Optical Devices for High Speed Communication Systems. Lecture Notes

Transcription

1 Optical Devices for High Speed Commuicatio Systems Lecture Notes

2 Optoelectroic Devices & Commuicatio Networks Motreal λ λ Switch λ 3 WDM Amplifier λ Add/Drop WDM λ Ottawa Toroto λ λ 3 WDM Switch Amplifier λ

3 Optoelectroic Devices for Commuicatio Networks» Optical Sources» LD» Laser» Optical Diodes» WDM» Fiber Optics» Optical Amplifiers» Optical Atteuators» Optical Isolators» Optical Switches» Add/Drop Devices

4 Optoelectroic Devices for Commuicatio Networks Requiremets to uderstad the cocepts of Optoelectroic Devices:. We eed to study cocepts of light properties. Some cocepts of solid state materials i particular semicoductors. 3. Light + Solid State Materials

5 Light Properties Wave/Particle Duality Nature of Light Reflectio Sell s Law ad Total Iteral Reflectio (TIR) Reflectio & Trasmissio Coefficiets Fresel s quatios Itesity, Reflectace ad Trasmittace Refractio - Refractive Idex Iterferece - Multiple Iterferece ad Optical Resoators Diffractio Frauhofer Diffractio Diffractio Gratig

6 Light Properties Dispersio Polarizatio of Light lliptical ad Circular Polarizatio Birefriget Optical Devices lectro-optic ffects Mageto-Optic ffects

7 Some Cocepts of Solid State Materials Cotets The Semicoductors i quilibrium Noequilibrium Coditio Geeratio-Recombiatio Geeratio-Recombiatio rates Photolumiescece & lectrolumiescece Photo Absorptio Photo missio i Semicoductors Basic Trasitios Radiative Noradiative Spotaeous missio Stimulated missio Lumiescece fficiecy Iteral Quatum fficiecy xteral Quatum fficiecy Photo Absorptio Fresel Loss Critical Agle Loss ergy Bad Structures of Semicoductors PN juctios Homojuctios, Heterojuctios Materials III-V semicoductors Terary Semicoductors Quaterary Semicoductors II-VI Semicoductors IV-VI Semicoductors

8 Light The ature of light Wave/Particle Duality Nature of Light c hν h mc p λ h λ --Particle ature of light (photo) is used to explai the cocepts of solid state optical sources (LASR, LD), optical detectors, amplifiers, --The wave ature of light is used to explai refractio, diffractio, polarizatio, used to explai the cocepts of light trasmissio i fiber optics, WDM, add/drop/ modulators,

9 The wave ature of Light

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11 The wave ature of Light Polarizatio Reflectio Refractio Diffractio Iterferece To explai these cocepts light ca be treated as rays (geometrical optics) or as a electromagetic wave (wave optics, studies related to Maxwell quatios). A electromagetic wave cosist of two fields: lectric Field Magetic Field

12 x x Directio of Propagatio k z z y B y A electromagetic wave is a travellig wave which has time varyig electric ad magetic fields which are perpedicular to each other ad the directio of propagatio, z. 999 S.O. Kasap, Optoelectroics (Pretice Hall) A electromagetic wave cosist of two compoets; electrical field ad magetic field compoets. k is the wave vector, ad its magitude is π/λ Light ca treated as a M wave, x ad By are propagatig through space i such a way that they are always perpedicular to each other ad to the directio of propagatio z.

13 The wave ature of Light We ca treat light as a M wave with time varyig electric ad magetic fields. x ad B Y which are propagatig through space i such a way that they are always perpedicular to each other ad to the directio of propagatio z. ( ω t k + ) ( r, t) r φ 0 cos. 0

14 z B ad B have costat phase i this xy plae; a wavefrot k Propagatio x x o si(ωt kz) z A plae M wave travellig alog z, has the same x (or B y ) at ay poit i a give xy plae. All electric field vectors i a give xy plae are therefore i phase. The xy plaes are of ifiite extet i the x ad y directios. 999 S.O. Kasap, Optoelectroics (Pretice Hall)

15 The wave ature of Light ( r, t ) ( ω t kr + φ ) 0 cos 0 y Directio of propagatio k x ( z, t) Re[ 0 e e jφ 0 j ( ωt kz ) ] θ r r (r,t) φ ωt kz+ φ 0 costat z O A travellig plae M wave alog a directio k 999 S.O. Kasap, Optoelectroics (Pretice Hall) Durig a time iterval Δt, a costat phase moves a distace Δz, Phase velocity V Δz Δt dz dt ω νλ k ω πν Δ φ kδ z π Δ z λ

16 Wave frots (costat phase surfaces) Wave frots k Wave frots lectric field compoet of M wave: λ λ P r k P λ O z A perfect plae wave A perfect spherical wave A diverget beam (a) (b) (c) ( r, t ) ( ω t kr + φ ) A cos ω r 0 cos ( t kr) 0 xamples of possible M waves 999 S.O. Kasap, Optoelectroics (Pretice Hall) Plae wave Spherical wave These are the solutios of Maxwell s equatio εμ Maxwell s Wave quatios t

17 Wave frots y (b) x w o O z Beam axis θ Gaussia Itesity (c) (a) (a) Wavefrots of a Gaussia light beam. (b) Light itesity across beam cross sectio. (c) Light irradiace (itesity) vs. radial distace r from beam axis (z). 999 S.O. Kasap, Optoelectroics (Pretice Hall) w r Wo is called waist radius ad Wo is called spot size θ 4λ π ( w 0 ) Is called beam divergece

18 Refractive Idex V εμ V c ε μ Phase velocity Speed of light ε ε rε 0 c v ε r k(medium) k λ(medium) λ/ Isotropic ad aisotropic materials?

19 ω + δω ω δω max max δk δω Wave packet ω Two slightly differet wavelegth waves travellig i the same directio result i a wave packet that has a amplitude variatio which travels at the group velocity. 999 S.O. Kasap, Optoelectroics (Pretice Hall) dz/dt δω/δk or V g dω/dk group velocity

20 N g Wavelegth (m) ω vk c ( π λ) λ dω c v g ( medium) dk d λ dλ Refractive idex ad the group idex N g of pure SiO (silica) glass as a fuctio of wavelegth. 999 S.O. Kasap, Optoelectroics (Pretice Hall) c N g

21 vδt z Area A k Propagatio directio B A plae M wave travellig alog k crosses a area A at right agles to the directio of propagatio. I time Δt, the eergy i the cylidrical volume AvΔt (show dashed) flows through A. 999 S.O. Kasap, Optoelectroics (Pretice Hall) I M wave a magetic field is always accompayig electric field, Faraday s Law. I a isotropic dielectric medium x vby c/ (By), where v is the phase velocity ad is idex of refractio of the medium.

22 y Structure of Fiber Optics y Claddig Core φ r z Fiber axis The step idex optical fiber. The cetral regio, the core, has greater refractive idex tha the outer regio, the claddig. The fiber has cylidrical symmetry. We use the coordiates r, φ, z to represet ay poit i the fiber. Claddig is ormally much thicker tha show. 999 S.O. Kasap, Optoelectroics (Pretice Hall)

23 A B y θ θ a A C π θ θ π/ k x θ z B Two arbitrary waves ad that are iitially i phase must remai i phase after reflectios. Otherwise the two will iterfere destructively ad cacel each other. 999 S.O. Kasap, Optoelectroics (Pretice Hall)

24 A Guide ceter θ k θ A C a y y π θ a x y z Iterferece of waves such as ad leads to a stadig wave patter alog the y- directio which propagates alog z. 999 S.O. Kasap, Optoelectroics (Pretice Hall)

25 Field of evaescet wave (expoetial decay) y Field of guided wave (y) m 0 (y,z,t) (y)cos(ωt β 0 z) Light The electric field patter of the lowest mode travelig wave alog the guide. This mode has m 0 ad the lowest θ. It is ofte referred to as the glazig icidece ray. It has the highest phase velocity alog the guide. 999 S.O. Kasap, Optoelectroics (Pretice Hall) ( y z, t) cos k y + φ cos ωt β z + k y + φ, 0 m m m m m ( y, z, t) ( y) cos( ωt β z) m m

26 y Claddig (y) m 0 m m Core a Claddig The electric field patters of the first three modes (m 0,, ) travelig wave alog the guide. Notice differet extets of field peetratio ito the claddig. 999 S.O. Kasap, Optoelectroics (Pretice Hall)

27 High order mode Low order mode Itesity Light pulse Claddig Core Broadeed light pulse Itesity Axial Spread, Δτ 0 t t Schematic illustratio of light propagatio i a slab dielectric waveguide. Light pulse eterig the waveguide breaks up ito various modes which the propagate at differet group velocities dow the guide. At the ed of the guide, the modes combie to costitute the output light pulse which is broader tha the iput light pulse. 999 S.O. Kasap, Optoelectroics (Pretice Hall)

28 Sell s Law ad Total Iteral Reflectio (TIR) A t siθ siθ siθ siθ V V i i t t V V i i r r A i λ y O Refracted Light A z A λ t k t B t θ t θ t B θ i θ r θ i θ r k i A B λ k r B r Icidet Light B i A r Reflected Light Vi Vr, therefore θi θr A light wave travellig i a medium with a greater refractive idex ( reflectio ad refractio at the boudary. 999 S.O. Kasap, Optoelectroics (Pretice Hall) > ) suffers Whe θt reaches 90 degree, θi θc called critical agle si θ c, We have total iteral reflectio (TIR)

29 Trasmitted (refracted) light θ t k t vaescet wave k i Icidet light θ i θ i k r > θ c θ c θ i >θ c TIR Reflected light (a) (b) (c) Light wave travellig i a more dese medium strikes a less dese medium. Depedig o the icidece agle with respect to θ c, which is determied by the ratio of the refractive idices, the wave may be trasmitted (refracted) or reflected. (a) θ i < θ c (b) θ i θ c (c) θ i > θ c ad total iteral reflectio (TIR). 999 S.O. Kasap, Optoelectroics (Pretice Hall) v t, ε r ε 0 μ 0 y ( x y z) e α, exp j( ωt k z), i0 c v ε r iz Isotropic ad aisotropic materials α π si θ i λ α is the atteuatio coefficiet ad / α is called peetratio depth

30 Trasverse electric field (T) Trasverse magetic Field (TM) i r i0 e r 0 e j( ωt k i. r j ( ωt k r ). r ) y x ito paper z i,// Icidet wave k i θ t θ i θ r i, r,// t,// Trasmitted wave k t t, r, k r Reflected wave (a) θ i < θ c the some of the wave is trasmitted ito the less dese medium. Some of the wave is reflected. i,// Icidet wave i, θ i θ r θ t 90 t, vaescet wave r,// r, Reflected wave (b) θ i > θ c the the icidet wave suffers total iteral reflectio. However, there is a evaescet wave at the surface of the medium. > Light wave travellig i a more dese medium strikes a less dese medium. The plae of icidece is the plae of the paper ad is perpedicular to the flat iterface betwee the two media. The electric field is ormal to the directio of propagatio. It ca be resolved ito perpedicular ( ) ad parallel (//) compoets 999 S.O. Kasap, Optoelectroics (Pretice Hall) t t 0 e j( ωt k t. r )

31 Fresel s quatios: usig Sell s law, ad applyig boudary coditios: r r0, i0, cosθ i cosθ + i [ si θ ] i [ si θ ] i t t0, i0, cosθ + i cosθ i [ ] si θ i r // r0,// i0,// [ si θi ] cos i [ si θi ] + cos i θ θ t // t0,// i0,// cosθ + cosθ i i [ ] si θ i /

32 Polarizatio agle ta θ p Magitude of reflectio coefficiets (a) r θ p θ c r // Icidece agle, θ i Phase chages i degrees (b) φ // θ p θ c TIR φ Icidece agle, θ i Iteral reflectio: (a) Magitude of the reflectio coefficiets r // ad r vs. agle of icidece θ i for.44 ad.00. The critical agle is 44. (b) The correspodig phase chages φ // ad φ vs. icidece agle. 999 S.O. Kasap, Optoelectroics (Pretice Hall) ta θ [ si θ ] i cosθ i ad ta θ // + π [ si θ ] i cosθ i

33 xteral reflectio θ p r // r Icidece agle, θ i The reflectio coefficiets r // ad r vs. agle of icidece θ i for.00 ad S.O. Kasap, Optoelectroics (Pretice Hall)

34 0 r o V I ε ε 0, 0, r R i r // 0,// 0,// // r R i r // + R R R 0, 0, t T i t // 0,// 0,// // t T i t ( ) // 4 T T T + Light itesity Reflectace for ormal icidet Trasmittace

35 d 3 A B Surface Atireflectio coatig Semicoductor of photovoltaic device Illustratio of how a atireflectio coatig reduces the reflected light itesity 999 S.O. Kasap, Optoelectroics (Pretice Hall)

36 λ /4 λ /4 Reflectace A B C 0 λ (m) λ o Schematic illustratio of the priciple of the dielectric mirror with may low ad high refractive idex layers ad its reflectace. 999 S.O. Kasap, Optoelectroics (Pretice Hall)

37 Light Ligh Light Light > A plaar dielectric waveguide has a cetral rectagular regio of higher refractive idex tha the surroudig regio which has a refractive idex. It is assumed that the waveguide is ifiitely wide ad the cetral regio is of thickess a. It is illumiated at oe ed by a moochromatic light source. 999 S.O. Kasap, Optoelectroics (Pretice Hall)

38 B λ Light y κ θ k A β θ θ d a x z C A light ray travellig i the guide must iterfere costructively with itself to propagate successfully. Otherwise destructive iterferece will destroy the wave. 999 S.O. Kasap, Optoelectroics (Pretice Hall) ΔΦ (AC) k(ab + BC) - Φ m(π), k k π/λ m0,,, π λ ( a ) cos θ m φ m m π Waveguide coditio β m π k siθ m siθ m λ k m π k cosθ m cosθ m λ

39 Field of evaescet wave (expoetial decay) y Field of guided wave (y) m 0 (y,z,t) (y)cos(ωt β 0 z) Light The electric field patter of the lowest mode travelig wave alog the guide. This mode has m 0 ad the lowest θ. It is ofte referred to as the glazig icidece ray. It has the highest phase velocity alog the guide. 999 S.O. Kasap, Optoelectroics (Pretice Hall) ( y z, t) cos k y + φ cos ωt β z + k y + φ ( y, z, t) ( y) cos( ωt β z) m, 0 m m m m m m

40 y Claddig (y) m 0 m m Core a Claddig The electric field patters of the first three modes (m 0,, ) travelig wave alog the guide. Notice differet extets of field peetratio ito the claddig. 999 S.O. Kasap, Optoelectroics (Pretice Hall)

41 High order mode Low order mode Itesity Light pulse Claddig Core Broadeed light pulse Itesity Axial Spread, Δτ 0 t t Schematic illustratio of light propagatio i a slab dielectric waveguide. Light pulse eterig the waveguide breaks up ito various modes which the propagate at differet group velocities dow the guide. At the ed of the guide, the modes combie to costitute the output light pulse which is broader tha the iput light pulse. 999 S.O. Kasap, Optoelectroics (Pretice Hall) y (m) is the field distributio alog y axis ad costitute a mode of propagatio. m is called mode umber. Defies the umber of modes travelig alog the waveguide. For every value of m we have a agle θm satisfyig the waveguide coditio provided to satisfy the TIR as well. Cosiderig these coditio oe ca show that the umber of modes should satisfy: m (V Φ)/π πa λ V is called V-umber ( ) V For V π/, m 0, it is the lowest mode of propagatio referred to sigle mode waveguides. The cut-off wavelegth (frequecy) is a free space wavelegth for v π/

42 (a) T mode (b) TM mode y B // B y θ θ // y θ θ B z z B O z x (ito paper) Possible modes ca be classified i terms of (a) traselectric field (T) ad (b) trasmagetic field (TM). Plae of icidece is the paper. 999 S.O. Kasap, Optoelectroics (Pretice Hall)

43 y y Claddig λ > λ c λ > λ v g Core v g > v g ω < ω cut-off ω < ω (y) Claddig The electric field of T 0 mode exteds more ito the claddig as the wavelegth icreases. As more of the field is carried by the claddig, the group velocity icreases. 999 S.O. Kasap, Optoelectroics (Pretice Hall)

44 y y Claddig Core φ r z Fiber axis The step idex optical fiber. The cetral regio, the core, has greater refractive idex tha the outer regio, the claddig. The fiber has cylidrical symmetry. We use the coordiates r, φ, z to represet ay poit i the fiber. Claddig is ormally much thicker tha show. 999 S.O. Kasap, Optoelectroics (Pretice Hall) Alog the fiber Meridioal ray Fiber axis 3, 3 (a) A meridioa ray always crosses the fibe axis. Fiber axis 3 Skew ray (b) A skew ray does ot have to cross the fiber axis. It zigzags aroud the fiber axis. Ray path alog the fiber Illustratio of the differece betwee a meridioal ray ad a skew ray. Numbers represet reflectios of the ray. 999 S.O. Kasap, Optoelectroics (Pretice Hall) Ray path projected o to a plae ormal to fiber axis For the step idex optical fiber Δ ( )/ is called ormalized idex differece

45 (a) The electric field of the fudametal mode (b) The itesity i the fudametal mode LP 0 (c) The itesity i LP (d) The itesity i LP Core Claddig LPs (liearly polarized waves) propagatig alog the fiber have either T or TM type represeted by the propagatio of a electric field distributio lm(r,φ) alog z S.O. Kasap, Optoelectroics (Pretice Hall) r The electric field distributio of the fudametal mod i the trasverse plae to the fiber axis z. The light itesity is greatest at the ceter of the fiber. Itesity patters i LP 0, LP ad LP modes. LP ( r. ϕ) j( ωt β z) exp lm lm LP is the field of the LP mode ad βlm is its propagatio costat alog z.

46 V-umber V πa πa λ λ ( ) ( ) Δ Δ ( ) ( ) / / V cut off πa λ c ( ). 405 Normalized idex differece For V.405, the fiber is called sigle mode (oly the fudametal mode propagate alog the fiber). For V >.405 the umber of mode icreases accordig to approximately V M

47 b 0.8 LP 0 b ( / K ) β LP LP LP V Normalized propagatio costat b vs. V-umber for a step idex fiber for various LP modes. 999 S.O. Kasap, Optoelectroics (Pretice Hall)

48 siα NA max ( ) ( 0 / ) α<α max A B α>α max 0 Lost B θ < θ c Claddig θ > θ Propagates c Fiber axis A Core 999 S.O. Kasap, Optoelectroics (Pretice Hall) Maximumacceptace agle α max is that which just gives total iteral reflectio at the core-claddig iterface, i.e. whe αα max the θθ c. Rays with α>α max (e.g. ray B) become refracted ad peetrate the claddig ad are evetually lost. siα max NA 0 V π a λ NA