Attenuation (or Loss) of optical signal in optical Fibre:
The difference in the power of the input optical signals and output optical output signals in optical fibre is known as attenuation in the optical fibre. It is measured in decibels per kilometer $(\frac{dB}{Km})$ and caused by the absorption and scattering of the optical signal in optical fibre.
The optical signal strength is reduced when the signal travels in optical fibre over a long distance. The expression for the attenuation of optical signal in optical fibre:
$\alpha = - \frac{10}{x(Km)} log \left[ \frac{P_{x}}{P_{\circ}} \right]$
Where
$P_{x} \rightarrow $ Power of optical signal at a position $x$ from origin
$P_{\circ} \rightarrow $ Power of optical signal at origin
The Losses in optical fibre are wavelength-dependent and the attenuation factor depends on the fibre material and manufacturing tolerance.
Types of Attenuation or Loss
A.) Absorption Attenuation or Loss
B.) Scattering Attenuation or Loss
C.) Bending Attenuation or Loss
A.) Absorption Attenuation or Loss:
The absorption of optical signals in optical fibre depends on the amount of the material in optical fibre. There are two types of absorption on optical fibre:
1.) Intrinsic Material Absorption
2.) Extrinsic Material Absorption
1.) Intrinsic Material Absorption: It is a fundamental minimum loss due to absorption when the optical signal passes through the optical fibre. This absorption occurs due to material in optical fibre with no impurities.
2.) Extrinsic Material Absorption: It is a loss due to absorption when the optical signal passes through the optical fibre. This absorption occurs due to a material having impurities ( such as $Fe^{+2}, Cu^{+2}, Cr^{+3}, and \: OH^{-}$ ion from water dissolved in glass) in the optical fibre material.
B.) Scattering Attenuation or Loss:
When the optical signal interacts with a particle then the energy of the optical signal is reduced and it goes in another direction. In scattering, the optical signal is not absorbed but it goes to any other direction which also causes the loss of the optical signal. Scattering is the loss of optical signal due to imperfections in the optical fibre i.e. the basic structure of the optical fibre. There are two types of scattering that occur in the optical fibre i.e.
1.) Linear Scattering:
2.) Nonlinear Scattering
1.) Linear Scattering: The amount of power of the optical signal transferred from an optical wave is proportional to power. There is no change in the frequency of the optical signal.
Types of Linear Scattering
i.) Rayleigh scattering in optical fibre
ii.) Mie scattering in optical fibre
i.) Rayleigh scattering in optical fibre: When the optical signal interacts with the lattice of the core it causes the scattering because the size of the lattice is smaller than the wavelength of the incident optical signal. This interaction is also known as elastic scattering.
In optical fibres, This scattering controls the intrinsic loss mechanism in the low-absorption between absorption tails of the ultraviolet and infrared. This is caused by random heterogeneity in the material of the core lattice that leads to changes in the refractive index. These changes cause attenuation in the optical signal by scattering in optical fibre.
ii.) Mie scattering in optical fibre: When the optical signal interacts with the lattice of the core that causes the scattering because in this scattering the size of a lattice is comparable to the wavelength of the incident optical signal. This interaction is also known as elastic scattering.
In optical fibres, This scattering occurs when the optical signal interacts with inhomogeneities in the fibre core or cladding that are larger than the wavelength of the incident optical signal.
2.) Nonlinear scattering: It is an inelastic scattering that occurs when an optical signal interacts with a material in a non-linear manner. Non-linear scattering occurs, when the intensity of the incident optical signal is very high to change the refractive index of material or when the optical signal interacts with molecules or particles that have non-linear optical properties.
In non-linear scattering, the intensity of the scattered optical signal is not proportional to the intensity of the incident optical signal, and the scattered optical signal can be polarized in different planes than the incident optical signal.
In other words,
In non-linear scattering the wavelength, frequency, or phase of scattered optical signal is different than the incident optical signal. The energy and momentum of the scattered optical signal are not conserved, hence, the scattered optical signal has different characteristics than the incident optical signal.
Types of Non-linear Scattering:
i.) Raman Scattering
ii.) Brillouin Scattering
iii.) Self-phase modulation (SPM)
iv.) Cross-phase modulation (XPM)
v.) Four-wave mixing (FWM)
i.) Raman Scattering: It is an inelastic scattering that occurs when a photon of optical signal interacts with molecules of vibrational modes in the material of the core then this photon excites the molecule to a virtual state before being re-emitted in a different direction with a different energy and frequency.
The frequency shift of the scattered optical signal is directly related to the molecule's vibrational energy, which is a characteristic property of the material.
Stimulated Raman scattering $(SRS)$ is an optical process (i.e. nonlinear process ) that enhances scattering by stimulating the molecules of vibrational modes. In SRS, a pump beam of high intensity is used to amplify the Raman signal which leads to a strong and more easily detectable output optical signal.
ii.) Brillouin Scattering: It is an inelastic scattering that occurs when an optical signal interacts with a material, usually a solid or a liquid, causing the material to vibrate.
It can also be said to be a scattering that occurs due to the interaction of an incident optical signal with the acoustic wave in a material.
The vibrating material scatters the optical signal, shifting its frequency by an amount proportional to the frequency of the vibration.
The scattering of the light by the vibrating material is called the Brillouin scattering. This scattering can be either stimulated or spontaneous. It depends on the material that is excited by an external stimulus or its own oscillations.
Stimulated Brillouin scattering (SBS) is used to control the optical signals in optical fibers and other waveguides. When the frequency of the incident optical signal is tuned to the frequency of the vibrational modes of the fiber then the scattered optical signal is shifted to a new frequency which allows for attenuation or amplification of the optical signal.
Brillouin scattering has various applications in materials science. It is used to study the mechanical properties of materials and to determine the stress and strain in solid materials.
iii.) Self-phase modulation (SPM): It is a non-linear effect that occurs when the optical signal of high intensity travels through an optical fiber. The intensity of the optical signal causes a change in the refractive index of the optical fiber that causes a phase shift in the optical signal.
This phase shift can cause the optical signal to spread out in time and frequency which leads to distortion of the transmitted signal.
In other words, The optical signal pulses change their spectrum due to their own intensity from an induced varying refractive index of the medium.
iv.) Cross-phase modulation (XPM): It is a non-linear effect that occurs when two optical signals, typically from two different channels, interact with each other in an optical fiber.
The interaction between the optical signals causes a change in the refractive index of the fiber, that causes a phase shift in one of the optical signals.
This phase shift can distort the optical signal which can lead to crosstalk between different channels in a fiber optic communication system.
v.) Four-wave mixing (FWM): It is a non-linear effect that occurs when two or more incident optical signals interact with each other in a non-linear medium and produce a new wave with a different frequency and phase.
It is used for wavelength conversion of optical signals and signal processing in optical fibers.
C.) Bending Attenuation or Loss: It is caused by the bending of optical fibre or physical stress on the fibre.
Types of Bend Loss
a.) Microbend Loss
b.) Macrobend Loss
a.) Microbend Loss: It is caused by small discountinuities or imperfections in the optical fibre. Microbend loss increses due uneven coating applications and improper cabling procedures. The external force is also a source of micro bending.
b.) Macrobend Loss: It is caused when the fibre bend's radius of curvature is larger than the fibre diametre. These bends are a great source of loss when the radius of curvature is less than several centimetres.
The total emf of the $n$ - cell = $nE$
The total emf of the $n$ - cell = $E$
The total emf of the $n$ - cell in each row of $m$ parallel rows of the cells = $nE$
