Numerical Study of an Ion-Exchanged Glass Waveguide Using Both Two-Dimensional and Three-Dimensional Models

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1 Dubl Isttute of Techology Artcles School of Electrcal ad Electroc Egeerg Numercal Study of a Io-Exchaged Glass Wavegude Usg Both Two-Dmesoal ad Three-Dmesoal Models Pegfe Wag Dubl Isttute of Techology pegfe.wag@dt.e Yulya Semeova Dubl Isttute of Techology yulya.semeova@dt.e Je Zheg Jl Uversty Qag Wu Dubl Isttute of Techology qag.wu@dt.e Agus Hatta Dubl Isttute of Techology ahatta@dt.e See ext page for addtoal authors Follow ths ad addtoal wors at: Part of the Egeerg ommos Recommeded tato Wag P. et al. (0) Numercal study of a o-exchaged glass wavegude usg both two-dmesoal ad three-dmesoal models Optcs & Laser Techology. Vol. 43 o. 4 pp do:0.06/.optlastec Ths Artcle s brought to you for free ad ope access by the School of Electrcal ad Electroc Egeerg at ARROW@DIT. It has bee accepted for cluso Artcles by a authorzed admstrator of ARROW@DIT. For more formato please cotact yvoe.desmod@dt.e arrow.adm@dt.e bra.wdds@dt.e. Ths wor s lcesed uder a reatve ommos Attrbuto- Nocommercal-Share Ale 3.0 Lcese

2 Authors Pegfe Wag Yulya Semeova Je Zheg Qag Wu Agus Hatta ad Gerald Farrell Ths artcle s avalable at ARROW@DIT:

3 Numercal study of a o-exchaged glass wavegude usg both two-dmesoal ad three-dmesoal models Pegfe Wag Yulya Semeova Je Zheg Qag Wu Agus Muhamad Hatta ad Gerald Farrell Photocs Research eter School of Electroc ad ommucatos Egeerg Dubl Isttute of Techology Kev Street Dubl 8 Irelad; State Key Laboratory of Itegrated Optoelectrocs ollege of Electroc Scece ad Egeerg Jl Uversty hagchu 300 P. R. ha E-mal: pegfe.wag@dt.e Abstract: A umercal study s carred out to compare the two-dmesoal (-D) case ad three-dmesoal (3-D) case for the modellg of a o-exchaged glass wavegude. It s show that dfferet wavegude wdths o the photomas correspod to dfferet o cocetrato dstrbutos after a aealg process. A umercal example s preseted of two wavegude sectos wth dfferet wdths dcates that due to the abrupt chage of the wavegude wdth a 3-D theoretcal model s requred for a accurate predcto of the parameters of o-exchaged glass wavegudes. The good agreemet betwee the modelled ad measured results proves that the developed 3-D umercal model ca be beefcally utlzed the geeralzed desg of optcal devces based o o-exchage wavegudes. Keywords: Itegrated optcs devce glass wavegude o exchage aealg. Itroducto Io-exchaged glass wavegudes have bee vestgated extesvely for applcatos the area of tegrated optcs due to ther superor characterstcs such as lowpropagato loss ad the relatvely smple fabrcato techque volved. A oexchaged glass wavegude has a graded dex profle whch dstgushes t from a wavegude wth a step-dex profle such as a slca-o-slco bured wavegude a polymer wavegude or a slco-o-sulator wavegude. Defg the dex profle s

4 a mportat prelmary step the smulato ad desg of plaar lghtwave crcuts. For o-exchaged glass wavegudes oe commoly used method s based o a approxmato of the refractve dex profle by a sem-gaussa fucto the horzotal drecto (parallel to the glass surface) ad by a complemetary error fucto the vertcal drecto whch requres the so-called dffuso depth parameters d x ad d y to be estmated expermetally [-4]. Ths smulato method wors well for some smple o-exchaged tegrated crcuts devces such as chael or tapered wavegudes. However for more complex optcal devces such as a bured wavegude ad a array-wavegude gratg multplexer smulatos based o the o dffuso equato model are more desrable sce the sem-gaussa fucto has a lmted accuracy. It s ow that a durg fabrcato the desred refractve dex profle s acheved by cotrol of the expermetal parameters: o-exchage tme aealg tme temperature ad the wavegude wdths defed by the photomas layout. Usg tal values of these parameters t s possble to derve the o-cocetrato dstrbuto [5-] ad hece the refractve dex profle ca be foud by solvg the dffuso equato umercally. Usg the calculated refractve dex profle a smulato ca be carred out to determe the optcal performace of the devce. Based o ths smulato further teratos of process above ca be carred utl the desred optcal performace s acheved ad wth t a owledge of correct values of the expermetal parameters eeded. Therefore ths paper modellg of the refractve dex profle of a o-exchaged glass wavegude through umercal calculato of the dffuso equato s cosdered. I practce tegrated optcal compoets based o plaar lghtwave crcuts usually cosst of wavegude sectos wth dfferet wdths. Ref. [0] preseted a vestgato of the depedece of bural-depth o wavegude wdth for a bured oexchaged glass wavegude. I ths paper the fluece of the wavegude wdth of the photomas o the o cocetrato dstrbuto s vestgated for o-exchaged glass wavegudes based o thermal o-exchage ad aealg. Both -D ad 3-D models are preseted. The results for the -D modellg dcate that for the oexchaged wavegude dfferet wavegude wdths result a sgfcatly dfferet dstrbuto for the o cocetrato after aealg. For o-exchaged wavegude

5 devces that requre a abrupt chage the wavegude wdth for example a multmode terferece based coupler or a arrayed-wavegude gratg a 3-D model s preseted. A umercal example of a structure cosstg of two wavegude sectos wth dfferet wdths s preseted. Through comparso betwee the smulato results obtaed wth the -D ad 3-D models t s foud that for the case of a abrupt chage of the wavegude wdth a 3-D model s ecessary to esure a accurate predcto of the o cocetrato the trasto rego ear the terface. Addtoally the mode patters for a o-exchaged wavegude based multmode terferometer (MMI) are vestgated ad preseted. The vestgato volves both theoretcal modelg ad expermetal verfcato. The 3-D umercal model shows a good agreemet wth the measured mode patter results for the o-exchaged optcal devces.. Modellg of a o-exchage process for the -D case A z B x y Fg. Schematc dagram of the o-exchage process. Fg. presets a schematc dagram of the o-exchage process wthout a appled voltage. The olear dffuso equato for o-exchage s [5-] DA = t α α α ( ) () D where s the ormalzed o cocetrato of A os. α = A D D A ad are the self-dffuso coeffcets for A os ad B os respectvely. Ths o-lear B D B 3

6 equato has o aalytcal solutos ad therefore some umercal algorthms have bee used prevous vestgatos such as the explct Dufort-Frael method [] ad the method of Peacema ad Rachford (PR-ADI) [3]. Our umercal calculato dcates that both methods ca produce smlar smulato results but the explct Dufort-Frael method s computatoally faster. For the same computer hardware specfcatos the calculato tme for the explct Dufort-Frael method ca be reduced to less tha a half of the calculato tme eeded wth the other two methods. Furthermore ths method ca be easly expaded for a 3-D case. Therefore the explct Dufort-Frael method s used ths paper. Whe the wavegude s uform the z-drecto.e. = 0 a -D model ca z be used. Deotg equato has the form: f D = ad α A f α = f the the -D dffuso ( α ) x 4x y [ ] [ ] [ ] [ ] = x y y x 4y () The correspodg boudary codto ca be foud from Ref. [5]. To cosder the fluece of the wavegude wdth o the refractve dex profle a umercal example of a Ag -Na o-exchage process s preseted. From Ref. [6] 6 D A = 5. 0 ad = α. The o-exchage ad aealg tmes are 0 ad 35 mutes respectvely. Wavegude wdths of ad 0 µm o the photomas are cosdered. The smulato results for the o cocetrato dstrbuto are preseted Fg.a ad Fg.b. 4

7 Normalzed cocetrato W=3 µm W=5 µm W=7 µm W=0 µm X (µm) (a) Normalzed cocetrato W=3 µm W=5 µm W=7 µm W=0 µm Y (µm) (b) Fg. Normalzed dstrbutos of the o cocetrato after thermal o-exchage (a) x- drecto; (b) y-drecto. 5

8 Fg. a presets the ormalzed o cocetratos the x-drecto parallel to the glass surface ad Fg. b presets the ormalzed o cocetrato the y-drecto the mddle of the wavegude. It ca be see that the y-drecto there s o apparet dfferece betwee the o cocetrato dstrbutos for dfferet wavegude wdths. Thermal aealg s usually carred out after o-exchage whch has bee show [4] to mprove the fber couplg effcecy ad decrease the propagato loss. The calculated o cocetrato dstrbutos after the thermal aealg process are preseted Fg. 3a ad Fg. 3b. 0.7 Normalzed cocetrato W=3 µm W=5 µm W=7 µm W=0 µm X (µm) (a) 6

9 0.7 Normalzed cocetrato W=3 µm W=5 µm W=7 µm W=0 µm Y (µm) (b) Fg. 3 Normalzed o cocetrato dstrbutos after the thermal aealg process (a) x-drecto; (b) y-drecto. Fg. 3 shows that after thermal aealg the o cocetrato profles dffer sgfcatly for dfferet wavegude wdths cludg the ampltude of the maxmum cocetrato. Ths umercal example shows that dfferet wavegude wdths correspod to sgfcatly dfferet o cocetrato profles. Ths -D model s sutable for a wavegude wth a uform wdth or a slowly varyg tapered wavegude the z-drecto. However the -D model preseted above caot predct the o cocetrato dstrbutos the case of a abrupt chage of the wavegude wdth for example the trasto rego of a multmode terferometer therefore a 3-D model s requred for predcto such a tegrated devce fabrcated through the o-exchage or dffuso process. 3. Modellg of a o-exchage process wth a 3-D model Smlar to the -D model wth the explct Dufort-Frael method the dffuso equato for the 3-D case s: 7

10 8 [ ] [ ] [ ] [ ] [ ] [ ] z z y y x x z y x z y x = (3) osder a structure cosstg of two wavegude sectos (secto I ad secto II) wth a dfferet wavegude wdths of 0 w ad w as show Fg.4. I practce such a structure correspods to the etry secto of a MMI devce. For the umercal calculato t s assumed that m w µ 3 0 = ad m w µ 5 =. The area of the calculato rego s µm the x-z plae ad the terface betwee the two wavegude sectos les at 00 z m µ =. w 0 w z x Secto II Secto I Fg. 4 Schematc structure of a two-wavegude secto wth the wdths w 0 ad w. Usg the same expermetal parameters as the -D case wth the threedmesoal model the o cocetrato profle the x-z plae at the surface of the glass s preseted Fg. 5. From Fg. 5 the terface betwee the two wavegude sectos ca be clearly see. The correspodg o-cocetrato dstrbutos the x-drecto ad y-drecto are plotted Fg. 6a ad Fg. 6b. The calculated results wth the -D model are also preseted Fg. 6a ad Fg. 6b. The -D model results were obtaed by cosderg the wavegude sectos I ad II depedetly. It ca be see that the o cocetrato ear the terface s dfferet from the profle for wdths of 3 µm ad 5 µm. From the calculated results oe ca see that at the

11 terface ad the rego aroud the terface wavegude secto I the o cocetrato obtaed by the 3-D model has a dfferet dstrbuto by comparso wth the results obtaed from the -D case. For the o cocetrato dstrbuto the y-drecto there s o apparet dfferece for dfferet wavegude sectos. However Fg. 6 (a) ad (b) oe ca also see that the trasto rego of the proposed multmode terferometer that s 95µ m Z 00µ m alog the propagato drecto the -D model preseted Sec. caot calculate the dstrbuto of o cocetrato for both x ad y-drecto cases. Fg. 5 Io cocetrato profle the x-z plae at the surface of glass. 9

12 Z>=0 µm Results wth the D model Results wth the 3D model Normalzed cocetrato Z=00 µm Z=95 µm 0. Z=80 µm X (µm) (a) Results wth the D model Results wth the 3D model Normalzed cocetrato Z=80 µm Z>=0 µm Z=00 µm Z=95 µm Y (µm) (b) Fg.6 Normalzed o cocetrato dstrbutos after the thermal o-exchage process for the structure Fg. 4 (a) x-drecto; (b) y-drecto. 0

13 The calculated o cocetrato dstrbuto the x-z plae at the surface of glass after 35 mutes of thermal aealg s preseted Fg.7. It ca be see that the wavegude boudares are ot as clear as the dstrbuto preseted Fg. 5 ad the trasto rego betwee sglemode ad multmode wavegudes s exteded. The correspodg o-cocetratos the x-drecto ad y-drecto at dfferet z- coordates are plotted Fg.8a ad Fg.8b. Fg. 7 Io cocetrato profle the x-z plae at the surface of the glass after aealg.

14 Normalzed cocetrato Results wth the D model Results wth the 3D model Z>=0 µm Z=0 µm Z=00 µm Z=95 µm Z=80 µm X (µm) (a) 0.7 Results wth the D model 0.6 Results wth the 3D model Normalzed cocetrato Z=95 µm Z>=0 µm Z=0 µm Z=00 µm Z=80 µm Y (µm) (b) Fg. 8 Normalzed o cocetrato dstrbutos after the thermal aealg process for the structure Fg. 4 (a) x-drecto; (b) y-drecto.

15 From the modellg results preseted Fg. 8 t ca be see that dstrbutos of the o cocetrato are sgfcatly dfferet from the correspodg results preseted Fg. 6. I Fg. 6 the o-cocetrato the wavegude rego II s detcal to the results obtaed by the -D model but Fg. 8a oe ca see that oly whe z >= 0 µm does the dstrbuto of o cocetrato agree wth that obtaed by the -D model. From ths example oe ca see the sgfcat fluece of the abrupt chage of the wavegude wdth o the correspodg dex profle ad f the - D model s used the dstrbuto of o-cocetrato aroud the terface betwee the two wavegude sectos caot be obtaed. The trasto rego betwee sglemode ad multmode wavegudes s exteded from 5 µm (see Fg. 6 (a) & (b)) to 5 µm at least due to the aealg process whch results o dffuso. Ths suggests that the 3-D model developed s essetal for the accurate predcto for a o-exchaged wavegude whch udergoes a aealg process. 4. Optcal performace of the o-exchaged devce To llustrate the optcal performace of the o-exchaged wavegude devce wth a abrupt chage of wavegude wdth a smulato usg a 3-D beam propagato method s carred out based o the dfferet dex profles obtaed wth both -D ad 3-D models. The maxmum chage of refractve dex due to the o-exchage s assumed to be = ad the refractve dex of the substrate s.504 at a wavelegth of.55 µm. The o-exchage ad aealg tmes are 0 ad 35 mutes respectvely. I the smulatos preseted earler ths paper the devce legth cosdered s 00 µm but practce fabrcatg a 00 µm log devce ad subsequetly polshg the ed facets to acheve the requred optcal qualty s very dffcult. Hece a loger devce legth was requred practce whch prcple would mea that smulatos carred out for a devce legth of 00 µm could ot be readly compared wth expermetal results for the fabrcated loger devce. However our smulatos t was foud that perodc real mages occur wth the secto of the multmode wavegude due to the well-ow self-focusg prcple for a graded dex wavegude [5 6]. It was foud that the profle of the optcal feld dstrbuto of the proposed MMI devce the x-y plae at a dstace of 500 µm from the put facet s 3

16 the same as that at a dstace of 5000 µm. Hece practce a 5000 µm log devce s fabrcated wth the wavegude wdth trasto at a dstace of 00 µm from the put facet. The loger devce legth allows the ed facets to be easly polshed to acheve the desred optcal qualty ad to adust the total legth precsely to 5000 µm. Addtoally the computato wdow the smulato alog the z-drecto s exteded from 00 µm to 500 µm. The smulato results are preseted Fg. 9a ad Fg. 9b respectvely. The put lght used the theoretcal models has a wavelegth of 550 m. omparg Fg. 9a ad Fg. 9b t s clear that the lght propagato dffers due to the dfferet dex profles obtaed by the -D ad 3-D models. For example Fg. 9 (a) there s o chage the testy profle the rego up to the 00 µm trasto pot betwee the sglemode ad multmode wavegudes obtaed by the -D model but Fg. 9 (b) oe ca see that creasg atteuato occurs the rego up to the trasto pot. The correspodg smulated mode patters of the devce at a legth of 5000 µm are preseted Fg. 0a ad Fg. 0b. The mode patters have the same shape at 5000 µm as those at 500 µm. Fg. 0a s based o the dex profle obtaed by the -D model ad Fg. 0b s based o the dex profle obtaed by the 3-D model. Through comparso of Fg. 0a ad Fg. 0b t s foud that there s a sgfcat dfferece the optcal feld testy ad mode patter from the output port for the -D ad 3-D models. Ths suggests that for a graded-dex wavegude structure volvg a abrupt chage the wavegude wdth a 3-D model s requred to accurately predct the optcal performace of the devce. 4

17 (a) (b) Fg.9 Lght propagato the x-z plae (both -D ad 3-D plots) at the surface of the glass based o the refractve dex profle obtaed by (a) -D model; (b) 3-D model. (a) 5

18 (b) Fg.0. Optcal feld dstrbuto the x-y plae (cross-secto vew) based o the refractve dex profle obtaed by (a) -D model; (b) 3-D model. 5. Expermetal evaluato I order to verfy the theoretcal models for the o-exchaged tegrated devce the o exchaged glass MMI devce descrbed earler ths paper was fabrcated. The chemcal composto of the soda-lme glass used the expermets s gve Table. Table. hemcal composto of the soda-lme slcate glass employed the expermets Oxde Weght (%) SO 73.5 Na O 4.35 ao 8.0 Al O K O 0.3 MgO 3.50 TO 0.0 Fe O

19 I order to defe the wavegude patter o the soda-lme slcate glass a 300- m-thc alumum flm was deposted upo the pre-cleaed glass surface ad stadard photolthographc techques were employed to defe the opegs the flm where o-exchage could tae place. The glass sldes wth the alumum mas opegs were mmersed a AgNO 3 -NaNO 3 molte salt composto at a temperature of 330 ; the temperature was cotrolled ad motored by a dgtal temperature sesor. The process of o-exchage of Ag wth the Na the glass slde was carred out for 0 mutes after o exchage the glass sample was removed from the molte salt ad the sample was the mmedately washed deozed water to remove resdual surface salt. After the cleag process a aealg process followed at the same temperature for a perod of 35 mutes. Fally the etre glass devce legth was accurately set to a legth of 5000 µm usg ed polshg ad the alumum mas was removed usg acd. As show Fg. a expermetal setup for measurg the mode patters was bult. The o-exchaged devce was mouted o a vacuum stage whch was coected to a vacuum pump. A tuable laser s used as a optcal source wth a output power of 0 dbm at a operatg wavelegth of 550 m. At the wavegude ed a mcroscope obectve focuses the output lght to a frared camera whch s cotrolled by a persoal computer. A stadard sglemode fber wth a tapered ed s employed to coect the laser source ad the sample the fber was alged X-Y drecto utl the measured trasmtted optcal power was maxmsed. Tuable laser source P Sglemode fber Y Io-exchaged wavegude devce Mcroscope obectve X Vacuum stage Ifrared camera Vacuum pump 7

20 Fg.. Schematc represetato of the o-exchaged wavegude measuremet setup The setup Fgure ca be used to obta the ear feld mode patters of the wavegude ed-facet. Fgure shows the ed-facet mode patter of the oexchaged MMI optcal devce at a wavelegth of 550 m. From Fg. 0b ad Fg. oe ca see that there s a good agreemet betwee the shape of mode patter calculated usg the 3-D theoretcal model ad the measured results. Y Z X Y 5 µm Fg.. Near-feld mode patter mage of the o-exchaged MMI devce at the propagato drecto of Z=5000 µm. 4. ocluso The modellg of a o-exchaged glass wavegude has bee vestgated ths paper for both the -D ad 3-D case. The -D model shows that dfferet wavegude wdth o the photomas correspod to dfferet o cocetrato dstrbutos after the aealg process. To llustrate the fluece of the abrupt chage of wavegude wdth o the dstrbuto of the o cocetrato a comparso has bee carred betwee the -D ad 3-D models. A umercal example s preseted based o two wavegude sectos wth dfferet wdths ad s has bee show that due to the abrupt chage of the wavegude wdth a 3-D model s requred for accurate modellg of such wavegude based devces. Furthermore the agreemet betwee the modelled ad measured results also suggests that the 3-D theoretcal umercal model developed ca be beefcally utlzed the geeralzed desg of o-exchage wavegude based optcal devces. 8

21 5. Acowledgemet Pegfe Wag s fuded by the Irsh Research oucl for Scece Egeerg ad Techology co-fuded by the Mare-ure Actos uder FP7. The research was partally supported by the Natoal Natural Scece Foudato of ha (No ) the ha-irelad Scece ad Techology ollaborato Research Fud ad the Iteratoal cooperato proect (No ) of Jl Provcal Scece & Techology Departmet of ha. Referece. M. N. Wess ad R. Srvastava Determato of o-exchaged chael wavegude profle parameters by mode-dex measuremets App. Opt. Vol. 34 No. 3 pp S. J. Hettrc J. I. Maceze R.D. Harrs J. S. Wlso D. P. Shepherd ad A.. Tropper Io-exchaged tapered-wavegude laser eodymum-doped BK7 glass Opt. Lett. Vol. 5 No. 9 pp A. Mlou H. Zheguag H.. heg R. Srvastava R. V. Ramaswamy Fber- ompatble K -Na Io-Exchaged hael Wavegudes: Fabrcato ad characterzato IEEE J. Quatum Electro. Vol. 5 No. 8 pp R. A. Betts F. Lu ad S. Dagas Wavelegth ad polarzato sestve optcal spltters fabrcated K /Na Io-exchaged glass IEEE Photo. Techol. Lett. Vol. No. 7 pp B. R. West P. Madasamy N. Peyghambara ad S. Hoae Modelg of o-exchaged glass wavegude structures J. No-rystalle Solds Vol. 347 pp J. T. A. arrere J. A. Fratz B. R. West S. Hoae ad R. K. Kostu Bed loss effects dffused bured wavegudes App. Opt. Vol. 44 No. 9 pp J. M. astro D. F. Geraghty B. R. West ad S. Hoae Fabrcato ad comprehesve modellg of o-exchaged Bragg optcal add-drop multplexers App. Opt. Vol. 43 No. 33 pp

22 8. B. Buchold. Glgeer D. ulema ad E. Voges Polarzato sestve o-exchaged array-wavegude gratg multplexers glass Fber ad Itegrated Optcs Vol. 7 pp S. Ylem B. R. West ad S. Hoae Io-exchaged glass wavegudes wth low brefrgece for a broad rage of wavegude wdths App. Opt. Vol. 44 No. 6 pp P. Madasamy B. R. West M. M. Morrell D.F. Geraghty S. Hoae ad N. Peyghambara Bured o-exchaged glass wavegudes: bural-depth depedece o wavegude wdth Opt. Lett. Vol. 8 No. 3 pp H. Saaros R. P. Salmo J. Saare T. Erola ad A. Tervoe Fast umercal soluto of olear dffuso equato for the smulato of oexchaged mcro-optcs compoets glass Opt. omm. Vol. 34 pp A. Tervoe : S. I. Naaf (Ed.) Itroducto to Glass Itegrated Optcs Artech House Norwood MA D. W. Peacema ad H. H. Rachford Jr. The umercal soluto of parabolc ad ellptc dfferetal equatos J. Soc. Idust. Appl. Math. Vol. 3 pp L. Palchett E. Gorgett D. Grado ad S. Sott Effcet couplg betwee aealed K -Na Io-exchaged chael wavegudes ad 0/5 sgle-mode fbers at λ=.3 µm IEEE J. Quatum Electro. Vol. 34 No. pp D. Marcuse Lght Trasmsso Optcs New Yor: Va Nostrad Rehold ompay L. B. Soldao ad E.. M. Pegs Optcal mult-mode terferece devces based o self-magg: Prcples ad applcatos J. Lghtwave Techol. Vol. 3 No. 4 pp