Integrated Optical Waveguides

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1 Su Opls Faha Raa Cll Uvs Chap 8 Ia Opal Wavus 7 Dl Slab Wavus 7 Iu: A va f ff a pal wavus a us f a u lh a hp Th s bas pal wavu s a slab wavus shw blw Th suu s uf h - Lh s u s h b al al fl a h -la fas Cla C Cla s aual wavus a uf a f h - bu a b appa as slab wavus f h wh W s uh la ha h hkss as shw blw A b sp f h u lh s s f h pal s Th slab wavu supps w ff ks f ppaa s: T asvs l : I hs h l fl has p h f ppaa T asvs a s: I hs h a fl has p h f ppaa

2 Su Opls Faha Raa Cll Uvs T su hs s w sa f awll s quas Th pl f f awll s quas s S I al Rah ] [ Bu f s pws uf ff s h s ah a assu S w hav ah Slal wh h assup f pws uf w a w f h fl 7 T s: F T s h l fl a b w as I ah f pws uf a la sasfs Gv a valu f h fqu w a f all slus f h abv qua whh s a valu qua wh fu a valu O w hav h l fl h a fl a b fu as fllws Th bua s slv h valu qua abv a as fllws: -p f h l fl s uus a h -la fas -p f h a fl s uus a h -la fas -p f h a fl s uus a h -la fas hs s auaall sasf wh abv s sasf Th slus a labl wh h 3 S h fl f h T s wh h p f h fus a h ppaa v h fqu s pll a F h T s w assu h slu / / s s / / / C k k C C

3 Su Opls Faha Raa Cll Uvs lu h abv slus h qua w k k Us h bua s v T s slus s v T s s slus a k k k k A slu a b ba aphall b pl h lf a h ss f h abv quas as shw blw wh h lf s s pl us blu ls a h s us ls Blw a a fqu h -h ass s Ths u-ff fqu s Th valus f f ah a skh h Fu blw

4 Su Opls Faha Raa Cll Uvs Cla C T T Cla Th ppaa vs bhav as a h u-ff fqus a aspall appah h uv a hh fqus I s applas wavu ss a hs suh ha supps l Ulss ssa w wll usuall p h 73 T s: Sla aalss a b f h T s Assu F pws uf sasfs Assu slu f h f / C / k s k C / s k / C / Th bua s slv h valu qua abv a as fllws: -p f h a fl s uus a h -la fas -p f h l fl s uus a h -la fas -p f h l fl wh b h squa f h s uus a h -la fas hs s auaall sasf wh abv s sasf Us h bua s v k a k k k s slus v T s s slus T s Th abv las a sla hs ba f h T s h ha h fas a h squas f h a la fav s Th al bhav f h T s s sla h T s

5 Su Opls Faha Raa Cll Uvs 7 ffv I a Gup I: Th ffv ff f a s f b h la ff Th ffv f ah quals a h u-ff fqus a appahs a hh fqus Th up vl f a s v v s w as v wh s all h up f h 7 Tw Dsal Wavus 7 Iu: I slab wavus lh s f l s h -s u a as avls h - I s aual wavus lh s f w ss a - ss a avls h - F apl h ss-s f a aula wavu s shw blw Ufual h a s f suh D wavus a as as pl as hs f slab wavu Th s a h T T All s hav a sall p f a fls h f ppaa Th a h fls a b w as W hav f h asvs ps f h fls as fllws

6 Su Opls Faha Raa Cll Uvs S h a slu s fful a ubs sval lvls f appas a l us a a suss blw 7 Slus f D Wavus: W slv h qua subj all h pp bua s f h a fls a all h fas Th pa s Df F fllws ha Slal a b shw ha quas a shw ha kw h asvs ps f h fl s uh s h - ps a b f h asvs ps W slv Tak h asvs p vs 3 W f v a usful psss f h fs w s h h ha s Nw bu Th h qua 3 s

7 Su Opls Faha Raa Cll Uvs Us h suls abv qua 3 bs Th abv valu qua s wha s slv h a slu Ths qua a b pu h f wh h ffal pas a Th abv qua s a valu qua a s slu vs h asvs ps f h l fl f h a h sp ppaa sa a b ba f a as ala pla a fl a b ba f h la F pws uf s all vavs f h a b pp pv apppa bua s a us a all h fas 73 Th S-Val Appa: I a ass f paal s asvs p f h l fl h as v h h p I suh ass w a assu ha h h asvs fl p s F apl f w kw a p ha as h w a assu ha s a slv h uh spl valu qua Th abv qua s all h s-val appa F pws uf ls w a als w as

8 Su Opls Faha Raa Cll Uvs pv w ak a ps h bua s a all h l fas as apppa f h -p f h l fl O h a p has b fu h a fl ps a b fu as fllws Wh h hal l fl p as h s a ss all pq s T pq s wh a slh abus f l Wh h val l fl p as h s a all pq s T pq s aa wh a slh abus f l Th w subsps p a q a h ub f s h a l fl p has h hal a val s spvl 7 Th Sala Fl Appa: If p f h asvs l fl as v h h asvs p a h ffs a ff s h suu a als lavl sall h a us h s-val appa a als awa wh h bua s h al p f h l fl a all l fas F apl f w kw a p ha as h w a slv h qua

9 Su Opls Faha Raa Cll Uvs assu ha h fl a s vav a uus ass all l fas Ths s all h sala fl appa O h a l fl p has b fu h a fl ps a b fu as h as f h s-val appa Sala fl appa ss u bu vs v aua asws f h ppaa v h ffv ff as l as s f awa f h u-ff fqu I s als v aua alula f fas as w wll s la Chaps F s pa f hs us w wll us h sala fl appa kp h puaal vha lw O savaa f h sala fl appa s ha s ll aual whh h sl- hls s h sala fl appa s aua a u-ff 75 Slab Wavu Appa: If h asp a f h wavu s suh ha s s uh la ha h h s h h s a h sp wavvs a ffv s a b appa b hs f h sp slab wavu as suss al 76 a w Wavus: Th flw f la fls s v b h pl v ] [ ] R[ S S F wavus l a a fls a f h f Th al flw pw a wavu s ba b a h v v h ss-s f h wavu S ] [ ] [ Assu h u b spsv h p u lh f h wavu s W s h aal up f al as Th supsp s s as aus fus wh h up f h pal Th fllw la a als b pv Thf h p u lh a b w as

10 Su Opls Faha Raa Cll Uvs W Th ffv ff f a s ff Th up vl f a s v v s fqul pss s f h up f h v wh s all h up O a pv h fllw la bw h pw a h p u lh W vw whh a als b w as W R I h slab-wavu appa assu T s wh h asvs p f h l fl v b bas h fllw psss f vaus quas f s W [ ] ff 77 ps f Wavu s a Ohal f s: Fqul slus vaus ass vlv pass s f all h wavu s I suh ass kwl f h hal f h s s usful Th l a h a fls f h -h a b w as S usful pps f h wavus s a ls blw: Wh h s a al h ppaa vs a als al a h asvs fl ps a b hs b al as wll quas a shw ha hs as h -ps f h fls a pul aa Wh h s a al h pl jua f h l fl vs h fl f h ppaa h pps -vs F apl f pss h fl f h fwa ppaa h pss h fl f h bakwa ppaa

11 Su Opls Faha Raa Cll Uvs Wh h s a al h av f h pl jua f h a fl vs h fl f h ppaa h pps -vs F apl f pss h fl f h fwa ppaa h pss h fl f h bakwa ppaa v Cs w ff s a p wh h sa ppaa v bu ff fqus h h hal bw h fls s pss as p p f p p f v Cs w ff s a p wh h sa fqu bu ff ppaa vs h h hal bw h fls s pss as p p f v Th s al wa f pa a ha fl f a paula fqu s a wavu s s f h wavu s b a b a 78 Lual vs Tasvs s f a Wavu: Cs h l sps las shw blw f h fs h s f a wavu Th a s a all h asvs s f h wavu s hs s sb h fl pfl ss a ha a asvs h f ppaa Th fl pfl h f ppaa s sb b h ppaa v Th sps f h lws s pl blw a slhl ff wa ha als shws h sps f av valus f h ppaa v ppaa h - Dff valus f sp ff lual s f h wavu

12 Su Opls Faha Raa Cll Uvs bua s a b us f h ub f ff lual s sp a asvs a val f fqu Th pbl s al f h s f sas f phs s If h lh f h wavu s L h h a L ff lual s a val S v h a L v ff lual s a val Th fa f aus f h fwa a bakwa ppaa s 7 uba Th f Wavus 77 uba Th f Wavus: Of s s h ha h ppaa v f a ha s f a sall ha s paa suh as h fqu h fav f h u Th ha h ppaa v a b ba f h pl la vaaal h a h sul s R F apl f h fqu s ha h us h abv qua bas h fala sul W v R If h fav s ha h bas R I h slab wavu appa assu a T a h asvs p f h l fl v b bas h fllw pss f h ha h ppaa v wh h fav ff

13 Su Opls Faha Raa Cll Uvs 78 Cf Fas: Cs h wavu shw blw Th fav f h s a ha f h la s + Supps h fav f h has b Th ha h ppaa v a b fu as fllws R R R R R N ha s h aal up f h wavu a s h up f h wavu Th vlap al f as pss h fa f h s f h wavu s all h asvs f fa f h wavu Th ha h ppaa v s as p ppal a als h fa f h al s h Supps w h fav f h la als has b h h al ha h ppaa v a b w as a spl su

14 Su Opls Faha Raa Cll Uvs I h slab wavu appa assu a T a h asvs p f h l fl v b bas h fllw pss f h asvs f fa f h Th wavu puba h a b us alula h ha h ppaa v h ps f aal lss a Supps h f h wavu bs lss a h aa pa f h fav aqus a - valu v b I hs as w a ak h puba b Th ha h wavu ppaa sa bs ~ ~ wh ~ ~ ~ Th ppaa v aqus a sall aa pa baus f pal lss h wavu Th aa pa f h ppaa v wll aus h wav a wh sa as ppaas h wavu

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