Modern Trends in Telecom & Information Superhighway. Institute of Information & Communication Technologies (IICT), Mehran UET, Jamshoro. Signal Loss in Optical Fibers. Attenuation . Attenuation .
Institute of Information & Communication Technologies (IICT),
Mehran UET, Jamshoro
Attenuation is the loss of optical power as light travels along the fiber. Signal attenuation is defined as the ratio of optical input power (Pi) to the optical output power (Po).
Signal attenuation (also known as signal loss or fiber loss) determines the maximum repeater-less separation between a transmitter and a receiver.
Metallic copper offers attenuation of 5 dB/km while fiber optic cable offers 0.2 dB/km.
The total attenuation (A), normally expressed in the logarithmic unit of the decibel, between an arbitrary point X and point Y located on the fiber is:
Px is the power output at point X. P y is the power output at point Y.
End users measure the total attenuation of a fiber at the operating wavelength, λ. At different wavelengths, attenuation offered by fiber optic cable is different
In optical fiber communications the attenuation is usually expressed in decibels per unit length (i.e., the attenuation coefficient (α) or attenuation rate), following:
L is the distance between points X and Y. α is a positive number because Px is always larger than Py. The attenuation coefficient will also vary with changes in wavelength, λ.
Attenuation in an optical fiber is caused by number of mechanisms normally influenced by absorption, scattering, and bending losses (discussed later in this lecture).
Intrinsic absorption is caused by basic fiber-material properties when an optical fiber were absolutely pure, with no imperfections or impurities.
Intrinsic absorption sets the minimal level of absorption.
In fiber optics, silica (pure glass) fibers are used predominately. Silica fibers are used because of their low intrinsic material absorption at the wavelengths of operation.
In silica glass, the wavelengths of operation range from 700 nanometers (nm) to 1600 nm. This wavelength of operation is between two intrinsic absorption regions. The first region is the ultraviolet region (below 400-nm wavelength). The second region is the infrared region (above 2000-nm wavelength).
Intrinsic absorption in the ultraviolet region is caused by electronic absorption bands.
The main cause of intrinsic absorption in the infrared region is the characteristic vibration frequency of atomic bonds. The interaction between the vibrating bond and the electromagnetic field of the optical signal causes intrinsic absorption. Light energy is transferred from the electromagnetic field to the bond.
Extrinsic absorption is caused by impurities (such as iron, nickel, and chromium) introduced into the fiber material during fabrication.
Extrinsic absorption is caused by the electronic transition of these metal ions from one energy level to another.
Extrinsic absorption also occurs when hydroxyl ions (OH-) are introduced into the fiber. The amount of water (OH-) impurities present in a fiber should be less than a few parts per billion.
Fiber attenuation caused by extrinsic absorption is affected by the level of impurities (OH-) present in the fiber. If the amount of impurities in a fiber is reduced, then fiber attenuation is reduced. Water or more precisely (OH-) ion, which is the main fiber impurity, creates an attenuation peak around 1430 nm.
During manufacturing, regions of higher and lower molecular density areas, relative to the average density of the fiber, are created. Light traveling through the fiber interacts with the density areas and as a consequence it is then partially scattered in all directions.
Scattering losses in glass arise from microscopic variations in the material density, from compositional fluctuations, and from structural in-homogeneities or defects occurring during fiber manufacture.
The molecular density of material used to manufacture fiber cable contains regions in which molecular density is higher or lower than the average density.
In addition, since glass is made up of several oxides, such as SiO2, GeO2, and P2O5, compositional fluctuations can occur.
These two effects results in the variation of refractive index.
Rayleigh scattering occurs when the size of the density fluctuation (fiber defect) is less than one-tenth of the operating wavelength of light.
Loss caused by Rayleigh scattering is proportional to the fourth power of the wavelength.
Rayleigh scattering, which is in almost all directions, is the physical limit to attenuation, increases dramatically when wavelength decreases, following a (1/λ4) variation.
This is the main reason why optical telecommunications use infrared light.
Rayleigh scattering of sunlight from particles in the atmosphere is the reason why the light from the sky is blue.
Rayleigh scattering Formula
For a single component glass, the Rayleigh scattering coefficient γR formula is:
where p = photo-elastic coefficient,
λ = operating wavelength
n = refractive index of the medium
βc = the compressibility coefficient specific to each material.
K = Boltzmann’s constant
TF = fictive temperature (the temperature at which the material attains isothermal equilibrium).
Transmission loss due to Rayleigh Scattering
The Rayleigh scattering coefficient is related to the transmission loss factor (transmitivity) of the fiber by:
Brillouin scattering occurs when light in a medium interacts with time dependent optical density variations and changes its energy (frequency) and path.
Stimulated Brillouin Scattering (SBS) may be regarded as the modulation of light through thermal molecular vibrations within the fiber. The scattered light appears as upper and lower sidebands which are separated from the incident light by the modulation frequency.
The incident photon in this scattering process produces acoustic phonon and as well as scattered photon.
The frequency shift is a maximum in the backward direction & zero in the forward direction.
Brillouin scattering is only significant above a threshold power density. Assuming that the polarization state of the transmitted light is not maintained, it may be shown that the threshold power PB is given by:
where d and λ are the fiber core diameter and the operating wavelength, respectively. αdB is the fiber attenuation coefficient and v is the source bandwidth in GHz.
Brillouin scattering can also be employed to sense mechanical strain and temperature in optical fibers
Stimulated Raman Scattering (SRS) is similar to Stimulated Brillouin scattering except that a high frequency optical phonon (i.e., quantum of an elastic wave in a crystal lattice) rather than an acoustic phonon is generated in the scattering process.
Also, SRS can occur in both the forward and reverse directions in an optical fiber, and may have an optical threshold of up to three orders of magnitude higher than the Brillouin threshold in a particular fiber.
Using the same criteria as those specified for the Brillouin scattering threshold, it may be shown that the threshold optical power for SRS PR in a long single-mode fiber is given by:
where d and λ are the fiber core diameter and the operating wavelength, respectively. αdB is the fiber attenuation coefficient.
SBS and SRS are not usually observed in multimode fibers because their relatively large core diameters make the threshold optical power levels extremely high.
Macrobendsare bends having a large radius of curvature relative to the fiber diameter. During installation, if fibers are bent too sharply, macrobend losses will occur.
These bends become a great source of loss when the radius of curvature is less than several centimeters. Light propagating at the inner side of the bend travels a shorter distance than that on the outer side. To maintain the phase of the light wave, the mode phase velocity must increase. When the fiber bend is less than some critical radius, the mode phase velocity must increase to a speed greater than the speed of light. However, it is impossible to exceed the speed of light. This condition causes some of the light within the fiber to be converted to high-order modes. These high-order modes are then lost or radiated out of the fiber.
Fiber sensitivity to bending losses can be reduced, if the refractive index of the core is increased, then fiber sensitivity decreases. Sensitivity also decreases as the diameter of the overall fiber increases. However, fibers with larger core size propagate more modes. These additional modes tend to be more lossy.
This assumes that the pulse broadening due to dispersion on the channel is τ which dictates the input pulse duration which is also τ. Hence, the maximum bit rate that can be obtained on an optical fiber link is 1/2τ .
Dispersion in digital OFC systems cause broadening of transmitted pulses as they travel along the channel.
If dispersion is severe, each pulse will overlaps with its neighbor, eventually becoming indistinguishable – Intersymbol Interference (ISI).
For no overlapping of light pulses down on an optical fiber link the digital bit rate Bt must be less than the reciprocal of the broadened pulse duration (2τ). Hence:
When a return to zero code is used the binary level is held for only part (usually half) of the bit period. For this signaling scheme the data rate is equal to the bandwidth in hertz (i.e., one bit per second per hertz) and thus:
The conversion of bit rate to bandwidth in hertz depends on the digital coding format used.
When a non return to zero (NRZ) code is used, the binary one level is held for the whole period τ. In this case there are two bit periods in one wavelength (i.e., two bits per second per hertz). Hence, the maximum bandwidth B is one half the maximum bit rate or
The amount of pulse broadening is dependent on the distance the light pulse travels. Thus the measurement of dispersive properties of a particular fiber is usually stated as the pulse broadening in time over a unit length of the fiber (i.e., ns/km)
In the absence of mode coupling or filtering, the pulse broadening increases linearly with distance.
Thus the actually capacity of fiber is defined as the Bandwidth x Length product. The typical best bandwidth-length products for the three fibers are 20 MHz km, 1 GHz km, and 100 GHz km for multimode step index, multimode graded index, and single mode step index fibers respectively.
Light propagates at a finite speed
fastest ray: one traveling down middle (“axial mode”)
slowest ray: one entering at highest angle (“high order” mode)
there will be a difference in time for these two rays
NOTE: GRIN fibers tend to have less modal dispersion because the ray paths are shorter
modal -time delay from path length differences- usually the biggest culprit in step-index
material-n() : different times to cross fiber -(note: smallest effect ~ 1.3 m)
Waveguide - changes in field distribution -(important for SM)
non-linear-n can become intensity-dependent
v = c/n
In optics, the mode contains all of the spectral components in the wavelength over which the source emits.
As the signal propagates along the fiber, each spectral component can be assumed to travel independently, and to undergo a time delay or group delay per unit length in the direction of propagation given by
here L is the distance traveled by the pulse, β is the propagation constant along the fiber axis, k = 2π/λ , and vg is the group velocity given as:
If the spectral width of the optical source is not too wide, the delay difference per unit wavelength along the propagation path is approximately .
For spectral components which are apart, the total delay difference over a distance L is:
is known as dispersion. It defines pulse spread as a function of wavelength and is measured in picoseconds per kilometer per nanometer.
modal example: step index ~ 24 ns km -1 GRIN ~ 122 ps km-1