1. Evolution Of Fiber Optic Systems

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1 OPTICAL FIBER COMMUNICATION UNIT-I : OPTICAL FIBERS STRUCTURE: 1. Evolution Of Fiber Optic Systems The operating range of optical fiber system term and the characteristics of the four key components of links 1) The optical fiber 2) Light sources 3) Photo detector 4) Optical amplifiers. There are three main operating windows of the optical fiber system. The 1 st generation links operated at 850nm, which was a low loss transmission window of early silica fibers. These links used GaAs - Based optical sources, silicon Photo detectors and multimode Fibers. The 2 nd generation links operated at 1300nm. Which have a larger bandwidth.(155 and 622 Mb/s) [multi and single mode are used in local area n\w] The 3 rd generation links operated at 1550nm provides lowest attenuation. InGaAs Indium Gallium Arsenide is a semi conductor composed of indium, gallium and arsenic. It is used in high power and high frequency electronics. The most successful and widely used devices are erbium-doped fiber amplifier (EDFA) operating at around 1550 nm. The use of Wavelength-Division Multiplexing (WDM) offers a further boost in fiber Transmission capacity. 2. Elements of an optical Fiber communication link:- Optical source: An optical source is an active component which converts the electrical energy in the form of current into optical energy in the form of light. Connector: These are removable Joints which allow easy, Fast, manual, Coupling and uncoupling of Fibers. An Optical Fiber Connecter terminates the end of an optical Fiber and enable quicker connection & Disconnection than splicing. Optical fiber Coupler: An optical Fiber coupler is a device that Distributes light from a main fiber into one or more branches.

2 Optical Splice: A fiber optic splice is a permanent Fiber Joint whose purpose is to establish an optical connection between two individual optical Fiber. Optical Fiber splices also permit repair of optical Fibers damaged during installation, accident or stress. Regenerator: Fig : Elements of an optical fiber Transmission link Regenerator are used to amplify as well as to reshape the weak Transmitted signal. A repeater is an electrical device that receives a signal and retransmits it at a higher level & higher power. Optical amplifier: An Optical amplifier is a device that amplifiers an optical signal Directly, without the need to First Convert it to an electrical signal.

3 Photo Detector: A Photo Detector is a device which converts the optical energy in the form of light into electrical energy in the form of current. 3. Basic optical laws & definitions:- The fundamental optical parameter of a material is the Refractive index. In a free space a light wave travels at a speed c = 3 *10 8 m/s. The speed of the light is related to the frequency v and wave length λ by c = cλ. The index of refraction n of the material is given n = c/v. Typical values of n are 1.00 for air, 1.33 for water, 1.50 for glass and 2.42 for diamond. Snell s Law The refraction of the light ray at the interface is a result of the difference in the speed of light in two materials that have different refractive indices. The relationship at the interface is known as Snell s Law. n 1 sin φ 1 = n 2 sin φ 2 (or) n 1 cos θ 1 = n 2 cos θ 2 Fig : Refraction and reflection of a light ray at a Material Boundary The angle φ 1 between the incident ray and the normal to the surface is known as the angle of incidence. The incident ray, the normal to the interface, and the reflected ray all lie in the same plane, which is perpendicular to the interface plane between the two materials. This is called as Plane of Incidence.

4 Fig : Representation of the Critical angle at a glass-air interface. If the angle of incidence φ1 is increased, a paint will finally be reached where the light ray in air is parallel to the glass surface. This point is known as the Critical angle of Incidence φ c. n 1 sin φ c = n 2 sin φ 2 ( φ 2 = 90.) n 1 sin φ c = n 2 sin 90. n 1 sin φ c = n 2 * 1. sin φ c = n 2 / n 1. φ c = sin -1 (n 2 / n 1). Fig : Representation of the Total Internal Reflection at a glass air interface. The angle of incidence φ 1 in an optically denser material becomes larger, the refracted angle φ 2 approaches π/2(90 ). Beyond this point no refraction is possible and the light rays become Totally Internally Reflected. The conditions required For Total Internal Reflection. The Condition required for Total Internal reflection can be determined by Snell s Law. (Or) When the incidence angle φ1 is greater than the critical angle, the condition for Total internal reflection is satisfied. i) Light should travel from denser medium to rarer medium. ii) The angle of incidence should be greater than the critical angle of the medium.

5 4. Optical Fiber Modes and Configuration: 4.1 Fiber Types An optical fiber is a dielectric waveguide that operates at optical frequencies. This fiber waveguide is normally cylindrical in form. It confines electromagnetic energy in the form of light to within its surfaces and guides the light in a direction parallel to its axis. The propagation of light along a waveguide can be described in terms of a set of guided electromagnetic waves called the modes of the waveguide. Each guided is a pattern of electric and magnetic field distributions that is repeated along the fiber at equal intervals. Fig : Schematic of a single fiber structure. The single solid dielectric cylinder of refraction Index n 1 is known as the Core of the Fiber. This core is surrounded by a solid dielectric Cladding which has refractive index n 2 that is less than n 1. A cladding is not necessary for light to propagate along the core of the fiber, it serves to reduce scattering loss and add mechanical strength to the fiber. In low and medium loss fibers the core material is generally glass and is surrounded by either a glass or plastic cladding. High loss plastic fibers with plastic cladding. 4.2 Two types of fiber i) Step Index Fiber ii) Graded Index Fiber i) Step Index Fiber The Refractive index of the core is uniform throughout and undergoes an abrupt change (or Step) at the cladding boundary. This is called a Step-Index Fiber. The light rays propagating through it are in the form of Meridional Rays. ii) Graded Index Fiber The core refractive Index is made to vary as a function of the Radial distance from the center of the fiber. This is called a Graded-Index Fiber The light rays propagating through it are in the form of Skew Rays.

6 Fig : Comparison of single mode and multimode step index and graded index optical fiber Both the Step and the Graded index fibers can be further divided into single mode and multimode classes. A single mode Fiber contains only one mode of propagation. Whereas multimode fibers contain many hundreds mode of propagation. Multimode fibers offer several advantages compared with single-mode fibers. i) The large core radius of multimode fibers make it easier to launch optical power into the fiber. ii) Another advantage is that light can be launched into a multimode fiber using LED source. iii) LED have less optical output power than laser diodes easier to make, less expensive and have longer lifetimes than laser diodes. A Disadvantages of multimode fibers is that they suffer from Intermodal Dispersion. When an optical pulse is launched into a fiber, the optical power in the pulse is distributed over all of the modes of the fiber. Each of the modes that can propagate in a multimode fiber travels at a slightly different velocity. This means that the modes in a given optical pulse arrive at the fiber end at slightly different times, This effect, which is known as Intermodal Dispersion.

7 4.3 Rays and Modes: The Electromagnetic light field that is guided along an optical fiber can be represented by Superposition of bounded modes. The step Index Fibers the core of radius a has a refractive index n 1, which is equal to This is surrounded by a Cladding of Index n 2. n 2 = n 1 (1- Δ) Δ = (n 1 - n 2 ) / n 1 n 1 The Refractive Index of the Core n 1 The Refractive Index of the Cladding Δ The Core - Cladding Index Difference 4.4 Rays Optics Representation: Two types of rays that can propagate in fiber i) Meridional rays ii) Skew rays. i) Meridional rays Meridional rays are the ray following zig-zag path when they travel through fiber and for every reflection it will cross the fiber axis. From Snell s law of refraction n 1 sin φ min = n 2 sin 90. sin φ min = n 2 / n 1.

8 By Appling Snell s law to the air-fiber face boundary, the condition can be related to the maximum entrance angle θ 0,max. n sin θ 0,max = (n 2 1 n 2 2 ) 1/2 Rays having entrance angles θ 0 < θ 0,max will be Totally Internally Reflected at the core cladding Interface. Numerical Aperture (NA) of a step Index Fiber for Meridional rays. NA = n sin θ 0,max = (n 2 1 n 2 2 ) 1/2 = n 1 2Δ n 1 The Refractive Index of the Core n 1 The Refractive Index of the Cladding Δ The Core - Cladding Index Difference Meridional rays can be divided into two general classes 1)Bound ray 2) Unbound ray Bound rays that are trapped in the core and propagate along the fiber axis according to the laws of geometrical optics, and unbound rays that are refracted out of the fiber core. ii) Skew Rays Skew rays are the ray following the helical path around the fiber axis when they travel the fiber and they would not cross the fiber axis at any time.

9 4.5 Wave Representation in a Dielectric Slab Wave Guide Let us consider wave propagation in an infinite Dielectric slab waveguide of thickness d. Its refractive Index n 1 is greater than the index n 2 of the material above and below the slab. A wave will propagate in the angle of incidence with respect to the upper and lower surfaces satisfies the condition given. n sin θ 0,max = (n 2 1 n 2 2 ) 1/2 We consider two rays, designated ray1 and ray2. The ray paths are denoted by solid lines and phase fronts by dashed lines. The phase change occurring in ray 1 when traveling from point A to point B minus. The phase change in ray 2 between points C and point D. As the wave travel through the material, it undergoes a phase shift Given by, where Δ = k 1 s k 1 = n 1 k and k = 2π / λ Δ = n 1 2 π s / λ k 1 => the propagation constant in the medium of refractive index of core n1. k => is the free space propagation constant. s => The distance, the wave has traveled in the material. The Phase changes occur both as the wave travels through the fiber medium and at the reflection points. In Ray 1 going from point A to point B, travels a distance s 1 = d / sinθ

10 Ray 2 does not incur any reflections in going from point C to point D. The distance from point A to point D is The distance between point C and D is The requirement for wave propagation Substituting the expressions for s 1 and s 2 into this equation Which can be reduced to Considering only electric waves with components normal to the plane of incidence Where n = n 1 / n 2 The negative sign indicate wave in medium is decaying. Substituting this expression into equation 2, The angle θ which satisfy the condition in this equation will propagate in the dielectric slab waveguide.

11 5. Mode Theory for Circular Waveguides: The propagation of light waves through an optical fiber in terms of electromagnetic waves. The modes are the solutions of the electromagnetic fields or Maxwell s equations in core and cladding of an optical fiber. For Transverse Electric (TE) modes E z = 0, H z 0 and Transverse Magnetic (TM) modes E z 0, H z = 0. HE and EH modes are called hybrid modes. In hybrid modes both E z and H z are Nonzero. In HE mode, E z > H z In EH mode, H z > E z Hybrid modes are the mixture of TE and TM modes. In the case of cylindrical fiber, there are two integers n and l is necessary to specify the mode numbers. For Meridional ray propagation, TE nl and TM nl modes are possible. For Skew ray, HE nl and EH nl modes also occur along with TE nl and TM nl modes. The two lowest-order modes are designated as HE and TE. The field components are called Linearly polarized (LP) modes and labeled as LP jm, where j and m are integers designating mode solutions. 5.1 Overview of Modes: The Electrical field distribution inside a slab wave guide for TE 0, TE 1, TE 2 modes. Fig: Electric field distributions for several of the lower order guided modes in a symmetrical slab waveguide.

12 The fields vary harmonically in the guided region of refractive index of core n 1 and decay exponentially outside of this region. For higher order modes, the fields are distributed more toward the edges of the guide and penetrate farther into the cladding region. For lower order modes, the fields are tightly concentrated near the center of the slab, with little penetration into the cladding region. In addition to bound and refracted modes, a third category of modes called leaky modes in optical fibers. The power radiation out of the waveguide results from a quantum mechanical phenomenon called as tunnel effect. A mode remains guided as long as β the propagation factor satisfies the condition n 2 k < β < n 1 k Where n 1, n 2 The refractive indices of the core cladding k 2 π / λ. The boundary between guided modes and leaky modes is defined by the cutoff condition β = n 2 k. When β decreases below n 2 k, power leaks out of the core into the cladding region. Leaky modes can carry significant amounts of optical power in short fibers. Most of the modes disappear after a few centimeters. 5.2 Key Modal Concepts: An important parameter connected with the cutoff condition is the V number defined by, V Total no of modes that a fiber support, NA Numerical Aperture This is a dimensionless number that determines how many modes a fiber can support. The V number is also used to express the number of modes M in a multimode fiber, when V is large. An estimate of the total number of modes supported in a fiber is, Where P is the total optical power in the fiber. As M is proportional to V 2, the power flow in the cladding decreases as V increases.

13 6. Single Mode Fibers: Single mode fibers are constructed by the dimensions of the core diameter be a few wavelengths (usually 8-12 μm) and by having small index differences between the core and the cladding. A single mode fiber have small core diameters to allow single mode propagation, the cladding diameter should be at least ten times more than the core. Core diameter : 8-12 μm Cladding diameter : generally 125 μm Numerical aperture : 0.08 to 0.15 μm. 6.1 Mode Field Diameter The fundamental parameter of a single mode fiber is the mode-field diameter (MFD). MFD can be determined from the mode-field distribution of the fundamental fiber mode. In single mode fibers not all the light that propagates through the fiber is carried in the core. This diagram illustrates this effect. Let us assume the distribution to be Gaussian: E(r) = E o exp(-r 2 / W 2 o) E(r) Field distribution of LP 01 mode r Radius E o Field at zero radius W o Width of electric field distribution

14 Fig : Distribution of light in a single mode fiber The MFD of LP 01 mode can then be defined as, E(r) Field distribution of LP 01 mode 6.2 Propagation Modes in Single-Mode fibers In single mode fiber, there are two independent degenerate, propagation modes. These modes are very similar but their polarization planers are orthogonal. They may be called as Vertical and Horizontal polarization. Two polarizations of the fundamental HE 11 mode in a single mode fiber. Fig : Two polarizations of the fundamental HE 11 mode in a single mode fiber. The modes propagate with different phase velocities and the difference between their refractive indices is called fiber Birefringence. B f = n y n x We may also define Birefringence as, β = k 0 (n y n x )

15 Where k 0 = 2 π / λ is the free space propagation constant. The length over which the two modes beat at a point is called fiber beat length which is given by, L p = 2 π / β L p Fiber beat length. 7. Graded- index Fiber Structures: The core refractive Index is made to vary as a function of the Radial distance from the center of the fiber. This is called a Graded-Index Fiber In the graded index fiber design the core refractive index decreases continuously with increasing radial distance r from the center of the fiber, but is generally constant in the cladding. Core diameter Cladding diameter Numerical aperture : μm : generally μm : 0.2 to 0.3 μm. The refractive index variation in the core is the power law relationship. r Radial distance from the fiber axis a the core radius n 1 The Refractive Index of the Core n 1 The Refractive Index of the Cladding Δ The Core - Cladding Index Difference α The shape of profile is dimensionless parameter.

16 Numerical aperture for graded index fibers is more complex than for step index fibers, since it is a function of position across the core end face. NA(r) = [n 2 (r) n 2 2] 1/2 NA(0) 1-(r/a) α for r a 0 for r > a Where the axial numerical aperture is defined as NA(0) = [n 2 (0) n 2 2] 1/2 = (n 2 1 n 2 2) 1/2 n 1 2Δ The number of bound modes in a graded index fiber is 8. Linearly Polarized Modes: The analysis is made on the principle that in a typical step-index fiber, the difference between the indices of refraction of the core and cladding is very small (Δ <<1). This is the basis of the weakly guiding fiber approximation. In this approximation, the electromagnetic field patterns and the propagation constants of the mode pairs HEv+1,m and EHv-1,m are similar. Using the recurrence relations for J v and k v two sets of equations are obtained. The positive sign yields, The negative sign yields, Taking inverse of the first equation, we get The parameters are given by,

17 The equations can be written in the unified form as, The above equations show that within the weakly guiding approximation, all modes are degenerate. Each LP0m mode is derived from a HE1m mode. Each LP1m mode comes from TE0m, TM0m and HE2m modes. Each LPvm mode (v >=2) is from a HEv+1,m and an EHv-1,m mode.

18 TWO MARKS: 1. What is meant by optical fiber Communication? Fiber-optic communication is a method of transmitting information from one place to another by sending pulses of light through an optical fiber. The light forms an electromagnetic carrier wave that is modulated to carry information 2. Mention the advantages of optical fiber Communication. Wider Bandwidth Low Transmission loss Immunity to crosstalk and EMI Signal Security Small size and Weight High Antenna Gain Dielectric Waveguide System reliability and Easy maintenance. 3. Mention the advantages of optical fiber as waveguide over conventional metallic waveguide. Optical fiber is made up of dielectric (glass) so there is no electromagnetic interference or cross talk Optical fiber cable is in small size with less weight and flexible. Optical fiber has low transmission loss 4. What is the necessity of cladding for an optical fiber? To provide proper light guidance inside the core To avoid leakage of light from the fiber To avoid mechanical strength for the fiber To protect the core from scratches and other mechanical damages 5. What is the principle used in the working of fibers as light guides? optical fiber. The phenomenon of total internal reflection is used to guide the light in the 6. Define Snell,s Law? The refraction of the light ray at the interface is a result of the difference in the speed of light in two materials that have different refractive indices. The relationship at the interface is known as Snell s Law. n 1 sin φ 1 = n 2 sin φ 2

19 7. Define angle of Incidence? The angle φ 1 between the incident ray and the normal to the surface is known as the angle of incidence. 8. Define Plane of Incidence? The incident ray, the normal to the interface, and the reflected ray all lie in the same plane, which is perpendicular to the interface plane between the two materials. This is called as Plane of Incidence. 9. Define Critical angle of Incidence? If the angle of incidence φ1 is increased, a paint will finally be reached where the light ray in air is parallel to the glass surface. This point is known as the Critical angle of Incidence φ c. φ c = sin -1 (n 2 / n 1) 10. Define Total Internal Reflection? When the incidence angle φ1 is greater than the critical angle, the condition for Total internal reflection is satisfied. 11. What are the condition for total internal reflection. Light should travel from denser medium to rarer medium. The angle of incidence should be greater than the critical angle of the medium. 12. What are the two types of fiber? Step Index Fiber Graded Index Fiber 13. What is Step Index Fiber? The Refractive index of the core is uniform throughout and undergoes an abrupt change (or Step) at the cladding boundary. This is called a Step-Index Fiber. The light rays propagating through it are in the form of Meridional Rays. 14. What is Graded Index Fiber? The core refractive Index is made to vary as a function of the Radial distance from the center of the fiber. This is called a Graded-Index Fiber The light rays propagating through it are in the form of Skew Rays. 15. Define Meridional Rays? Meridional rays are the ray following Zig-Zag path when they travel through fiber and for every reflection it will cross the fiber axis.

20 16. Define Skew Rays? Skew rays are the ray following the helical path around the fiber axis when they travel the fiber and they would not cross the fiber axis at any time. 17. Define Acceptance angle? The maximum angle φ max with which a ray of light can enter through the entrance end of the fiber and still be totally internally reflected is called acceptance angle of the fiber. 18. Define Numerical aperture of the fiber? Numerical Aperture(NA) of the fiber is the light collecting efficiency of the fiber and is a measure of the amount of light rays that can be accepted by the fiber. 19. What is Linearly polarized mode? NA = Sin φ a = (n 2 1 n 2 2) 1/2 The two lowest-order modes are designated as HE and TE. The field components are called Linearly polarized (LP) modes and labeled as LP jm, where j and m are integers designating mode solutions. 20. What are hybrid modes? Give two examples. Hybrid modes are the mixture of TE and TM modes that can be traveled through the optical fiber. In HE mode, E z > H z In EH mode, H z > E z 21. Define cutoff wavelength of the fiber. The cutoff wavelength is defined as the minimum value of wavelength that can be transmitted through the fiber. The wavelengths greater than the cutoff wavelength can be transmitted. 22. What is fiber birefringence? λ cuttoff = 2 π a (NA) / V The modes propagate with different phase velocities and the difference between their refractive indices is called fiber Birefringence. B f = n y n x We may also define Birefringence as, β = k 0 (n y n x )

21 23. What is Mode Field Diameter? The fundamental parameter of a single mode fiber is the mode-field diameter (MFD). MFD can be determined from the mode-field distribution of the fundamental fiber mode. 24. State the propagations modes in single mode fibers? Horizintal mode Vertical mode 25. What is the operating frequency of optical fiber? The operating Frequency of optical fiber is to Hz. 26. Comparison between Single Mode and Multimode Fiber. S.No Single Mode Fiber Multi mode Fiber 1 In single mode fiber only one mode can propagate through the fiber Multimode fiber allows a large number of paths or modes for the light rays traveling through it. The multi mode fiber the core diameter and the relative refractive index difference are larger than the single mode fiber. The single mode fiber has smaller 2 core diameter and the difference between the refractive indices of the core and cladding is very small. 3 No Dispersion There is signal degradation due to 4 Jointing of two fibers are very difficult material and inter dispersion. Jointing of two fibers is easy. 27. Comparison between Step index and graded index Fiber. S.No Step index fiber Graded index Fiber The Refractive index of the core is uniform throughout and undergoes an 1 abrupt change (or Step) at the cladding boundary. This is called a Step-Index Fiber. 2 The light rays propagating through it 3 are in the form of Meridional Rays. Meridional rays are the ray following Zig-Zag path when they travel through fiber and for every reflection it will cross the fiber axis. 4 Attenuation is more for multimode step index fiber 5 Numerical Aperture is more for multimode step index fiber The core refractive Index is made to vary as a function of the Radial distance from the center of the fiber. This is called a Graded-Index Fiber The light rays propagating through it are in the form of Skew Rays. Skew rays are the ray following the helical path around the fiber axis when they travel the fiber and they would not cross the fiber axis at any time. Attenuation is less Numerical Aperture is less.