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2Optical Fiber
“Signal Degradation”
2 EffectsPulse Spreading – Dispersion (Distortion)
Causes the optical pulses to broaden as they travel along a fiberOverlap between neighboring pulses creates errorsResulting in the limitation of information-carrying capacity of a fiber
Signal Attenuation – Losses
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Signal Attenuation Losses Determines the maximum repeaterless separation between optical transmitter & receiver
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Pulse Spreading
Successive pulses overlap as they spread
Initial instantaneous pulsesp y p
Spreading increases with distanceDegree of dispersion depends on fiber type
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Unintelligible
Multipath/Modal DispersionModes are oscillation/propagation pathsMode velocities differ in step-index multimodefiberfiberVisualize as difference in ray paths
Red ray goes shorter distance than blue
n2
n1
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Time Delay & Bandwidth Length product
Time delay between the two rays taking longest and shortest paths is a measure of pulse broadening; given by
Δ=⎥⎦
⎤⎢⎣
⎡−=
2
2
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nn
cLL
SinL
cndT
cφ
pulse broadening; given by
Time delay can be related to the information carrying capacity of the fiber through bit rate B
cn2
Derive ?
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1.
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Group Velocity, VgThe actual velocity at which the signal information & energy is traveling down the fiber. It is always less than the speed of light The observable delay experienced by the optical signal waveform & energy, is commonly referred to as group delayThe group velocity depends on frequency and is given by: dV ω=
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βdV g =
Basics about Plane Waves
Wave Front
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Phase Velocity
vp
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Group of Waves
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Carrier and Envelopevp
vg
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Group Velocity
vg
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Dispersion can be described as: Any phenomenon in which the velocity of propagation of any electromagnetic wave is wavelength dependentwavelength dependent. Any process by which any electromagnetic signal propagating in a physical medium is degraded because the various wavelength signals have different propagation velocities within the physical medium
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Types of DispersionIntermodal/Modal Dispersion
(already discussed)Intramodal Dispersion
1- Material Dispersion2- Waveguide Dispersion
Polarization-Mode Dispersion
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p
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Intramodal Dispersion/GVDThe propagation constant, β(ω), is frequency dependent over band width Δω, with the center frequency ω0, q y 0,Each frequency component has a specific delay time As the output signal is collectively represented by group velocity & group delay this phenomenon is called intramodal dispersion or Group Velocity Dispersion (GVD)
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p ( )In the case of optical pulse propagation down the fiber, GVD causes pulse broadening, leading to Inter Symbol Interference (ISI)
How to characterize dispersion?If the spectral width of the optical source is not too wide, For spectral components which are δλ apart, symmetrical around center wavelength, the total delay difference δτ over a distance L is:
ωβωωβω
ωω
ωτ
Δ=Δ⎟⎟⎠
⎞⎜⎜⎝
⎛=Δ⎟
⎟⎠
⎞⎜⎜⎝
⎛=Δ=Δ L
ddL
VL
dd
dd
Tg
g22
2
βτ dandL == 1where the group delay
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β2 is called GVD parameter, and shows how much a light pulse broadens as it travels along an optical fiber
ωτ
dVand
V ggg ==where, the group delay,
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The more common parameter is called Dispersion, and can be defined as the delay difference per unit length per unit wavelength as follows:
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21 βπcdD −=⎟⎟⎞
⎜⎜⎛
=
In the case of optical pulse, if the spectral width of the optical source is characterized by its rms value of the Gaussian pulse Δλ , the pulse spreading ΔT, over the length of L, can be well approximated by:
ΔT = DL Δλ
22 βλλ Vd g ⎟⎠⎜⎝
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ΔT = DL ΔλD has a typical unit of [ps/(nm–km)]
Material DispersionCladding
CoreEmitterVery shortli h l
vg(λ2)vg(λ1)
Input
Output
τt
Spread, ² τ
t0
λ
Spectrum, ² λ
λ1 λ2λo
Intensity Intensity Intensity
light pulse
All excitation sources are inherently non monochromatic and emit
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All excitation sources are inherently non-monochromatic and emit within a spectrum, Δλ, of wavelengths. Waves in the guide with different free space wavelengths travel at different group velocities due to the wavelength dependence of n1. The waves arrive at the end of the fiber at different times and hence result in a broadened output pulse.
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Material Dispersion
The refractive index of the material varies as a function of wavelength, n (λ)Material-induced dispersion for a plane wave propagation in homogeneous medium of refractive index n:
Th l d d t t i l di i i th fλωλ
πd
dncd
dnD ggM
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12=−= ⎥⎦
⎤⎢⎣⎡=⎥
⎦
⎤⎢⎣
⎡cn
dd
Vdd 2
2
1λλ
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The pulse spread due to material dispersion is therefore:
)(λλ matg DLT Δ=Δ
material dispersion
Wavelength dependence of Dispersion
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Waveguide Dispersion Waveguide dispersion is due to the dependency of the group velocity of the fundamental mode as well as other modes on the ‘V’ number (Normalized Frequency). ( q y)In order to calculate waveguide dispersion, we consider that n is independent of wavelength. Waveguide dispersion is given by:
⎥⎥⎦
⎤
⎢⎢⎣
⎡+
Δ−=
dVVbd
ddn
dVVbdV
nn
D ggW)()(2 2
2
2
2
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2 ωωλπ
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⎦⎣
where, group delay is expressed in terms of the normalized propagation constant, ‘b’, also called waveguide parameter
Total Dispersion, Zero Dispersion
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Minimum loss here
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Dispersion Shifted Fiber Profiles
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Polarization Mode DispersionEffect of fiber birefringence on polarization (electric field orientation) states of an optical signal Due to geometric irregularities, internal stresses, deviations in circularity, external factors like bending, twisting & pinchingResulting difference in propagation times between the two orthogonal modes causes pulse spreading, hence l di t PMD
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leading to PMD PMD varies randomly along the fiber, ps/√km
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Polarization Mode Dispersion
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Polarization Mode Dispersion
Corez
n 1 y // y Ex
Output light pulset
Δτ
Intensity
n 1 x // x
y
Ey
Ex
x
Ey
E
Δτ = Pulse spread
Input light pulse
t
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Suppose that the core refractive index has different values along two orthogonal directions corresponding to electric field oscillation direction (polarizations). We can take x and y axes along these directions. An input light will travel along the fiber with E x and E y polarizations having different group velocities and hence arrive at the output at different times
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Polarization Mode Dispersion
Polarization mode dispersion (PMD) is due to slightly different velocity for each polarization mode because of the lack of perfectly symmetric & anisotropicity of the ffiber If the group velocities of two orthogonal polarization modes are vgx and vgy , then the differential time delay ΔTpol between these two polarization over a distance L is
pol vL
vLT −=Δ
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The rms value of the differential group delay can be approximated as:
gygx vv
LDT PMDpol ≈Δ
Losses in Optical Fibers Coaxial cable Vs. Optical Fiber Attenuation
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Attenuation (fiber loss)Power loss along a fiber:
The parameter is called fiber attenuation coefficient
Z=0P(0) mW
Z= l lpePlP α−= )0()( mw
zpePzP α−= )0()(pα
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having the unit of for example [1/km] or [nepers/km]. A more common unit is [dB/km] that is defined by:
]km/1[343.4)()0(log10]dB/km[ plP
Pl
αα =⎥⎦
⎤⎢⎣
⎡=
Fiber loss in dB/km
dBmmWmWmWP 10
110log1010 10 =⎟⎟
⎠
⎞⎜⎜⎝
⎛==
Z = 0 Z = l]dBm)[0(P
]km[]dB/km[]dBm)[0(]dBm)[( lPlP ×−= α
????
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mWmWdBmP 50110127 1027
=⎟⎟⎠
⎞⎜⎜⎝
⎛==
????
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Fiber lossExample: 10mW of power is launched into an optical fiber that has an attenuation of a=0.6 dB/km. What is the received power after traveling a distance of 100 km?
Initial power is: P = 10 dBmInitial power is: Pin = 10 dBmReceived power is: Pout= Pin– α L = 10 dBm – (0.6)(100) = - 50 dBm
Example: 8mW of power is launched into an optical fiber that has an attenuation of a=0.6 dB/km. The received power needs to be -22dBm. What is the maximum transmission distance?
Initial power is: P = 10log (8) = 9 dBm
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Initial power is: Pin = 10log10(8) = 9 dBmReceived power is: Pout = 1mW 10-2.2 = 6.3 mWPout - Pin = 9dBm - (-22dBm) = 31dB = 0.6 LL = 51.7 km
Optical fiber attenuation vs. wavelength
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Attenuation in Optical Fibers
Three causes of LossesAbsorptionScatteringRadiative Losses
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Absorption-I (Extrinsic)
Absorption is caused by three different mechanisms:1- (a) Impurities in fiber material: from transition metal [iron,
chromium cobalt and copper] ions (must be in order ofchromium, cobalt and copper] ions (must be in order of 1~10 ppb)(b) OH ions with absorption peaks at wavelengths 1400 nm, 950 nm & 725nm (overtones of the fundamental absorption peak of water around 2700nm).
Reduction of residual OH contents to around 1 ppb, commercially available fibers have attenuation around
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commercially available fibers have attenuation around 0.3 dB/km in 1550 nm window.
An effectively complete elimination of water molecule results in the Allwave fiber
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850 nmwindow
1.3 µmwindow
1.55 µmwindow
Main OHMain OH absorption
Rayleigh Infrared
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RayleighScatteringminimum
AbsorptionOf silica
Absorption-II2- Intrinsic absorption (fundamental lower limit): electronic
absorption band (UV region) & atomic bond vibration band (IR region) in basic SiO2.
3 R di i d f3- Radiation defects
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2 Scattering lossesLinear scattering losses: transfer of optical power from one mode (proportionally to the mode power) into some other modemode power) into some other mode
Rayleigh scatteringMie scattering
Nonlinear scattering losses: Disproportionateattenuation, usually at high optical power levels in long SM fibers
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gStimulated Brillouin scatteringStimulated Raman scattering
Linear ScatteringRayleigh scattering: - Refractive index variations over small distances compared with wavelength due to:g
Microscopic variations in the material densityDefects during fiber manufactureCompositional fluctuations due to oxides
( )kmdBcRR /1
4α =
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( )kmdcRR /4λαwhere cR is the Rayleigh scattering coefficient and is the range from 0.8 to 1.0 (dB/km)·(mm)4
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Mie scattering: ---- inhomogeneities comparable in size to the guided wavelength due to non perfect cylindrical structure: e.gy g
Imperfections at core-cladding interfaceDiameter fluctuations Core-cladding refractive index differences along the fiber length
Mie scattering is typically very small in optical
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Mie scattering is typically very small in optical fibers
Nonlinear ScatteringInsignificant unless the power is greater than 100 mWStimulated Brillouin scattering:modulation of light through thermal molecular vibrations within the fiber: incident photonvibrations within the fiber: incident photon produces a phonon of acoustic frequency as well as a scattered photonStimulated Raman scattering: high frequency optical phonon is generated instead of acoustic phonon
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instead of acoustic phonon
Phonon is a quantum of elastic wave in lattice structure
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Absorption & Scattering Losses in Fibers
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Radiative Losses (Bending Loss)Macrobending Loss:
Lightwave suffers sever lossdue to radiation of the
t fi ld i thevanescent field in thecladding region. As the radiusof the curvature decreases, theloss increases exponentiallyuntil it reaches at a certaincritical radius.For any radius a bit smallerthan this point the losses
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than this point, the lossessuddenly becomes extremelylarge.Higher order modes radiateaway faster than lower ordermodes.
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Microbending Loss:Microscopic bends of the fiber axis that can arise when the fibers are incorporated into cables.The power is dissipated through the microbended fiber, because of the repetitive coupling of energy between guided
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modes & the leaky or radiation modes in the fiber
Losses in standard SM fiber
Wavelength SMF28 62 5/125Wavelength SMF28 62.5/125
850 nm 1.8 dB/km 2.72 dB/km1300 nm 0.35 dB/km 0.52 dB/km1380 nm 0.50 dB/km 0.92 dB/km1550 0 19 dB/k 0 29 dB/k
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1550 nm 0.19 dB/km 0.29 dB/km
