Lecture 26. Dielectric Slab Waveguides
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1 Lectue 6 Delectc Slab Wavegudes In ths lectue yu wll lean: Delectc slab wavegudes T and TM guded mdes n delectc slab wavegudes C 303 Fall 005 Fahan Rana Cnell Unvesty T Guded Mdes n Paallel-Plate Metal Wavegudes ( y ˆ ( e j = > sn 0 H H H = ˆ + ˆ = ˆ + ˆ Guded T mdes ae T-waves buncng bac and futh between tw metal plates and ppagatng n the -dectn! The -cmpnent f the wavevect can have nly dscete values ts quanted m = whee : m =, d, 3, KK C 303 Fall 005 Fahan Rana Cnell Unvesty
2 Delectc Wavegudes - I Cnsde T-wave undegng ttal ntenal eflectn: = ˆ + ˆ H θ θ H = ˆ + ˆ j ( ( + j ( + = yˆ e + yˆ Γ e > 0 Γ = when θ > θc vanescent wave > + = When θ > θ c : ( j α y T e e = ˆ < 0 = jα α = C 303 Fall 005 Fahan Rana Cnell Unvesty Delectc Wavegudes - II vanescent wave H θ θ H H > vanescent wave One can have a guded wave that s buncng between tw delectc ntefaces due t ttal ntenal eflectn and mvng n the -dectn C 303 Fall 005 Fahan Rana Cnell Unvesty
3 Delectc Slab Wavegudes W d Assumptn: W >> d y C 303 Fall 005 Fahan Rana Cnell Unvesty Delectc Vs Metal Wavegudes m = m = Metal Wavegudes (mdes ae tghtly cnfned Delectc Slab Wavegudes (mdes ae lsely cnfned C 303 Fall 005 Fahan Rana Cnell Unvesty 3
4 Delectc Slab Wavegudes T Mdes: Fmal Slutn d symmetc The T slutns ae f the fm: cs( j ( = yˆ d e < sn( Whee: > d < d α ( ( d = yˆ e + j e + α ( ( + d j = yˆ e e + = α = antsymmetc C 303 Fall 005 Fahan Rana Cnell Unvesty The sne and csne epesent the symmetc and antsymmetc slutns w..t. the -as Gven a fequency, the values f,, and α ae stll nt nwn T Mdes: Bunday Cndtns d Bunday cndtns: ( At =± d the cmpnent f -feld paallel t the nteface (.e. the y-cmpnent s cntnuus f all cs( d ( sn( d ( At =± d the cmpnent f H-feld paallel t the nteface (.e. the -cmpnent s cntnuus f all sn( d α ( cs( d C 303 Fall 005 Fahan Rana Cnell Unvesty 4
5 T Mdes: Tanscendental quatn d Dvdng ( by ( n the pevus slde gves: ( d α ct( d But: + = α = S we fnally get: ct ( d ( α + = ( Tanscendental equatn that can be used t slve f n tems f the fequency C 303 Fall 005 Fahan Rana Cnell Unvesty T Mdes: Gaphcal Slutn d Gaphc slutn f the tanscendental equatn ct ( d ( d Dffeent ed cuves f Inceasng values LHS RHS F the m-th T mde (T m mde the value f s n the ange (dependng n the fequency : ( m d m d m =,,3,KK C 303 Fall 005 Fahan Rana Cnell Unvesty 5
6 T Mdes: Cut-ff Fequences d ct ( d ( d Dffeent ed cuves f Inceasng values LHS RHS Cut-ff fequency f the m-th T mde can be btaned by settng the RHS equal t e f d = (m-/ m = ( m d ( d m =,,3,KK C 303 Fall 005 Fahan Rana Cnell Unvesty Delectc Wavegudes What s Cut-ff? d H θ θ H H > θ S what des cut-ff eally mean? It means that the wave s n lnge beng guded thugh ttal ntenal eflectn snce θ < θ c A wave wll nt be guded f: θ < θ < < sn < c ( θ < sn( θ ( < c = C 303 Fall 005 Fahan Rana Cnell Unvesty F the m-th T mde (T m mde the smallest value f s: ( m d S T m mde wll nt be guded f: < m = ( ( m ( m d = d ( 6
7 T Mdes: Nea Cut-ff Behav Dffeent ed cuves f nceasng values >> (T mde well cnfned n the 0 3 d > (T mde nea cut-ff mde nt well cnfned n the C 303 Fall 005 Fahan Rana Cnell Unvesty T Mdes: Dspesn Cuves d Hw des ne btan dspesn cuves? ( F a gven fequency fnd usng: ct ( d ( Then fnd usng: ( d = T 3 mde dspesn elatn T mde dspesn elatn = = T mde dspesn elatn 3 C 303 Fall 005 Fahan Rana Cnell Unvesty 7
8 TM Mdes: Fmal Slutn d The TM slutns ae f the fm: cs( j H( = yˆ H d e < sn( α ( ( d j H = yˆ H e e > d + + α + d j H = y H e e ˆ < d Whee: ( ( + = α = The sne and csne epesent the symmetc and antsymmetc slutns w..t. the -as Gven a fequency, the values f,, and α ae stll nt nwn C 303 Fall 005 Fahan Rana Cnell Unvesty TM Mdes: Bunday Cndtns d Bunday cndtns: ( At =± d the cmpnent f H-feld paallel t the nteface (.e. the y-cmpnent s cntnuus f all cs( d H H ( sn( d ( At =± d the cmpnent f -feld paallel t the nteface (.e. the -cmpnent s cntnuus f all sn( d α H H ( cs C 303 Fall 005 Fahan Rana Cnell Unvesty 8
9 TM Mdes: Tanscendental quatn d Dvdng ( by ( n the pevus slde gves: ( d α ( d ct But: + = α + = α = S we fnally get: tan( d ( = d ct( d ( d ( Tanscendental equatn that can be used t slve f n tems f the fequency C 303 Fall 005 Fahan Rana Cnell Unvesty TM Mdes: Gaphcal Slutn d Gaphc slutn f the tanscendental equatn ct ( d ( d Dffeent ed cuves f Inceasng values LHS RHS F the m-th TM mde (TM m mde the value f s n the ange (dependng n the fequency : ( m d m d m =,,3,KK C 303 Fall 005 Fahan Rana Cnell Unvesty 9
10 Fbe Optcal Cmmuncatns: Optcal Fbes 9.0 m 5 m Slca (SO and mateals C 303 Fall 005 Fahan Rana Cnell Unvesty Integated Optcs um An ptcal mc-ng flte (sepaates ut lght f a patcula cl SM An ptcal mc-spltte (splts lght tw ways SM Slab Wavegude S S SO SO S S C 303 Fall 005 Fahan Rana Cnell Unvesty 0
11 Integated Optcs: Semcnduct Quantum Well Lases tp metal InP/InGaAsP Wavegude.0 m thc plymde laye 3.0 m The delectc wavegude f a semcnduct quantum well lase wth metal n tp (f electcal cnnectn s shwn A mcchp cntanng seveal semcnduct lase stpes unnng n paallel s shwn. C 303 Fall 005 Fahan Rana Cnell Unvesty
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