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Opticlecture2 - Lea-fa r 4,2” Large alfwe we...

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Guiding of Light in Optical Fibers Reflection and Total Internal Reflection (Geometric Perspective) n2>n1 in this figure Figure 1: Reflection and refraction where the incident medium has a lower refractive index than the Incident Normal Reflected Ray Ray 9i 6r n1 ‘ 5 Medium 1 n2 : Medium 2 6t (n2<n1 in fibers) Transmitted Ray transmitting medium. What happens when a beam of light encounters a boundary between two media? There are typically 2 beams, reflected and transmitted (refracted) The direction of propagation of both of those beams are different from that of the incident beam 6, = 6,- Sing = 21— (Snell's Law) smfli n2 if 112 > n1, the transmitted beam is "bent" towards the normal if n2 < n1, the transmitted beam is "bent" away from the normal if n; < ii, there exists a 9i such that at = 1t/2 (90°), called the "critical angle" sin 66 = if n2 < n. and 9; > SC, there is no transmitted beam 21 ”1 may: 24+ L Incident Normal Reflected Ray - Ray more «369138 Medium 1 less dense n2<n1 in this figure; Transmitted Ray Figure 2: Reflection and refraction where the incident medium has a higher refractive index than the transmitting medium. This is the case where total internal reflection can occur. Geometrical Optics of the Waveguide An optical fiber consists of a cylindrical piece of glass set up in such a way that there is a core with a larger index than the cladding. In such a way, total internal reflection can be used to confine light in the core of the fiber with very little loss. Cladding (n2) V Figure 3: Step-index fiber geometry. In order to understand waveguides there is another geometry that is convenient. The slab waveguide consists of a high index core which is considered to extend to infinity in the y and +2 directions surrounded by lower index cladding. Core (n1) Cladding (n2) Figure 4: Slab waveguide geometry. The refractive index profile is shown below. The core is of thickness 2d, and the index of the core, n1 is slightly larger than the index of the cladding, n2. We will see that the difference in index need not be that large in order to effectively guide light. n2 -d +d Figure 5: Step refractive index profile. We see that as the incident angle, Si, is increased, the angle that the rays make at the interface between core and cladding decreases. Therefore there is some angle, 90, so that as long as light is incident at an angle, 9i < 90, the light will be guided. 2'6 cladding (n2) free space ray cladding (n2) n1 >n2 Figure 6: Light launched into a fiber or slab waveguide. _ n smflc 2—2 / n] no smfli Sn1 sm€,_ . 7r Snl sm(3——t9€) S n1 cos 66 NA = n1 cos 6’6 So NA is the "numerical aperture", and is the maximum value of (no sin 9i) for which the slab or fiber will guide. In air, no = 1, so we can further represent numerical aperture as: sinA=ubcosA= l—u2 This is a highly simplified picture of how an optical waveguide actually works, but it illustrates several interesting concepts: I Light can be confined and forced to travel through a waveguide structure by taking advantage of TIR Numerical aperture is a useful concept primarily because it is easy to experimentally measure 60. Fiber manufacturers specify their fibers in terms of numerical aperture 2«7 I - 3’8 Having ghoum, —Hng+ Only (£175 Inside, Nae ‘(I'Eer UWCLL CXCQEQ +146 Cri‘hCafi 3mg“: 9:: Com‘HIbq'fe. +0 ,3f0paja'§;om 1 dams”: (g pt)" [\M,‘ 4 re fiwww aliowab“{ 9 I a ' gynalZS Cv I Haw do we: €XC#€ ‘VLAe’sa rags afi {(1:33 5231mmruj offing- {iéer/£,c at“ Wk’a‘t angle, Vim/«31L {Fee—-$paca {8/5 {amp/rmga om “4e. a i r— {abet r" fwnter g3 (:42: normafl 1% c1344W3~Core 'M‘Lf‘rflacc 4 1/ p I cleéc‘ruj W3, core 'n . n‘g(\~t2£ +0 ‘ ‘1 n +e r gaca "cu-”- “fin-d— ! a? r—{Tber \L cfaalqlvrha ’ 9 5:” 0 z 35-43» Son = n, stt :: n, (:05 9C 5H4 9t; no V1 7’ 9£=_n;i-¢9c .‘.. allowable mcidemca angles 9‘: :‘S 90 == 611:, 11, 1,9596): £9:ny {VI-9 {WW Wameriraé apar-I'ure IVA =: 7155.959; =YL, YE!” 61,1596, = n, g?" gaff“ .. 2 9» .. Vb, ~VLX. I ‘ ”/4 *5 3V! ufperwflmhL vafua of 314561an or 50mi>a§€¥4f0m +0 “faVe piaae [rm afiber. F9? emwple: fipkafi rmamas: Core magi-55>") aiaéif’j ngm‘; A/l‘}: Lgsé‘kmfl: V2.+-,z. =15": 0.548 Si.“ i. gufolange. a)?” fake iMaca {9( $50.545 or f ’ ; "I'YL .‘I guidance angles m Core flee: SW1, 76:99‘4 I‘M-76130 1.55 Incowu'mj angle 9. S 90 615‘ MA: sLJ'O546: 33.20 lb : Tramsch/ed amala 9; 323966200— 67.30: 20.70 V ’7 '0 Figure 7: In the cylindrical fiber geometry we see that the rays are much less well behaved. ' The different "modes" propagate at different velocities cladding AV ' ——>v1 —>v2 core cladding Figure 8: An illustration of different waveguide "modes" in the ray picture. We see that this model gives some insight, but is inadequate to completely describe some other phenomena: . The geometry of the waveguide has an effect on how fast a signal travels through it . If one considers the fact that source of light actually consists of a range of frequencies, each propagating at a slightly different speed through the waveguide, and each having a slightly different index of refraction, one can recognize the effect of dispersion in the waveguide We learn more about guiding of light by considering the system in terms of a traveling electromagnetic Wave, and solving Maxwell's equations for the geometries under consideration. 2—62 2:10 3-2, Mer is flaw: BMd [0891 at; Taoka'lfCZES'O/wm Core 6 2.5km +\/{>:rca.52 Luavelemj+L1 (a {rage space 35 10: 1.5574,“,1 _ j“ 39:4,“, “Jaye/pblgf/L 15 kg: /0 : [96$ 7‘; 1.6 = / m4 . V0866; I‘m ‘561’ \j’=32’_o__ 3409 g [4 W J 7K] 5 71g " A55 fl fifiemumeov‘, due 710 $05525 {w {Iber I; Weaswkeg 'mc/g <9ch 43m ‘34» \5 a (34:0 WCESM vamemi/ VIQQQIQLJ far Eafiac rat/1385 ABVBHO: ‘0 Qfi'lo (SOLE/j I [W = Lama/g ..‘ ' _. _ ° —- :2 P0 — P ~i 9H6 nua'hom 0% IOdB — [0&5 a to £0803 75: _> 75:10 :04 ABM/1 L5 Power Fag/[E‘HOV‘ +0 [MW'H Oglm/IW : ’IOdBm / u I: O H 10 \t Z {O H lllllllllll ,¢,. me n : 20 H Fiber afifnqafi'gvm onn AB Per /@/M 0?? fiber gang/'12 l. __3¢fll: _ pa ”(1. to i0 “ eog E 0r 32 :2, [O / , i 0 Pi, / Rub: Reawphflcahew weedeoi 0&5??ng Power drop; (93 IO"5 QP‘HCaQ 3(8‘5fi W:{5fi9§dB/%W§ £2 ; {0—100 ”(XL -' - P4; to :’5 fkaL .L:.‘JL‘93.§Z 7.5sz A [moo mo l rppeygm Evflfé 50AM l “0+ {)(acfimg’ , 9 — 3 367L949! Coax (Esme; d~ BAB/kw lP—rf: (0 L L: gram ; M75144 . , 1 v) ~0.08 L M gwmfflé’x Mafle {I (96V M1 0ang/Iv’iw ”6&9; :1 [O Lréléwrg; 250 WW 4 a Repeflfl Qtffl‘éj 5; km W, wai‘e’ {"”€?E§>€;g“‘[;cn Fiber A tten ua tion P(z) = P(O)e “'Pz all, 2 —lln[P(z)] z P(O) In these equations P(z)[W] is the optical power measured after propagating a distance, z[m]. P(0)[W] is the initial optical power. The power attenuation coefficient, ccp, is in units of m'l. Attenuation is often expressed in dB/km as follows: a: g 10 log[P(z)] z[km] 13(0) Signal power is often represented in a funky way P[dBm] "decibels relative to 1 mW" P(dBm] = 10 log[——P—[fl—] 10‘3[W] One is also often interested in a transmission ratio: T =10—a[dB/km]z[km]/IO so that: P(z ) = Me) Sources of Loss in Fibers Me Material absorption Material molecular and atomic structure, impurity ions, especially OH' from water In fiber optic communications, material absorption is the limiting source of loss at wavelengths longer than 1550 run. Scattering effects Linear scattering (the amount of scattering is proportional to the power of the wave) such as Rayleigh scattering (that from inhomogeneities smaller than the wavelength of light, proportional to 105) and Mie scattering (that from inhomogeneities comparable in size to the wavelength) Nonlinear scattering (the amount of scattering is proportional to the P2 of the wave) such as Brillouin scattering and Raman Scattering. Nonlinear effects are normally insignificant at powers considered here. In fiber optic communications, Rayleigh scattering is the limiting source of loss at wavelengths shorter that 15 50 nm. Interface inhomogeneities Problems at the interface between core and cladding as well as problems on the input face of the fiber cause losses Bending losses Macrobends (large scale bend and twists of the fiber) and microbends (small scale variations in the core-cladding interface) asuring attenuation There are several techniques useful for experimentally quantifying attenuation in the lab or field. Insertion loss (most useful for lab work) Cutback method (opposite of insertion loss) (most useful when fabricating fibers) Optical Time—Domain Reflectometry (OTDR) (most useful in the field) 2—! Z 75 Optical Fibers: Index Plastic Jacket d2=125t1m I Cladding. A ’ w' , d2 ' Cladding Y Plastic Jacket d1=5um Schematic of a Step index Single Mode Fiber index i rT _ Single Mode (d1 =5um) St ld G d dl d n2-1.50 epn exor rae n ex Multimode (d1 - 50 um) Graded index i r terial' Fused Silica ' Plastic . . I .19" :2 “x a a Key Ether Eroperties ; s (m 2 ~ ‘33 - Loss (less than 0.2 dB/km at 1.55 pm) The emergence of the erbium-doped fiber amplifier has revolutionized fiber-optic communications . Dispersion (group velocity is a function of it) - Nonlinearity (intensity dependent refractive index) Dispersion and nonlinearity can compensate each other to form optical solitons -- pulses of light that travel without spreading Effect of ti Dispersion _ g _ , Distance «mi 1\ Fiber vs. Coax and Twisted Pair:* Attenuation (dB/km) 500 300 200 IOO PCS Fiber HCS Fiber l 2 5 IO 20 50 l00 200 500 1000 Signal Frequency (MHz) Attenuation Spectra of a Typical Fused Silica Fiber: 10.0 -‘ 9° '0 o Attenuation Coefficient (dB/km) p w 0.1 ' Fl. J. H033. Fiber-Optic Communications: Design Handbook, (Prentice—Hall. New Jersey,1990). 0.7 0.9 OH Rayleigh Absorption Scattering Infrared Abnorption 1.1 ' 1.3 1.5 1.7 1.90 Wavelength (pm) 0 d a) (mu—wwsd) 1111619111800 misaedssc 76 2-13 Main characteristics of optical fibers Much of the behavior of light can be understood by considering it a traveling electromagnetic wave - Light travels at c = 3 * 108 m/s I Different light frequencies correspond to different colors in dispersion" : =clf=1.3 um a2. =231 THz "min attenuatio ‘3 =clf=1.55 a : a: 3 < 0-H 02 Wavelength Figure 2: Relationship between attenuation and wavelength in glass. Wavelengths in the picture are "vacuum" wavelengths The frequency of light is set by the laser "source" The speed of propagation and wavelength depend on the propagation medium The ratio of the speed of light in vacuum, c, to the speed of light in a medium, v, is called the index of refraction n = c/v I Index of refraction also varies with the frequency of light, (we see this in prisms) Vacuum Silica Fiber HEM— 231THz 231THZ Wavelength I-ll—3*wnvs <2*wm Index of refraction Useful relationships are: I l» = c/f ( £ : 1)) I km = v/f I km = Mn I (where km refers to the wavelength in the medium) 2" )1" ...
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