Anlyss of whsperng-gllery mcrocvtyenhnced chemcl bsorpton sensors A. T. Rosenberger Deprtment of Physcs, Oklhom Stte Unversty, Stllwter, OK 7478-37, USA tr@okstte.edu Abstrct: A theoretcl nlyss of the operton of chemcl sensor bsed on cvty-enhnced optcl bsorpton s gven for system n whch the cvty s delectrc whsperng-gllery mcroresontor. Contnuouswve nput s ssumed, nd the detecton senstvty s chrcterzed n terms of n ectve bsorpton pth length. In the cse of tunble snglefrequency nput, t s shown tht montorng nlyte-nduced chnges n the throughput dp depth enbles detecton wth reltve senstvty greter thn tht of frequency-shft nd cvty-rngdown methods. In ddton, for the cse of brodbnd nput nd drop-port output, n nlyss pplcble to mcrocvty-enhnced bsorbnce spectroscopy experments s gven. 7 Optcl Socety of Amerc OCIS codes: (35.395) Mcro-optcs; (3.13) Absorpton; (3.575) Resontors; (6.37) Fber optcs sensors. References nd lnks 1. A. B. Mtsko nd V. S. Ilchenko, Optcl Resontors wth Whsperng-Gllery Modes Prt I: Bscs, IEEE J. Sel. Top. Quntum Electron. 1, 3-14 (6).. V. S. Ilchenko nd A. B. Mtsko, Optcl Resontors wth Whsperng-Gllery Modes Prt II: Applctons, IEEE J. Sel. Top. Quntum Electron. 1, 15-3 (6). 3. I. Terok, S. Arnold, nd F. Vollmer, Perturbton pproch to resonnce shfts of whsperng-gllery modes n delectrc mcrosphere s probe of surroundng medum, J. Opt. Soc. Am. B, 1937-1946 (3). 4. N. M. Hnumegowd, C. J. Stc, B. C. Ptel, I. Whte nd X. Fn, Refrctometrc sensors bsed on mcrosphere resontors, Appl. Phys. Lett. 87, 117 (5). 5. A. M. Armn nd K. J. Vhl, Hevy wter detecton usng ultr-hgh-q mcrocvtes, Opt. Lett. 31, 1896-1898 (6). 6. A. A. Svchenkov, A. B. Mtsko, M. Mohgeg, nd L. Mlek, Rngdown spectroscopy of stmulted Rmn sctterng n whsperng gllery mode resontor, Opt. Lett. 3, 497-499 (7). 7. R. W. Boyd nd J. E. Heebner, Senstve dsk resontor photonc bosensor, Appl. Opt. 4, 574-5747 (1). 8. M. J. Humphrey, E. Dle, A. T. Rosenberger, nd D. K. Bndy, Clculton of optml fber rdus nd whsperng-gllery mode spectr for fber-coupled mcrosphere, Opt. Commun. 71, 14-131 (7). 9. M. L. Gorodetsky nd V. S. Ilchenko, Optcl mcrosphere resontors: optml couplng to hgh-q whsperng-gllery modes, J. Opt. Soc. Am. B 16, 147-154 (1999). 1. M. C, O. Pnter, nd K. J. Vhl, Observton of Crtcl Couplng n Fber Tper to Slc- Mcrosphere Whsperng-Gllery Mode System, Phys. Rev. Lett. 85, 74-77 (). 11. G. Frc, S. I. Shopov, nd A. T. Rosenberger re preprng mnuscrpt to be clled Cvty-enhnced lser bsorpton spectroscopy usng mcroresontor whsperng-gllery modes. 1. M. L. Gorodetsky nd V. S. Ilchenko, Hgh-Q optcl whsperng-gllery mcroresontors: precesson pproch for sphercl mode nlyss nd emsson ptterns wth prsm couplers, Opt. Commun. 113, 133-143 (1994). 13. J. Zhng, B. N. Strecker, R. K. Shelton, S.-J. J, J. V. Hrynewcz, nd A. T. Rosenberger re preprng mnuscrpt to be clled A brodbnd whsperng-gllery mode mcrosphere bsorbnce spectrometer. 14. S. L. Westcott, J. Zhng, R. K. Shelton, N. M. K. Bruce, S. Gupt, S. L. Keen, J. W. Tllmn, L. B. Wld, B. N. Strecker, A. T. Rosenberger, R. R. Dvdson, W. Chen, K. G. Donovn, nd J. V. Hrynewcz re preprng mnuscrpt to be clled Brodbnd optcl bsorbnce spectroscopy usng whsperng gllery mode mcrosphere resontor. #86369 - $15. USD Receved 13 Aug 7; revsed 15 Sep 7; ccepted 17 Sep 7; publshed 4 Sep 7 (C) 7 OSA 1 October 7 / Vol. 15, No. / OPTICS EXPRESS 1959
1. Introducton Delectrc mcroresontors tht support whsperng-gllery modes (WGMs) re becomng ncresngly useful for numerous pplctons n optcs. These resontors cn be sphercl, cylndrcl, dsk-shped, or torodl; lght n WGM crcultes round the crcumference of the resontor, loclzed ner the surfce by totl nternl reflecton. The mpct of these devces s bsed on certn ttrctve propertes of WGMs, such s hgh qulty fctor (Q) nd low mode volume, nd on the possblty of cent couplng of lght nto nd out of these modes [1]. The hgh Q of WGM mens tht lght mkes mny round trps n the resontor. Ths feture, combned wth smll mode volume nd cent couplng usng prsms, nglepolshed fbers, or tpered fbers, mkes hgh ntrcvty power enhncement esy to cheve. Vrous pplctons such s flterng, lsng, modulton, nonlner optcs, sensng, nd spectroscopy re enbled by these propertes of WGMs []. In the pplcton re of lbel-free chemcl detecton nd spectroscopy, severl methods of usng WGM mcroresontors hve been reported. Prt of the WGM feld extends outsde the delectrc, nd t s ths evnescent porton tht ntercts wth the surroundng medum. Anlyte molecules n the mbent or on the resontor s surfce cn then be detected by mesurng the frequency shft of WGM cused by the nlyte s perturbton of the mbent s ndex of refrcton [3,4]. In ddton, nlyte bsorpton wll chnge the ectve Q of the WGM, nd the modfcton of mode lnewdth cn be mesured [5]. One cn lso envson usng cvty-rngdown spectroscopy [6]. The method descrbed n ths pper s more closely relted to other erler work [7] n tht wht s mesured s the nlyte bsorpton ect, for contnuous-wve nput, on ether the depth of the throughput dp (Secton ) or the strength of the drop sgnl (Secton 3). As explned below, the former cn be more senstve thn other tunble sngle-frequency methods, nd the ltter lends tself well to brodbnd spectroscopy. These technques wll be descrbed n the next two sectons nd dscussed further n Secton 4.. Tunble sngle-frequency operton Consder mcrocvty n whch lght s coupled nto WGM from n dbtclly tpered fber tngentlly n contct wth the resontor. Tunble sngle-frequency lght s njected t one end of the tpered fber nd the throughput spectrum tht s detected t the other end wll dsply Lorentzn dp for ech WGM resonnce excted. The mcrocvty cn be modeled s four-mrror rng cvty, s depcted n Fg. 1, n whch one of the mrrors s prtlly trnsmttng whle ll the others re ssumed to be perfect reflectors. The rng cvty model s vld nlog to fber-coupled mcroresontor when only sngle fber mode s excted. For lght ncdent on mcroresontor ths s ccomplshed by mkng the frst fber tper trnston dbtc. However, lght couplng out of the mcroresontor cn couple nto mny fber modes, nd ny lght coupled nto hgherorder modes wll be lost f the second tper trnston s lso dbtc. Fortuntely, t s possble to mke ths lossy couplng nto hgher-order fber modes neglgbly smll by properly choosng the dmeter of the tpered fber [8]. Fg. 1. Four-mrror rng cvty model. Left, mcrocvty nd tpered fber n contct. Lght cn couple from the fber nto the resontor nd vce vers. Rght, the four-mrror rng cvty equvlent. The top mrror s prtlly trnsmttng; ll others hve 1% reflectvty. #86369 - $15. USD Receved 13 Aug 7; revsed 15 Sep 7; ccepted 17 Sep 7; publshed 4 Sep 7 (C) 7 OSA 1 October 7 / Vol. 15, No. / OPTICS EXPRESS 196
A round-trp power loss αl, where α s the loss cocent nd L s the mcroresontor crcumference, s ssumed; t models the ntrnsc loss (prmrly surfce sctterng) of WGM mcroresontor. The mrror reflecton nd trnsmsson cocents r nd t, reltng to the feld mode mpltudes, re tken to be rel nd mgnry respectvely wthout loss of generlty; ths corresponds to the usul choce for fber or prsm couplng [7,9,1]. The ssumpton of neglgble power loss nto rdton modes requres tht these cocents stsfy the relton t = 1 r. Becuse Q s so hgh, even under condtons of lodng by the coupler, the ntrnsc round-trp loss nd the couplng loss (mrror trnsmssvty or probblty of photon tunnelng between fber nd mcroresontor) wll lwys be smll, so α L << 1 nd T = t << 1wll be ssumed throughout ths work. By summng the feld over round trps, the net reflected power frcton (fber throughput frcton) s found to be where δ πnl ( ν ν )/ c R δ αl / δ αl / r e e =, (1) δ 1 re e = s the round-trp phse ccumulton due to detunng of the nput frequency ν from resonnce ν (c s the speed of lght nd n the resontor s ndex of refrcton). The devton of the throughput frcton from unty gves the dp profle: TαL TαL M δ = 1 Rδ = 1 sn. () 4 1 1 ( T + αl) + 4 δ ( T + αl) + δ Ths functon s the usul Ary profle, wth mxm t δ = pπ, p =, 1,,. The spcng of π between djcent modes s the free spectrl rnge (FSR) n phse. (Recll tht the FSR n frequency s gven to good pproxmton by c /(nl). Becuse mny hgher-order WGMs cn be excted, the ctul spcng between djcent modes s much less thn the FSR.) The full wdth t hlf-mxmum of WGM resonnce s thus seen to be gven by Δ δ = T + αl, the totl round-trp loss. The fnl expresson n Eq. (), vld when δ << 1, shows the Lorentzn profle of dp. The dp depth on resonnce ( δ = ) s determned by the rto of the couplng loss to ntrnsc loss, x = T / αl, nd s gven by 4x M =. (3) ( 1+ x) If x = 1, crtcl couplng s obtned nd the dp depth ttns ts mxmum vlue of 1%; the mcroresontor s sd to be undercoupled f x < 1 nd overcoupled for x > 1. Whle the couplng loss remns constnt, the ectve ntrnsc loss cn be chnged by ntercton of the evnescent frcton ( f ) of the WGM wth the surroundng medum. The ectve loss cocent cn then be wrtten s α = α + fα + fα s, where the three terms denote true ntrnsc loss, bsorpton (nd perhps lso sctterng) by the nlyte, nd bsorpton n the solvent (or mbent). Absorpton by the nlyte cuses chnge n dp depth tht, when smll (wek nlyte bsorpton), s proportonl to the chnge n nlyte bsorpton cocent, n nlogy wth t Beer s lw. A theoretcl ectve bsorpton pth length L cn then be obtned from the dp depth dependence on the bsorpton cocent of the nlyte: 4 #86369 - $15. USD Receved 13 Aug 7; revsed 15 Sep 7; ccepted 17 Sep 7; publshed 4 Sep 7 (C) 7 OSA 1 October 7 / Vol. 15, No. / OPTICS EXPRESS 1961
dm M 1 x f dα 1+ x α + fα s L t dα. (4) In the bsence of solvent bsorpton, ths ectve bsorpton pth length cn be expressed s L t 1 x f =. (5) 1 + x α Ths ectve length s defned n the low-nlyte-bsorpton lmt, α << 1 (or fα << α ), whch s the condton for Eq. (4) to hold. Note tht n the strongly undercoupled or overcoupled lmts (x << 1 or x >> 1) the reltve detecton senstvty s determned by the ntrnsc loss only. Ths cn be dvntgeous, snce hvng the tpered fber n contct wth the mcroresontor tends to produce overcouplng, especlly when the system s mmersed n lqud. Thus n the strongly overcoupled cse, ths method hs greter reltve senstvty (here, frctonl chnge n dp depth) thn the frequency-shft, mode-wdth, or rngdown methods, ll of whose reltve senstvtes re determned by the totl loss. Recll tht the totl loss determnes the lnewdth nd the cvty lfetme, nd n the overcoupled lmt couplng loss domntes. The reltve frequency-shft senstvty s mesured s frcton of the lnewdth, the chnge n mode wdth s reltve to the full wdth, nd rngdown mesures the frctonl chnge n the overll lfetme. e An expermentl ectve bsorpton pth length L cn be found by mesurng the dp depth n the bsence of nlyte (M ) nd n the presence of nlyte (M + ΔM ): L e L t 1 M ln. (6) α M + ΔM As wth Eq. (4), ths holds for smll chnges n dp depth or α L e << 1. Comprson of expermentl nd theoretcl ectve bsorpton pth lengths for detecton of tmospherc trce gses shows good greement [11], s dscussed brefly n Secton 4. Ths method lso llows for senstve detecton of n nlyte n strongly bsorbng solvent. In Eq. (4), f fα >> α, the ectve bsorpton pth length cn stll be s lrge s s 1 / α s. In ect, solvent bsorpton cn shft the sensor from one senstve regme to nother from strongly overcoupled to strongly undercoupled, enblng bsolute nlyte senstvty,.e., ctul sgnl mpltudes, tht would be dffcult to cheve n sngle-pss drect bsorpton through the sme ectve pth length. 3. Brodbnd operton In ths model mcrosphere, wth one prsm coupler used to excte precessng modes [1], s tken to be nlogous to rng cvty wth two dentcl prtlly-trnsmttng mrrors. Here we wll concentrte on the trnsmtted sgnl (drop power output, enbled by precesson nd detected by spectrometer) rther thn the reflected sgnl (throughput). See Fg. below. Frst consder sngle-frequency response. Summng over round trps nd rbtrrly tkng the second prtlly-trnsmttng mrror to be t hlf the round-trp dstnce from the nput mrror (the fnl result wll not depend on ths choce), gves the drop power frcton: D δ αl / 4 δ / e αl / δ 1 ( T + αl) 1 1 ( Δδ ) 1 1 ( Δδ ) + ( sn ) Te T = = = D 1 r e e + 4 sn δ δ In ths system the mode wdth s Δδ = T + αl nd the resonnt drop frcton s D.. (7) #86369 - $15. USD Receved 13 Aug 7; revsed 15 Sep 7; ccepted 17 Sep 7; publshed 4 Sep 7 (C) 7 OSA 1 October 7 / Vol. 15, No. / OPTICS EXPRESS 196
drop throughput Fg.. Hemsphercl prsm couplng scheme. The mcrosphere s n V-groove chnnel for the solvent nd nlyte. Left, polr vew showng nput nd output couplng. Rght, equtorl vew llustrtng how precessed lght s collected t the drop port. Now, consder the cse where the nput s brodbnd nd the drop sgnl s detected by spectrometer, whch ntegrtes over frequency ntervl tht we wll tke to be equl to the FSR (for convenence; gn, the fnl result wll not depend on ths choce, nd the spectrometer resoluton ntervl my be greter thn or less thn the FSR, s long the condtons noted below re stsfed). Assumng the nput power, the reflecton nd trnsmsson cocents, nd the ntrnsc loss ll to be ndependent of frequency over ths ntervl, the ntegrted drop frcton D I, the frcton of the ncdent power n the ntegrton ntervl tht s trnsmtted out the drop port, s gven by ( Δδ ) D D = 4T for Δδ >> 1 D I =. (8) Δ / 4 = Δ for Δ << 1 4 D δ T δ δ 1+ Δδ The spectrometer sgnl wll be proportonl to ths ntegrted frcton tmes the ncdent power n the detecton ntervl. Note the functonl dependence of the detected sgnl on the lnewdth (or totl loss) Δδ = T + αl n the two lmtng cses of lrge nd smll lnewdth. The frst lmtng cse sys tht when the lnewdth flls the ntegrton ntervl, the drop frcton equls wht would be found by usng sngle-frequency source tuned to WGM resonnce; ths holds for ether low Q or mny overlppng modes n the ntegrton ntervl, so tht ntegrton ntroduces no ddtonl lnewdth dependence. The second lmtng cse s the usul one for well-seprted modes, nd s the sme s tht whch results from pproxmtng ech WGM s nrrow trnsmtted lneshpe s Lorentzn; ths holds s long s the ntegrton ntervl s wde compred to the WGM lnewdth. Let the ectve loss cocent now nclude, n ddton to ntrnsc loss, contrbuton due to bsorpton (nd sctterng) by the nlyte fllng the evnescent frcton f of the WGM: α = α + fα. The ect of the nlyte on the resonnt (sngle-frequency) drop sgnl D, when nlyte bsorpton s smll frcton of the totl loss, cn be wrtten n terms of n pproxmte ectve bsorpton pth length L s defned below: D ( T + ) 1 L + fα L ( 1+ α L ) 4T D fl = =, where L. = (9) α T + α L Here, L s the ectve bsorpton pth length s defned n the low-nlyte-bsorpton lmt. However, the lst expresson for D s vld even for lrge nlyte bsorpton, tht s, there re no restrctons on the sze of α L s long s f α L << 1. Then, for brodbnd nput, the ntegrted drop frcton n the presence of nlyte, D I, wll lso be gven by Equton (9) n the lrge lnewdth lmt. For precessng-mode dropport output collected wthout beng sptlly fltered by n perture [13], ths lmt pples, for the followng reson. The ncdent focused lght (Fg. ) ncorportes bundle of wvevectors nd so exctes precessng modes over rnge of ngles wth respect to the #86369 - $15. USD Receved 13 Aug 7; revsed 15 Sep 7; ccepted 17 Sep 7; publshed 4 Sep 7 (C) 7 OSA 1 October 7 / Vol. 15, No. / OPTICS EXPRESS 1963
equtorl plne. The round-trp dstnce depends on ths ngle n spherod, so the precessng modes re frequency-shfted by mounts dependng on ngle. The result s mny modes (not just rnge of dfferent ngles, but lso rnges of dfferent rdl orders nd dfferent polr orders) tht overlp to fll the ntegrton ntervl, so when the nlyte bsorpton brodens the lnewdth nd reduces the trnsmsson of ech mode, the brodenng s not notced, becuse the ntegrton ntervl remns flled. Thus only the decrese n mpltude s observed, just s n the sngle-frequency resonnt cse. The overlppng of modes lso mens tht the exct vlue of the spectrometer resoluton ntervl does not mtter. Ths lrge-lnewdth-lmt functonl dependence of the ntegrted drop sgnl on α L s gven n Eq. (9) hs been tested n recent expermentl work [14], descrbed brefly below. 4. Dscusson nd summry A method for whsperng-gllery mcrocvty-enhnced chemcl sensng hs been descrbed. Two mplementtons of ths method hve been consdered n detl. The frst nvolves usng tunble sngle-frequency lser nd observng chnges n the depth of the throughput dp cused by bsorpton by the nlyte n the evnescent frcton of WGM. The reltve senstvty ws shown to be determned by the ntrnsc loss only, n the cses of strong underor overcouplng. In these cses, sgnfcnt dp cn stll be observed; for exmple, x =.5 or x = produce M =.18. In ths exmple, n the overcoupled cse, the totl loss s twenty-one tmes the ntrnsc loss, so ~ enhncement n reltve senstvty compred to frequency-shft or rngdown methods s obtned. For wvelength on the order of 1 nm nd typcl mcroresontor vlues, for exmple crcumference L ~ 1 mm, Q ~ 1 8, evnescent frcton f ~.% (n r) or f ~ % (n wter or methnol), ectve nlyte bsorpton pth lengths on the order of centmeters cn be expected, even n strongly bsorbng solvents (α s ~ 1 cm -1 ). Usng cylndrcl mcroresontor wth Q ~ 5 1 6 [11], expermentl ectve pth lengths of bout 1 cm re found for trce mounts of methne, ethylene, or methyl chlorde n r t tmospherc pressure. The dp depth s montored by lockng WGM to the lser s the lser s scnned over bsorpton lnes for wvelengths round 1.65 μm. Agreement wth theoretcl ectve pth lengths s very good. The second mplementton uses brodbnd source nd spectrl detecton, usng spectrometer wth resoluton ssumed to be of the order of the resontor s FSR (the FSR s bout GHz for 33-μm dmeter mcrosphere, or. nm for wvelengths round 55 nm). Precessng modes n mcrosphere re employed to gve drop spectrum tht s modfed by nlyte bsorpton. In ths cse, the totl loss determnes the senstvty, but wth prsm couplng t s more lkely tht the system wll be n the undercoupled lmt. The setup shown n Fg. hs been used for the detecton of Lssmne Green B dye n ph 5 ctrte buffer usng 635-nm LED lght source [14]. Effectve pth lengths of bout 1 cm were observed, nd the behvor of the drop sgnl s functon of concentrton (hence α ) ws n most cses s predcted by Eq. (9). Although the greement so fr between expermentl results nd the theoretcl model presented here s encourgng, ths nlyss hs neglected certn ects tht mght need to be tken nto ccount to do detled comprson wth future expermentl results. One of these s sturton (or reverse sturton) of the bsorpton n the nlyte nd perhps lso n the solvent. Another s the ect of the delectrc mcroresontor s surfce on the nlyte, through the orentton of molecules tht dsorb onto the surfce or by the nducton of concentrton grdent ner the surfce. Acknowledgments The uthor cknowledges support from the Ntonl Scence Foundton (ECS-3994), the Oklhom Stte Regents for Hgher Educton, nd ICx Nomdcs, nd dscussons wth Jeromy P. Rezc, Syk I. Shopov, nd Brn N. Strecker. Specl thnks go to George Frc for extensve dscussons nd for provdng Fg. 1. Fgure ws dpted from one generously suppled by Jngqun Zhng. #86369 - $15. USD Receved 13 Aug 7; revsed 15 Sep 7; ccepted 17 Sep 7; publshed 4 Sep 7 (C) 7 OSA 1 October 7 / Vol. 15, No. / OPTICS EXPRESS 1964