OPTICAL FIBER COMMUNICATION basic and characterstics

Optical fiber communication BLDEACETvijaypur

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Overview of Optical Fiber Communication Introduction: History :Some of the historical developments in the field of communication that led to present day optical fiber communication are listed below: Optical fiber communication methods(special interest):     

Optical Transmission Links: 1.A fire signal method,(Earliest known Greeks) 2.reflecting mirror method(Chinese dynasty, for sending alarms) Invention of laser proved to be a turning point (1960) Practical light wave communication started in 1978 (worldwide) G.Bell informed speech transmission possible using light beam(in 1880) The discovery of the of photonic bandgap phenomena which can be created in structures which propagate light, such as crystals or optical fibers.

Different generation of optical fiber communication: The below table shows repeater spacing needed as function of bitrate at different wavelengths. Bit Rate(Mbps -> Gbps) 45Mbps 100Mbps-1.7Gbps 10Gbps 10Tbps 40-160Tbps

Repeater Spacing(Km)

Operating λ(μm)

10 50 100 >10 x 103 km 24 x 103 – 35 x 103

1.3 1.55 1.45-1.6 1.53-1.57

General Systems   

Baseband transmission (signal is transmitted directly over a channel). Ex- Telegraph analog Morse developed Telegraph in 1837 A typical optical fiber communication system consist of optical source to convert information in electric form to optical form as shown in figure below. The general communication system consist of : Information source:This can be any source like text ,voice ,video. But


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each source differ with each other with respect to bitrate etc. Transmitter modulator:This device modulates the information source so that it should be compatible to transmission channel. The process of modulation ensures immunity towards noise to information . Receiver:This is responsible for recovering the original signal. If we correlate the above two block diagram ,we observe that optical fiber system additionally consists of optical source,e.g LED or LASER for conversion from electrical form to optical form. Optical detector (photo diode e.g:avalanche or pin ) for conversion from optical form to electrical form. At destination side the recovered signal is further processed to bring it back to its base band form.

Advantages of Optical Fiber Communication:       

Long Distance Transmission - O.F have low transmission loss. Large Information Capacity - O.F have wider B.W, 1013 – 1016 Hz. Small size & Light weight - O.F have low weight and small dimension. Immunity to electrical interference - O.F is made from dielectric material, Ex. Glass, Plastic polymer. Enhanced Safety – O.F have high degree of operational safety. No problems of ground loops, sparks, etc. Increased Signal Security – O.F have a high degree of security. Since optical signal is well confined within the core. Low transmission loss compared to copper.( ≅ 0.2 dB/km)


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System reliability & Ease of maintenance – Low loss property of O.F results in less requirement of repeaters(intermediate), Lifetime of optical fiber (predicted) ≈ 20-30yrs. Thus, these two factors tend to reduce time & cost.

Disadvantages:       

High investment cost. Need for expensive transmitter and receiver. More difficult and expensive to splice compared to wires. At high optical powers, is susceptible to fiber fuse Cannot carry electrical power to operate terminal devices. Opaqueness extensive military use, it is known that most fibers become opaque when exposed to radiation. Chemical effects : The glass (fiber material) can be affected by various chemicals including hydrogen gas.

Applications: 

    

As sensors to measure strain, temperature, pressure and other quantities (Qty measured modulates : intensity, phase, polarization, wavelength, transmit time of light in the fibers). In illumination application(Frisbee). For decorative applications (signs ,art & artificial Christmas tree). For endoscopy, to view object through small hole) Ex: Medical Endoscopy. An optical fiber with certain rare earth element (Ex: Erbium) is used as the gain medium of laser or optical amplifier. To provide low level power to electronics situated in difficult electrical environment.

Ray theory: Optical laws that guides light 1. Refractive index : Fundamental optical parameter of material Index of refraction(η) = Air η = 1 H2O η = 1.33 Silica η = 1.45 2. Reflection & Refraction :

C V

=

Speed of light in vaccum Speed of light in matter


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Refraction : Due to bending of light(since n2 > n1) n1sinφ1 = n2sinφ2 δN = phase shift normal to plane of incidence. δP = phase shift parallel to plane of incidence. When light is totally internally reflected a phase change ‘δ’ occurs in the reflected wave. This phase change depends on angle “θ1 < according to relation δN tan( )= 2 tan(

 

δP )= 2

√ n 2 cos 2 θ 1−1 nsin θ 1

n=

π 2

– φc “

n1 n2

n √ n 2 cos 2 θ1 −1 sin θ 1

Ordinary light consist of many electro-magnetic waves that vibrate in a variety of direction. Polarizer is a material that transmits only one polarization component & blocks other


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Acceptance Angle(θa): For the ray to be propagated,along the length of the fiber,it should enter into total internal reflection phenomenen.But this can be accomplished by launching the ray within the half conical angle to the fiber axis.This angle is called as Acceptance angle(θa ).

Θo(max) =sin-1(√n12 – n22) Numerical aperture (N.A): This gives interrelation between acceptance angle & R.I. of three media (viz : core, cladding and air) N.A indicates light gathering capability of a fiber. It is used to calculate source fiber optical power coupling efficiency. Θ2 + φ + Θ2 =

π 2

π 2 -φ

=π


Snells

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law says :

n0sinθ1 = n1sinθ2 : (at air core interface) ……...(1) Consider ∆ ABC => θ2=

π 2

-φ

,

here φ > φc

(critical angle)

Eq(1) becomes n0sinθ1=n1(1-sin2θ)1/2 ……….(2) If limiting case of total internal reflection is considered then Φ Ξ Φc (i.e sinΦc=n1/n2) and θ1=θa (acceptance angle) n0sinθa=n1(1-sin2θ)1/2 = (n1 - n2)1/2

……….(3),Eq3 is known as NA (also defines NA of

step index fiber) aperture(NA). Or NA= n1(2Δ)1/2

where Δ Ξ ( n1 - n2 )/ n1 –--- Relative refractive index diffeerence

Ex. A silica fiber with core diameter large enough to be considered by ray theory analysis has a core R.I 1.5 & clad R.I = 1.47. Determine critical angle,NA for the fiber ,Acceptance angle in air for the fiber. A: Critical angle = 78.5, Acceptance angle = 17.4, NA = 0.3 Skew Rays : 

Don’t cut across the fiber axis,as compared to meridional rays. Traces a helical path in fiber.


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γ

 

-> angle between proj of the ray (in two dimensions) & rad of fiber core. Helical path traced gives a direction change of 2γ at each reflection. Point of emergence (from fiber) in air depends upon the no. of reflection, the rays undergo rather than input condition to fiber (meridional ray).


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Resolving the direction of the ray path AB to core radius at B. γ -> angle between core radius and proj of the ray onto a plane BRSS’ normal to core axis. Θ-> between ray and a line drawn parallel to core axis. To resolve ray path AB relative to radius BR in perpendicular planes (through which ray traverses) requires multiplication by cosγ and sinθ & equating it to cosφ Thus the reflection at point B at an angle φ may be given by: cos γ sin θ = cos φ

Using the trigonometrical relationship sin 2 φ + cos 2 φ = 1,above equation becomes cos γ sin θ = cos φ = (1 − sin 2 φ )1/2 

Consider limiting case of Total internal reflection : φ becomes equal to the critical angle φ c for the core–cladding interface , Using sin φ c = n 2 /n 1 . cos γ sin θ ≤ cos φ c = (1- n22/n12)1/2

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Use snells law at Point ‘A’ n cosin θa = n 1 sin θ Θas – maximum input angle or acceptance angle for skewing



Thus acceptance condition for skew rays is:

where θ as represents the maximum input angle or acceptance angle for skew rays.


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Cylindrical Fiber :

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At Core clad interface, coupling of electric and magnetic field component may results in hybrid mode creation depending upon whether E field is greater or H field (i.e. HE or EH) for that mode V – Normalized Frequency(dimensionless), a – core radius

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Mode- Mode refers to the no. of paths for the light rays within the cable. Modes TE(Ez=0),TM(Hz=0) – occurs due to meridional rays. Order of the mode is equal to the no. of field zeros across the guide. Order of the mode also depends upon the angle that the ray congruence corresponding to this mode makes with axis of fiber. Hybrid modes (Ez = Hz ≠ 0) Also present in cylindrical waveguide(due to skew rays)

No. of modes (M) = 1/2[πd NA/λ]1/2 d=core diameter,NA=numerical aperture 

Waveguide perturbations:Wave guide perturbations are deviation of fiber characteristics. This is due to one or more of the fallowing reasons: a. Deviation of fiber axis from straightness b. Variation in core diameter. c. R.I variation Fiber types : Optical fiber are classified depending upon the fallowing characteristics of the fiber. 1.No of Modes : i)Single mode ii)Multi mode


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Each mode is a pattern of electric and magnetic field distribution that is repeated along the fiber at equal interval W.P may change propagation characteristics of the fiber Depending upon particular perturbation, coupling of energy from one mode to another may take place.

2.Fiber profiles 1.Step index Fibers:   

Core is of constant R.I(n1) Clad of slightly lower R.I R.I profile makes a step change at core-cladding interface. n(r)=

{

n 1 r
If a mode is away from its fc,then energy will be concentrated more in core. At fc, field penetrates into clad relative amount of power flow in core & clad in axial direction( ez)


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Sz=1/2(EXH*).ez over a fiber cross-section.

2.Graded Index Fiber(inhomogeneous core fiber)

 

Constant R.I in core Decreasing R.I n(r) w.r.t radial distance from a maximum value of n1 at the axis to a constant value n2 beyond core radius ‘a’ in the cladding(α – shape of index profile)

n(r) = n 1 [1 − 2Δ(r/a) 2 ] 1/2

= n 1 (1 − 2Δ) 1/2 = n 2

r < a (core)

r ≥ a (cladding)

if α = ∞ ; reduces to step index profile n(r)=n1.    

Meridional rays seems to follow curved path(fig) Variation in R.I creates many refraction(fig) Multi mode graded index exhibit for less inter modal dispersion than multi mode step index. Skew Rays follow a lower index region (at greater speeds)

Ex. Graded index fiber with a parabolic R.I profile has a dr = 50μm. Fiber has a NA=0.2. Estimate total no. of guided modes propagating in the fiber if λ=1μm.


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Single Mode Fibers     

Advantages of SM: Signal dispersion caused (due to delay difference) between different modes in a multi-mode fiber may be avoided. Multi-mode don’t lend themselves for single mode fiber. If we want to use multimode fiber for single mode propagation,all other mode(existing should be attenuated by leakage or absorption). Suitable Normalized frequency can be used for this purpose 0 < V < 2.405. Advantages: i. Exhibit greatest Transmission BW & lowest losses of the fiber transmission media. ii. Have superior Transmission quality over other fibers. iii. Compatible with developing Integrated optics technology. iv. Offer a substantial upgrade capability (future proofing).

Problem: A step index fiber(multimode) with NA=20m supports 1000 modes at λ= 850nm. Calculate, diameter of core and how many modes fiber supports at λ=1320nm & λ= 1550nm. A: a=60.49μm , M=207.07(for 1320nm) ,M=300.63(for 1550nm). Cut-off Wavelength – Single mode operation possible if λc=(2Пan1 /Vc ) (2Δ)1/2 ------------------------------1 Vc = cut off normalized frequency λc = wavelength above which a particular fiber becomes single mode but λ=(2П/V) an1(2Δ)1/2

-----------------------------2

Divide eqn2 by eqn1 , gives λc/ λ =V / Vc , λc=v λ /2.405

where Vc =2.405

Ex. Determine λc for step index fiber to exhibit single mode when R.I(core)=1.46, r(core)=4.5μm,with relative R.I difference 0.25%. Answer. λc = 1.21μm Mode field Diameter:  

The geometric distribution of light describe the performance characteristic of single mode fiber. MFD is a function of optical source wavelength, the core radius & R.I profile of the fiber.


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For Gaussian distribution the MFD is given by the ‘1/e2’ width of the optical fiber. (1/e = 0.37, 1/e2 = 0.135) MFD is used to predict fiber properties. Ex: Splice loss, bending loss, cutoff wavelength ‘e’,waveguide dispersion.

MFD=

2W0= (spot size) , is full width of far field distribution E2(r) – Far field intensity distribution.


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3.Fiber Material:This is third type of fiber classification. This is based on type of material used while during manufacture of the fiber. That is wether glass,plastic or any other specific technique used while during manufacture of the fiber.ex: Photonic Crystal Fiber 

Fiber material should satisfy the following requirements: 1. It must be possible to make long, thin, flexible fiber 2. Must be transparent at a particular optical wavelength(so as to guide light efficiently) 3. Physically compatible materials that have different R.I for core & cladding must be available Ex. Glass, Plastics(satisfy above requirements)

GLASS FIBERS 1.Majority of fibers are made 2.Range of fibers manufactured is more moderate loss- with large core for short transparent low loss for large transmission) 3.Usage is more 4.Less Attenuation

PLASTIC FIBERS 1.Less fibers are made 2.Range of fiber very less

3.Use is less 4.High Attenuation

Glass Fibers:      

Silica (SiO2) is commonly used (pure sand)[RI=1.458, λ=850nm],Resistance to high temperature(1000 ℃ ) Dopants(Ex. B2O3,GeO20 are added to silica. To produce two similar material but with slightly different R.I (for core & clad) GeO2, P2O5 increases R.I(fig) Fluorine or B2O3 decreases R.I(fig) Ex. GeO2-SiO2 ->Core; SiO2 Cladd SiO2 -> Core, B2O3-SiO2 Cladd


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Active Glass Fibers : 

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Incorporating certain rare earth elements into Silica, allow to perform amplification, attenuation & phase retardation, ionic concentration of rare earth elements are low, this avoids clustering effects, which is necessary for amplification. Ex. Erbium & Neodymium , Thulium

Plastic Optical fiber:    

For delivering high speed services directly to work station. Core is made of polymethyl acrylate(or per fluorinated polymer). Core diameter is 1020 times larger when compare to glass fiber. Tough & Durable (but great losses) Larger diameter allows a relaxation of connector tolerances without sacrificing coupling efficiencies.

Photonic Crystal Fiber: (Holey fiber or Microstructure fiber)    

It is a new fiber structure. Difference: Cladding(sometime core), contains air holes (which runs along the length). Material properties (of core and cladding) define “The light transmission characteristics” in ordinary fiber. But internal microstructure (in PCF) defines another dimension of light control. Ex. Size and spacing of holes, R.I of constituent material.


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Light guidance takes place due to “Photonic bandgap effect”.

Types: i. ii.

Index Guiding Photonic Bandgap

Advantages: i.Low losses ii. Capable to transmit high optical powers iii. High resistance to darkening effect from nuclear radiation. i. Index Guiding PCF:     

Has solid core. Cladding region, contains air holes running along the length of fiber. Air holes lower the effective index of refraction(in cladding). Micro structure array must create a step-index. Support single mode operation over λ=(300nm – 2000nm).

ii. Photonic Bandgap fiber: 

Fiber has a hollow core.

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Functional principal analogous to periodic crystalline lattice in a semiconductor (which blocks electrons from occupying a bandgap region). Hollow core act as a defect, which creates a region in which the light propagates. Fiber Optic Cable structure: Cable structure provides strength to optical fiber. Therefore, the fibers needs to be incorporated in some type of cable structure. Cable structure will vary depending upon situations: i. Whether the cable is to be pulled into underground. ii. Buried directly in the ground. iii. Submerged under water.

Cable structure: Maximum allowable axial load, determines the length of cable that can be reliably installed.

Ex. In copper cables the wires themselves are principal load-bearing members of the cable and elongation of >20% is possible without fracture. On the other hand, extremely strong optical fiber tends to break at 4% elongation. Steel wires can be used as a strength member for optical fiber cables. Plastic strength synthetic yarns are also used. Since they can avoid the effects of electromagnetic induction & also weight. Tight-Buffered design:


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Each fiber is individually encapsulated within its own 900μm diameter plastic buffer structure. Buffer is nearly 4 times the diameter and 5 times the thickness of 250μm protective coating material. Significance: The construction feature contributes to the excellent moisture and temperature performance.

Underwater Cable(Submarine cable): 

These cables are normally exposed to high water pressure. Therefore, these cables have various water blocking layers.


  

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Have one or more polyethylene sheath Have a heavy outer armor jacket Submarine cable structure contains copper wires to provide electrical power for submersed optical amplifier.

Specialty Fibers: 

Specialty fibers are designed to interact with light and theory manipulate or control some characteristics of an optical signal.

Application: i. Optical signal amplification, optical power coupling, dispersion, compensation, wavelength conversion and sensing of physical parameters viz. temperature, stress, pressure. ii. Optical devices like light transmitter, light signal modulators, optical receiver, light couplers and splitters use the specialty fibers.

Erbium-Doped Fiber:  

A length of Er-doped fiber(10-30m) serves as a gain medium for amplifying optical signal (in either C-Band 1530-1560nm or L-band 1560-1625nm) Specific Erbium-doped fiber yields a variety of optical amplifier designs (for pumping laser power).

Photosensitive Fiber: Here R.I changes when exposed to UV light. The required sensitivity can be provided by doping the fiber with Ge or B ions. Application: Used to create fiber Bragg grating (for light coupling mechanisms for pump laser, optical filters) Others: Bend_insensitive fiber, polarization_preserving fiber Termination fibers: Optical device with multiple parts will have one or more unused open branches. Back reflection from these parts can cause instabilities and need to be suppressed. Termination fibers can be used for this purpose. Ex. A termination that has a return loss of more than 65dB can be achieved by splicing about 25cm of a termination fiber onto the end of unused fiber branches.


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Ray Tracing Approach(Geometrical optics) is another method of studying propagation characteristics of light signal. This method provides a good approximation to the light acceptance & guiding properties of optical fiber. The ratio of fiber radius to wave length is known as small-wavelength limit.


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2.Transmission characteristics of optical fibers Introduction: 

Attenuation and bandwidth(BW) are the two main characteristics which affect the performance of optical fibers.



Little earlier than 1970,an optical fiber with an attenuation< 20dBkm-1 was known.

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BW is limited due to signal dispersion.

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Modal noise,polarization are the other transmission characteristics.

Figure:Attenuation v/s wavelength

Attenuation: This determines the “The Maximum transmission distance” prior to signal restoration(or reproduced and amplified).Figure above shows attenuation variation as function of wavelength and also photon energy. It is clear from graph that low and wavelengths (say .7um< and above 2um ) attenuation is high. So care should be taken while selecting wavelength for a particular task. ΑdB=10/Llog10(Pi/Po)


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αdB→Signal attenuation/unit length,L→Fiber length Ex:When mean optical power into an 8km length of fiber is 12µW.The mean optical power at the fiber o/p is 3µW. Determine: (a) Overall signal attenuation(in dB) through the fibers assuming there are no fiber connectors(splices). (b) The signal attenuation/Km. (c) Overall signal attenuation for a 10Km optical link using the same fiber with splices at 1Km interval,each giving an attenuation o 1dB. (d) Numerical input/output power ratio in (c) . (a) α=10log10Pi/Po=16dB (b)

αdB=16/8=2dBKm-1

(c) Now loss incurred along 10Km is αdBL=2*10=20dB. The link also has nine splices(at 1Km intervals) each with an attenuation of 1dB.Therefore Loss due to splices=1dB*9=9dB signal attenuation=20+9=29dB. Pi/Po=1029/10=794.3

Absorption: Material absorption,loss occurs due to 1. Material composition 2. Fabrication process. Material absorption is a loss mechanism attributed to the material composition and the fabrication process , which results in the dissipation of some of the transmitted optical power as heat in the waveguide.Glass has little intrinsic absorption due to its basic material structure in the near-infrared region as shown in figure. (1) Intrinsic Absorption:Due to interaction with one or more of the major components.




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Strong absorption band occurs due to oscillations of structure units Impurities viz:SiO(λ=9.2μm),P-O(8.1 μm)

By suitable choice of both core and cladd composition,absorption can be overcome. (2) Extrinsic Absorption: 

Due to the impurity within the glass. Impurities viz:Cu,Fe,Ni etc are found in glass.



But this can be overcome by glass refining technique (ex:phase oxidation)

Linear Scattering losses : 

Causes transfer of sum or all of optical power contained within one propagating mode to another mode .



Results in attenuation of transmitted light due to leakage or radiation.

There are two types of Linear Scattering: 1.Rayleigh

2.Mie

1.Rayleigh:It is a dominant intrinsic loss mechanism ,occurs due to microscopic variation in material density. Glass composed of randomly connected network of molecular structure. The structure may have regions in which molecular density is either high or lower. It happens due to slight fluctuation in mixing of ingredients. It is impossible to eliminate random changes, When light ray strikes such zones it gets scattered in all directions. Therefore losses due to rayleigh scattering cannot be completely removed. 2.Mie:This occurs due to non perfect cylindrical structure in optical fiber. i.e. irregularities in core cladding interface. Depending upon the fiber material,design & manufacturing process, Mie scattering can cause significant losses. Non homogeneousness in the fiber is a great concern .This can be can be eliminated by: 1.Removing imperfections. 2.By coating of fiber. 3.Increasing fiber guidance by increasing relative R.I. difference.


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Non linear scattering Results in disproportionate attenuation,usually at high optical power levels. Observed at high optical power densities in long single-mode fibers. It results in high optical gain but with a shift in frequency, thus contributing to attenuation for light transmission at a specific wavelength. Two types:1.Brillouin scattering 2.Raman scattering 1.Stimulated Brillouin scattering(SBS) :It can 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.But it is is only significant above a threshold power density.Threshold power P B is given by: P B = 4.4 × 10 −3 d 2 λ2 α db ν watts 2.Raman scattering:Similar to SBS,But SRS can occur in both the forward and backward directions in an optical fiber.The threshold optical power is given by: P R = 5.9 × 10 −2 d 2 λα db watts Both occurs usually at high optical power densities in long single-mode fibers.

Example : Silica has an estimated fictive(assumed) temperature of 1400 K with an isothermal compressibility of 7 × 10 −11 m 2 N −1. The refractive index and the photoelastic coefficient for silica are 1.46 and 0.286 respectively. Determine the theoretical attenuation in decibels per kilometer due to the fundamental Rayleigh scattering in silica at optical wavelengths of 0.63, 1.00 and 1.30 μm. Boltzmann’s constant = 1.381 × 10 −21. J K −1. . Solution: The Rayleigh scattering coefficient may be obtained from Eq.1 for each wavelength. However, the only variable in each case is the wavelength, and therefore the constant of proportionality of Eq. (1) applies in all cases. Hence: γ R = 8 π 3 n 8 p 2 β c KT F / 3 λ 4 ------------------------------------1 = 248.15 × 20.65 × 0.082 × 7 × 10 −11 × 1.381 × 10 −23 × 1400 3 × λ 4 = 1.895 × 10 −28 /λ 4


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At a wavelength of 0.63 μm: γ R =1.895 × 10 −28 / 0.158 × 10 −24 = 1.199 × 10 -3

The transmission loss factor for 1 kilometer of fiber may be obtained using L( km) = exp(−γ R l) = exp(−1.199 × 10 −3 × 10 3 ) = 0.301 The attenuation due to Rayleigh scattering in decibels per kilometer may be obtained as Attenuation = 10 log 10 (1/ per km ) = 10 log 10 3.322 = 5.2 dB km −−1. At a wavelength of 1.0 μm: γ R =1.895 × 10 −28 = 1.895 × 10 −4 m −110 −24 L(in km) = exp(−1.895 × 10 −4 × 10 3 ) = exp(−0.1895) = 0.827 Bend loss 

Radiation losses at bends.



Guidance mechanism is inhibited,due to more energy in evanescent(fading) field,this exceeds velocity of light in clading region.



Therefore part of mode in the cladding needs to travel faster than velocity of light in core medium.


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Two types: 1.Macroscopic bend:Bends having radii greater than fiber diameter ex:when fiber turns around a corner 2.Microscopic bend:Bend of fiber axis. ex:Occurs when fiber is incorporated into cables.

Fig: Loss due to curving of fiber

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Figure: Loss due to microscopic bend in fiber



So as to maintain a wavefront perpendicular to propagation direction.



Radiation attenuation co-efficient,αr=C1 exp(-C2R) r-radius of curvature of fiber

c1,c2-constant,independent of R 

Large bending losses occurs at critical radius of curvature.

Rc=3n12λ/4π(n12-n22)3/2 & RCS=(20λ/(n12-n22))(2.748-0.996λ/λC)-3 

Macrobending losses may be reduced by:

a) Designing fibers with large RI differences. b)Choose operational wavelength small. Ex:Two step index fibers with: a) A multimode fiber with a core RI=1.5 a relative RI diffeerence=3%, operating wavelength=0.82μm,RC=9.08μm


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b) A D(core)=8μm,single mode fiber wth a RI(core)=1.5,a relative RI difference of 0.3% and λ(operating)=1.55μm Relative RI difference,∆=(n12-n22 )/2n12 Rc=9μm λc=2πan1(2∆)1/2/2.405=1.214μm Rc=7.77μm Dispersion:”Broadening of transmitted light pulses as they traverse through along the channel.” Two types: 1.Intermodal:Occurs only in multimode fiber. This occurs due to modal delays contributed by each mode. 2.Intramodal:(chromatic) modal delay is result of each mode having different value of group velocity at single frequency,occurs only in single mode.

Fig:Each pulse broadens and overlaps with its neighbors


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If overlapping of successive pulses have to be avoided then Bt<=1/2T(i.e. digital bit rate less than 1/(broadened pulse duration)) 

Btmaximum =2B B-maximum bandwidth(NRZ)



Btmax =B (RZ)

Ex:A multimode graded index fiber exhibit total pulse broadening of 0.1μs over distance=15km. Estimate a) maximum possible bandwidth on link,assume zero ISI b)pulse dispersion /per unit length c)bandwidth-length product

a)Bt=1/2T=1/(2*10-6)=5MHz b)dispersion =0.1*10-6/15 = 6.67ns/km c)BtL=5*15=75MHz km

Intra model dispersion (Chromatic dispersion ) 

Occurs in all types of fibers.i.e step-index and graded-index



Result due to finite spectral Bandwidth ( of Optical source)



Each optical source emits a band frequencies, this may lead to propagation delay difference between the different spectral components.



Thus causing broadening of each transmitted mode, hence intramodal dispersion.

There are wo types Intra model dispersion:1) Material dispersion 2) Waveguide dispersion 1) Material dispersion : This results from the different group velocities of the various spectral components launched into the fiber from the optical source.Phase velocity of a plane wave propagating in dielectric medium varies nonlinearly with respect to wavelength.


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Phase velocity of a wave is the rate at which the phase of the wave propagates in space(vp=λ/ T).The red and green dots in figure below demonstrate the variation in phase of

a wave. Group delay is the time delay of the amplitude envelope of the various sinusoidal component of a signal through a device under test, and is a function of frequency for each component. All frequency components of a signal are delayed when passed through a device such as an amplifier, a loudspeaker, or propagating through space or a medium, such as air. This signal delay will be different for the various frequencies unless the device has the property of being linear phase.

A material is said to exhibit material dispersion when the second order differential of the refractive index with respect to wavelength is not zero (i.e.d²n/dλ²≠ 0).

Figure:Material dispersion v/s wavelength τg = dβ/dω= 1/c (n1-λdn1/dλ) --------------------------------(1) Phase velocity , vp = ω/β n1= R I of care Group velocity , vg = δω/δβ


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Pulse delay due to material dispersion in a fiber of length 'L' , τm = L/c(n1 – λdn1/ dλ) --------------- (2) Expanding (2) using Taylor series , σm ( RMS pulse broadening ) =σλ dτm/ dλ + σλ 2 d²λm/dλ² + –--------------(3) Considering Only dominant term in (3) i.e σm = σλ dτm/dλ -----------(4) Diff. (2) wrt λ , i.e dτm/ dλ = - Lλ/c d²n/ dλ² ------------- (5) Put (5) in (4) ,σm ≈ σλL/C |d2n/dλ2| Where M=1/L dτm/dλ=λ/c | d2n1/dλ | - Material dispersion parameter

In case of Polarization mode dispersion, light energy confines into two orthogonal polarization state ( or modes ) as shown in figure. As fiber material is non uniform through out. Each mode will travel at slightly different velocity thereby causing dispersion.

Figure :Polarization mode dispersion In an ideal optical fiber, the core has a perfectly circular cross-section.The fundamental mode then has two orthogonal polarizations (orientations of the electric field) that travel at the same speed.In a realistic fiber, however, there are random imperfections that break the circular symmetry, causing the two polarizations to propagate with different speeds.


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Wave guide dispersion : Waveguide of optical fiber also create intra modal dispersion . 

Part of optical power propagating along a fiber is confined to core.



Propagating power in Cladd travel faster than the part in core thereby causing mismatch in phase when both part reaches the other end of fiber.

Intermodal Dispersion (ID):ID occurs due to propagation delay differences between modes within a multimode fibers. Purely singly mode fiber doesn't exhibit intermodal dispersion

Multimode step index fiber: Delay differences between the axial ray and meridional ray gives an estimation of pulse broadening ( due to intermodal dispersion ) * Both traveling with same velocity.

* Delay differences due to respective path length * Time taken by axial ray to travel a distance L, Tmin =dist/vel=L/c/n1=Ln1/c * Now time taken by meridional ray ( max), Tmax =(L/cosθ)/(c/n1)=Ln1/ccosθ -----------(2)


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*Use Snell's law at core-clad interface,ie sinФc=n2/n1=cosθ ------(3) put above equation in (2), Tmax=Ln12/cn2 -----------(4) *Now delay difference i.e, (4)-(1) ═> δTs=Tmax- T min=Ln12/cn2-Ln1/c ═> δTs= Ln12/cn2((n1-n2)/n2) ≈ Ln12∆/cn2 when ∆<<1 aslo δTs= Ln1/c((n1-n2)/n2) ≈ Ln1∆/c ═> δTs=L(NA)2/2n1c RMS pulse broadening:If i/p to fiber is a pulse of unit area -∞∫∞P1(t)dt=1 *But P(t) has a constant amplitude of 1/ δTs over the range – δTs/2<

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Ex:A 6Km optical link consists of multimode fiber (step index) with RIcore=1.5,realtive RI difference of 1% estimate (a)Delay difference between fastest & slowest mode of fiber o/p. (b)Also determine rms pulse broadening. An LED operating at λ=850nm hs a spectral width of 45nm.What is pulse spreading in ns/Km due to material dispersion Dmat=-λ/c d2n/dλ2, for LED (a)λ=850nm,│d2n/dλ2│=0.025 M=1/c λ│λ 2d2n/dλ2│=9.8ps/nm/Km,σm= 4.5*1*9.8=441ps/Km

Ex:A multimode step index fiber has a numerical aperture of 0.3 and a core refractive index of 1.45. The material dispersion parameter for the fiber is 250 ps nm −1 km −l which makes material dispersion the totally dominating chromatic dispersion mechanism. Estimate (a) the total rms pulse broadening per kilometer when the fiber is used with an LED source of rms spectral width 50 nm and (b) the corresponding bandwidth–length product for the fiber. Solution: (a) The rms pulse broadening per kilometer due to material dispersion may be obtained from Eq.1, where:

-----------------------------(1)

The rms pulse broadening per kilometer due to intermodal dispersion for the step index fiber is given by Eq. (2 ) As Overall fiber dispersion 125


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-------------2

The total rms pulse broadening per kilometer may be obtained using Eq.3

---------------------------------3

where σ c ≈ σ m as the waveguide dispersion is negligible and σ n = σ s for the multimode step index fiber. (b) The bandwidth–length product may be estimated from the relationship given in Eq.4 ---------------------4


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3.Optical sources and detector Energy bands

Figure1a:

Figure1a shows Resultant free elect-hole moves under

Figure1b

the influence of external electric field.

Figure1b shows equal electron hole-pair concentration in an intrinsic semiconductor created by thermal excitation of electron across the band gap. * An electron during transition from conduction band to valence band(cb-vb), absorbs a emitting photon, both energy and momentum must be conserved as shown in figure. * A photon may have considerable energy ,but less momentum. * Semiconductors are of two types , depending upon band gap energy as the function of momentum(K). 1.Direct bandgap:Electron & hole have same value of momentum.

OPTICAL FIBER COMMUNICATION basic and characterstics

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