Time Domain Modelling of Optical Add-drop filter based on Microcavity Ring Resonators

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1 IOSR Jour of ecroc d Commuco geerg IOSR-JC e-issn: p- ISSN: Voume Iue 6 Ver. II Nov - Dec.5 PP Tme Dom Modeg of Opc Add-drop fer bed o Mcrocv Rg Reoor Nbe A. Abuh Ro e Fh Awfe 3 Sh Ob 4 Deprme of ecrc d ecroc geerg Fcu of geerg Uver of Au-b geerg Deprme cer Uver cer A 4YR.UK 3 Deprme of ecrc d ecroc geerg Fcu of Scece geerg d Techoog Uver of Sebh-b. 4 Cere for Phooc d Smr Mer Zew C of Scece d Techoog Shekh Zed Drc 6 h of Ocober c G gp Abrc: I h pper ccure of wo-dmeo D couped rg reoor bed o hghde-cor crred ou. The ormed rmo pecr for ge-rg d doube-rg cofguro hve bee veged b ug robu d ccure Mureouo Tme Dom MRTD echque wh couco wh u perfec mched er UPM borbg boudr codo h rgorou erme he compuo wdow. The reo-mode qu fcor Q free pecr rge FSR re umerc veged. The vro of he rucure prmeer uch he mmerc d mmerc gp e g ed o drmc chge of Q d he eco ro of he devce. Sude of he rmo chrcerc for he rg dmeer of 3.4 μm how he pob for chevg Q ever houd d FSR of 9 TZ 8m he.55 μm wveegh rge. Keword:- mureouo me dom mcrocv umerc rg reoor me dom mehod. I. Iroduco Rece dvce mcro d ofbrco echoog hve brough ew ere budg opc devce wh phc dmeo comprbe o opc wveegh [ ]. I prcur mcrocv reoor bed o whperg-ger-mode WGM p gfc roe m ppco rgg from quum eecrodmc o eecommuco devce d opc eor [3-8]. A prcur wveegh gh he bu e wvegude c evece couped hrough he gp o WGM of he reoor f proper phe mchg codo e. B me of refrcve de cor bewee core d cddg gh whch rveg medum of crcur geomer uch rg c be reo cofed b o er refeco TIR[9]. Thee mode c reoe wh hgh qu fcor Q he cv where he og phoo feme ow he fed wh he cv o be bu from coderb weker pu [] []. orc he org cocep of opc rg reoor bck de o 969[] where reve opc rg reoor mde drec er wre pomer[3] d o-echged g ubre[4] were demored. owever due o ow-de-cor bewee he reoor medum d he urroudg mer he rdu eeded o be of he order of ever cemere o bed oe [] [5]. I he few er reerch ere h bee rog dreced o he deg of opc rg reoor bed o hgh-de-cor emcoducor mer [ 6 7]. Thee reerch effor hve cer demored h hee rucure ur perm reo of mrdu mcrocve wh eggbe bedg oe reug rge ogud mode pcg. For h reo he ebe he egro of rge umber of devce o opc crcu foreee for ver rge ce egred VSI phooc []. For cve devce ppco wde rge of reerch ude c be foud erure o rog gudg emcoducor rg er wh dmeer rgg from o 5 µm. d rge wvegude wdh from 4 o µm [8] [9] []. I order o cqure gh oupu hee rg reoor re couped o oupu b me of Y uco. Thk o eg emcoducor fbrco echque gh he bu wvegude c be evece couped hrough he gp o whperg ger mode of he reoor f he proper phe mchg codo e. Opc mcrorg reoor MRR bed o hgh-de-cor emcoducor wvegude re be o uppor rog cofed WGM wh dmeer m - µm[]. If he free pecr rge FSR of he rg c be mde wde eough o ccommode he e of WDM che wh he commuco wdow oe c cheve he go of droppg oe che b oe fer whou ffecg he oher che. To eure FSR rger h he opc commuco wdow 3m rg rdu of e h 5 μm requred. Sce he MRR hve bee recoged compced rucure d co be ed b ug mpe echque he chrcero of hee devce uu ecee fu-wve eecromgec muor. I order o chooe prcur muo pproch geer wo crer hve o be ke o ccou. Fr he dered reu eeded o be ccomphed wh vbe reource d ecod DOI:.979/ Pge

2 Tme Dom Modeg of Opc Add-drop fer bed o Mcrocv Rg Reoor CPU muo me h o be opmed o ob hee reu. Sce he fr pec reed o he covergece re of he ued echque rge compuo probem c be uded wh hgh coverge gorhm. O he oher de he eecuo muo me o o ree o he co of me per me ep bu o deped o he umber of me ep h hve o be crred ou. Amog he eg fu-wve echque Fe Dfferece Tme Dom FDTD kow popur frmework for ow-co feb ude d perm deg opmo before fbrcg he devce[]. Ahough h echque rghforwrd d dpbe pu hev burde o compuer reource pec whe modeg compe probem wh rge compuo voume. The more ophced MRTD echque ued here o e MRR devce [-3]. Th echque w roduced b Krumpho d Keh 996 [4] for he mcrowve rge d h bee rece eeded o for he opc rge [3]. Th mehod ue hgh order of ppromo of dervve pce o reduce he umerc phe error of FDTD. B dog o MRTD doe o requre he ue of ver fe meh e o dcree he rucure geomer d hgh umerc ccurc c be cheved whe mgg he compuo burde. Therefore he pob of vg CPU rug me mke he MRTD effce erve umerc cheme o he commo ued FDTD for he deg of mcrorg rucure. I h pper MRTD h bee ued o e he rmo chrcerc of dffere order of MRR. The m focued o he erco of dffere reo mode where dffere vego hve bee crred ou o epore he effec of dffere prmeer of he rucure o rmed d couped power. Prmeer uch gp e he dce bewee wo rg d he wdh of rg d wvegude hve bee vred d e of dffere reu hve bee preeed. Th pper orged foowg. Foowg h roduco bref mhemc gve eco. The muo reu re preeed eco 3. F cocuo re drw. II. A Srg from Mwe equo d for D rucure - pe he rvere eecrc mode T wh compoe d derved uder umpo h - he homogeeou dreco d he - he propgo dreco. b r c Wh repec o he u ce how Fg. he eecromgec fed re epded combo of cg fuco pce d r fuco me ug h where d re he dcree dee me d pce repecve Φ he cg fuco repreeg he mpg pce h he r fuco d compoe o whch he erve proce of upde pped o. he epo coeffce for DOI:.979/ Pge

3 Tme Dom Modeg of Opc Add-drop fer bed o Mcrocv Rg Reoor DOI:.979/ Pge Fgure : ecrc d mgec fed epo pced de -D MRTD u ce. Subug he fed epo he form of 4 o he cr Mwe equo d eg hem wh he du of he borhogo cg fuco m ~ wh m= b ppg he mehod-of-mome ed o he dcreed upde equo [3]: 3 3b 3c where µ ε re permeb d permv of he free pce repecve ε he reve permv of he medum d Δ me ep. Δ d Δ re he p creme he dreco of d repecve. The ec e d for he effecve uppor of he b fuco h deerme he umber of epo coeffce codered he ummo d equ o 5 for CDF4 whe repree he coeco coeffce h c be umerc ccued ug [3] ' ' d 4 The vue of he coeco coeffce for he ce of CDF4 re repored []. I order o eure he umerc b of he MRTD cheme he me erv Δ h o be mer h cer m foow c 5 wh 6

4 Tme Dom Modeg of Opc Add-drop fer bed o Mcrocv Rg Reoor DOI:.979/ Pge where Δ=Δ=Δ c he peed of he gh d he Cour umber repree he b fcor whch covee fed o. hrough he pper [3]. The u perfec mched er UPM re ver effce d robu w o erme he compuo dom wh er of rfc borber h cpbe of ver-ow refeco d h bee uccefu corpored wh MRTD cheme boudr codo. A empe he dcreed equo o upde compoe hrough he dpceme vecor D re repored here D D 7 D D 7 b where ε he reve permv of he medum d σ d σ re he eecrc coducve of he UPM og d dreco repecve. Aogue equo re derved for he mgec fed compoe [3]. For he be performce of UPM borbg boudr codo he prmeer σ = choe o vr pce m m d m 8 where = d he deph of he UPM d m d for he order of he poom vro. The choce of σ m h mme refeco from he boudre [5] r m 5 m 9 where Δ he p dcreo doped = d he deph of he UPM d m d for he order of he poom vro. The choce of σ m h mme refeco from he boudre [5] r m 5 m 9 where Δ he p dcreo doped. III. Reu Ad Dcuo A fr rucure he ge MRR how Fg. h bee codered where he wdh W =.3 µm he rg dmeer d = 3.4 µm d he core d he cddg hve refrcve dce of core = 3. d c = repecve.

5 Tme Dom Modeg of Opc Add-drop fer bed o Mcrocv Rg Reoor Fgure : Schemc of mcrorg reoor couped o wo rgh wvegude. The rucure dcreed o uform meh wh ce e Δ = Δ = Δ = 7.5 m d ermed b -ce UPM o borb he refeced power.. I mpor o oce h he choe Δ bou wce he vue requred b prevou of MRR rucure b me of FDTD foud []. Where he me eve of ccurc c be cheved d he pob o ve he CPU rug me o c be obed. A Gu hped pue pce wh cer frequec f = T λ =.5µm modeed wh Gu pue me h bee ued o ece he rucure o cover he frequec rge of ere. A how Fg. dffere croeco re choe order o record he me dom vro he cde rmed d refeced fed. B me of F Fourer Trform FFT of he recoded me-depede fed he couped power por C d he rmed power por B re ccued b dvdg he couped d rmed pecr b cde pecrum por A repecve. The effec of he gp e g o couped power κ d Q how Fg.3 he reoce mode of 53 m. Fgure 3: ffec of he gp wdh o he reoce qu fcor d coupg coeffce. DOI:.979/ Pge

6 Tme Dom Modeg of Opc Add-drop fer bed o Mcrocv Rg Reoor I ppre h cree of g h gfc effec o boh Q d κ. Sce wh he cree gp e he coupg effcec of he reoce mode decree due o m frco of power echged whe he Q vue cree. The coupg effcec c be ehced order o compee he oe he cv d h w mprove he rmo. owever he qu fcor w be degrded. For h reo he opmum vue of gp e eed o be crefu choe order o cheve reobe hgh qu fcor whe he coupg effcec wh derbe rge. Accordg o Fg. 3 good comprome c be cheved b choog he g = 8 m where he vue of he κ d Q re.4 % d 398 repecve. Ne he rmo por B for 3.4 µm-dmeer rg d 8 m of g codered. The meured rmo pecrum of ge-rg reoor roud λ =.55 μm preeed Fg. 4. Fgure 4: MRTD-compued Trmo for.7-µm-rdu mcrorg reoor couped o rgh.3-µmwde wvegude. From h fgure he oced reoce wveegh d Q d correpodg coupg effcec re ed be I. TAB I Reoce D from Fg.4 for 3.4 μm-dmeer MRR d w =.3 μm m F T λ re m Q The Q of he m h reoce erced drec from power pecrum b formg he ro of he reo wveegh λ m o he wdh of he reoce δλ he hf-power po. The FSR whch defed he pcg bewee wo dce reo wveegh rge bewee 6 o 8 m. The reeco ro or o/off ro whch he ro of power rmed reoce wveegh o he power o rmed reoce wveegh pprome 6dB. Fg.5 how he vro of eco ro fuco of gp e. DOI:.979/ Pge

7 Tme Dom Modeg of Opc Add-drop fer bed o Mcrocv Rg Reoor Fgure 5: ffec of he gp wdh o he o-off ro. A c bee ee from Fg. 5 he eco ro c be ered b vrg he coupg effcec κ. owever he Q w be o ffeced h mer dced from Fg. 3. ve hough he reeco ro requred beg rge eough o mme he crok he qu fcor eeded o be hgh ome ppco reed o WDM. I order o cree he eco ro whe he reobe qu fcor c be o obed doube pre mcrocv rg reoor DPMRR uggeed. The rucure how Fg. 6 co of wo pre rg reoor cered bewee wo rgh wvegude. Fgure.6: pre couped mcrorg reoor doube rg ce. The foowg eeco of prmeer re choe foowg: he dmeer of rg re d = 3.4 µm he core d he cddg hve refrcve dce of core = 3. d c = repecve he wdh of rg d rgh wvegude re W =.3 µm he gp wdh bewee he ouer rg d rgh wvegude e o be 8 m. The rucure eced he me mer ge rg. The dce from cere o cere deoed b Λ bewee wo rg e o 5 μm. The rmo chrcerc how Fg. 7 cheved ug DPMRR. DOI:.979/ Pge

8 Tme Dom Modeg of Opc Add-drop fer bed o Mcrocv Rg Reoor Fgure.7: MRTD-compued Trmo for.7-µm-rdu doube mcrorg reoor couped o rgh.3- µm-wde wvegude where he dce bewee wo rg 5 µm. The oced reoce wveegh erced d Q of he m h reoce ccued drec from power pecrum he me mer ge rg ce. Thee reu re ed be II. Tbe II Rece D From Fg. 7 For 3.4-μm-Dmeer PDMRR d w =.3 μm m F T λ re m Q A how h be here gh chge he qu fcor. Whe he o- off ro rge bewee 4 o db dffere reoce wveegh. The effec of chge he gp e bewee he pu d oupu wvegude d he rg codered. Two pe of chge of g d g re dcued. Chge boh gp dec d chge o oe of he gp e whe keepg he oher co. Fgure 8 d 9 how he effec of he mmerc chge where g= g =9 m d mmerc chge where g=9 m d g=45 m. The dce bewee wo rg e o Λ=5µm. Bed o he coupg whch decree hgh frequece he Q houd cree wh frequec. Such behvour oberved Fg. 8. DOI:.979/ Pge

9 Tme Dom Modeg of Opc Add-drop fer bed o Mcrocv Rg Reoor Fgure.8: ffec of mmerc d mmerc chge of boh epro dce o he qu fcor. owever he gp wdh g g re reduced he coupg effcec bewee he rgh pu wvegude d he cv cree whe he rmed power hroughou por decree. Due o he decree he eve of rmed power hroughou por hgher o-off ro cheved whe he eve of he Q decreed. Fgure 9 how he MRTD reu for DPMRR for mmerc gp wdh. Fgure. 9: ffec of mmerc d mmerc chge of boh epro dce o he o-off ro. Keepg he gp wdh g co d g creed d he he coupg bewee he pu wvegude d he cv cree. Due o he cree he eve of coupg power he eve of rmed power hroughou por decree. O he oher hd keepg he gp wdh g co f g creed he he coupg bewee he oupu wvegude d he cv decree. A more power remed he cv he Q creed whe he eve of o-off ro decree. Fgure how he eecrc fed per bewee he wvegude d he cv whe uod coue wve h bee eced d reched he ed e. The wveegh of he uod fed 655 m 8. T. A how h fgure er % of he power wched o he cv whch ur wched o he oupu wvegude. DOI:.979/ Pge

10 Tme Dom Modeg of Opc Add-drop fer bed o Mcrocv Rg Reoor Fgure.: Suod ed-e mpude drbued.7-µm-rdu mcrorg reoor: ON-reoce 655 m I he me mer he ed-e -fed compued for eco oreo wveegh 65 m 85.7 T ured Fg. A how h fgure o coupg occurred bewee he pu wvegude d he cv d % of he g rmed oupu por B. Fgure.: Suod ed-e mpude drbued.7-µm-rdu mcrorg reoor: OFF-reoce 65 m IV. Cocuo I h pper opc mcrocv rg reoor bed o hgh-de-cor wvegude hve bee ed b ug MRTD formuo bed o CDF 4 cg fuco d rgorou UPM boudr codo. The pproch h proved good eve of ccurc ercg d udg he reoce behvour of h rucure. The opmo of umber of mpor prmeer cudg coupg coeffce qu fcor d reeco ro h bee dcued. A hgh-order rucure cog of wo rg reoor pre wh cere dce of µm h how ereg poe creg he o-off ro where derbe o mme he cro k of he devce. Furhermore b ug mmerc gp e he reeco ro of he devce h gfc creed of bou 6 % compred o he be reu he mmerc gp e ce. DOI:.979/ Pge

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