Geometrical Optics Fiber optics

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1 Phys 322 Lecture 15 Chapter 5 Geometrical Optics Fiber optics

2 First optical commuicatio Alexader Graham Bell : photophoe 4 years after ivetig a telephoe!

3 Fiberoptics: first lightguide 1870: water as a light guide Joh Tydall

4 Fiber optics: commuicatios 1960: First laser 1966: couplig with fibers for commuicatio 1970: 1% of light trasmitted over 1 km (losses 20 db/km) Today: over 96% of power trasmitted over 1 km Why light? - frequecies ~10 15 Hz Theoretical badwidth limit: each oscillatio is 1 bit, badwidth is ~10 14 bytes/secod (100,000 GB/s) Speech ~3 kb/s: ca support ~10 billio phoe coectios over oe fiber simultaeously! DVD quality videophoe: ~10 millio chaels! Note: Moder fiber systems record 100 Tb/s

5 What is a Optical Fiber? A optical fiber is a waveguide for light cosists of : core claddig buffer jacket ier part where wave propagates outer part used to keep wave i core protective coatig outer protective shield

6 Desig of optical fibers Core: Thi glass ceter of the fiber that carries the light Claddig: Surrouds the core ad reflects the light back ito the core Buffer coatig: Plastic protective coatig core > claddig

7 Microstructure fiber I microstructure fiber, air holes act as the claddig surroudig a glass core. Such fibers have differet dispersio properties. Air holes Core Such fiber has may applicatios, from medical imagig to optical clocks.

8 Propagatio of light i a optical fiber Light travels through the core boucig from the reflective walls. The walls absorb very little light from the core allowig the light wave to travel large distaces. Some sigal degradatio occurs due to imperfectly costructed glass used i the cable. The best optical fibers show very little light loss -- less tha 10%/km at 1,550 m. Maximum light loss occurs at the poits of maximum curvature.

9 Fiberoptics: sigle core fiber losses Cosider large fiber: diameter D >> ca use geometric optics Path legth traveled by ray: l L / cos Number of reflectios: l N 1 D / si t t Example: L = 1 km, D = 50 m, f =1.6, i = 30 o N = 6,580,000 Note: frustrated iteral reflectio, irregularities losses! Usig Sell s Law for t : N D Lsi 2 f i si 2 1 i

10 Step Idex Fiber: TIR escapes core claddig t escapes core core i i stuck i core i i For total iteral reflectio eed c < f si t c ti i c for TIR i critical agle (pg 122)

11 Remider: Numerical Aperture A measure of a les size is the umerical aperture. It s the product of the medium refractive idex ad the margial ray agle. NA = si() f Why this defiitio? Because the magificatio ca be show to be the ratio of the NA o the two sides of the les. High-umerical-aperture leses are bigger.

12 Numerical Aperture NA si describes light gatherig capability for: leses microscope objectives (where may ot be 1) optical fibers NA photos gathered

13 Numerical aperture (NA) of a i Step Idex Fiber c f t 90- t Claddig - trasparet layer core of a fiber (reduces losses ad f/#) max must be > critical agle NA outside si max NA step f 2 i 2 c NA step f 2 2 c NA i air

14 Fiber ad f/# si max 2 f i 2 c Agle max defies the light gatherig efficiecy of the fiber, or umerical aperture NA: NA i si max 2 f 2 c Ad f/# is: 2NA f /# 1 Largest NA=1 Typical NA = 0.2 1

15 Budles Coheret budles: flexible image carriers Budles ca collect light from larger area ad be still flexible Flexible light carriers Fibers are arraged i a coheret fashio

16 Data trasfer limitatios 1. Distace is limited by losses i a fiber. Losses are measured i decibels (db) per km of fiber (db/km), i.e. i logarithmic scale: 10 L log Po P i Po P Example: P o /P i over 1 km 10 db 1:10 20 db 1: db 1:1000 i 10 L /10 P o - output power P i - iput power L - fiber legth Workaroud: use light amplifiers to boost ad relay the sigal 2. Badwidth is limited by pulse broadeig i fiber ad processig electroics

17 Atteuatio Rayleigh Scatterig page 297 IR absorptio absorptio ad scatterig i fiber i the IR: low-oh versus high-oh

18 Pulse broadeig Dispersio: The Basics Light propagates at a fiite speed fastest ray slowest ray fastest ray: oe travelig dow middle ( axial mode ) slowest ray: oe eterig at highest agle ( high order mode) will be a differece i time for these two rays

19 Types of Dispersio i Fibers modal material waveguide o-liear time delay from path legth differeces usually the biggest culprit i step-idex () : differet times to cross fiber (ote: smallest effect ~ 1.3 m) chages i field distributio (importat for SM) ca become itesity-depedet NOTE: GRIN fibers ted to have less modal dispersio because the ray paths are shorter

20 Effect of Dispersio iitial pulse farther dow farther still time time time modal example: step idex ~ 24 s km -1 GRIN ~ 122 ps km -1

21 Fibers carry modes of light umber of modes D 0 NA 2 a mode is : a solutio to the wave equatio a give path/distributio of light (pg 196) higher # modes gives more light, which is ot always desirable

22 Example of # of 850m Silica step-idex fiber has f = 1.452, c = (NA = 0.205) SELFOC graded idex fiber with same NA diameter (micros) # step-idex modes # GRIN modes E3 37 E3 230 E E3 46 E E3 high # modes implies classical optics

23 NA ad # of Modes killed ray propagated ray large NA small NA

24 Pulse broadeig Multimode fiber: there are may rays (modes) with differet OPLs ad iitially short pulses will be broadeed (itermodal dispersio) For ray alog axis: t mi L v f L 2 For ray eterig at max : t l v L c max The iitially short pulse will be broadeed by: Makig c close to f reduces the effect! L f f t tmax tmi 1 c c f f f c c

25 Pulse broadeig: example f = 1.5 c =1.489 Estimate the badwidth limit for 1000 km trasmissio. Solutio: L f t c f c s Eve the shortest pulse will become ~37 s log Badwidth ~ s 27 kbps Multimode fibers are ot used for commuicatio! 5 s 37s kilobits per secod = ONLY 3.3 kbytes/s

26 Graded Idex Fiber c varies quadratically f c like a restorig force!

27 Types of fibers c c f c c f c c f GRIN step-idex siglemode step-idex multimode

28 Sigle mode fiber To avoid broadeig eed to have oly oe path, or mode Sigle mode fiber: there is oly oe path, all other rays escape from the fiber clad core jacket Geometric optics does ot work aymore: eed wave optics. Sigle mode fiber core is usually oly 2-7 micro i diameter

29 Sigle mode fiber: broadeig clad core jacket Trasform limited pulse product of spectral full width at half maximum (fwhm) by time duratio fwhm: ft 0.2 Problem: shorter the pulse, broader the spectrum. refractio idex depeds o wavelegth A 10 fs pulse at 800 m is ~40 m wide spectrally If secod derivative of is ot zero this pulse will broade i fiber rapidly Solitos: special pulse shapes that do ot chage while propagatig

30 Critical Bed radius

31 A example: I eed a fiber that will coduct NIR light. I have to keep a tight pulse patter. It must couple ito a LED. What do I do?

32 Puttig It All together (a) I eeded a fiber that will coduct NIR light. get a low OH fiber (b) I had to keep a tight pulse patter. you wat low dispersio: SM or a GRIN fiber, low diameter, low NA (c) It must couple ito a LED. The LED has a high divergece agle; better get a bright oe. A laser might be better, ad use a GRIN les to couple. These are desig cosideratios, as well as cost!

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