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2.5.12 Properties of optical fibres

An optical fibre consists of at least two distinct regions known as the core and cladding. When the refractive index of the core, n₁, is made higher than the refractive index of the cladding, n₂, a light beam may be confined to the core region of the fibre. The most commonly used material for the fabrication of optical fibres is silicon dioxide in which the refractive index can be modified by the addition of dopants such as GeO₂, P₂O₅, F and B₂O₃ (Waynant, 1993). There are two categories of optical fibre which differ in both propagation properties and in their construction. Multi-mode fibre has a 40 to 300 µm core diameter and a cladding diameter in the range 125 µm to over 300 µm; light can travel via many paths or modes. Single-mode fibre has a core diameter of the order 3 to 10 µm and a cladding diameter of 125 µm. The fibre parameter (Snyder, 1983), V, provides information on the number of modes in a fibre and is defined as

where ρ is the core radius, λ is the wavelength of radiation and Δ is the profile height parameter given by

A step profile fibre having a uniform core and uniform cladding is single-moded when V < 2.405 and the cut-off wavelength, λ_c, above which only one mode can propagate is given by

The mode field is the single-mode field distribution giving rise to a radial intensity distribution in the fibre. The mode field diameter (MFD) 2W is defined (Petermann, 1983) from the far field intensity distribution F²(q), where q = (1/λ) sin θ, θ being the far field angle,

2W = (2/π)

2

q3F2(q) dq

qF2(q) dq

−1/2

Attenuation of a signal within a fibre occurs as a result of absorption, material scattering and perturbation of the optical path by bending the fibre. The attenuation A(λ) at wavelength λ is given by

   A(λ) = 10 log₁₀[P₁(λ)/P₂(λ)] dB

where P₁ and P₂ are the optical powers traversing cross-sections 1 and 2 separated by distance L; for a uniform fibre the attenuation coefficient a(λ) = A(λ)/L. Absorption losses arise from charge transfer bands in the ultraviolet region and vibration or multiphonon bands in the near infrared, and from impurities and atomic defects in the fibre. The most significant impurities which affect the absorption are O–H and various transition metals; these impurities must be kept below 10 ppb in low loss fibres. In silica fibres minima in the absorption occur around 850 nm, 1310 nm and 1550 nm. Scattering is due to the interaction of the radiation with the inhomogeneity of the material on a microscopic scale. In such cases the attenuation due to scattering is proportional to λ⁻⁴, Rayleigh scattering. Attenuation also arises if the fibre is bent away from the straight position due to radiation being radiated away from the core. The two categories of bending loss are macrobending loss which occurs when the fibre is wound on a spool or mandril, and microbending loss due to small random deviations of the fibre from a straight line. The macrobending loss of the fundamental mode of a single mode fibre is proportional to R^−1/2 exp(– UR) where R is the radius of the bend and U is a constant determined by the fibre parameters (Snyder, 1983).

Several effects contribute to distort the shape of light pulses propagating down a fibre. In multi-mode fibres, different modes have different optical paths and so a pulse comprising several modes will spread out as it propagates (intermodal dispersion). In a circularly symmetric, single mode fibre the intermodal dispersion is zero and the remaining intramodal dispersion arises from the finite spectral width of the light source, since the group delay of the mode varies with wavelength. This results from the wavelength dependence of refractive index (material dispersion) and from the propagation characteristics of the guiding structure (waveguide dispersion).

The generic characteristics of optical fibres widely used in telecommunication networks are detailed in Recommendations of the Telecommunication Standardization Sector (formerly the Consultative Committee for International Telephony and Telegraphy, CCITT) of the International Telegraph Union.

References

CCITT Recommendation G651–Characteristics of a 50/125 μm multi-mode graded index optical fibre cable.
CCITT Recommendation G652–Characteristics of a single-mode optical fibre cable.
CCITT Recommendation G653–Characteristics of a dispersion-shifted single-mode optical fibre cable.
CCITT Recommendation G654–Characteristics of a 1550 nm wavelength loss-minimised single-mode optical fibre cable.
K. Petermann (1983) Constraints for fundamental-mode spot size for broadband dispersion-compensated single-mode fibres, Electron. Lett., 19, 712–714.
A. W. Snyder and J. D. Love (1983) Optical Waveguide Theory, Chapman & Hall, ISBN 0-412-09950-0.
R. W. Waynant and M. N. Ediger (eds) (1993) Electro-optics Handbook, McGraw-Hill, ISBN 0-07-068663-7.

Typical parameters of telecommunication fibres

    ^a Values in the range 2–2.5 dB/km are achieved.
    ^b Values in the range 0.5–0.8 dB/km are achieved.
    ^c Values in the range 0.3–0.4 dB/km are achieved.
    ^d Values in the range 0.15–0.25 dB/km are achieved.

S.Pollitt

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