1. UNIT II TRANSMISSION CHARACTERISTICS OF OPTICAL FIBERS Dr.Gnanasundari/Prof/ECE/SNSCE/OCN/Unit II

2. Attenuation (fiber loss) Power loss along a fiber: The parameter is called fiber attenuation coefficient in a units of for example [1/km] or [nepers/km]. A more common unit is [dB/km] that is defined by: Z=0 P(0) mW Z= l mw [3-1] [3-2] Dr.Gnanasundari/Prof/ECE/SNSC E/OCN/Unit II

3. Optical Fiber communications, 3 rd ed.,G.Keiser,McGrawHill, 2000 Optical fiber attenuation vs. wavelength Dr.Gnanasundari/Prof/ECE/SNSC E/OCN/Unit II

4. Types of Attenuation Absorption Loss: Caused by the fibre itself or by impurities in the fibre,such as water and metals. Scattering Loss: Intrinsic loss mechanism caused by the interaction of photons with the glass itself. Bending loss: Loss induced by physical stress on the fibre. Dr.Gnanasundari/Prof/ECE/SNSC E/OCN/Unit II

5. Absorption Absorption is caused by three different mechanisms: 1- Impurities in fiber material: from transition metal & particularly from OH ions with absorption peaks at wavelengths 2700 nm, 400 nm, 950 nm & 725nm. 2- Intrinsic absorption (fundamental lower limit): electronic absorption band (UV region) & atomic bond vibration band (IR region) in basic SiO2. 3- Radiation defects Dr.Gnanasundari/Prof/ECE/SNSC E/OCN/Unit II

6. Material Absorption Losses Material absorption is caused by absorption of photons within the fiber. – When a material is illuminated, photons can make the valence electrons of an atom transition to higher energy levels – Photon is destroyed, and the radiant energy is transformed into electric potential energy. This energy can then Be re-emitted (scattering) Frees the electron (photoelectric effects) (not in fibers) Dissipated to the rest of the material (transformed into heat) In an optical fiber Material Absorption is the optical power that is effectively converted to heat dissipation within the fiber. Two types of absorption exist: – Intrinsic Absorption, caused by interaction with one or more of the components of the glass – Extrinsic Absorption, caused by impurities within the glass Dr.Gnanasundari/Prof/ECE/SNSC E/OCN/Unit II

7. Intrinsic Absorption 1 Less significant than extrinsic absorption. For a pure (no impurities) silica fibre a low loss window exists between 800 nm and 1600 nm. Graph shows attenuation spectrum for pure silica glass. Intrinsic absorption is very low compared to other forms of loss. It is for this reason that fibres are made up of silica and optical communications systems work between about 800 to 1600 nm. Dr.Gnanasundari/Prof/ECE/SNSC E/OCN/Unit II

8. Intrinsic Absorption 2 Intrinsic absorption in the ultraviolet region is caused by electronic absorption bands. Basically, absorption occurs when a light particle (photon) interacts with an electron and excites it to a higher energy level. The main cause of intrinsic absorption in the infrared region is the characteristic vibration frequency of atomic bonds. In silica glass, absorption is caused by the vibration of silicon- oxygen (Si-O) 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. Dr.Gnanasundari/Prof/ECE/SNSC E/OCN/Unit II

9. Extrinsic Absorption (metallic ions) Extrinsic absorption is much more significant than intrinsic Caused by impurities introduced into the fiber material during manufacture – Iron, nickel, and chromium Caused by transition of metal ions to a higher energy level Modern fabrication techniques can reduce impurity levels below 1 part in 10 10. For some of the more common metallic impurities in silica fibre the table shows the peak attenuation wavelength and the attenuation caused by an impurity concentration of 1 in 10 9 Dr.Gnanasundari/Prof/ECE/SNSC E/OCN/Unit II

10. Extrinsic Absorption (OH ions) Extrinsic absorption caused by dissolved water in the glass, as the hydroxyl or OH ion. In this case absorption due to the same fundamental processes (between 2700 nm and 4200 nm) gives rise to so called absorption overtones at 1380, 950 and 720 nm. Typically a 1 part per million impurity level causes 1 dB/km of attenuation at 950 nm. Typical levels are a few parts per billion Absorption Spectrum for OH in Silica Narrow windows circa 800, 1300 nm and 1550 nm exist which are unaffected by this type of absorption. Dr.Gnanasundari/Prof/ECE/SNSC E/OCN/Unit II

11. Scattering Losses in Fibre Scattering is a process whereby all or some of the optical power in a mode is transferred into another mode. Frequently causes attenuation, since the transfer is often to a mode which does not propagate well. (also called a leaky or radiation mode). Dr.Gnanasundari/Prof/ECE/SNSC E/OCN/Unit II

12. Types of Scattering Loss in Fibre Two basic types of scattering exist: Linear scattering: Rayleigh and Mie Non-linear scattering: Stimulated Brillouin and Stimulated Raman. Rayleigh is the dominant loss mechanism in the low loss silica window between 800 nm and 1700 nm. Raman scattering is an important issue in Dense WDM systems Dr.Gnanasundari/Prof/ECE/SNSC E/OCN/Unit II

13. Rayleigh Scattering (I) Dominant scattering mechanism in silica fibres Scattering causes by inhomogeneities in the glass, of a size smaller than the wavelength. Inhomogeneities manifested as refractive index variations, present in the glass after manufacture. Difficult to eliminate with present manufacturing methods Rayleigh loss falls off as a function of the fourth power of wavelength:  in this empirical formula is expressed in microns (μm) The Rayleigh scattering coefficient Ar is a constant for a given material. For 1550 nm the loss is approximately 0.18 dB per km. Dr.Gnanasundari/Prof/ECE/SNSC E/OCN/Unit II

14. Rayleigh Scattering (II) The Rayleigh scattering coefficient Ar depends: -The fibre refractive index profile -The doping used to achieve a given core refractive index For a step index germanium doped fibre Ar is given by: Ar = 0.63 + 2.06.NA dB/km For a graded index near-parabolic profile fibre Ar is given by: Ar = 0.63 + 1.75.NA dB/km Exercise: Show that for a graded index fibre with a numerical aperture of 0.275 operating at 1330 nm the Rayleigh scattering loss is approximately 0.36 dB/km. Dr.Gnanasundari/Prof/ECE/SNSC E/OCN/Unit II

15. Scattering Loss Small (compared to wavelength) variation in material density, chemical composition, and structural inhomogeneity scatter light in other directions and absorb energy from guided optical wave. The essential mechanism is the Rayleigh scattering. Since the black body radiation classically is proportional to (this is true for wavelength typically greater than 5 micrometer), the attenuation coefficient due to Rayleigh scattering is approximately proportional to. This seems to me not precise, where the attenuation of fibers at 1.3 & 1.55 micrometer can be exactly predicted with Planck’s formula & can not be described with Rayleigh-Jeans law. Therefore I believe that the more accurate formula for scattering loss is Dr.Gnanasundari/Prof/ECE/SNSC E/OCN/Unit II

16. Absorption & scattering losses in fibers Optical Fiber communications, 3 rd ed.,G.Keiser,McGrawHill, 2000 Dr.Gnanasundari/Prof/ECE/SNSC E/OCN/Unit II

17. Typical spectral absorption & scattering attenuations for a single mode-fiber Optical Fiber communications, 3 rd ed.,G.Keiser,McGrawHill, 2000 Dr.Gnanasundari/Prof/ECE/SNSC E/OCN/Unit II

18. Bending Loss (Macrobending & Microbending) Macrobending Loss: The curvature of the bend is much larger than fiber diameter. Lightwave suffers sever loss due to radiation of the evanescent field in the cladding region. As the radius of the curvature decreases, the loss increases exponentially until it reaches at a certain critical radius. For any radius a bit smaller than this point, the losses suddenly becomes extremely large. Higher order modes radiate away faster than lower order modes. Optical Fiber communications, 3 rd ed.,G.Keiser,McGrawHill, 2000 Dr.Gnanasundari/Prof/ECE/SNSC E/OCN/Unit II

19. Microbending Loss 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 modes & the leaky or radiation modes in the fiber. Optical Fiber communications, 3 rd ed.,G.Keiser,McGrawHill, 2000 Dr.Gnanasundari/Prof/ECE/SNSC E/OCN/Unit II

20. Dispersion in Optical Fibers Dispersion: Any phenomenon in which the velocity of propagation of any electromagnetic wave is wavelength dependent. In communication, dispersion is used to describe any process by which any electromagnetic signal propagating in a physical medium is degraded because the various wave characteristics (i.e., frequencies) of the signal have different propagation velocities within the physical medium. There are 3 dispersion types in the optical fibers, in general: 1- Material Dispersion 2- Waveguide Dispersion 3- Polarization-Mode Dispersion Material & waveguide dispersions are main causes of Intramodal Dispersion. Dr.Gnanasundari/Prof/ECE/SNSC E/OCN/Unit II

21. Group Velocity Wave Velocities: 1- Plane wave velocity: For a plane wave propagating along z-axis in an unbounded homogeneous region of refractive index, which is represented by, the velocity of constant phase plane is: 2- Modal wave phase velocity: For a modal wave propagating along z-axis represented by, the velocity of constant phase plane is: 3- For transmission system operation the most important & useful type of velocity is the group velocity,. This is the actual velocity which the signal information & energy is traveling down the fiber. It is always less than the speed of light in the medium. The observable delay experiences by the optical signal waveform & energy, when traveling a length of l along the fiber is commonly referred to as group delay. [3-4] [3-5] Dr.Gnanasundari/Prof/ECE/SNSC E/OCN/Unit II

22. Group Velocity & Group Delay The group velocity is given by: The group delay is given by: It is important to note that all above quantities depend both on frequency & the propagation mode. In order to see the effect of these parameters on group velocity and delay, the following analysis would be helpful. [3-6] [3-7] Dr.Gnanasundari/Prof/ECE/SNSC E/OCN/Unit II

23. Input/Output signals in Fiber Transmission System The optical signal (complex) waveform at the input of fiber of length l is f(t). The propagation constant of a particular modal wave carrying the signal is. Let us find the output signal waveform g(t). z-=0 Z=l [3-8] [3-9] Dr.Gnanasundari/Prof/ECE/SNSC E/OCN/Unit II

24. [3-10] [3-11] [3-14] Dr.Gnanasundari/Prof/ECE/SNSC E/OCN/Unit II

25. Intramodal Dispersion As we have seen from Input/output signal relationship in optical fiber, the output is proportional to the delayed version of the input signal, and the delay is inversely proportional to the group velocity of the wave. Since the propagation constant,, is frequency dependent over band width sitting at the center frequency, at each frequency, we have one propagation constant resulting in 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). This phenomenon arises due to a finite bandwidth of the optical source, dependency of refractive index on the wavelength and the modal dependency of the group velocity. In the case of optical pulse propagation down the fiber, GVD causes pulse broadening, leading to Inter Symbol Interference (ISI). Dr.Gnanasundari/Prof/ECE/SNSC E/OCN/Unit II

26. Dispersion & ISI Optical Fiber communications, 3 rd ed.,G.Keiser,McGrawHill, 2000 A measure of information capacity of an optical fiber for digital transmission is usually specified by the bandwidth distance product in GHz.km. For multi-mode step index fiber this quantity is about 20 MHz.km, for graded index fiber is about 2.5 GHz.km & for single mode fibers are higher than 10 GHz.km. Dr.Gnanasundari/Prof/ECE/SNSC E/OCN/Unit II

27. How to characterize dispersion? Group delay per unit length can be defined as: If the spectral width of the optical source is not too wide, then the delay difference per unit wavelength along the propagation path is approximately For spectral components which are apart, symmetrical around center wavelength, the total delay difference over a distance L is: [3-15] [3-16] Dr.Gnanasundari/Prof/ECE/SNSC E/OCN/Unit II

28. is called GVD parameter, and shows how much a light pulse broadens as it travels along an optical fiber. The more common parameter is called Dispersion, and can be defined as the delay difference per unit length per unit wavelength as follows: In the case of optical pulse, if the spectral width of the optical source is characterized by its rms value of the Gaussian pulse, the pulse spreading over the length of L, can be well approximated by: D has a typical unit of [ps/(nm.km)]. [3-17] [3-18] Dr.Gnanasundari/Prof/ECE/SNSC E/OCN/Unit II

29. Material Dispersion Dr.Gnanasundari/Prof/ECE/SNSC E/OCN/Unit II

30. Material Dispersion The refractive index of the material varies as a function of wavelength, Material-induced dispersion for a plane wave propagation in homogeneous medium of refractive index n: The pulse spread due to material dispersion is therefore: [3-19] [3-20] is material dispersion Dr.Gnanasundari/Prof/ECE/SNSC E/OCN/Unit II

31. Material Dispersion Diagrams Optical Fiber communications, 3 rd ed.,G.Keiser,McGrawHill, 2000 Dr.Gnanasundari/Prof/ECE/SNSC E/OCN/Unit II

32. 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. In order to calculate waveguide dispersion, we consider that n is not dependent on wavelength. Defining the normalized propagation constant b as: solving for propagation constant: Using V number: [3-21] [3-22] [3-23] Dr.Gnanasundari/Prof/ECE/SNSC E/OCN/Unit II

33. Waveguide Dispersion Delay time due to waveguide dispersion can then be expressed as: [3-24] Optical Fiber communications, 3 rd ed.,G.Keiser,McGrawHill, 2000 Dr.Gnanasundari/Prof/ECE/SNSC E/OCN/Unit II

34. Waveguide dispersion in single mode fibers For single mode fibers, waveguide dispersion is in the same order of material dispersion. The pulse spread can be well approximated as: [3-25] Optical Fiber communications, 3 rd ed.,G.Keiser,McGrawHill, 2000 Dr.Gnanasundari/Prof/ECE/SNSC E/OCN/Unit II

35. Polarization Mode dispersion Dr.Gnanasundari/Prof/ECE/SNSC E/OCN/Unit II

36. Polarization Mode dispersion The effects of fiber-birefringence on the polarization states of an optical are another source of pulse broadening. Polarization mode dispersion (PMD) is due to slightly different velocity for each polarization mode because of the lack of perfectly symmetric & anisotropicity of the fiber. If the group velocities of two orthogonal polarization modes are then the differential time delay between these two polarization over a distance L is The rms value of the differential group delay can be approximated as: [3-26] [3-27] Dr.Gnanasundari/Prof/ECE/SNSC E/OCN/Unit II

37. Chromatic & Total Dispersion Chromatic dispersion includes the material & waveguide dispersions. Total dispersion is the sum of chromatic, polarization dispersion and other dispersion types and the total rms pulse spreading can be approximately written as: [3-28] [3-29] Dr.Gnanasundari/Prof/ECE/SNSC E/OCN/Unit II

38. Total Dispersion, zero Dispersion Optical Fiber communications, 3 rd ed.,G.Keiser,McGrawHill, 2000 Fact 1) Minimum distortion at wavelength about 1300 nm for single mode silica fiber. Fact 2) Minimum attenuation is at 1550 nm for sinlge mode silica fiber. Strategy: shifting the zero-dispersion to longer wavelength for minimum attenuation and dispersion. Dr.Gnanasundari/Prof/ECE/SNSC E/OCN/Unit II

39. Optimum single mode fiber & distortion/attenuation characteristics Fact 1) Minimum distortion at wavelength about 1300 nm for single mode silica fiber. Fact 2) Minimum attenuation is at 1550 nm for sinlge mode silica fiber. Strategy: shifting the zero-dispersion to longer wavelength for minimum attenuation and dispersion by Modifying waveguide dispersion by changing from a simple step-index core profile to more complicated profiles. There are four major categories to do that: 1- 1300 nm optimized single mode step-fibers: matched cladding (mode diameter 9.6 micrometer) and depressed-cladding (mode diameter about 9 micrometer) 2- Dispersion shifted fibers. 3- Dispersion-flattened fibers. 4- Large-effective area (LEA) fibers (less nonlinearities for fiber optical amplifier applications, effective cross section areas are typically greater than 100 ). Dr.Gnanasundari/Prof/ECE/SNSC E/OCN/Unit II

41. Optical Fiber communications, 3 rd ed.,G.Keiser,McGrawHill, 2000 Single mode fiber dispersion Dr.Gnanasundari/Prof/ECE/SNSC E/OCN/Unit II

42. Optical Fiber communications, 3 rd ed.,G.Keiser,McGrawHill, 2000 Single mode fiber dispersion Dr.Gnanasundari/Prof/ECE/SNSC E/OCN/Unit II

43. Single mode Cut-off wavelength & Dispersion Fundamental mode is with V=2.405 and Dispersion: For non-dispersion-shifted fibers (1270 nm – 1340 nm) For dispersion shifted fibers (1500 nm- 1600 nm) [3-30] [3-31] [3-32] Dr.Gnanasundari/Prof/ECE/SNSC E/OCN/Unit II

44. Dispersion for non-dispersion-shifted fibers (1270 nm – 1340 nm) is relative delay minimum at the zero-dispersion wavelength, and is the value of the dispersion slope in. [3-33] [3-34] [3-35] Dr.Gnanasundari/Prof/ECE/SNSC E/OCN/Unit II

45. Dispersion for dispersion shifted fibers (1500 nm- 1600 nm) [3-36] [3-37] Dr.Gnanasundari/Prof/ECE/SNSC E/OCN/Unit II

46. Optical Fiber communications, 3 rd ed.,G.Keiser,McGrawHill, 2000 Example of dispersion Performance curve for Set of SM-fiber Dr.Gnanasundari/Prof/ECE/SNSC E/OCN/Unit II

47. Optical Fiber communications, 3 rd ed.,G.Keiser,McGrawHill, 2000 Example of BW vs wavelength for various optical sources for SM-fiber. Dr.Gnanasundari/Prof/ECE/SNSC E/OCN/Unit II

48. MFD Optical Fiber communications, 3 rd ed.,G.Keiser,McGrawHill, 2000 Dr.Gnanasundari/Prof/ECE/SNSC E/OCN/Unit II

49. Bending Loss Optical Fiber communications, 3 rd ed.,G.Keiser,McGrawHill, 2000 Dr.Gnanasundari/Prof/ECE/SNSC E/OCN/Unit II

50. Bending effects on loss vs MFD Optical Fiber communications, 3 rd ed.,G.Keiser,McGrawHill, 2000 Dr.Gnanasundari/Prof/ECE/SNSC E/OCN/Unit II

51. Bend loss versus bend radius Optical Fiber communications, 3 rd ed.,G.Keiser,McGrawHill, 2000 Dr.Gnanasundari/Prof/ECE/SNSC E/OCN/Unit II

53. Temporal changes in a medium with Kerr nonlinearity and negative GVD. Since dispersion tends to broaden the pulse, Kerr Nonlinearity tends to squeeze the pulse, resulting in a formation of optical soliton. Dr.Gnanasundari/Prof/ECE/SNSC E/OCN/Unit II