# Fiber Attenuation Loss

This is a continuation from the previous tutorial - ** landscape lenses and the influence of stop position**.

Optical intensity of light decreases during transmission in a straight fiber because of various absorption and scattering mechanisms. This is represented mathematically in Eq. (2.3) when the longitudinal propagation constant, \(\beta\), is a complex number. The imaginary part of \(\beta\) is the longitudinal decay constant.

The decrease in optical power during transmission is often referred to as ‘‘attenuation’’ or ‘‘loss.’’ For modern silica-based fibers, the attenuation within the wavelength range from about 1300 to 1600 nm is dominated by Rayleigh scattering, which results from intrinsic nanoscopic density fluctuations in the glass.

Rayleigh scattering loss has wavelength dependence approximately \(1/\lambda^4\), as illustrated in the dashed line in Fig. 2.7.

In addition, sources of attenuation in optical fibers result from electronic and vibrational absorption from the silica, intended dopants, and impurities, and possibly from scattering by stress patterns frozen into the core layers during draw.

The most commonly used model for the spectral loss, \(\alpha\), in dB/km has been

\[\tag{2.19}\alpha=A\frac{1}{\lambda^4}+B+C(\lambda)\]

where \(A\) is the Rayleigh scattering coefficient, \(B\) represents the combined wavelength-independent scattering loss mechanisms such as microbending, waveguide imperfections, and other scattering losses, and \(C(\lambda)\) represents all other wavelength-dependent loss mechanisms such as the OH^{-} absorption peaks.

Walker proposed modeling \(C(\lambda)\) as

\[\tag{2.20}C(\lambda)=\alpha_{uv}+\alpha_{IR}+\alpha_{12}+\alpha_{13}+\alpha_{POH}+\alpha_M+\alpha_{XS}\]

where the UV absorption band edge is modeled by

\[\tag{2.20a}\alpha_{uv}=K_{uv}\cdot{w}\cdot\exp(C_{uv}/\lambda)\]

the infrared absorption band edge is modeled by

\[\tag{2.20b}\alpha_{IR}=K_{IR}\cdot\exp(-C_{IR}/\lambda)\]

and the OH^{-} absorption peaks at 1240 and 1383 nm are modeled by the superposition of Gaussian terms

\[\tag{2.20c}\alpha_{12}=\sum_{i=1}^2A_{12,i}\exp\left[-(\lambda-\lambda_{12,i})^2/2\sigma_{12,i}^2\right]\]

and

\[\tag{2.20d}\alpha_{13}=\sum_{i=1}^4A_{13,i}\exp\left[-(\lambda-\lambda_{13,i})^2/2\sigma_{13,i}^2\right]\]

respectively, where \(A_{12,i}\) and \(A_{13,i}\) are the individual Gaussian peak amplitudes, \(\lambda_{12,i}\), \(\lambda_{13,i}\) are the individual Gaussian peak center wavelengths, and \(\sigma_{12,i}\) and \(\sigma_{13,i}\) are the individual Gaussian peak widths.

If phosphorous doping is present in the fiber, the absorption from P-OH, \(\alpha_{POH}\), is

\[\tag{2.20e}\alpha_{POH}=A_{POH}\cdot\exp\left[-(\lambda-\lambda_{POH})^2/2\sigma_{POH}^2\right]\]

where \(A_{POH}\) is the peak amplitude, \(\lambda_{POH}\) is the peak center wavelength, and \(\sigma_{POH}\) is the peak width.

The macrobending loss, \(\alpha_M\), is modeled by Walker as

\[\tag{2.20f}\alpha_M=A_M\lambda^{-2}\cdot\exp\left[M_1\lambda^{-1}(2.478-M_2\lambda)^3\right]\]

where \(A_M\), \(M_1\), and \(M_2\) are parameters determined by the fiber properties and the bend radius.

For high-performance fibers, the excess loss term, \(\alpha_{XS}\), will normally be small and contain measurement error and noise, as well as systematic errors associated with the accuracy of the various terms of the loss model.

The next tutorial discusses about ** laser amplification**.