Successfully reported this slideshow.
We use your LinkedIn profile and activity data to personalize ads and to show you more relevant ads. You can change your ad preferences anytime.

FOT_MEng2004_FEUP

856 views

Published on

  • Be the first to comment

FOT_MEng2004_FEUP

  1. 1. Fibre Optic Technology Mestrado Eng. Electrotécnica e de Computadores
 (2003/2005)
 António Lobo Prof. Associado da UFP Prof. Convidado da FEUP
  2. 2. © A.Lobo (2004) 2 Course Topics 1. Optical Fibre: Basic Characteristics 2. Light Propagation in Fibres and Related Optical Effects 3. Types of Optical Fibre 4. Passive Fibre Optic Devices 5. Active Fibre Optic Devices 6. Other Fibre Optic (Hybrid) Devices 7. Fibre Device Fabrication Techniques
  3. 3. © A.Lobo (2004) 3 Reading Material Optical Fiber Communications ▪ G. Keiser, Optical Fiber Communications, 3rd Ed., McGraw-Hill (2000). ▪ J. M. Senior, Optical Fiber communications, Prentice Hall (1985). ▪ G. P. Agrawal, Non-Linear Fiber Optics, 2nd Ed., Academic Press (1995). ▪ H. Kolimbiris, Fiber Optics Communications, Pearson Prentice Hall (2004). Optical Fiber Technology ▪ K.T.V. Grattan and B.T. Meggitt, Optical Fiber Sensor Technology, Vol. 1 and 2, Chapman & Hall (1995). ▪ B. Culshaw and J. Dakin, Optical Fiber Sensors: Principles and Components, vol.II, Artech House (1988). ▪ B. Culshaw and J. Dakin, Optical Fiber Sensors: Components and Subsystems, vol.III, Artech House (1997). ▪ R. Kashyap, Fiber Bragg Gratings, Academic Press (1999). ▪ C. Hentschel, Fiber Optic Handbook, HP Electronics Instruments Dept, ISBN:3-9801677-0-4. ▪ D. Derickson, Fiber Optic Test and Measurement, Hewlett-Packard Co., Prentice-Hall Publs. (1998). ▪ Jeff Hecht, Understanding Fiber Optics, 4th Ed., Pearson Prentice Hall (2002). General Optics ▪ E. Hecht, Optics, 4th Ed., Addison Wesley (2002) ▪ M. Born and E. Wolf, Principles of Optics, 7th Ed. Cambridge Univ. Press (1999). Other material ▪ Class notes and handouts with each of the class topics provided in this syllabus. ▪ Optical Fiber Sensors (OFS) Conference Proceedings. ▪ Optical Fiber Communications (OFC) Conference Proceedings.
  4. 4. © A.Lobo (2004) 4 Assessment to Final Grade The grade is based on the following: ◗ Final examination (50%) ◗ Home Assignments (20%) ◗ Term Paper Project (30%) Examination is based on class lectures, reading assignments, homework problems and class handouts. A Term Paper is required.
  5. 5. © A.Lobo (2004) 5 Term Paper Project LISTING OF POTENTIAL SUBJECTS FOR TERM PAPER (Paper is due May 29, 2004) 1. Optical fibre propagation in fibres 2. Non-linear optical fibre effect 3. High strength fibres 4. Fibre optic sensors (many choices here) 5. Environmental effects in fibres 6. Fibre optic cable designs 7. Wavelength division multiplexing devices 8. Fibre optic filters. 9. Fibre Bragg gratings 10. Microstructured Fiber Devices 11. Fibre optic modulators 12. Dispersion compensation devices 13. Plastic optical fibre for communications 14. Aging effects in fibre optics 15. Photonic crystal fibres 16. Active fibre optic devices in communications 17. Optical power propagation in fibres 18. Fibre Lasers 19. Long wavelength fibre applications 20. All-Fibre optic signal processing 21. Optical fibre technology for automotive applications 22. Optical fibre technology for biomedical applications 23. Optical fibre technology for environmental applications
  6. 6. © A.Lobo (2004) 6 Acknowledgements ▪ Prof. David Jackson – Head of Applied Optics Group, School Physical Sciences, Univ. Kent (UK). ▪ Prof. Philip Russell – Head of Optoelectronics Group, Univ. Bath & CTO of Blaze Photonics Ltd. (UK) ▪ Prof. Govind Agrawal – Optical Communications Group, Univ. Rochester (USA). ▪ Prof. Xiaoyi Bao – Fiber Optics Group, Univ. Ottawa (Canada). ▪ Prof. Jose L. Santos – Head of UOSE, INESC Porto & FCUP, Univ. Porto (Portugal). ▪ Dr. Adrian Podoleanu - Applied Optics Group, School Physical Sciences, Univ. Kent (UK). ▪ Dr. David Webb – Photonics Research Group, Aston Univ. (UK). ▪ Dr. Hector Guerrero – Lab. Optoelectronica, Dept. Ciencias Espacio, INTA (Spain). ▪ Dr. Ralf Pechstedt, Bookham Technology Plc. (UK). ▪ Prof. Y. J. Rao – Dept. optoelectronics Eng., Chongquing Univ. & General Manager of Chongqing Bao Tong Optical Fiber Technology Ltd. (China) ▪ Dr. Christian Hentschel – Boeblingen Instruments Div., Hewlett-Packard GmbH (Germany).
  7. 7. © A.Lobo (2004) 7 1. Optical Fibre: Basic Characteristics ▪ Roman Times (Italy) Glass is drawn into fibers ▪ ?? (Venice) Decorative flowers made of glass fibers ▪ 1626 Snell (Holland) Snell’s Law ▪ 1713 Reaumur (France) Makes spun glass fibers ▪ 1841 Colladon (Swiss) Light guiding in jet of water of Geneva ▪ 1854 Tyndall (UK) Light guiding in a thin water jet ▪ 1880 Wheeler (USA) System of light pipes to illuminate homes ▪ 1888 Roth & Reuss (Austria) Bent glass to illuminate body cavities ▪ 1897 Rayleigh (UK) Analysis of waveguide ▪ 1926 Hansell (USA) Principles of fiber optic imaging bundle ▪ 1930 Lamm (Germany) Assembles first bundle of transparent fibers ▪ 1953-54 Heel (Holland) Simple bundles of clad fiber ▪ 1954 Hopkins, Kapany (UK) Image transmission w. unclad fiber bundles ▪ 1956 Curtiss (USA) Makes the first glass-clad fiber ▪ 1957 Hirschowitz & Curtiss (USA) First test fiber-optic endoscope in a patient ▪ 1960 Goubau & Christian (USA) Hollow optical guides w. periodic lenses 1.1 Historical Introduction
  8. 8. © A.Lobo (2004) 8 1. Optical Fibre: Basic Characteristics ▪ 1960 (May) Maiman et.al. (USA) First laser (ruby laser) ▪ 1960 (Dec.) Javan et.al. (USA) Operation of He-Ne laser ▪ 1961 Kapany and Snitzer (UK) Mode analysis of optical fiber – SingleMode Fiber ▪ 1962 Hall’s et. Al. (USA) Operation of semiconductor laser ▪ 1964 Goubau and Christian (USA) Light guide with periodic lenses ▪ 1966 Kao and Hockham (UK) Suggest that fiber loss could be <20 dB/km ▪ 1967 Kawakami (Japan) Proposes graded-index optical fiber ▪ 1970 Maurer, Keck, Schultz (USA) Fiber transmission loss 17dB/km @ 633 nm ▪ 1070-71 Dyot & Kapron (USA) Find pulse spreading lower at 1.2 to 1.3 µm ▪ 1972 Gambling et.al. (UK) Gigahertz bandwidth over 1km ▪ 1974 Kaiser & Astle (USA) Air-silica microstructured optical fiber ▪ 1975 Payne and Gambling (UK) Calculate zero material dispersion at 1.3 µm ▪ 1976 Horiguchi & Osanai (Japan) First fiber w. 0.47dB/km @ 1.2 µm & Open 3rd Window @ 1.55 µm. 1.1 Historical Introduction
  9. 9. © A.Lobo (2004) 9 1. Optical Fibre: Basic Characteristics ▪ 1978 NTT (Japan) Makes SMF w. 0.2dB/km @ 1.55 µm ▪ 1981 British Telecom (UK) Transmits 140Mb/s in 49 km of SMF @ 1.3 µm ▪ 1987 Payne et.al.(UK) Develops EDFA @ 1.55 µm ▪ 1988 Mollenauer (USA) Soliton transmission on 4000 km of SMF ▪ 1991 Russell (UK) Proposes the Photonic Crystal optical fiber ▪ 1993 Nakazawa (Japan) Soliton signals over 180 million kms ▪ 1993 Mollenauer et.al.(USA) 10 Gbits through 11000 km of SMF using soliton system ▪ 1995-96 Russell et.al. (UK) Demonstrates the first Photonic Crystal optical fiber ▪ 1999 Cregan, Russell et.al. (UK) Demonstrates the Photonic Bandgap optical fiber 1.1 Historical Introduction
  10. 10. © A.Lobo (2004) 10 1. Optical Fibre: Basic Characteristics 1.2 Fibre Optic Physical Structure Core (8-12 µm) Cladding (125 µm) Buffer Coating (250 ou 900 µm) R. Maurer, P. Schultz, D.Keck (Corning Corp., 1970) Human Hair ~ 70 µm
  11. 11. © A.Lobo (2004) 11 1. Optical Fibre: Basic Characteristics 1.2 Fibre Optic Physical Structure
  12. 12. © A.Lobo (2004) 12 1. Optical Fibre: Basic Characteristics 1.3 Index of Refraction and Index Difference r r o o c n v εµ ε µ ε µ = = = c = speed of light in vacuum (≈ 3×108 m/s) v = speed of light in medium 1 o o c ε µ = Permeability in vacuum = 4π×10-7 N s2/C2 Permitivity in vacuum = 8.854 ×10-12 C2/N m2 For most materials in the optical region: 1r rnµ ε≈ ⇒ ≈ Substance n Fused silica 1.458 Diamond 2.419 @ λ = 589.29 nm (Sodium D light)
  13. 13. © A.Lobo (2004) 13 1. Optical Fibre: Basic Characteristics 1.3 Index of Refraction and Index Difference 2 2 2 2 1 j j j A n λ λ λ = + − ∑ Sellmeier’s Equation Absorption Bands Visible
  14. 14. © A.Lobo (2004) 14 1. Optical Fibre: Basic Characteristics 1.3 Index of Refraction and Index Difference 2 2 2 2 1 withj j j j j A n b b λ λ λ = + = − ∑ A1=0.6961663 b1=0.004629148 A2=0.4079426 b2=0.01351206 A3=0.8974994 b3=97.934062 Refractive index variation of fused silica
  15. 15. © A.Lobo (2004) 15 1. Optical Fibre: Basic Characteristics 1.3 Index of Refraction and Index Difference 1 2 1 for 1 n n n − Δ ≈ Δ ≪ 2 2 1 2 2 12 n n n − Δ = and 1 2n n> Refractive Index Difference, also called Refractive Index Contrast
  16. 16. © A.Lobo (2004) 16 1. Optical Fibre: Basic Characteristics 1.4 Total Internal Reflection 1 1 2 2sin sinn nφ φ⋅ = ⋅ Snell’s Law Increasing θ1 progressively until θ2 = π/ 2 : 2 1 sin c n n φ = Critical angle “Critical angle is the minimum angle necessary to obtain total internal reflection”
  17. 17. © A.Lobo (2004) 17 1. Optical Fibre: Basic Characteristics 1.5 Numerical Aperture and Acceptance Angle 2 2 1 2NA sino An n nθ= = − Numerical Aperture (NA) “Numerical Aperture express de ability of the fibre to collect light” or “Numerical Aperture measures spreading of light from the end of the fibre”
  18. 18. © A.Lobo (2004) 18 1. Optical Fibre: Basic Characteristics Relation between Numerical Aperture and Index Difference 1NA 2n≅ Δ Fibre type NA Δ Step-Index SM 0.1 2×10-3 Graded-index MM 0.2 1×10-2 Step-index MM 0.3 2×10-2
  19. 19. © A.Lobo (2004) 19 1. Optical Fibre: Basic Characteristics 1. Using the Snell’s relation, how can you estimate the amplitudes of the optical rays? 2. “An optical ray at any angle θ less than the critical angle (θc) propagate along the fiber.” Is this true? 3. Definition of NA described before for singlemode fibre is frequently wrong! Why? 4. Why the index of refraction is frequency dependent? Questions to think:
  20. 20. Light Propagation in Fibres and Related Optical Effects FIBRE OPTIC TECHNOLOGY COURSE António Lobo Prof. Associado (UFP)
  21. 21. © A.Lobo (2004) 2 2. Light Propagation in Fibres and Related Optical Effects 2.1 The Wave nature of light. 2.2 Rays and Modes representation. 2.3 Mode Theory for fibres. 2.4 The Cut-off wavelength and V-number. 2.5 Singlemode and multimode fibre propagation. 2.6 Mode Field Diameter (MFD) 2.7 Phase velocity and group velocity. 2.8 Absorption and Scattering losses 2.9 Dispersion: Group delay and Material dispersion. 2.10 Chromatic Dispersion (CD). 2.11 Polarization effects and Birefringence. 2.12 Polarization Dependence Loss (PDL) 2.13 Polarization Mode Dispersion (PMD). 2.14 Non-linear Optical Effects ◗ Stimulated Raman Scattering ◗ Stimulated Brillouin Scattering ◗ Four-Wave Mixing ◗ Self-Phase and Cross-Phase Modulation
  22. 22. © A.Lobo (2004) 3 2. Light Propagation in Fibres and Related Optical Effects 2.1 Wave Nature of the Light ❧ Waves ◗ Electromagnetic radiation consisting of propagating electric and magnetic fields (interference & diffraction) ❧ Photons ◗ Quanta of energy (photoelectric effect) The two views are related: the energy in a photon is proportional to the frequency of the wave. DUAL NATURE
  23. 23. © A.Lobo (2004) 4 2. Light Propagation in Fibres and Related Optical Effects 2.1 Wave Nature of the Light Waves [ ]( , ) cos ( v ) A r t k r t r ψ " # = ⋅ ±% & ' ( [ ]( , ) cos )x t A kx tψ ω= ⋅ ± 2 2 2 1 v t ψ ψ ∂ ∇ = ⋅ ∂
  24. 24. © A.Lobo (2004) 5 2. Light Propagation in Fibres and Related Optical Effects 2.1 Wave Nature of the Light A Single Photon (“short” packet wave) Photon ❧ Quanta of Energy: Photon (photoelectric effect) E hν= E → Energy of 1 photon in Joules (J) h → Planck’s constant: 6.626×10-34 J-s ν→frequency in Hz
  25. 25. © A.Lobo (2004) 6 2. Light Propagation in Fibres and Related Optical Effects 2.1 Wave Nature of the Light c → Speed of light = 2.9979 ×108 m/s; λ → Wavelength in meters; ν→Frequency in Hz n→Refractive index (vaccum=1.0000; standard air= 1.0003; silica fibre: 1.44 to 1.48) c nλν=
  26. 26. © A.Lobo (2004) 7 2. Light Propagation in Fibres and Related Optical Effects 2.1 Wave Nature of the Light 21 o o S E B c E Bε µ = × = × ! ! ! ! !y zE cB= Poynting Vector
  27. 27. © A.Lobo (2004) 8 2. Light Propagation in Fibres and Related Optical Effects 2.2 Rays and Modes representation. About Reflection (Fresnel Equations): E ⊥Plane-of-Incidence v 0 B k E k E = × = !! ! ! ! i cos( ) cos( ) i oi r r t ot t t E E k r t E E k r t ω ω = − = − !! ! ! i !! ! ! i ot oi orE E E= + ! ! ! cos cos cos cos 2 cos cos cos or i i t t oi i i t t ot i i oi i i t t E n n r E n n E n t E n n θ θ θ θ θ θ θ ⊥ ⊥ ⊥ ⊥ # $ − = =& ' +( ) # $ = =& ' +( )
  28. 28. © A.Lobo (2004) 9 2. Light Propagation in Fibres and Related Optical Effects 2.2 Rays and Modes representation. About Reflection (Fresnel Equations): E ||Plane-of-Incidence cos cos cos cos 2 cos cos cos or t i i t oi i t t i ot i i oi i t t i E n n r E n n E n t E n n θ θ θ θ θ θ θ " # − = =% & +' ( " # = =% & +' ( ! ! ! !
  29. 29. © A.Lobo (2004) 10 2. Light Propagation in Fibres and Related Optical Effects 2.2 Rays and Modes representation. Total Internal Reflection (case: ni > nt):θi ≥ θc sin t c i n n θ = Critical Angle: 2 2 2 2 2 2 2 2 2 2 2 2 2 2 cos sin cos sin cos sin cos sin t t i i i i t i i i i t i i i i t i i i i t n i n n r n i n n n in n n r n in n n θ θ θ θ θ θ θ θ ⊥ − − = + − − − = + − ! * * 1 e 0 1 r i t r r r r I I I R ⊥ ⊥ "= = ⇒ = =$ = % ! ! sint t i ii k xn n t t otE E e e θ ωβγ % &−( ) = ∓ " " Evanescent wave: Goos-Hänchen depth 1 0 4 2 x n λ < Δ < Δ
  30. 30. © A.Lobo (2004) 11 2. Light Propagation in Fibres and Related Optical Effects 2.2 Rays and Modes representation. Total Internal Reflection (case: ni > nt):θi ≥ θc * 2 2 1 i i r rr r r e e− ΔΦ − ΔΦ = = = = 2 2 2 1 2 2 2 1 2 sin tan cos sin tan cost i i t i i i i i t i n n n n n n n θ θ θ θ − ⊥ − $ %− & 'ΔΦ = & '* + $ %− & 'ΔΦ = & '* + ! ⊥ΔΦ ΔΦ! 2 1 i t n n = = Polarization TE →ΔΦ⊥ Polarization TM →ΔΦ||
  31. 31. © A.Lobo (2004) 12 2. Light Propagation in Fibres and Related Optical Effects 2.2 Rays and Modes representation. About Reflection (case: ni > nt): Phase-shifts tan t p i n n θ = Brewster Angle: The component of electric field normal to plane- of-incidence undergoes a phase shift of π radians upon reflection when the incident medium has a lower index than the transmitting medium.
  32. 32. © A.Lobo (2004) 13 2. Light Propagation in Fibres and Related Optical Effects 2.2 Rays and Modes representation. 1 1 2 2 sin tan 1 ; is an integer sin 2 kn a m m π φ φ − $ %Δ − − =' ( ) * Propagation Condition: The optical field distribution that satisfies this phase matching condition is called MODE Goos-Hänchen shift (ΔΦ⊥) n1 n2 n2
  33. 33. © A.Lobo (2004) 14 2. Light Propagation in Fibres and Related Optical Effects 2.2 Rays and Modes representation. Formation of modes
  34. 34. © A.Lobo (2004) 15 2. Light Propagation in Fibres and Related Optical Effects 2.2 Rays and Modes representation. At angles for which the condition of self-consistently (i.e., as a wave reflects twice it duplicates itself) is satisfied, the two waves interfere and create a pattern that does not change with z direction. z
  35. 35. © A.Lobo (2004) 16 2. Light Propagation in Fibres and Related Optical Effects 2.2 Rays and Modes representation. V ξ 1 2V kn a= Δ sin 2 φ ξ = Δ Single-mode condition 1.571 2 cV v π < = = Normalized frequency: Propagation constant: Dispersion Equation 1 cos 2 m V π ξ ξ − + = (Slab Waveguide)
  36. 36. © A.Lobo (2004) 17 2. Light Propagation in Fibres and Related Optical Effects 2.3 Mode Theory for fibres. Coordinate System Notação 2 grad div rot lap f f A A A A f f = ∇ = ∇ = ∇× = ∇ ! ! i ! ! Cylindrical Coordinates (r,φ,z)
  37. 37. © A.Lobo (2004) 18 2. Light Propagation in Fibres and Related Optical Effects 2.3 Mode Theory for fibres. Maxwell´s Equations 0 B E t E B E t E B µε µσ ρ ε ∂ ∇× = − ∂ ∂ ∇× = + ∂ ∇ = ∇ = ! ! ! ! ! ! i ! i 1 0 B E dl dS t E B dl E dS t E dS dV B dS µε µσ ρ ε ∂ ⋅ = − ⋅ ∂ ' (∂ ⋅ = + ⋅) * ∂+ , ⋅ = ⋅ ⋅ = ∫ ∫∫ ∫ ∫∫ ∫∫ ∫∫∫ ∫∫ ! ! !! ! ! !! ! !! !! " " # #
  38. 38. © A.Lobo (2004) 19 2. Light Propagation in Fibres and Related Optical Effects 2.3 Mode Theory for fibres. Maxwell´s Equations (2) 0 B E t D H J t D B ρ ∂ ∇× = − ∂ ∂ ∇× = + ∂ ∇ = ∇ = ! ! ! ! ! ! i ! i 2 1 2 1 2 1 2 1 0 0 0 t t t t n n n n E E H H D D B B σ − = − = − = − = ! ! ! ! Boundary Conditions (for conductors) o o D E E P B H H M J E ε ε µ µ σ = = + = = + = ! ! ! ! ! ! ! ! ! ! Constitutive Equations
  39. 39. © A.Lobo (2004) 20 2. Light Propagation in Fibres and Related Optical Effects 2.3 Mode Theory for fibres. 2 2 2 2 2 2 0 0 E E t H H t µε µε ∂ ∇ − = ∂ ∂ ∇ − = ∂ ! ! ! ! In dielectric, non-conducting media, σ = 0 Wave Equations (1) 2 2 2 2 2 2 0 0 E E E t t H H H t t µε µσ µε µσ ∂ ∂ ∇ − − = ∂ ∂ ∂ ∂ ∇ − − = ∂ ∂ ! ! ! ! ! !
  40. 40. © A.Lobo (2004) 21 2. Light Propagation in Fibres and Related Optical Effects 2.3 Mode Theory for fibres. 2 2 2 2 2 2 ( ) ( ) 0 ( ) ( ) 0 E r n k E r H r n k H r ∇ + = ∇ + = ! !! ! ! !! ! Wave Equations (2) Helmholtz Equations 2 2 2 2 2 n k c ω µεω= = Waves in photonics are often monochromatic, with a frequency that stays the same across the material boundaries, that is: ( , ) ( ) j t E r t E r e ω = ! !! !
  41. 41. © A.Lobo (2004) 22 2. Light Propagation in Fibres and Related Optical Effects 2.3 Mode Theory for fibres. Coordinate System Notação 2 grad div rot lap f f A A A A f f = ∇ = ∇ = ∇× = ∇ ! ! i ! ! Cylindrical Coordinates (r,φ,z)
  42. 42. © A.Lobo (2004) 23 2. Light Propagation in Fibres and Related Optical Effects 2.3 Mode Theory for fibres. ( ) ( ) ( , ) ( , ) ( , ) ( , ) j t z j t z E r t E r e H r t H r e ω β ω β φ φ − − = = ! !! ! !! 2 2 2 2 2 2 ( ) ( ) 0 ( ) ( ) 0 E r n k E r H r n k H r ∇ + = ∇ + = ! !! ! ! !! ! 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 ( , ) 0 1 1 ( , ) 0 z z z z z z z z z z E E E E n r k E r r r r z H H H H n r k H r r r r z φ φ φ φ ∂ ∂ ∂ ∂ + ⋅ + ⋅ + + = ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ + ⋅ + ⋅ + + = ∂ ∂ ∂ ∂ The longitudinal component of the electric field does not change though either propagation or reflection at the cylindrical surface
  43. 43. © A.Lobo (2004) 24 Since the equations for Er and Eθ are coupled, we first solve for Ez (Hz is a solution of the same Helmholtz equation and its solutions have the same form ). We find all other field components form Ez and Hz using Mawell’s equations. We look for solution of the form: 2. Light Propagation in Fibres and Related Optical Effects 2.3 Mode Theory for fibres. ( , , ) ( ) ( ) ( )zE r z R r Z zφ φ= ⋅Φ ⋅ 2 2 2 2 2 2 2 2 2 ( ) 0 R R Z r r r knr r r zφ ∂ ∂ ∂ Φ ∂ + + + + = ∂ ∂ ∂ ∂ In the core we find: ( ) ( ) ( ) ( ) ( ) j z j z j j Z z ae be ce de R r gJ r hN r β β νφ νφ ν ν φ κ κ − − = + Φ = + = + 2 2 2 ( ) and 0,1,2,...onkκ β ν= − =
  44. 44. © A.Lobo (2004) 25 2. Light Propagation in Fibres and Related Optical Effects 2.3 Mode Theory for fibres. We can simplify these solutions noting that: • Often we have only forward going waves, thus a =0. • The Neumann function Nν(κr) goes to minus infinity at r =0, so it is unphysical (h =0). Therefore Jν(κr) is the proper solution in the core.
  45. 45. © A.Lobo (2004) 26 2. Light Propagation in Fibres and Related Optical Effects 2.3 Mode Theory for fibres. 2 2 ( ) j z Z Z z be z β β− ∂ = ⇒ = − ∂ 2 2 2 2 2 2 2 0 R R r r r R r r r ν κ # $∂ ∂ + + − =' ( ∂ ∂ ) * • Due to predominant propagation of the field along the z axis an oscillatory characteristic is assumed for the z dependence • We need both the clockwise and counter-clockwise circulating exponentials that describe the φdependence of the eigenmodes 2 2 2 ( ) j j ce deνφ νφ φ ν φ φ − ∂ Φ Φ = + ⇒ = − ∂ Bessel Equation 2 2 2 ( ) and 0,1,2,...onkκ β ν= − =
  46. 46. © A.Lobo (2004) 27 2. Light Propagation in Fibres and Related Optical Effects 2.3 Mode Theory for fibres. 2 2 2 0 r ν κ # $ − >& ' ( ) CASE 1: CORE CASE 2: CLADDING Modified Bessel functions Bessel functions 2 2 2 0 r ν κ # $ − <& ' ( ) ( ) ( ) j z z j z z E AJ r e H BJ r e νφ β ν νφ β ν κ κ − − = = ( ) ( ) j z z j z z E CK r e H DK r e νφ β ν νφ β ν γ γ − − = = A,B,C and D are constants determined by the boundary conditions 2 2 γ κ= −
  47. 47. © A.Lobo (2004) 28 2. Light Propagation in Fibres and Related Optical Effects 2.3 Mode Theory for fibres. After some maths…. We get this “small” CHARACTERISTIC EQUATION for an optical fibre ( ) ( ) 2' ' ' ' 2 1 2 2 2 1 ( ) ( ) ( ) ( )1 1 1 1 ( ) ( ) ( ) ( ) 1 1 o J a K a J a K an a J a a K a a J a n a K a n k a a ν ν ν ν ν ν ν ν κ γ κ γ κ κ γ γ κ κ γ γ βν κ γ % &% & % & ' (⋅ + ⋅ ⋅ ⋅ + ⋅ ⋅ =' ( ' (' (* +* + * + , -% & . /= ⋅ +' ( ' (. /* +0 1 2 2 2 1 2 2 2 2 ( ) ( ) o o n k n k κ β γ β = − = − ( ) ( ) 2 22 V a aκ γ= + 2 2 1 2where oV k a n n= − The characteristic equation is used with: to find values for κ, γ, β and neff
  48. 48. © A.Lobo (2004) 29 2. Light Propagation in Fibres and Related Optical Effects 2.3 Mode Theory for fibres. About the Effective Index (neff) A plane wave propagates with a phase term ejnkz, where k=2π/λo is the free-space wave-vector. We can define an effective index for a guided wave that has a phase factor ejβz with: 2 eff o nπ β λ ≡ Then; 2 12 2 o o n nπ π β λ λ < < 2 1effn n n< < The effective index is an “average” index seen by the guided mode.
  49. 49. © A.Lobo (2004) 30 2. Light Propagation in Fibres and Related Optical Effects 2.3 Mode Theory for fibres. Meridional Modes (ν = 0) For modes that correspond to bouncing meridional rays, there is no φ dependence. The characteristic equation simplifies greatly. Modes are of two types – TE0µ (Ez=0) and TM0µ (Hz=0) with µ=1,2, …. The values κ, γ can be found graphically Curves of the characteristic equation of the TE0µ and TM0µ modes
  50. 50. © A.Lobo (2004) 31 2. Light Propagation in Fibres and Related Optical Effects 2.3 Mode Theory for fibres. Skew Modes (ν ≠ 0) Modes have both Ez≠0 and Hz≠0 and thus are called “hybrid” modes. The hybrid modes are labeled EHνµ and HEνµ depending on whether Ez or Hz is dominant. The values κ, γ can be found graphically Curves of the characteristic equation of the HE1µ modes
  51. 51. © A.Lobo (2004) 32 2. Light Propagation in Fibres and Related Optical Effects 2.3 Mode Theory for fibres. Field Distributions in Optical Fibers (1) 1 0 1 0 0 ( ) ( ) 0 r r E E J r H J r H φ µ µ φ κ κ− ∼ ∼ ∼ ∼ 1 0 1 0 ( ) 0 0 ( ) r r E J r E H H J r µ φ φ µ κ κ −∼ ∼ ∼ ∼ TE Modes TM Modes This Bessel function (J1) has a zero at the origin and one maximum in the core
  52. 52. © A.Lobo (2004) 33 2. Light Propagation in Fibres and Related Optical Effects 2.3 Mode Theory for fibres. Field Distributions in Optical Fibers (2) 1 21 1 21 1 21 1 21 ( )cos(2 ) ( )sin(2 ) ( )sin(2 ) ( )cos(2 ) r rE J r H J r E J r H J rφ φ κ φ κ φ κ φ κ φ − − − ∼ ∼ ∼ ∼ HE21 Mode This Bessel function (J1) has a zero at the origin and one maximum in the core
  53. 53. © A.Lobo (2004) 34 2. Light Propagation in Fibres and Related Optical Effects 2.3 Mode Theory for fibres. Linearly Polarized (LP) Modes When the refractive index of the core n1 ≈ n2 , the characteristic equation (CE) can be simplified. This is called the “weakly guiding approximation”. The CE can be written in the unified form as: 1 1 ( ) ( ) ( ) ( ) m m m m J a K a J a K a κ γ κ κ γ γ− − = 1 for TM and TE modes 1 for EH modes 1 for HE modes m ν ν →# $ = + →% $ − →' LP modes can be constructed from sums of EH and HE modes that have the same propagation constant.
  54. 54. © A.Lobo (2004) 35 2. Light Propagation in Fibres and Related Optical Effects 2.3 Mode Theory for fibres. Linearly Polarized (LP) Modes
  55. 55. © A.Lobo (2004) 36 2. Light Propagation in Fibres and Related Optical Effects 2.4 The Cut-off wavelength and V-number. ( ) ( ) 2 22 V a aκ γ= + 2 2 2 1 2 1 2o oV k a n n k an= − = Δ 2 2 2 1 2 2 2 2 o o u a a k n w a a k n κ β γ β = = − = = − This is a dimensionless number that determines how many modes a fibre can support 2 22 2 2 2 2 1 2 ( / )ok nw b V n n β − = = − Normalized Propagation Constant* 2 2 1 2 2 cutoff a n n V π λ = − Cut-off Wavelength * D. Gloge, “Weakly guiding fibers”, Applied Optics 10, 2252-2258 (1971)
  56. 56. © A.Lobo (2004) 37 2. Light Propagation in Fibres and Related Optical Effects 2.4 The Cut-off wavelength and V-number. min 1 2.405 3.7cutoff V V anλ λ < = > = Δ Singlemode Condition ( ) ( ) 10log ( ) straight loop P R P λ λ λ " # = $ %$ % & ' See recommendation ITU-T G.650
  57. 57. © A.Lobo (2004) 38 2. Light Propagation in Fibres and Related Optical Effects 2.5 Singlemode and multimode fibre propagation. 2.405V ≤ Single-mode Condition Single-modeRegion LP Step-index singlemode fibre
  58. 58. © A.Lobo (2004) 39 2. Light Propagation in Fibres and Related Optical Effects 2.5 Singlemode and multimode fibre propagation. 2 2 V M = 2 2 1 2NA n n= − 2 2 2 2 1 2sin n nπ θ πθ πΩ = ≈ = − Numerical Aperture Solid Angle Total number of Modes in the fibre (Step-index Fibre)
  59. 59. © A.Lobo (2004) 40 2. Light Propagation in Fibres and Related Optical Effects 2.5 Singlemode and multimode fibre propagation. In the weakly guiding approximation, the big steps in this figure become perfectly vertival (eg. TE01, TM01 and HE21 have the same V at cutoff. Groups of modes with the same cutoff also have the same propagation constant. Singlemode Condition
  60. 60. © A.Lobo (2004) 41 2. Light Propagation in Fibres and Related Optical Effects 2.5 Singlemode and multimode fibre propagation.
  61. 61. © A.Lobo (2004) 42 2. Light Propagation in Fibres and Related Optical Effects 2.5 Singlemode and multimode fibre propagation. HE11 mode Solid lines – E field Dashed lines – H field With permission of C.D. Cantrell and D.M. Hollenbeck, “Fiberoptic Mode Functions: A Tutorial”, Erick Jonsson School of Eng. and Computer Science, Univ. Texas at Dallas, Course EE6314.
  62. 62. © A.Lobo (2004) 43 2. Light Propagation in Fibres and Related Optical Effects 2.5 Singlemode and multimode fibre propagation. Solid lines – E field Dashed lines – H field HE21 mode With permission of C.D. Cantrell and D.M. Hollenbeck, “Fiberoptic Mode Functions: A Tutorial”, Erick Jonsson School of Eng. and Computer Science, Univ. Texas at Dallas, Course EE6314.
  63. 63. © A.Lobo (2004) 44 2. Light Propagation in Fibres and Related Optical Effects 2.5 Singlemode and multimode fibre propagation. Solid lines – E field Dashed lines – H field TM01 mode TE01 mode With permission of C.D. Cantrell and D.M. Hollenbeck, “Fiberoptic Mode Functions: A Tutorial”, Erick Jonsson School of Eng. and Computer Science, Univ. Texas at Dallas, Course EE6314.
  64. 64. © A.Lobo (2004) 45 2. Light Propagation in Fibres and Related Optical Effects 2.5 Singlemode and multimode fibre propagation. Optical Power in the Mode ( ) ( )* * *1 1 2 2 z z r rS E H u E H E Hθ θ= × ⋅ = − ! ! ! ( ) 2 2 * * 0 0 0 0 1 2 a a core z r rP S r dr d r E H E H dr d π π θ θφ φ= ⋅ ⋅ = − ⋅ ⋅∫ ∫ ∫ ∫ ( ) 2 2 * * 0 0 1 2 cladding z r r a a P S r dr d r E H E H dr d π π θ θφ φ ∞ ∞ = ⋅ ⋅ = − ⋅ ⋅∫ ∫ ∫ ∫ 22 2 2 2 1 1 ( )( ) 1 1 ( ) ( ) 1 core m total m m cladding core total total P K aa P V K a K a P P P P γκ γ γ− + $ % = − −& ' ( ) = −
  65. 65. © A.Lobo (2004) 46 2. Light Propagation in Fibres and Related Optical Effects 2.5 Singlemode and multimode fibre propagation. Optical Power in the Mode LPml
  66. 66. © A.Lobo (2004) 47 2. Light Propagation in Fibres and Related Optical Effects 2.6 Mode Field Diameter (MFD). Gaussian Beam (1) 2 ( ) r w oE r E e ! " −$ % & ' = 2 2 ( ) o r w oI r I e ! " − $ % & ' =
  67. 67. © A.Lobo (2004) 48 2. Light Propagation in Fibres and Related Optical Effects 2.6 Mode Field Diameter (MFD). Gaussian Beam (2) 1/22 2 ( ) 1 ( ) 1 o R R z w z w z z R z z z ! "# $ % &= + ' ( % &) *+ , ! "# $ = +% &' ( ) *% &+ , 2 o R w z π λ = 2 ow λ π Θ =Divergence Angle: Rayleigh Range: for large ( ) o z z w z w λ π ⇒ ≈ H. Kolgelnik and T. Li, “Laser beams and resonators”, Applied Optics 5, 1550-1566 (1966)
  68. 68. © A.Lobo (2004) 49 2. Light Propagation in Fibres and Related Optical Effects 2.6 Mode Field Diameter (MFD). Petermann I Integral (Near-Field): M. Artiglia et al, “Mode Field Diameter Measurements in Single-Mode Optical Fibers”, Journal of Lightwave Technology, Vol. 7, No. 8. (1989) 1/2 2 3 0 2 0 ( ) 2 2 ( ) I E r r dr MFD E r r dr ∞ ∞ " # ⋅% & % &= ⋅ % & ⋅% & % &' ( ∫ ∫ Petermann II Integral* (Far-Field): 1/2 3 2 ( )sin cos ( )sin cos II I d MFD I d θ θ θ θ θ θ θ θ λ π θ θ θ θ − − % & ⋅( ) ( )= ⋅ ( ) ⋅( ) ( )* + ∫ ∫*TIA/EIA FOTP-191, ITU-T G.650E
  69. 69. © A.Lobo (2004) 50 2. Light Propagation in Fibres and Related Optical Effects 2.6 Mode Field Diameter (MFD). Near-Field Profiles 100X 40X J. L. Guttman, “Mode-Field Diameter and “Spot Size” Measurements of Lensed and Tapered Specialty Fibers”, NIST Symposium on Optical Fiber Measurements, September 24-26, 2002
  70. 70. © A.Lobo (2004) 51 2. Light Propagation in Fibres and Related Optical Effects 2.6 Mode Field Diameter (MFD). Far-Field Profiles J. L. Guttman, “Mode-Field Diameter and “Spot Size” Measurements of Lensed and Tapered Specialty Fibers”, NIST Symposium on Optical Fiber Measurements, September 24-26, 2002 a.) Fiber #1 b.) Fiber #2
  71. 71. © A.Lobo (2004) 52 2. Light Propagation in Fibres and Related Optical Effects 2.6 Mode Field Diameter (MFD). Petermann II Integral* (Far-Field): 1/2 3 2 ( )sin cos ( )sin cos II I d MFD I d θ θ θ θ θ θ θ θ λ π θ θ θ θ − − % & ⋅( ) ( )= ⋅ ( ) ⋅( ) ( )* + ∫ ∫(*TIA/EIA FOTP-191, ITU-T G.650E) • Errors [1,2] • Obliquity Factor and Aperture Field •Elliptical Fiber [3] • Radial Symmetry for Hankel Transform • Field Within Fiber vs Field at Focus [1] M. Young, “Mode-field Diameter of single-mode optical fiber by far-field scanning”, Applied Optics, Vol. 37, No. 24, August 1998 [2] R. C. Wittmann and M. Young, “Are the Formulas for Mode-Field Diameter Correct?”, NIST SOFM 1998 [3] M. Artiglia et al, “Mode Field Diameter Measurements in Single-Mode Optical Fibers”, Journal of Lightwave Technology, Vol. 7, No. 8. August 1989
  72. 72. © A.Lobo (2004) 53 2. Light Propagation in Fibres and Related Optical Effects 2.6 Mode Field Diameter (MFD). 1.5 6 1.619 2.879 0.65w a V V ! " = + +# $% & D. Marcuse, Bell Systems Tech. Journal 56, 703-718 (1977) Marcuse Model:
  73. 73. © A.Lobo (2004) 54 2. Light Propagation in Fibres and Related Optical Effects 2.6 Mode Field Diameter (MFD). 1.5 6 1.619 2.879 0.65w a V V ! " = + +# $% & For the best fit between a Gaussian function and the Bessel function in the core we can use the Marcuse Model: Satisfying this condition gives about 96% overlap between the Gaussian and the Bessel function mode profiles. At the cut-off condition (V ≈ 2.405) we obtain: 1.1w a≈
  74. 74. © A.Lobo (2004) 55 2. Light Propagation in Fibres and Related Optical Effects 2.6 Mode Field Diameter (MFD). 1.5 6 1.237 1.429 0.761w a V V ! " = + +# $% & Other MFD models 1.5 6 1.289 1.041 0.759w a V V ! " = + +# $% & 1.5 6 1.66 0.987 0.616w a V V ! " = + +# $% & ( ) 1.5 1 for V>1 ln w a V =Snyder and Sammut Model Myslinski Model Desurvire Model Whitley Model Several models have been developed to obtain better agreement with experimentally observed data (particularly gain factors →Erbium doped fibres)
  75. 75. © A.Lobo (2004) 56 2. Light Propagation in Fibres and Related Optical Effects 2.7 Absorption and Scattering losses. 3 8 2 4 8 3 R T B Fn p k T π γ β λ = SCATTERING NON-LINEAR LINEAR • Rayleigh (diameter physical anomalies < λ/10) • Mie (diameter physical anomalies > λ/10) • Brillouin (acoustic phonon →SBS) • Raman (optical phonon →SRS) n – refractive index of the material, βT – isothermal compressibility, p – photoelastic coefficient, TF – Solidification temperature, kB – Boltzman constant, L - the fibre length. Rayleigh Scattering Coefficient RL RayleighF e γ− = Transmission Loss factor
  76. 76. © A.Lobo (2004) 57 2. Light Propagation in Fibres and Related Optical Effects 2.7 Absorption and Scattering losses. ABSORPTION INTRINSIC INDUCED Curvature (micro and macrobending) EXTRINSIC Interaction of free electrons and the λ within the fibre material. Impurities atoms in glass material (metal ions) 4.582 3 [ ] [ / ] 1.108 10 UV m UV dB km Ce e λ λ µλ α − = = × 48.48 11 [ ] [ / ] 4 10 m IR dB km eλ µ α − = × Urbach’s rule (empirical relationship) Macrobending (critical radius) 2 1 2 2 1 2 3 4 ( ) MMF n R n n λ π = − 3 2 2 1 2 20 0.996 2.748SMF cutoff R n n λ λ λ − # $ = −% &% &− ' (
  77. 77. © A.Lobo (2004) 58 2. Light Propagation in Fibres and Related Optical Effects 2.7 Absorption and Scattering losses. ATTENUATION z dz P P+dP 1 (0) ( ) (0) ln [1/km or 1/m] ( ) LdP P L P L P e dz L P L α α α− # $ = − ⇒ = ⇒ = & ' ( ) (0) (0) 10log 10log 10 log 4.343 ( ) ( ) L LP P e e L e P L P L α α α α " # " #= ⇔ = = =% & ' ( ' ( 10 (0) [ / ] log ( ) [ / ] 4.343 [1/ ] P dB km L P L dB km km α α α " # = $ % & ' = scattering absorption bendingα α α α= + +
  78. 78. © A.Lobo (2004) 59 2. Light Propagation in Fibres and Related Optical Effects 2.7 Absorption and Scattering losses.
  79. 79. © A.Lobo (2004) 60 2. Light Propagation in Fibres and Related Optical Effects 2.7 Absorption and Scattering losses. Theoretically expected minimum attenuation Governed by: 1. Rayleigh scattering at short λ 2. Multi-phonon absorption at long λ
  80. 80. © A.Lobo (2004) 61 2. Light Propagation in Fibres and Related Optical Effects 2.7 Absorption and Scattering losses. Fibre λ (nm) α (dB/km) MMF-GI 850 2.5 SMF 1300 0.5 SMF 1550 ≤0.25 F-POF (Fluorinated) 800 to 1340 60 ZBLAN 1550 0.02 SMFF (Fluoride glass) 2300 0.005 Typical minimum attenuation values for several fibres
  81. 81. © A.Lobo (2004) 62 2. Light Propagation in Fibres and Related Optical Effects 2.8 Phase velocity and group velocity. phv ω β =g d v d ω β = 1 1 g c v dn n d λ λ = " # −% & ' ( Group Velocity Phase Velocity Guide Group Index (ng) 1 ph c v n =
  82. 82. © A.Lobo (2004) 63 2. Light Propagation in Fibres and Related Optical Effects 2.9 Dispersion: Group delay and Material dispersion. 1 g L d L d L L v d c dk β β τ β ω = = = ⋅ = Group Delay 1 o d D L d τ λ = ⋅ Dispersion Parameter Origin of the Dispersion: Frequency dependence of the mode index n(ω) 2 0 1 0 2 0 1 ( ) ( ) ( ) ( ) ... 2 n c ω β ω ω β β ω ω β ω ω= = + − + − + 1 2 2 3 2 2 2 2 2 2 1 1 1 2 2 g g ndn n c d c v dn d n d n d n c d d c d c d β ω ω ω λ β ω ω ω ω π λ % & = + = =' ( ) * % & = + ⋅ ⋅' ( ) * ! !
  83. 83. © A.Lobo (2004) 64 2. Light Propagation in Fibres and Related Optical Effects 2.9 Dispersion: Group delay and Material dispersion. 2 1 22 2 2d c d n D d c d β π λ β λ λ λ = = − − ⋅!Dispersion Parameter: Group Velocity Dispersion (GVD): 1 2 2 1 1 g g g dvd d d d v v d β β ω ω ω # $ = = = − ⋅' (' ( ) * (Contains the information about the variation of the group velocity with wavelength) 2 g g d L d L t L LD d v d v δ δω β δω δλ δλ ω λ % & % & = = ⋅ = = ⋅( ) ( )( ) ( ) * + * + If a pulse with spectral width (Δδ) input to a fibre with length L, the output pulse broadening is: Limitation on the bit rate: 2 1 or 1t B t BL BLD B δ δ β δω δλ< = ⋅ ⋅ <
  84. 84. © A.Lobo (2004) 65 2. Light Propagation in Fibres and Related Optical Effects 2.9 Dispersion: Group delay and Material dispersion. 2 1 2 1 g mat dn d n D c d c d λ λ λ = ⋅ = − ⋅ Material Dispersion 0gdn dλ = Zero-dispersion wavelength = 1276 nm Negative Dmat Positive Dmat
  85. 85. © A.Lobo (2004) 66 2. Light Propagation in Fibres and Related Optical Effects 2.10 Chromatic Dispersion (CD) 2 2 2 2 2 1 2 ( / )ok n b n n β − = − Normalized propagation constant*: 2 1 2 ( / )ok n b n n β − ≅ − for small Δ 2 (1 )o o effk n b k nβ = + Δ = * See D. Gloge, “Weakly guiding fibers”, Applied Optics 10, 2252-2258 (1971) D. Gloge, “Dispersion in weakly guiding fibers”, Applied Optics 10, 2442-2445 (1971). 2 1 2 1 g mat dn d n D c d c d λ λ λ = ⋅ = − ⋅ 2 2 2 ( ) wg n d Vb D V c dVλ Δ = − mat wgD D D= +
  86. 86. © A.Lobo (2004) 67 2. Light Propagation in Fibres and Related Optical Effects 2.10 Chromatic Dispersion (CD) 2 2 2 ( ) wg n d Vb D V c dVλ Δ = − Waveguide Dispersion
  87. 87. © A.Lobo (2004) 68 2. Light Propagation in Fibres and Related Optical Effects 2.10 Chromatic Dispersion (CD) Anomalous dispersionNormal dispersion λD ≈ 1320 nm
  88. 88. © A.Lobo (2004) 69 2. Light Propagation in Fibres and Related Optical Effects 2.10 Chromatic Dispersion (CD) Anomalous Dispersion (D > 0) Normal Dispersion (D < 0)
  89. 89. © A.Lobo (2004) 70 2. Light Propagation in Fibres and Related Optical Effects 2.10 Chromatic Dispersion (CD) P.K. Bachman et.al., “Dispersion-flattened single-mode fibres prepared with PCVD: Performance, limitations, design and optimization”, J. Lightwave Technology 4, 858-863 (1986)
  90. 90. © A.Lobo (2004) 71 0( ) ( )oD Sλ λ λ= − 4 0 ( ) 1 4 oS D λ λ λ λ " #$ % = −' () * + ,' (- . 2. Light Propagation in Fibres and Related Optical Effects 2.10 Chromatic Dispersion (CD) Typical values for S0 are 0.092 ps/(km·nm2) for SMF, and between 0.06 and 0.08 ps/ (km·nm2) for DSF 1 ( ) gd D L d τ λ λ = ⋅ Slope (ps/km·nm2) (See recommendation ITU-T G.652)
  91. 91. © A.Lobo (2004) 72 2. Light Propagation in Fibres and Related Optical Effects 2.10 Chromatic Dispersion (CD)
  92. 92. © A.Lobo (2004) 73 k h v k h v 2. Light Propagation in Fibres and Related Optical Effects 2.11 Polarization effects and Birefringence. 0 cos( )x x x xE e E t zω β φ= − + ! ! 0 cos( )y y y yE e E t zω β φ= − + ! ! TOTAL x yE E E= + ! ! ! nkn λ π ==β 2 x y POLARIZATION
  93. 93. © A.Lobo (2004) 74 time h v time h v 2. Light Propagation in Fibres and Related Optical Effects 2.11 Polarization effects and Birefringence. -4 -2 2 4 h,(V/m) -3 -2 -1 1 2 3 v,(V/m) 0 0cos( ) cos( )TOTAL x x y yE e E t z e E t zω β ω β π= − + − + ! ! ! LINEAR POLARIZATION
  94. 94. © A.Lobo (2004) 75 2. Light Propagation in Fibres and Related Optical Effects 2.11 Polarization effects and Birefringence. time h v time h v -1 -0.5 0.5 1 h,(V/m) -1 -0.5 0.5 1 v,(V/m) 0 sin( ) cos( )TOTAL x x yE E e t z e t zω β ω β# $= − + −& ' ! ! ! CIRCULAR POLARIZATION
  95. 95. © A.Lobo (2004) 76 2. Light Propagation in Fibres and Related Optical Effects 2.11 Polarization effects and Birefringence. time h v time h v -2 -1 1 2 h,(V/m) -4 -2 2 4 v,(V/m)ELLIPTICAL POLARIZATION 0 1 0 2sin( ) cos( )TOTAL x x y yE e E t z e E t zω β φ ω β φ= − + + − + ! ! !
  96. 96. © A.Lobo (2004) 77 2. Light Propagation in Fibres and Related Optical Effects 2.11 Polarization effects and Birefringence. Birefringence effect of polarized light in the fibre Birefringence Beat Length ( ) or equivalently, 2 ( ) x y x y B n n n n π β λ = − Δ = − 2 BL B π λ β = = Δ π/2 2π0 π/4 3π/4 π 5π/4 3π/2 7π/4
  97. 97. © A.Lobo (2004) 78 2. Light Propagation in Fibres and Related Optical Effects 2.11 Polarization effects and Birefringence. Jones Calculus* - applicable only to polarized waves (*) E. Hecht, “Optics”, 4Ed. Addison Wesley, Chapter 8, 2002. A1 0 0 x y i x in i y E e E E e ϕ ϕ " # = $ % $ %& ' ! xout out yout E E E ! " = # $ % & ! 11 12 21 22 xout xin yout yin E Ea a E Ea a ! " ! "! " =# $ # $# $ % &% & % & 0 0 0 1 1 x x x i ix in xi x E e E E e E e ϕ ϕ ϕ " # " # = =$ % $ % & '& ' ! 45º 11 12 E ! " = # $ % & !02 xi xE eϕ Dividing both terms by:
  98. 98. © A.Lobo (2004) 79 2. Light Propagation in Fibres and Related Optical Effects 2.11 Polarization effects and Birefringence. Jones Matrix from E. Hecht, “Optics”, 4Ed. Addison Wesley, Chapter 8, 2002.
  99. 99. © A.Lobo (2004) 80 2. Light Propagation in Fibres and Related Optical Effects 2.11 Polarization effects and Birefringence. [from D.Derickson, “Fiber Optic Test and Measurement” Prentice Hall, Ch. 6 (1998)] Measurement of the Jones Matrix of an optical element
  100. 100. © A.Lobo (2004) 81 2. Light Propagation in Fibres and Related Optical Effects 2.11 Polarization effects and Birefringence. Stokes Parameters – applicable to both totally or partially polarized light. The elements describe the optical power in particular reference polarization states. 0 1 2 45º 45º 3 total LH LV L L RC LC S I S I I S I I S I I + − " # " # $ % $ %−$ % $ %= $ % $ %− $ % $ % −$ % $ %& ' & ' 2 2 2 1 2 3 0 S S S DOP S + + =
  101. 101. © A.Lobo (2004) 82 2. Light Propagation in Fibres and Related Optical Effects 2.11 Polarization effects and Birefringence. Normalized Stokes Parameters 0 1 20 3 1 1 1 2 3 S Ss Ss S Ss ! "! " # $# $ # $# $ = # $# $ # $# $ # $% & % & 2 2 2 1 2 3DOP s s s= + +
  102. 102. © A.Lobo (2004) 83 2. Light Propagation in Fibres and Related Optical Effects 2.11 Polarization effects and Birefringence. Poincaré Sphere – graphical tool in real, 3D space that allows convenient description of polarized signals and of polarization transformations caused by propagation through devices.
  103. 103. © A.Lobo (2004) 84 2. Light Propagation in Fibres and Related Optical Effects 2.11 Polarization effects and Birefringence. Measurement of retardance θ of a near λ/4-wave retarder [from D.Derickson, “Fiber Optic Test and Measurement” Prentice Hall, Ch. 6 (1998)]
  104. 104. © A.Lobo (2004) 85 2. Light Propagation in Fibres and Related Optical Effects 2.11 Polarization effects and Birefringence. Twisting of a singlemode fibre [from Agilent HP8509C Application Note]
  105. 105. © A.Lobo (2004) 86 2. Light Propagation in Fibres and Related Optical Effects 2.11 Polarization effects and Birefringence. Muller Matrix – applicable to any degree of polarization. 00 01 02 030 0 10 11 12 131 1 20 21 22 232 2 30 31 32 333 3 out in out in out in out in m m m mS S m m m mS S m m m mS S m m m mS S ! " ! "! " # $ # $# $ # $ # $# $= ⋅ # $ # $# $ # $ # $# $ # $# $ # $& '& ' & '
  106. 106. © A.Lobo (2004) 87 2. Light Propagation in Fibres and Related Optical Effects 2.11 Polarization effects and Birefringence. Two polarization modes Ex , Ey of a singlemode fibre © R. Ulrich, TU Hamburg-Harburg
  107. 107. © A.Lobo (2004) 88 2. Light Propagation in Fibres and Related Optical Effects 2.11 Polarization effects and Birefringence. From K.T.V.Grattan & B.T. Meggitt, “Optical Fiber Sensor Technology”, Chapman & Hall (1995)
  108. 108. © A.Lobo (2004) 89 2. Light Propagation in Fibres and Related Optical Effects 2.11 Polarization effects and Birefringence. From K.T.V.Grattan & B.T. Meggitt, “Optical Fiber Sensor Technology”, Chapman & Hall (1995)
  109. 109. © A.Lobo (2004) 90 2. Light Propagation in Fibres and Related Optical Effects 2.12 Polarization Dependence Loss (PDL) . Device Under Test (DUT) Constant Power 100% Polarized Time Pmáx Pmin max min 10logdB P PDL P ! " = # $ % & PDL measures the peak-to-peak difference in transmission for light with various states of polarization.
  110. 110. © A.Lobo (2004) 91 2. Light Propagation in Fibres and Related Optical Effects 2.13 Polarization Mode Dispersion (PMD). PMD is a fundamental property of singlemode optical fibre and components in which signal energy at a given wavelength is resolved into two orthogonal polarization modes of slightly different propagation velocity. The resulting difference in propagation time between polarization modes is called the differential group delay (Δτ). g L d L v d n d n L c c d β τ ω ω ω Δ Δ = = Δ Δ Δ% & = + ⋅( ) * + d L L d φ β φ β τ ω ω Δ = Δ → = = Δ Δ Also, Frequency-domain manifestation
  111. 111. © A.Lobo (2004) 92 2. Light Propagation in Fibres and Related Optical Effects 2.13 Polarization Mode Dispersion (PMD). PMD is characterized by the PMD-vector, Ω(ω), in Stokes space, around which an output state of polarization (SOP), s , rotates when the carrier frequency is changed. ' dS S S dω = = Ω× ! ! !! τΔ = Ω ! And the differential group delay (DGD) is:
  112. 112. © A.Lobo (2004) 93 2. Light Propagation in Fibres and Related Optical Effects 2.13 Polarization Mode Dispersion (PMD). CASE 1 - Ideal fibre section (βx = βy) , , ( ) x in in y in E E E ω " # = $ % & ' ! ( )out in j L in E J E e Eβ ω − $ % $ %= & ' & ' = ! ! ! i ! 0 ( ) 0 j L j L e J e β β ω − − $ % = & ' ( ) ! 0τΔ =
  113. 113. © A.Lobo (2004) 94 2. Light Propagation in Fibres and Related Optical Effects 2.13 Polarization Mode Dispersion (PMD). CASE 2 - linearly birefringent fibre section (βx ≠ βy) , , ( ) x in in y in E E E ω " # = $ % & ' ! 0 ( ) 0 x y j L j L e J e β β ω − − $ % = & ' & '( ) ! 2d L n d L n c π τ ω λ % & Δ = ⋅ Δ) * + , ≅ Δ ⋅ , , ( ) x y j L x in out j L y in e E E e E β β ω − − $ % = & ' & '( ) !
  114. 114. © A.Lobo (2004) 95 2. Light Propagation in Fibres and Related Optical Effects 2.13 Polarization Mode Dispersion (PMD). CASE 3 - Birefringence axes aligned: PM fibre 0 ( ) 0 x y j L total j L e J e β β ω − − $ % = & ' & '( ) ! out out dS S dω = Ω× ! !! Ω ! τΔ = Ω !
  115. 115. © A.Lobo (2004) 96 2. Light Propagation in Fibres and Related Optical Effects 2.13 Polarization Mode Dispersion (PMD). CASE 4 - Random orientation of birefringence axes aligned: standard long-length fibre [ ] [ ] [ ] [ ] [ ] [ ]2 2 1 1total n nJ R J R J R J= ⋅ ⋅⋅⋅⋅ ⋅ ⋅ ⋅ ! ( )out out dS S d ω ω = Ω × ! !!
  116. 116. © A.Lobo (2004) 97 2. Light Propagation in Fibres and Related Optical Effects 2.13 Polarization Mode Dispersion (PMD). • Frequency domain scenario: PMD vector and principal states of polarization (PSP) 1,20 if outout out dS S PSP dω = = ! ! • Time domain scenario: Pulse splitting
  117. 117. © A.Lobo (2004) 98 2. Light Propagation in Fibres and Related Optical Effects 2.13 Polarization Mode Dispersion (PMD). • Frequency domain scenario : frequency dependence of PSP 0( ) ( ) ....ωω ω ωΩ = Ω + Ω Δ + ! ! ! 0 d d ω ω ω ω = Ω Ω = ! ! 1st order approximation is valid within “PSP-bandwidth”: 1 PSPω τ Δ ≅ Δ • Time domain scenario: multi-path pulse transmission [See J.L. Santos, Ph.D. Thesis, Chap.7, Univ. Porto, (1992)]
  118. 118. © A.Lobo (2004) 99 2. Light Propagation in Fibres and Related Optical Effects 2.13 Polarization Mode Dispersion (PMD). 2 2 2 2 3 2 e τ α τ π α Δ −Δ ⋅ with 8τ α πΔ = Probability of finding DGD at value Δτ is given by the Maxwellian density distribution
  119. 119. © A.Lobo (2004) 100 2. Light Propagation in Fibres and Related Optical Effects 2.13 Polarization Mode Dispersion (PMD). Consequences of PMD ❧ DGD (Δτ) causes: ◗ Pulse broadening ◗ Reduction of eye openings / increase in BER ◗ Additional power penalty ◗ Increase of outage probability ❧ Instantaneous Δτ ◗ Is a random variable ◗ It varies due to environment (temnperature, strain) ◗ It can surpass its mean value by far 2 PMD Lτ τΔ = Δ ∝
  120. 120. © A.Lobo (2004) 101 2. Light Propagation in Fibres and Related Optical Effects 2.14 Non-linear Optical Effects. ❧ Self-Phase Modulation (SPM) – pulses distiort as they propagate. ❧ Cross-Phase Modulation (XPM) – pulses interfere with one another ❧ Modulation Instability (MI) – CW beams break into pulses ❧ Solitons – a nonlinear way of transmitting pulses ❧ Four-Wave Mixing (FWM) ❧ Optical Kerr Effect – electric field imposed induces linear birefringence ❧ Stimulated Brillouin Scattering (SBS) – inelastic scattering from acoustic phonons ❧ Stimulated Raman Scattering (SRS) – inelastic scattering from molecular resonances ❧ Supercontinuum Generation (SG) – “white light” generation Parametric Process (light induced modulation) Non-Parametric Process Observed effect
  121. 121. © A.Lobo (2004) 102 2. Light Propagation in Fibres and Related Optical Effects 2.14 Non-linear Optical Effects. Nonlinear optics is a result of anharmonic excitation of the medium. The induced polarization is given by: ( )0 1 2 3 ...P E EE EEEε χ χ χ= ⋅ + ⋅ + ⋅ + ! ! ! ! ! ! ! where χ1, χ2, χ3 are 1st, 2nd, 3rd order susceptibilities. χ2 vanishes in centro-symmetric materials like glass, so the lowest-oder nonlinear term is χ3. One manifestation of this is the nonlinear refractive index: where n2K is the nonlinear Kerr coefficient and is directly related to χ3. In most glasses, n2 is positive, so the refractive index of the material increases at higher intensities. The value of n2K for SiO2 is ~3.2×10-20 m2W-1. 2 0 2Kn n n E= +
  122. 122. © A.Lobo (2004) 103 2. Light Propagation in Fibres and Related Optical Effects 2.14 Non-linear Optical Effects. ❧ Nonlinear Coefficient (γ) – measure of the strength of the nonlinar response of a particular fibre at frequency ω0 with effective area Aeff and n2k known. 2 0K eff n cA ω γ = ❧ Effective Length (Leff) – effective nonlinear length of a fibre with physical length L and loss given by α. 1 L eff e L α α − − = ❧ Nonlinear Length (LNL) – the fibre length required for nonlinear effects to become important, for a given peak pump power. Explicity, the length for development of a phase shift of unity. 0 1 NLL Pγ = ❧ Dispersion Length (Ld) – length over which the pulse length τ0 is significantly dispersed in a fibre with β2. 2 0 2 dL τ β = DEFINITIONS
  123. 123. © A.Lobo (2004) 104 2. Light Propagation in Fibres and Related Optical Effects 2.14 Non-linear Optical Effects. λo Rayleigh radiation (λo) Brillouin radiation (λo±0.08 nm) Raman radiation (λo ±80 nm ) Scattering spectra of an optical fibre Wavelength Energy Incident radiation (λo=1550 nm) 2 s B o nV n l =Anti-Stokes Stokes ElectrostrictionRaman shift ≈ -13 THz @ 1.55 µm Brillouin shift ≈ -11 GHz @ 1.55 µm
  124. 124. © A.Lobo (2004) 105 2. Light Propagation in Fibres and Related Optical Effects 2.14 Non-linear Optical Effects. 2.14.1 Stimulated Raman Scattering (SRS) (Spontaneous) Raman Scattering: a very small amount of light in any molecular is inelastic scattered. A lower-frequency photon is produced, and the extra energy goes into exciting a molecular vibrationsl or rotational mode. Stimulated Raman Scattering (SRS): the lower-frequency radiation beats with the pump beam to provide a field beating at the Raman frequency. This drives the Raman oscillations directly, so that the shifted radiation experiences gain at the expense of the pump beam. 0 P zS SRS S S S dI g I I e I dz α α− = − The growth of the Stokes wave along the fibre in both spontaneous and stimulated emission may be expressed in the form: Raman gain
  125. 125. © A.Lobo (2004) 106 2. Light Propagation in Fibres and Related Optical Effects 2.14 Non-linear Optical Effects. 2.14.1 Stimulated Raman Scattering (SRS) 16 effSRS th SRS eff kA P g L ≅ 17 W km @ 1.55 µm SRS th effP L⋅ ≈ ⋅ Relative polarization factor (1 ≤ k ≤ 2)
  126. 126. © A.Lobo (2004) 107 2. Light Propagation in Fibres and Related Optical Effects 2.14 Non-linear Optical Effects. 2.14.2 Stimulated Brillouin Scattering (SBS) SBS Characteristics: ❧ Low power threshold ❧ Backward propagating Stokes wave ❧ Small Stokes shift (low phonon energy) ❧ Acoustic phonon lifetime is long (10ns), so gain bandwidth is narrow. ❧ Need narrow linewidth pump source for efficient excitation. 21 1 pump effSBS th B SBS eff A P g L ν ν Δ# $ ≅ +& ' Δ( ) 0.03 W km @ 1.55 µm SBS th effP L⋅ ≈ ⋅ Electrostriction
  127. 127. © A.Lobo (2004) 108 2. Light Propagation in Fibres and Related Optical Effects 2.14 Non-linear Optical Effects. 2.14.3 Four-Wave Mixing (FWM) 2 6 3 4 2 2 31024 ( ) eff L ij FWM i j eff L P L PP e n c A α χπ η λ − ' (' ( = ⋅* +* + * +, - , - see A.R. Chraplyvy, Journal Lightwave Technology 8, 1548-1557 (1990).
  128. 128. © A.Lobo (2004) 109 2. Light Propagation in Fibres and Related Optical Effects 2.14 Non-linear Optical Effects. 2.14.4 Self-Phase (SPM) and Cross-Phase Modulation (XPM) Kerr nonlinearity Linear regime 2 effSPM th K eff A P n L λ π ≅ 1.5 W km @ 1.55 µm SPM th effP L⋅ ≈ ⋅ ( )2 2SPM K d n E dt νΔ ∝
  129. 129. © A.Lobo (2004) 110 2. Light Propagation in Fibres and Related Optical Effects 2.14 Non-linear Optical Effects. 2.14.4 Self-Phase (SPM) and Cross-Phase Modulation (XPM) ( )2 0 2 2 0 2 2 2 K K nL L n n E n n n E π φ π φλ λ $ = % ⇒ = +' %= + ( ( ) 0 0 2 0 2 ' ' 2 ' K d dt L d n E dt φ ω ω ω ω ω π ω ω λ = + ⇔ = + ⇒ ⇒ = + ( ) ( ) 2 0 2 0 0 ' ( ) 0 ' ( ) K K d E t dt d E t dt ω ω ω ω ω ω > ⇒ = − < ⇒ = + Pulse is CHIRPED
  130. 130. © A.Lobo (2004) 111 2. Light Propagation in Fibres and Related Optical Effects 2.14 Non-linear Optical Effects. Limitations over WDM Limitations on the channel power imposed by four nonlinear effects (assumed λ=1.55 µm and fibre loss of 0.2 dB/km) see A.R. Chraplyvy, Journal Lightwave Technology 8, 1548-1557 (1990).
  131. 131. © A.Lobo (2004) 112 2. Light Propagation in Fibres and Related Optical Effects 2.14 Non-linear Optical Effects. Soliton Propagation 2 0 2 3.11 FWHM P T β γ ! Fundamental soliton peak power
  132. 132. Types of Optical Fibre FIBRE OPTIC TECHNOLOGY COURSE António Lobo Prof. Associado (UFP)
  133. 133. © A.Lobo (2004) 2 3. Types of Optical Fibre 3.1 Optical Fibre Fabrication. 3.2 Standard Singlemode Fibre. 3.3 Step-Index and Graded-Index Multimode Fibre. 3.4 Dispersion Shifted Fibre. 3.5 Dispersion Flattened Fibre. 3.6 Non-Zero Dispersion Shifted Fibre. 3.7 Dispersion Compensating Fibre. 3.8 E-Band Fibre. 3.9 Polarization Maintaining Fibres: PANDA, Bow-Tie, Elliptical and Side-Hole types. 3.10 Rare-Earth Doped Fibres: Erbium, Ytterbium, Neodymium, Praseodymium. 3.11 Long Wavelength Fibres (Fluoride and Chalcogenide). 3.12 Plastic Fibre. 3.13 Hollow Fibre. 3.14 Photonic Crystal Fibre.
  134. 134. © A.Lobo (2004) 3 3. Types of Optical Fibre 3.1 Optical Fibre Fabrication Fibre Drawing (Double-Crucible Method) Cabelte S.A.
  135. 135. © A.Lobo (2004) 4 3. Types of Optical Fibre 3.1 Optical Fibre Fabrication Modified Chemical Vapour Deposition (MCVD) Prof. J. Knight, Optoelectronics Group, Dept. Physics, University of Bath (UK) & Blaze Photonics Ltd. (UK)
  136. 136. © A.Lobo (2004) 5 3. Types of Optical Fibre 3.2 Standard Singlemode Fibre (SMF) ❧ Generally standard singlemode fibre, have a step-index refractive profile. ❧ Main disadvantages: coupling difficulties with incoherent optical sources (like LEDs), small NA ❧ One of the most advanced commercial singlemode fibres: SMF-28 (by Corning) Main Characteristic (Measurement methods comply with ITU-T G.650 and IEC 793-1) ❧ Attenuation coefficient: ≤0.40 dB/km @ 1310 nm , ≤0.3 dB/km @ 1550 nm ❧ NA = 0.13 ❧ Cut-off wavelength: < 1260 nm ❧ Core diameter: 8.3 µm ❧ MFD: 9.30±0.50 µm @ 1310 nm, 10.50 ±1.00 µm @ 1550 nm ❧ Zero dispersion wavelength: 1301.5 nm ≤ λ0D ≤ 1321.5 nm ❧ Zero dispersion slope (So): 0.092 ps/nm2#km ❧ PMD (máx): ≤ 0.2 ps/√km ❧ Refractive index difference (Δ): 0.36% ❧ Effective group index refraction (Ng): 1.4675 @ 1310 nm, 1.4681 @ 1550 nm
  137. 137. © A.Lobo (2004) 6 3. Types of Optical Fibre 3.2 Standard Singlemode Fibre (SMF) SMF-28 From Plasma Optical Fiber B.V. (Eindhoven)
  138. 138. © A.Lobo (2004) 7 3. Types of Optical Fibre 3.2 Standard Singlemode Fibre (SMF) Depressed cladding 1300 nm Optimized SMF
  139. 139. © A.Lobo (2004) 8 3. Types of Optical Fibre 3.3 Step-Index (SI-MMF) and Graded-Index Multimode Fibre (GI-MMF) ❧ SI-MMF are very similar to step-index SMF, but differ in their core diameter. ❧ SI-MMF have fibre core diameters around 50 to 62.5 µm, and cladding with 125 µm. ❧ GI-MMF are defined by a progressive decrease of refractive index from the centre of the core with radius a toward the cladding, while still maintaining the fundamental relationship: n1 > n2. ❧ Different modes can interfere with each other generating modal noise. ❧ Refractive index profiles difficult to realize in practice → expensive and some flutctuations from ideal profile are inevitable. 1( ) 1 2 y r n r n a ! " = − Δ% & ' ( Where y is the core characteristic refractive index profile: ❧ y = ∞ for step-index profile ❧ y = 1 for triangular profile ❧y = 2 for parabolic profile From Plasma Optical Fiber B.V. (Eindhoven)
  140. 140. © A.Lobo (2004) 9 3. Types of Optical Fibre 3.4 Dispersion Shifted Fibre (DSF) ❧ DSF is a singlemode fibre with very low dispersion at 1550 nm operating wavelength. Main Characteristics (Measurement methods comply with ITU-T G.650 and IEC 793-1) ❧ Attenuation coefficient: ≤0.25 dB/km @ 1550 nm Cut-off wavelength: ≤ 1260 nm ❧ NA = 0.17 Core diameter: 8.3 µm MFD: 8.10 ±0.65 µm @ 1550 nm ❧ Zero dispersion wavelength: 1535 nm ≤ λ0D ≤ 1565 nm ❧ Zero dispersion slope (So): 0.085 ps/(nm2·km) ❧ Total dispersion coefficient: ≤ 2.7 ps/(nm·km) ❧ PMD (máx): ≤ 0.5 ps/√km
  141. 141. © A.Lobo (2004) 10 3. Types of Optical Fibre 3.5 Dispersion Flattened Fibre (DF-SMF) ❧ DF-SMFF is a singlemode fibre with very low dispersion simultaneously at 1330 nm and 1550 nm operating wavelengths. Main Characteristics ❧ Attenuation coefficient: ≤0.5 dB/km @ 1310 nm , ≤0.3 dB/km @ 1550 nm ❧ Dispersion coefficient: ≤3.5 ps/(nm·km) @ 1310 nm , ≤ 3.5 ps/(nm·km) @ 1550 nm From Plasma Optical Fiber B.V. (Eindhoven)
  142. 142. © A.Lobo (2004) 11 3. Types of Optical Fibre 3.6 Non-Zero Dispersion Shifted Fibre (NZ-DSF) ❧ NZ-DSF is a singlemode fibre specially designed for Dense Wavelength Division Multiplexing (DWDM) technology. Non-linear effects such as Four-Wave Mixing (FWM) are minimized, by moving the zero-dispersion wavelength outside the band used by EDFAs.. Main Characteristics ❧ Dispersion coefficient: -3.5 to -0.1 ps/(nm·km) over the range 1530 to 1560 nm ❧ PMD: ≤ 0.5 ps/√km ❧ Attenuation coefficient: ≤0.25 dB/km @ 1550 nm From Corning Corp.
  143. 143. © A.Lobo (2004) 12 3. Types of Optical Fibre 3.6 Non-Zero Dispersion Shifted Fibre (NZ-DSF)
  144. 144. © A.Lobo (2004) 13 3. Types of Optical Fibre 3.6 Non-Zero Dispersion Shifted Fibre (NZ-DSF) Large Area NZ-DSF Fibre nonlinearities are inversely proportional to the core effective area, and so, increasing the effective area will ultimately reduce nonlinearities through the reduction of light density propagating along the core. The large effective area NZ-DSF is based on a triangular core and raised index ring. Corning Corp. developed the LEAF NZ-DSF with a effective area of 72 µm2 as compared with to 55 µm2 standard NZ-DSF. Shifts the zero dispersion wavelength to the 1550 nm range Enhances the cross-sectional effective area while simultaneously achieving a relative low bending loss Refractive Index Profile
  145. 145. © A.Lobo (2004) 14 3. Types of Optical Fibre 3.6 Non-Zero Dispersion Shifted Fibre (NZ-DSF) Large Area NZ-DSF 2K input eff n LP Nonlinearity A → From Corning Corp.
  146. 146. © A.Lobo (2004) 15 3. Types of Optical Fibre 3.6 Non-Zero Dispersion Shifted Fibre (NZ-DSF) Increasing the optical power on a SMF (G.652) 10,6 10,7 10,8 10,9 11,0 11,1 11,2 -45 -40 -35 -30 -25 -20 -15 -10 νTLS@25.7ºC νBrillouin OpticalPower(dBm) Frequency Shift (GHz) VOA=6dB 9,0 9,5 10,0 10,5 11,0 11,5 12,0 -45 -40 -35 -30 -25 -20 -15 -10 -5 0 VOA=5dB νTLS@25.5ºC νBrillouin OpticalPower(dBm) Frequency Shift (GHz) With permission of M. Melo and M.O. Berendt, Multiwave Networks Lda.. (Portugal)
  147. 147. © A.Lobo (2004) 16 3. Types of Optical Fibre 3.7 Dispersion Compensating Fibre (DCF) ❧ DCF is a singlemode fibre with very high waveguide dispersion. The overall dispersion of this fibre is opposite in sign and much larger in magnitude than that of standard fibre, so they can be used to cancel out or compensate the dispersion in SMF. Main Characteristics ❧ Dispersion coefficient (typ.): -80 to -150 ps/(nm·km) @ 1550 nm ❧ Dispersion slope: -0.40 ps/(nm2·km) @ 1550 nm ❧ PMD: 0.25~0.5 ps/√km ❧ Attenuation: ≤0.55 dB/km @ 1550 nm a b From Fujikura Technical Review, 2001
  148. 148. © A.Lobo (2004) 17 3. Types of Optical Fibre 3.8 E-Band Fibre (E-SMF) E-SMF is a singlemode fibre specially designed for the Extend-Band (or E-Band) transmission window, which is located at the wavelength range region from 1360 nm to 1460 nm, but with possibility to operate also in the other bands, such as, C-band. Main Characteristics: ❧ Attenuation (máx): 0.35 dB/km @ 1310 nm , 0.31 dB/km @ 1385 nm, 0.22 dB/km @ 1550 nm ❧ Zero dispersion wavelength: 1300 nm ≤ λ0D ≤ 1322 nm ❧ Zero dispersion slope (So): 0.092 ps/nm2#km ❧ PMD (typ.): ≤ 0.08 ps/√km Commercial Examples: ❧ Corning SMF-28e® fibre → Corning Corp. ❧ AllWave® fibre → Lucent Technologies Inc. ❧ LightScope ZWP™ fibre → CommScope Inc. ❧ TeraSPEED ™ fibre → Avaya Inc. ❧ BBG ® -SMF-WF fibre → Hitachi Cable Ltd. DEFINITION OF SIGNAL WAVELENGTH BAND (ITU-T) Band Name Wavelength (nm) O-band (Original) 1260 - 1360 E-band (Extended) 1360 - 1460 S-band (Short Wavelength) 1460 - 1530 C-band (Conventinal) 1530 - 1565 L-band (Long Wavelength) 1565 - 1625 U-band (Ultralong Wavelength) 1625 - 1675
  149. 149. © A.Lobo (2004) 18 3. Types of Optical Fibre 3.8 E-Band Fibre (E-SMF) SMF E-SMF (5th window) “water peak” around 1385 nm
  150. 150. © A.Lobo (2004) 19 3. Types of Optical Fibre 3.9 Polarization Maintaining Fibre (PMF) PMF is a singlemode fibre specially designed to maintain the state of polarization (SOP) of guided polarized light. In the most common optical fiber telecommunications applications, PM fiber is used to guide light in a linearly polarized state from one place to another. Commercial Types: ❧ PANDA fibre ❧ BowTie fibre ❧ Elliptical shape (core or cladding ) fibre ❧ D-shaped fibre ❧ Side-Hole fibre ❧ Side-Pit fibre ❧ Spun fibre 2 ( )F SL n n π φ λ Δ = Δ − Birefringence (typ.): 2×10-4 to 7 ×10-4
  151. 151. © A.Lobo (2004) 20 3. Types of Optical Fibre 3.9 Polarization Maintaining Fibres (PMF) Fast axis Slow axis Bow Tie PANDA Side-Hole Elliptical Stressed Cladding D-shaped Elliptical Core Elliptical Core
  152. 152. © A.Lobo (2004) 21 3. Types of Optical Fibre 3.10 Rare-Earth Doped Fibres. For more details see: www.webelements.com ❑ Erbium (Er) ❑ Ytterbium (Yb) ❑ Neodymium (Nd) ❑ Praseodymium (Pr) ❑ Thulium (Tm) ❑ Holmium (Ho) Lanthanides are best characterized by observation that they possess incomplete inner 4f levels and, to a large extent, they form ions that exist solely in the 3+ state. This state is formed by the removal of two outer 6s electrons and one inner 4f electron. What are Rare Earth Ions?
  153. 153. © A.Lobo (2004) 22 3. Types of Optical Fibre 3.10 Rare-Earth Doped Fibres. Optical properties of the Rare Earth Ions Fluorescence Up-Conversion
  154. 154. © A.Lobo (2004) 23 3. Types of Optical Fibre 3.10 Rare-Earth Doped Fibres. Erbium Doped Fibre (ErDF) ABSORPTION BANDS: ❧ 520 nm ❧ 650 nm ❧ 800 nm ❧ 980 nm (free from excited-state absorption ESA) ❧1480 nm
  155. 155. © A.Lobo (2004) 24 3. Types of Optical Fibre 3.10 Rare-Earth Doped Fibres. Neodymium Doped Fibre (NdDF) ABSORPTION BANDS: ❧ 520 nm ❧ 590 nm ❧ 820 nm
  156. 156. © A.Lobo (2004) 25 3. Types of Optical Fibre 3.10 Rare-Earth Doped Fibres. Thulium Doped Fibre (TmDF) ABSORPTION BANDS: ❧ 520 nm ❧ 590 nm ❧ 820 nm
  157. 157. © A.Lobo (2004) 26 3. Types of Optical Fibre 3.10 Rare-Earth Doped Fibres. Holmium Doped Fibre (HoDF) Pumped at 640 nm
  158. 158. © A.Lobo (2004) 27 3. Types of Optical Fibre 3.10 Rare-Earth Doped Fibres. Praseodymium Doped Fibre (PrDF)
  159. 159. © A.Lobo (2004) 28 3. Types of Optical Fibre 3.10 Rare-Earth Doped Fibres. Ytterbium Doped Fibre (YbDF) ABSORPTION BANDS: ❧ 520 nm ❧ 590 nm ❧ 840 nm This transition is significantly broadened
  160. 160. © A.Lobo (2004) 29 3. Types of Optical Fibre 3.11 Long Wavelength Fibres (Fluoride and Chalcogenide). ❧ Fluorozirconate fibers transmit light between 0.4 and 5 µm. ❧ Silver Halide compounds fiber (AgBrCl) transmit light between 3 and 16 µm. ❧ Synthetic crystalline sapphire (Al2O3) can transmit light between 0.5 and 3.1 µm
  161. 161. © A.Lobo (2004) 30 3. Types of Optical Fibre 3.12 Plastic Fibre (POF). Fluorinated POF characteristics: ❧ Attenuation: <150 dB/km @ 650 nm 1.5 mm diameter ❧ NA: 0.4 ❧ Index profile: Step-index and also GI-index PMMA – Polymethyl Metacrylate
  162. 162. © A.Lobo (2004) 31 3. Types of Optical Fibre 3.13 Hollow Fibre (HOF). Hollow optical fiber with an inner core ring Hollow silica tube filled with HCBD (hexachlorobutadiene) D. N. Payne and W. A. Gambling, Electronics Letters, vol. 8, p374, 1972 K. Oh, FOR Lab., Dept. of Information and Communications Kwangju Institute of Science and Technology (K-JIST)
  163. 163. © A.Lobo (2004) 32 3. Types of Optical Fibre 3.13 Hollow Fibre (HOF). K. Oh, FOR Lab., Dept. of Information and Communications Kwangju Institute of Science and Technology (K-JIST) S. Choi, K. Oh, W. Shin, U. C. Ryu, Electron. Lett., vol. 37, no.13 , pp.823-825, Jun. 2001. New type of Mode Coupler based on tapered HOF
  164. 164. © A.Lobo (2004) 33 3. Types of Optical Fibre 3.14 Photonic Crystal Fibre (PCF). Stack-and-Draw Fabrication Process Prof. J. Knight, Optoelectronics Group, Dept. Physics, University of Bath (UK) & Blaze Photonics Ltd. (UK)
  165. 165. © A.Lobo (2004) 34 3. Types of Optical Fibre 3.14 Photonic Crystal Fibre (PCF). How can one make this….? Differential Pressure ! Prof. J. Knight, Optoelectronics Group, Dept. Physics, University of Bath (UK) & Blaze Photonics Ltd. (UK)
  166. 166. © A.Lobo (2004) 35 3. Types of Optical Fibre 3.14 Photonic Crystal Fibre (PCF). Extrusion (Soft glass) Prof. J. Knight, Optoelectronics Group, Dept. Physics, University of Bath (UK) & Blaze Photonics Ltd. (UK)
  167. 167. © A.Lobo (2004) 36 3. Types of Optical Fibre 3.14 Photonic Crystal Fibre (PCF). Prof. J. Knight, Optoelectronics Group, Dept. Physics, University of Bath (UK) & Blaze Photonics Ltd. (UK)
  168. 168. © A.Lobo (2004) 37 3. Types of Optical Fibre 3.14 Photonic Crystal Fibre (PCF). Prof. J. Knight, Optoelectronics Group, Dept. Physics, University of Bath (UK) & Blaze Photonics Ltd. (UK)
  169. 169. © A.Lobo (2004) 38 3. Types of Optical Fibre 3.14 Photonic Crystal Fibre (PCF). Prof. P.St Russell, Head of Optoelectronics Group, Dept. Physics, University of Bath (UK) & CSO of Blaze Photonics Ltd. (UK) Endlessly SMF PM fibre Multicore PCF Highly Nonlinearity PCF Hollow Core PCF Hollow Core Visible PCF
  170. 170. © A.Lobo (2004) 39 3. Types of Optical Fibre 3.14 Photonic Crystal Fibre (PCF). Random Hole Fibre (RHOF) Virginia Polytechnic Institute and State University , USA High NA PCF Crystal Fiber A/S (Denmark) High NA Yb-Doped PCF Crystal Fiber A/S (Denmark)
  171. 171. © A.Lobo (2004) 40 3. Types of Optical Fibre
  172. 172. Passive Fibre Optic Devices FIBRE OPTIC TECHNOLOGY COURSE António Lobo Prof. Associado (UFP)
  173. 173. © A.Lobo (2004) 2 4. Passive Fibre Optic Devices 4.1 Directional Couplers: Splitters and Combiners. 4.2 WDM Couplers. 4.3 Tap Couplers 4.4 Biconical Fibre Filter. 4.5 Fibre Bragg Gratings. 4.6 Long Period Fibre Gratings. 4.7 Gain Equalizing Filters. 4.8 Mach-Zehnder and Michelson Filters (Interleavers). 4.9 Fibre Ring Filters. 4.10 Fibre Fabry-Perot Filters. 4.11 Fibre Polarizer. 4.12 Fibre Depolarizer. 4.13 Fibre Polarization Controller. 4.14 Fibre Optic Attenuator.
  174. 174. © A.Lobo (2004) 3 4. Passive Fibre Optic Devices 4.1 Directional Couplers: Splitters and Combiners Directional Coupler. Theory of Coupled Modes © R. Ulrich, TU Hamburg-Harburg Between the waveguides 1 and 2 optical power is coupled continuously back and forth (in both directions, 1→2 and 2→1). This results in a periodic spatial variation of the powers Pi(z) in the waveguides (i=1,2) with a periodicity Lc (coupling length)
  175. 175. © A.Lobo (2004) 4 4. Passive Fibre Optic Devices 4.1 Directional Couplers: Splitters and Combiners Theory of Coupled Modes: The coupled pendulums
  176. 176. © A.Lobo (2004) 5 4. Passive Fibre Optic Devices 4.1 Directional Couplers: Splitters and Combiners Directional Coupler: Coupled Mode Theory (*) Coupled Wave Equations: and 2 1 2 1 ( )1 12 2 ( )2 21 1 j z j z dA j A e dz dA j Ae dz β β β β κ κ − − + − = − = − 12 21κ κ κ= = (*) for more detailed analysis see K. Okamoto, Fundamentals of Optical Waveguides, Academic Press (2001) – Chap.4 mode coupling coeff. (coupler with geometric symmetry) Solutions assumed in the form: (for codirectional couplers: β1>0, β2>0) 1 1 1 2 2 2 ( ) ( ) jqz jqz j z jqz jqz j z A z a e a e e A z a e a e e δ δ + − − − + − − ⎡ ⎤= +⎣ ⎦ ⎡ ⎤= +⎣ ⎦ With initial conditions: 1 1 1 2 2 2 (0) (0) a a A a a A + − + − + = + =2 1( ) 2 β β δ − = and 2 2 q κ δ= +
  177. 177. © A.Lobo (2004) 6 4. Passive Fibre Optic Devices 4.1 Directional Couplers: Splitters and Combiners Directional Coupler: Coupled Mode Theory(*) Substituting the assumed solutions into the coupled wave equations and applying the initial conditions, we obtain: (*) for more detailed analysis see K. Okamoto, Fundamentals of Optical Waveguides, Academic Press (2001) – Chap.4 1 1 2 2 1 2 ( ) cos( ) sin( ) (0) sin( ) (0) ( ) sin( ) (0) cos( ) sin( ) (0) j z j z A z qz j qz A j qz A e q q A z j qz A qz j qz A e q q δ δ δ κ κ δ −⎡ ⎤⎛ ⎞ = + −⎢ ⎥⎜ ⎟ ⎝ ⎠⎣ ⎦ ⎡ ⎤⎛ ⎞ = − + −⎢ ⎥⎜ ⎟ ⎝ ⎠⎣ ⎦
  178. 178. © A.Lobo (2004) 7 4. Passive Fibre Optic Devices 4.1 Directional Couplers: Splitters and Combiners Directional Coupler: Coupled Mode Theory For the most practical case, in which light is coupled into waveguide 1 only at z=0, we have the conditions of A1(0)=Ao and A2(0)=0. Then the optical power flow along the z-direction is given by: 2 1 2 1 2 2 2 2 2 2 ( ) ( ) 1 sin ( ) ( ) ( ) sin ( ) o o A z P z F qz A A z P z F qz A = = − = = 2 1( ) 2 β β δ − = 2 2 q κ δ= + ( ) 2 2 1 1 F q κ δ κ ⎛ ⎞ = =⎜ ⎟ ⎝ ⎠ + Power-coupling efficiency
  179. 179. © A.Lobo (2004) 8 4. Passive Fibre Optic Devices 4.1 Directional Couplers: Splitters and Combiners Directional Coupler 0 1 2 3 4 5 6 0 0.2 0.4 0.6 0.8 1 0 1 2 3 4 5 6 0 0.2 0.4 0.6 0.8 1 0 1Fδ = ⇒ = 0.5Fδ κ= ⇒ = P1 P1 P2 P2 Normalized distance (qz) Normalized distance (qz) For 50% coupling it is a necessary condition that δ ≤ κ 2 22 2 cL q π π κ δ = = + Coupling Length: Lc Lc/2 NormalizedPowers
  180. 180. © A.Lobo (2004) 9 4. Passive Fibre Optic Devices 4.1 Directional Couplers: Splitters and Combiners Directional Fibre Coupler Side-Polished coupler (adjustable CR) Fused coupler (fixed CR, possibly λ-dependent) © R. Ulrich, TU Hamburg-Harburg
  181. 181. © A.Lobo (2004) 10 4. Passive Fibre Optic Devices 4.1 Directional Couplers: Splitters and Combiners © C. Hentschel,, HP GmbH
  182. 182. © A.Lobo (2004) 11 4. Passive Fibre Optic Devices 4.1 Directional Couplers: Splitters and Combiners Combiner Splitter
  183. 183. © A.Lobo (2004) 12 4. Passive Fibre Optic Devices 4.1 Directional Couplers: Splitters and Combiners 1 3 (dB) 10log P CR P ⎛ ⎞ = ⎜ ⎟ ⎝ ⎠ Coupling Ratio (CR) By varying the parameters δ and κ it is possible to adjust CR in a very wide range.
  184. 184. © A.Lobo (2004) 13 4. Passive Fibre Optic Devices 4.2 WDM Couplers. © R. Ulrich, TU Hamburg-Harburg Normal -3dB coupler at 1550 nm has interaction coupling length is typically 0.9 mm, whereas for a WDM coupler that length can be from 100 to 500 mm. Lc is depends on the optical wavelength λ
  185. 185. © A.Lobo (2004) 14 4. Passive Fibre Optic Devices 4.3 Tap Couplers. Tap Coupler Pin (95 to 99%) Pin (5 to 1%) Pin Used for monitor
  186. 186. © A.Lobo (2004) 15 4. Passive Fibre Optic Devices 4.4 Biconical Fibre Filter. n1 n2 n3 Refraction Index Profile Core Int. Cladding Ext. Cladding Biconical Filter 1487 1507 1527 1547 1567 1587 -68 -66 -64 -62 -60 TransmittedPower(dBm) Wavelength (nm) Depressed-cladding fibre 1 2 1 sin ( 2 fT m π λ λ ⎡ ⎤⎛ ⎞ ≈ + −⎜ ⎟⎢ ⎥Λ⎝ ⎠⎣ ⎦ A.B. Lobo Ribeiro, Ph.D. thesis, FCUP (1996) • A.C. Boucouvalas, J. Lightwave Technol. 3, 1151-1158 (1985). • A.C. Boucouvalas and G Georgiou, IEE Proc. 134, Pt.J, 191-195 (1987)
  187. 187. © A.Lobo (2004) 16 4. Passive Fibre Optic Devices 4.5 Fibre Bragg Grating. 2B effnλ = Λ Periodic refraction index change Bragg Condition
  188. 188. © A.Lobo (2004) 17 4. Passive Fibre Optic Devices 4.5 Fibre Bragg Grating. 4 2 effn λ Λ = λ1 λ2 λ3 λ4 λ1 λ2 λ3 λ4 2 ( ) coseff zn z n n z π δ ⎛ ⎞ = + ⎜ ⎟ Λ⎝ ⎠ 4 2 effnλ = Λ 2 tanh z peak B L n R π δ λ ⎛ ⎞⋅ = ⎜ ⎟ ⎝ ⎠ 2 2 2 2 B z B eff B L n n L λ π δ λ π λ ⎛ ⎞ Δ = + ⎜ ⎟ ⎝ ⎠ L Peak Reflectivity Stop-Band Width (FWHM) Rpeak ΔλB
  189. 189. © A.Lobo (2004) 18 4. Passive Fibre Optic Devices 4.5 Fibre Bragg Grating. Fibre Bragg Grating: Coupled Mode Theory(*) (*) for more detailed analysis see R. Kashyap, Fiber Bragg Gratings, Academic Press (1999) – Chap.4 2 2 2 2 2 2 sinh ( ) ( ) cosh ( ) L R L α λ ρ α β Ω = = Ω − Δ 2 2 2 2 z eff eff n n n π δ α β π π β λ ⋅ Ω = Λ = Ω − Δ ⎛ ⎞ ⎛ ⎞ Δ = −⎜ ⎟ ⎜ ⎟ Λ⎝ ⎠⎝ ⎠ 2 (arg ) ( ) 2 d c d λ ρ τ λ π λ = − L = 20 mm sinh( ) sinh( ) cosh( ) L L i L α ρ β α α α −Ω = Δ − Group delay: Reflectivity: ΩL = 4
  190. 190. © A.Lobo (2004) 19 4. Passive Fibre Optic Devices 4.5 Fibre Bragg Grating. Chirped Fibre Bragg Grating (CFBG) (*) for more detailed analysis see R. Kashyap, Fiber Bragg Gratings, Academic Press (1999) – Chap.4 2chirp eff chirpnλΔ = ΔΛ 0( ) 2 ( ) G chirp g L v λ λ τ λ λ − ≈ ⋅ Δ λ1 λ2 λ3 Pulse compression after CFBG λ1 λ2 λ3 In most fibre at 1550 nm, short wavelength light tends to travel faster Λ L
  191. 191. © A.Lobo (2004) 20 4. Passive Fibre Optic Devices 4.5 Fibre Bragg Grating. Chirped Fibre Bragg Grating (CFBG) (*) for more detailed analysis see R. Kashyap, Fiber Bragg Gratings, Academic Press (1999) – Chap.4 Uniform Grating Chirped Grating Chirped Grating with Apodization ( )( ) cos ( )eff zn z n n z zδ κ= + ⋅ δnz z
  192. 192. © A.Lobo (2004) 21 4. Passive Fibre Optic Devices 4.6 Long-Period Fibre Grating. LPG promotes coupling between the propagating core mode and co-propagating cladding modes ΛLPG , ,( )LPG i eff clad i LPGn nλ = − Λ The long-period grating (LPG) has a period typically in the range 100 µm to 1 mm L = 10mm, ΛLPG = 450 µm (SMF-28 fibre)
  193. 193. © A.Lobo (2004) 22 4. Passive Fibre Optic Devices 4.6 Long-Period Fibre Grating. 2FBG effnλ = Λ , ,( )LPG i eff clad i LPGn nλ = − Λ
  194. 194. © A.Lobo (2004) 23 4. Passive Fibre Optic Devices 4.6 Long-Period Fibre Grating. Concatenated LPGs
  195. 195. © A.Lobo (2004) 24 4. Passive Fibre Optic Devices 4.7 Gain Equalizing Filter. © Teraxion Inc. Gain Flattening Filter (GFF) with Concatenated Chirped-FBG (*) (*) M. Rochette, M. Guy, S. LaRochelle, J. Lauzon and F. Trépanier, Photonics Technology Letters 11, 536-538 (1999).
  196. 196. © A.Lobo (2004) 25 4. Passive Fibre Optic Devices 4.7 Gain Equalizing Filter. K. Mizuno et.al., Furukawa Review no.19, 53-58 (2000).
  197. 197. © A.Lobo (2004) 26 4. Passive Fibre Optic Devices 4.7 Gain Equalizing Filter. Comparison of GFF technologies Source: Teraxion Inc.
  198. 198. © A.Lobo (2004) 27 4. Passive Fibre Optic Devices 4.8 Mach-Zehnder and Michelson Filters (Interleavers). 0 1 2 3 4 0 1 0 4π3π2ππ λ/2 Pontos de quadratura Iout /Iin φ (radianos) high sensitivity points Mach-Zehnder Michelson 1 2 1 2 1 2 2 ( ) 1 ( ) cos ( ) out I I I I I I I γ τ φ ⎡ ⎤ = + ⋅ ± ⋅⎢ ⎥ +⎢ ⎥⎣ ⎦ 2 n L π φ λ = Δ 1 2L L LΔ = − 1 22( )L L LΔ = −
  199. 199. © A.Lobo (2004) 28 4. Passive Fibre Optic Devices 4.8 Mach-Zehnder and Michelson Filters (Interleavers). Optical interleavers • Channel spacing management via optical interferometry (e.g., Michelson, Mach-Zehnder) e.g. from 25 GHz to 50 GHz, or vice versa. • Interleavers are needed in density populated WDM systems with 2.5 Gbit/s, 10 Gbit/s and even 40 Gbit/s transmitter/receivers
  200. 200. © A.Lobo (2004) 29 4. Passive Fibre Optic Devices 4.8 Mach-Zehnder and Michelson Filters (Interleavers). Cascaded Mach-Zehnders: 16-Channel Frequency Selector 0 1 2 3 4 5 6 0.2 0.4 0.6 0.8 1 0 1 2 3 4 5 6 0 0.2 0.4 0.6 0.8 1 MZ1 ΔL 2ΔL 4ΔL 8ΔL MZ2 MZ3 MZ4
  201. 201. © A.Lobo (2004) 30 4. Passive Fibre Optic Devices 4.8 Mach-Zehnder and Michelson Filters (Interleavers). Cascaded Mach-Zehnders: 1×4 Demultiplexer 0 1 2 3 4 5 6 0 0.2 0.4 0.6 0.8 1 0 1 2 3 4 5 6 0 0.2 0.4 0.6 0.8 1 MZ1 ΔL MZ2 MZ3 ΔL/2 ΔL/2 λ1, λ2, λ3, λ4 λ1 λ3 λ2 λ4
  202. 202. © A.Lobo (2004) 31 4. Passive Fibre Optic Devices 4.9 Fibre Ring Filter. Ring (direct coupled) 0 180 360 540 720 0 1 4π3ππ 2π0 k = 0.5 k = 0.2 k = 0.1 Iout /Iin φ (radianos) 2 2 2 (1 ) 1 4(1 )sin ( / 2) out in k I I k k δ φ ⎡ ⎤ = − −⎢ ⎥− −⎣ ⎦ 2 (1 ) L k e α δ − = − Ring: Direct coupled Phase (!) NormalizedTransmittedPower k - power coupling coefficient of the coupler (1-δ) – power coupling loss of the coupler α – attenuation coeff. of the fibre ring L – ring length Iin Iout
  203. 203. © A.Lobo (2004) 32 0 180 360 540 720 0 1 (a) Acoplamento Cruzado k = 0.5 k = 0.8 k = 0.9 I out /I in φ (radianos) 4π3π2ππ0 4. Passive Fibre Optic Devices 4.9 Fibre Ring Filter. 2 2 2 (1 ) (1 ) 1 (1 ) 4 sin ( / 2 / 4) out in k I I k k δ φ π ⎡ ⎤− = − −⎢ ⎥− − −⎣ ⎦ 2 (1 ) L k e α δ − = − Phase (!) NormalizedTransmittedPower Ring (cross-coupled) Ring: Cross-coupled •  An advantage of this configuration is that the entire ring can be made of one fibre, i.e., without cutting and splicing the fibre Iin Iout
  204. 204. © A.Lobo (2004) 33 4. Passive Fibre Optic Devices 4.9 Fibre Ring Filter. Fibre Ring Filter: Sagnac Interferometer (*) (*) X. Fang, H.Ji, C.T. Allen, K. Demarest and L. Pelz, IEEE Photonics Technology Letters 9, 458-460 (1997). PMF SMF 3 dB 0 10 20 30 40 50 60 0 0.2 0.4 0.6 0.8 1 2 ( ) sin 2 out in I I φ γ τ ⎛ ⎞ = ⋅ ⎜ ⎟ ⎝ ⎠ Phase (!) NormalizedTransmittedPower Iin Iout
  205. 205. © A.Lobo (2004) 34 4. Passive Fibre Optic Devices 4.10 Fibre Fabry-Perot Filter. L M M 0 180 360 540 720 0 1 4π3π2ππ0 R = 80% R = 50% R = 25% R = 4% Iout /Iin φ (radianos) NormalizedTransmittedPower Phase (!) 2 2 2 1 1 2 1 sin 1 2 A R T R R φ ⎛ ⎞ −⎜ ⎟ −⎝ ⎠= ⎛ ⎞ ⎛ ⎞ +⎜ ⎟ ⎜ ⎟ − ⎝ ⎠⎝ ⎠ T 2 2 4 1 sinnL n π θ φ λ − = For normal incidence: θ = 0º 1 FSR R Finesse FWHM R π = = − A – Absorption loss of the mirror R – Reflectivity of the mirror For more detailed analysis see E. Hecht, Optics, 4ed. Chap.9. FSR
  206. 206. © A.Lobo (2004) 35 4. Passive Fibre Optic Devices 4.10 Fibre Fabry-Perot Filter. www.micronoptics.com
  207. 207. © A.Lobo (2004) 36 4. Passive Fibre Optic Devices 4.11 Fibre Polarizer. Surface Plasmon Polarizer A Surface plasmon is an electromagnetic wave that propagates along the interface of two materials, one of which has a negative dielectric constant. The plasmon is a transverse magnetic effect and exhibits the property of strongly attenuating one polarization component from an optical beam while the other polarization is unaffected. Thus only the TM polarization is coupled to the plasmon and the TE polarization is unaffected. © R. Ulrich, TU Hamburg-Harburg © R. Ulrich, TU Hamburg-Harburg TMo Plasmonβ β= Phase-Matching Condition
  208. 208. © A.Lobo (2004) 37 4. Passive Fibre Optic Devices 4.11 Fibre Polarizer. Surface Plasmon Polarizer Thin-film metal layer Fibre Core Silica Block Optical Fibre Fibre Cladding ~50 nm P. Perumalsamy, In-Line Fiber Polarizer, M.Sc. Thesis, Virginia Polythecnic Institute, Virgina, USA (1998).
  209. 209. © A.Lobo (2004) 38 4. Passive Fibre Optic Devices 4.12 Fibre Depolarizer. #1 #2 #n Depolarization occurs by averaging over many different polarization states of the recirculating beams. Advantages are: • All-fibre SMF device • Low cost structure • Insensitive to input polarization state • Infinitesimal DOP is possible with increasing numbers of cascaded fibre rings (*) B. Paisheng and C. Lin, Electronics Letters 34, 1777-1778 (1998). Passive Fibre Depolarizer 3 dB
  210. 210. © A.Lobo (2004) 39 4. Passive Fibre Optic Devices 4.13 Fibre Polarization Controller. Fibre Coil Polarization Controller (*) (*) H.C. Lefevre, Electronics Letters 16, 778-780 (1980). A.B. Lobo Ribeiro, M.Sc. Thesis, Univ. Kent, UK (1992). 2 0.836 ( , ) r N m R m N λ ⋅ ⋅ ⋅ = R – radius of the coil r – nominal radius of the fibre (2r =125 µm, standard SMF) N – number of turns of fibre on the coil m –fractional-wave order (m=2, 4 or 8) to get a λ/m wave plate λ – wavelength of the light Free-space optics approach Fibre optic approach
  211. 211. © A.Lobo (2004) 40 4. Passive Fibre Optic Devices 4.13 Fibre Polarization Controller. Fibre Squeezer Polarization Controller(*): The PolaRITE TM (*) www.generalphotonics.com Babinet Compensator: see E. Hecht, Optics, 4ed. Chap.8. Free-space optics approach (Babinet-Soleil compensator) Fibre optic approach (PolaRITE TM) 1 2 2 ( ) o ed d n n π ϕ λ Δ = − ⋅ −
  212. 212. © A.Lobo (2004) 41 4. Passive Fibre Optic Devices 4.13 Fibre Polarization Controller. PM Fibre Twist Polarization Controller(*) (*) www.fiberpro.com PMF SMF SMF Free-space optics approach (with λ/4-wave plates) • No Fiber Squeezing • No Damage on Fiber Jacket TWIST
  213. 213. © A.Lobo (2004) 42 4. Passive Fibre Optic Devices 4.14 Fibre Optic Attenuator. Pin Pout ( ) 10 log 10in out P IL dB OD P ⎛ ⎞ = ⋅ = ×⎜ ⎟ ⎝ ⎠ OD : Optical Density For example: An attenuator with optical density of 2, has a 20 dB ILoss Standard SMF Standard SMF Air Gap λ = 1300 nm Fresnel reflection 3.5% → return loss of 14.5 dB ( ) 10 log in back P RL dB P ⎛ ⎞ = ⋅ ⎜ ⎟ ⎝ ⎠ Pback More accurate analysis based on electric fields: INTERFERENCE ANALYSIS
  214. 214. © A.Lobo (2004) 43 4. Passive Fibre Optic Devices 4.14 Fibre Optic Attenuator. Standard SMF Standard SMF Absorbing SMF (GeAl core+Rare Earth ions) S. Chia, AMP Journal of Technology 5, 19-23 (1996) from AMP Inc. Response of insertion loss to temperature cycling between -40ºC and 85ºC of five individual samples of a 5 dB OA measured at 1550 nm. ± 0.30 dB 5 dB attenuator.
  215. 215. Active Fibre Optic Devices FIBRE OPTIC TECHNOLOGY COURSE António Lobo Prof. Associado (UFP)
  216. 216. © A.Lobo (2004) 2 5. Active Fibre Optic Devices 5.1 Thermally Tunable Fibre Filter and Modulator. 5.2 Twin-Core Fibre Switch. 5.3 Acousto-Optic Tunable Fibre Filter. 5.4 Piezoelectric Tunable Fibre Filter. 5.5 Acousto-Optic Fibre Modulator. 5.6 Piezoelectric Fibre Modulator. 5.7 Electric Poling Fibre Modulator. 5.8 Fibre Amplifier.
  217. 217. © A.Lobo (2004) 3 5. Active Fibre Optic Devices 5.1 Thermally Tunable Fibre Filter and Modulator. Temperature-induced optical phase shifts in fibres (*) (*) N. Lagakos, J.A. Bucaro and J. Jarzynski, Applied Optics 20, 2305-2308 (1981). 1 z T L n n n T L n n T nρ φ ε φ Δ Δ Δ ∂ Δ⎛ ⎞ ⎛ ⎞ = + = + ⋅Δ +⎜ ⎟ ⎜ ⎟ ∂⎝ ⎠ ⎝ ⎠ 2 nLπ φ λ = εz , εr – Axial (z) and radial (r) strains in the core. ρ – core density. n – effective refractive index p11 , p12 – are the Pockels coefficients of the core. [ ] 2 11 12 12 1 1 ( ) 2 z r z n n p p p T n T Tρ φ ε ε ε φ ⎧ ⎫Δ ∂⎛ ⎞ = + − + +⎨ ⎬⎜ ⎟ Δ ∂ Δ⎝ ⎠ ⎩ ⎭ 5 -1 0.7 10 C bare T φ φ −Δ = × Δ o 5 -1 1.7 10 C jacket T φ φ −Δ = × Δ o
  218. 218. © A.Lobo (2004) 4 5. Active Fibre Optic Devices 5.1 Thermally Tunable Fibre Filter and Modulator. Optical phase sensitivity of the fibre due to a physical parameter 2 X n L n S L X L X X φ π λ Δ ∂ ∂⎡ ⎤ = = ⋅ +⎢ ⎥Δ ∂ ∂⎣ ⎦ Physical Parameter (X) Sensitivity (SX) Axial Deformation (ε) 107 rad m-1 strain-1 Temperature (T) 100 rad m-1 °C-1 Hydrostatic Pressure (P) 5*10-5 rad m-1 Pa-1 (For a wavelength of 850 nm)
  219. 219. © A.Lobo (2004) 5 5. Active Fibre Optic Devices 5.1 Thermally Tunable Fibre Filter and Modulator. Temperature-induced optical phase shifts in metal coated fibres (*) (*) C.T. Shyu and L. Wang, J. Lightwave Technology 12, 2040-2048 (1994). Standard SMF Standard SMF Metallic film 2 ( )o nT T I R hA t t V cρ ∂ − − Θ∂Θ = = ∂ ∂ ( ) 2 / ( ) 1 tnI R t e hA τ− Θ = − ( ) 2 / ( ) 1 tnI R t e hA τβ φ − Δ = −R – Electrical resistance of the metallic film. ρ , c – density and specific heat of the fibre (respectively). V , A – volume and surface area of the metallic film. k – thermal conductivity of the film h – heat transfer coefficient In cV hA ρ τ = T φ β Δ = Δ → Fibre glass material
  220. 220. © A.Lobo (2004) 6 5. Active Fibre Optic Devices 5.1 Thermally Tunable Fibre Filter and Modulator. Temperature-induced optical phase shifts in metal coated fibres (*) (*) C.T. Shyu and L. Wang, J. Lightwave Technology 12, 2040-2048 (1994). gold coating In Coating length: 3 cm Resistance: 60.6 Ω
  221. 221. © A.Lobo (2004) 7 5. Active Fibre Optic Devices 5.1 Thermally Tunable Fibre Filter and Modulator. Thermally fibre modulator (*) (*) - C.T. Shyu and L. Wang, J. Lightwave Technology 12, 2040-2048 (1994). - B.J. White et. al., J. Lightwave Technology 5, 1169-1174 (1987). Metallic film In cos (ωt) Test current Detected optical signal Predicted signal 100 Hz
  222. 222. © A.Lobo (2004) 8 5. Active Fibre Optic Devices 5.1 Thermally Tunable Fibre Filter and Modulator. Thermally tunable fibre Bragg grating filter (*) 1 1B X B n S X X X n X λ λ Δ ∂Δ ∂ = = ⋅ + ⋅ Δ ∂ ∂ Physical Parameter (X) Sensitivity (SX) Axial Deformation (ε) 0.78×10-6 µs t r a i n -1 Temperature (T) 8×10-6 °C-1 Hydrostatic Pressure (P) 2.7×10-6 MPa-1 2B nλ = Λ B X
  223. 223. © A.Lobo (2004) 9 0.0 0.1 0.2 0.3 150 200 250 300 350 400 Time (min.) Is (mA) Vaplicado 0.8 0.9 1.0 1.1 1.2 1.3 1.4 (a) Vout /Vref 5. Active Fibre Optic Devices 5.1 Thermally Tunable Fibre Filter and Modulator. Thermally tunable fibre Bragg grating filter (*) (*) P.M. Cavaleiro, F.M. Araújo and A.B.Lobo Ribeiro, Electronics Letters 34, 1133-1135 (1998) silver film In SMF fibre with FBG 0.0 0.5 1.0 1.5 2.0 2.5 3.0 835.2 835.4 835.6 835.8 836.0 836.2 836.4 836.6 BraggWavelength(nm) Electrical current - squared (A 2 ) Coating length: 2 cm Resistance: 1.2 Ω
  224. 224. © A.Lobo (2004) 10 5. Active Fibre Optic Devices 5.1 Thermally Tunable Fibre Filter and Modulator. Thermally tunable fibre Bragg grating filter (*) (*) L.Lin et. al., IEEE Photonics Technology Letters 15, 545-547 (2003) Ti-Pt-Ni metal alloyed coating (2 µm) In SMF fibre with FBG Coating length: 4 cm Resistance: 7.5 Ω
  225. 225. © A.Lobo (2004) 11 11.2 nm Wavelength (nm) OpticalPower(dBm) 5. Active Fibre Optic Devices 5.1 Thermally Tunable Fibre Filter and Modulator. Thermally tunable fibre Bragg grating (*): Laser Application (*) J.J. Pan et.al., Lightwaves 2020 Inc., US Pat.6018534 0.009 nm/ºCB T λΔ Δ ; 0.16 nm/ºCB DFBT λΔ Δ ;
  226. 226. © A.Lobo (2004) 12 5. Active Fibre Optic Devices 5.2 Twin Core Fibre Switch. Twin Core Fibre (*) (*) - P.J. Severin, in Proc. SPIE vol.1314 – Fiber Optics 90, 348-364 (1990). - R. Romaniuk, J. Dorosz, in Proc. SPIE vol.4887 (2001) 2 21 2 22 ( ) 1 sin ( ) sin o o P z kz F P F P z kz F P F ⎛ ⎞ = − ⎜ ⎟ ⎝ ⎠ ⎛ ⎞ = ⎜ ⎟ ⎝ ⎠ 2 2 1 1 1 2 F k β β = −⎛ ⎞ +⎜ ⎟ ⎝ ⎠ Power-coupling efficiency: Cladding (125 µm) 4 µm Cores (10 µm)
  227. 227. © A.Lobo (2004) 13 5. Active Fibre Optic Devices 5.2 Twin Core Fibre Switch. Twin Core WDM coupler/filter (*) 1530 1535 1540 1545 1550 1555 1560 0 0.2 0.4 0.6 0.8 1 Wavelength [nm] NormalizedPowers P1 P2 (*) twin core fibre sample provided by Prof. P.J. Severin (Philips Eindhoven) L = 20 cm P2 P1 Po Cores: 9 µm Cores separation: 2 to 5 µm Cladding: 100 µm
  228. 228. © A.Lobo (2004) 14 1530 1535 1540 1545 1550 1555 1560 0 0.2 0.4 0.6 0.8 1 5. Active Fibre Optic Devices 5.2 Twin Core Fibre Switch. (*) twin core fibre sample provided by Prof. P.J. Severin (Philips Eindhoven) P1 Po Piezoelectric Transducer V Wavelength [nm] NormalizedPower(P1/Po) Length variation of 100 µm on 20 cm
  229. 229. © A.Lobo (2004) 15 5. Active Fibre Optic Devices 5.2 Twin Core Fibre Switch. R. Vallée and D. Drolet, Applied Optics 33, 5602-5610 (1994) P1 Po TWIST
  230. 230. © A.Lobo (2004) 16 5. Active Fibre Optic Devices 5.3 Acousto-Optic Tunable Fibre Filter. FREQUENCY SHIFTER Optical Frequency ωo Optical Frequency ωo ± ωac Acoustic Frequency ωac ( Acoustic frequency (ωa) can be generated electrically or optically) sin 2 4 o o ac B B ac acV λ λ ω π Θ = ⇒ Θ ≅ Λ Diffracted beam angle at: For more information see: www.brimrose.com
  231. 231. © A.Lobo (2004) 17 5. Active Fibre Optic Devices 5.3 Acousto-Optic Tunable Fibre Filter. (*) W. P. Risk, R. Youngquist, R.C. Kino, H.J. Shaw, Optics Letters 9, 309 (1984) Surface Acoustic Wave (SAW) device (*) (Used to produce surface acoustic waves) cos SAW a a B B V f L L Λ Θ = =Phase-matching condition: Velocity of the SAW Fibre beat length SAW wavelength
  232. 232. © A.Lobo (2004) 18 5. Active Fibre Optic Devices 5.3 Acousto-Optic Tunable Fibre Filter. Flexure-wave fibre device (*) (*) B.Y. Kim, J.N. Blake, H.E. Engan, H.J. Shaw, Optics Letters 11, 389-391 (1986). York HB600 fibre (HiBi fibre), with beat length of 1.5 mm and an acoustic frequency of ~0.2 MHz, producing a frequency shift of ~790 kHz
  233. 233. © A.Lobo (2004) 19 5. Active Fibre Optic Devices 5.3 Acousto-Optic Tunable Fibre Filter. Flexure-wave fibre device (*) (*) T. E. Dimmick, G. Kakarantzas, T. A. Birks, and P. St. J.Russell, in Proc. OFC‘2000, FB4 pp.25-27, 2000. 11 21 2 ac HE HE π β β Λ = − Resonance condition:
  234. 234. © A.Lobo (2004) 20 5. Active Fibre Optic Devices 5.3 Acousto-Optic Tunable Fibre Filter. Flexure-wave fibre device (*) (*) T. E. Dimmick, G. Kakarantzas, T. A. Birks, and P. St. J.Russell, in Proc. OFC‘2000, FB4 pp.25-27, 2000. Filter bandwidth 0.8 ac L λ λ ΛΔ = 2.9 nm bandwidth (4 cm) < 10 cm
  235. 235. © A.Lobo (2004) 21 1.53 1.54 1.55 1.56 1.57 0.2 0.4 0.6 0.8 1 5. Active Fibre Optic Devices 5.4 Piezoelectric Tunable Fibre Filter. L M M PZTOptical fibre A = 0 R = 95 % L = 20 µm ΔL = +1 µm2 2 2 1 1 2 1 sin 1 2 A R T R R φ ⎛ ⎞ −⎜ ⎟ −⎝ ⎠= ⎛ ⎞ ⎛ ⎞ + ⎜ ⎟ ⎜ ⎟ − ⎝ ⎠⎝ ⎠ FSR ≈ 60 nm FWHM ≈ 2 nm Finesse ≈ 30 Wavelength (µm) Transmittance Tunable Fibre FP Filter
  236. 236. © A.Lobo (2004) 22 5. Active Fibre Optic Devices 5.4 Piezoelectric Tunable Fibre Filter. www.micronoptics.com
  237. 237. © A.Lobo (2004) 23 5. Active Fibre Optic Devices 5.4 Piezoelectric Tunable Fibre Filter. Strain-induced optical phase shifts in fibres (*) (*) A. Bertholds, R. Dändliker, J. Lightwave Technology 5, 895-900 (1987). ( ) 2 T const n L nL π φ λ= Δ = Δ + Δ 2 nLπ φ λ = εz , εr – Axial (z) and radial (r) strains in the core (εr= ν εz) ν – Poisson ratio (=0.17 for silica). n – effective refractive index (= 1.456 at λ=1550 nm) p11 , p12 –Pockels coefficients of the core (p11=0.121 , p12=0.27 for silica) [ ] 2 11 12 12 2 ( ) 2 z r z n nL p p p π φ ε ε ε λ ⎧ ⎫ Δ − + +⎨ ⎬ ⎩ ⎭ ; 6 -1 -1 4 10 rad m strain L φ ε Δ ≈ × ⋅ ⋅ Δ for λ = 1550 nm
  238. 238. © A.Lobo (2004) 24 5. Active Fibre Optic Devices 5.4 Piezoelectric Tunable Fibre Filter. PZT PZT FBG (*) A. Iocco, H.G. Limberger, R.P. Salathé, Electronics Letters 33, 2147-2148 (1997). Tunable FBG Filter (*)
  239. 239. © A.Lobo (2004) 25 5. Active Fibre Optic Devices 5.4 Piezoelectric Tunable Fibre Filter. (**) C. S. Goh et.al., IEEE Photonics Tech. Letters 14, 1306-1308 (2002). Tunable FBG Filter (**)
  240. 240. © A.Lobo (2004) 26 5. Active Fibre Optic Devices 5.5 Acousto-optic Fibre Modulator. All-fibre AO Frequency Shifter (*) (*) D.O. Culverhouse et.al., IEEE Photonics Tech. Letters 8, 1636-1637 (1996).
  241. 241. © A.Lobo (2004) 27 5. Active Fibre Optic Devices 5.5 Acousto-optic Fibre Modulator. ZnO-Coated Optical Fibre AO Phase Modulator(*) (*) A. Roeksabutr and P.L. Chu, J. Lightwave Technology 16, 1203-1211 (1998). 3 11 12( ) rn l p p π φ ε λ Δ ≈ + Optical phase shift: Max. phase shift (exp):~700 mrads @ 670 MHz
  242. 242. © A.Lobo (2004) 28 r R 5. Active Fibre Optic Devices 5.6 Piezoelectric Fibre Modulator. 32 11 12 12 (1 ) ( )4 2 2 eff eff n p p rNC n p V R νφ π λ ⎧ ⎫+ +Δ ⎪ ⎪⎡ ⎤ = + −⎨ ⎬⎢ ⎥⎣ ⎦⎪ ⎪⎩ ⎭ (rad/volt) for more details see: G. Martini, Optical & Quantum Electronics 19, 179 (1987). N – number of fibre turns wrapped on the PZT ν – Poisson ratio of silica (0.17) p11 , p12 –Pockels coefficients of the fibre core C – radial displacement of PZT per unit of voltage (p.ex. C≈0.61 nm/V for a PZT-5H)
  243. 243. © A.Lobo (2004) 29 5. Active Fibre Optic Devices 5.6 Piezoelectric Fibre Modulator.
  244. 244. © A.Lobo (2004) 30 5. Active Fibre Optic Devices 5.6 Piezoelectric Fibre Modulator. (*) M.N. Zervas and I.P. Giles, Optics Letters 13, 404-406 (1988). Fibre-Loop Phase Modulator(*) 2 phase resonance loop V f L = Resonance Frequency of the loop As the advantage to remove the phase shift dependence on the PZT characteristics
  245. 245. © A.Lobo (2004) 31 5. Active Fibre Optic Devices 5.7 Electric Poling Fibre Modulator. The fibre is 127 mm diameter with two holes of 45 mm diameter. The optical fibres are thermally poled at around 250°C with an electric field in the order of 4kV. The electrodes are inserted to lengths in excess of 20 cm. (150 VAC at 4.5 kHz) EO coefficient can be calculated. EO coefficients of ~0.2 pm/V have been measured in 1.55 µm silica single mode fibres (for a LiNbO3: 7~30 pm/V) See: Applied optics Group, Univ. Kent, Canterbury (U.K.) - www.kent.ac.uk/physical-sciences/aog 4.5 kHz 2 2 2 NL Kn L E π φ λ Δ = n2K ≈ 3.2×10-20 m2/W 2 2eff o Kn n n E= + 2 11 2 for 10 V/mK on E n E≈ ≈
  246. 246. © A.Lobo (2004) 32 5. Active Fibre Optic Devices 5.8 Fibre Amplifier. Gain (EDFA) Power Supply (PUMP) IN OUT FEEDBACK (Resonant Cavity) FIBER LASER
  247. 247. © A.Lobo (2004) 33 5. Active Fibre Optic Devices 5.8 Fibre Amplifier. S-Ring Fibre Laser (*) (*) O.G. Okhotnikov, A.B.Lobo Ribeiro, J.A.R. Salcedo, Applied Physics Letters 63, 2726-2728 (1993).

×