1. UPM, DIAC. Open Course. March 2010 2. FIBER 2.1 Nature of Light 2.2 Refractive Index 2.3 Fiber Structure 2.4 Waves 2.5 Rays

2. 2-2 2.1 NATURE OF LIGHT (I) Concept —Light can be explained as – Rays: using Optical Geometry – Waves: using Electromagnetic Theory – Photons: using Photoelectric Effect – ?: using Quantum Mechanic We will need – Optical Geometry → to explain light propagation – Electromagnetic Theory → to understand spectrum – Photoelectric Effect → to show lasers and photodetectors

3. 2-3 2.1 NATURE OF LIGHT (II) Spectrum —Light as a wave

4. 2-4 2.1 NATURE OF LIGHT (III) Polarization —Light as a wave – An electromagnetic wave has electric (E) and magnetic (H) fields. They are perpendicular – The orientation and phase of E defines the polarization (linear, circular or elliptical) Circular polarization

5. 2-5 2.2 REFRACTIVE INDEX (I) Refractive Index of a medium i – Measures how much the speed of light is reduced – “n” typical value: 1.5 –  i : material’s relative permittivity REAL in fiber (dielectric)  i =  ’ – j·  ’’ ;  ’’ negligible in a dielectric – c  3·10 8 m/s, light speed in vacuum Maximum speed of any physical phenomena c = 299,792,458 m/s (set by definition)

6. 2-6 2.2 REFRACTIVE INDEX (II) Snell’s Laws (Optical Geometry) – Light = rays – Light propagation → straight-line (homogeneous medium) (In refraction there is always a reflected ray)

7. 2-7 2.3 FIBER STRUCTURE (I) What is a fiber? – Dielectric waveguide (usually cylindrical) An only wire It does not carry electricity – Carries light (inside) – Tiny size (like a human hair) – Can transmit high data rates AS FIBER HAS SO MANY PROS, OPTICAL COMMUNICATIONS ARE USUALLY MADE VIA FIBER

8. 2-8 2.3 FIBER STRUCTURE (II) Structure – Core: doped SiO 2 Carries the light (most of it) Typical values: 8-10; 50; 62.5  m  (diameter) – Cladding: pure/doped SiO 2 Confines light into the core (like a mirror) Typical values: 125  m  – (Coating: outer protection)

9. 2-9 2.3 FIBER STRUCTURE (III) Main parameters – Core’s size, radius “a” – Cladding’s refractive index n 2 – Core’s refractive index n 1, or n 1 (r) if it varies

10. 2-10 2.3 FIBER STRUCTURE (IV) Fiber types

11. 2-11 2.3 FIBER STRUCTURE (V) Step-Index Fiber – n 2 = constant (cladding) – n 1 = constant (core) – Relative Index Difference Typical values (SiO 2 ): n 1 ≈ 1.461 n 2 ≈ 1.460 Δ SI = 0.01-0.05

12. 2-12 2.3 FIBER STRUCTURE (VI) Graded Index Fiber – n 2 = constant (cladding) – n 1 = n(r) variable! (core) – Relative Index Difference

13. 2-13 2.3 FIBER STRUCTURE (VII) – Index profile parameter “g” – Most important values Step-Index fiber: g → ∞ Graded index fiber: g ≈ 2

14. 2-14 2.4 WAVES (I) Modal Theory – Maxwell eqs. Wave eqs. MODES – MODES: different ways for light to propagate – Number of solutions —depends on n 1, n 2 a (core radius), diameter Ø = 2a Approximate expression mediumsolutions Be careful! This is an approximation, M is discrete

15. 2-15 2.4 WAVES (II) g: constant which appears in refractive profile n 1 (r) – g  (0,  ) – Usually g  1 V: “Normalized Frequency”. It appears in Maxwell equations – Fiber types: according to the number of propagating modes SINGLE-MODE: M = 1 MULTIMODE: M > 1 SI: Step Index GI: Graded Index

16. 2-16 2.4 WAVES (III) How is M controlled? – g/(g+2): varies little g = 1  1/3 g =   1 – : varies little (fiber only propagates light in a narrow window) – (n 1 2 -n 2 2 ) 1/2 : varies little (technology) In particular: M = 1 – V SI < 2.405 (g   ) – V GI < 3.518 (g = 2) SO, THE KEY PARAMETER IS “a” a   M = 1 a   M > 1

17. 2-17 2.4 WAVES (IV) Fiber types

18. 2-18 2.4 RAYS (I) Ray Theory – Core: carries light – Cladding: confines light into the core – In order to propagate light Air/core interface: refraction (lighting horizontally) Core/cladding interface: reflection (n 1 > n 2 ) Air: n 0 ≈ 1

19. 2-19 2.4 RAYS (II) Snell’s Laws —core/cladding interface

20. 2-20 2.4 RAYS (III) – Refractive index values To achieve total reflection in the interface  sin(  i ) > n 2 /n 1 If n 2 > n 1    i / sin(  i ) > n 2 /n 1 > 1 If n 2 = n 1  there is no interface (ray escapes) Therefore: n 2 < n 1

21. 2-21 2.4 RAYS (IV) Critical Angle —to propagate light  L : limit angle of propagation  OL : limit angle of acceptance

22. 2-22 2.4 RAYS (V) Numerical Aperture – Light capturing ability of the fiber – Definition – Step-Index Fiber

23. 2-23 2.4 RAYS (VI) – Graded Index Fiber —same expression is applied

24. 2-24 2.4 RAYS (VII) Ray Paths – SI Fiber Straight line paths They all have the same velocity (n 1 constant) – GI Fiber Curved trayectories Velocity changes: shorter paths travels more slowly

25. 2-25 2.4 RAYS (VIII) Rays & Modes – A mode prefers a specific propagation angle – Although modes and rays behave differently… – For our purposes: one mode ≈ one ray – Then, multimode ≈ multi-ray

26. 2-26 2.4 RAYS (IX) Application —Desert Mirages (I)

27. 2-27 2.4 RAYS (X) Application —Desert Mirages (II)