5 Calculation of optical properties of fibers and parameters of cable transfer
5.1 Determination of optical fiber parameters
Optical fiber is a guiding system for propagation of electromagnetic waves. For their propagation by fiber is used known phenomenon of total internal reflection at the boundaries of two dielectric media core with a refractive index n1 and a shell with a refractive index n2, with n1> n2.
According to [6] to the relative difference between the refractive indices of OF stepped refractive index profile (RIP) is the formula:
. (5.1)
For these OF the numerical aperture is defined as:
. (5.2)
To determine the mode of OF normalized frequency is used:
, (5.3)
where
- the operating wavelength, mkm;
d - core diameter of OF, mkm (for standard OF d = (8,6 ... 9,5) mkm).
If V <2,405, then the work mode is single-mode, otherwise - multimode.
Critical frequency of OF at which only one type of wave can propagate (NE11) is determined by the expression:
,
where
–
value of the mode
НЕ11
– 2,405;
с – speed of light (с = 3·108 m/s).
Critical wavelength of OF is determined by the expression:
. (5.4)
5.2 Determination of losses in optical fiber
Coefficient of attenuation in the OF due to own and additional losses [6], which appears as the result of the production of optical fiber:
, (5.5)
where
–total
self losses in OF, dB/km;
– additional
losses in OF, dB/km.
Total self losses in OF are defined as [6]:
, (5.6)
where
– rayleigh scattering losses in OF, dB/km;
– losses
in material, related to the polarization, dB/km;
– signal
losses caused by absorption in the infrared region of the spectrum,
dB/km;
– loss
in OF on hydroxyl residue water ОН,
dB/km.
Rayleigh losses can be defined by the formula [6]:
, (5.7)
where
– wavelength,
nm.
When
calculating Rayleigh losses in singlemode OF
складову component
in expression (5.7)
should
be taken approximately equal to 0.
Losses in material related to losses on polarization increases linearly with increasing frequency according to the expression [6]:
. (5.8)
where
– dielectric loss tangent in the core of
OF.
These losses can be found using the expression [5]:
. (5.9)
Signal loss associated with absorption in the infrared region of the spectrum. They are defined by the expression [6]:
. (5.10)
Losses in OF on hydroxyl OH residue water level [6]:
. (5.11)
Experimentally, the additional losses in OC is approximately (20 - 40)% of their losses and are calculated by the formula [6]:
. (5.12)
5.3 Calculation of running dispersion of the signal in single mode optical fiber
A Root mean value of linear dispersion of single-mode fiber is:
, (5.13)
where
– working
wavelength, nm;
– wavelength
range of the laser (table|
4.5);
– chromatic
dispersion coefficient of OF, ps/(km·nm).
Chromatic dispersion coefficient for fibers with shifted dispersion is calculated by the formula [9]
, (5.14)