, the presence of
defects or rare-earth ions can increase the absorption, even within in the
transmission windows of 1.3 to 1.6 microns in silica optical fiber.
Fj can be neglected in low-loss optical fibers in the telecommunications
transmission band, so that the real part, the refractive index, is [32]

With i = 3, we arrive at the well-known Sellmeier expression for the
refractive index, and for silica (and pure germania), the A i (i = 1 -» 3)
are the electronic resonances at 0.0684043 (0.0690) and 0.1162414
(0.1540) /mi, and lattice vibration at 9.896161 (11.8419) /mi. Their
strengths A t have been experimentally found to be 0.6961663 (0.8069),