Supplementary Information - Nanocouplers for free-space excitation of whispering-gallery microlasers

Transcription

1 Supplemetary Iformatio - Naocouplers for free-space excitatio of whisperig-gallery microlasers Jiagag Zhu 1*, Şahi K. Özdemir 1*, Huzeyfe Yilmaz 1, Bo Peg 1, Mark Dog, Matthew Tomes, Tal Carmo, ad La Yag 1* 1 Departmet of Electrical ad Systems Egieerig, Washigto Uiversity, St. Louis, MO 6313, USA Departmet of Electrical ad Computer Egieerig, Uiversity of Michiga, A Arbor, MI 4819, USA *Correspodece to: yag@ese.wustl.edu, ozdemir@ese.wustl.edu, jzhu@seas.wustl.edu

2 Supplemetary Figures Supplemetary Figure S1 Experimetal images. a, Image of a microtoroid with diameter of about 8 m coupled with a tapered fiber, top view. b, side view of a. c, Optical image of the fiber les made from a sigle mode fiber (SMF-8e). d, Polystyree aoparticles (radii 5 m) deposited o the surface of a microtoroid.

3 Supplemetary Method 1 Fabricatio ad Experimet setup To study the free space light couplig usig aocouplers, we fabricated passive microtoroids with major diameters of 6-15 m usig commercially available silico wafers with m oxide layer. We also fabricated active microtoroids usig sol-gel method 16, either usig a Ytterbiumdoped (Yb 3+ cocetratio: x1 18 /cm 3 to x1 19 /cm 3 ) sol-gel silica layer (3 layer coatig, 1.5 m total thickess) o silico or by coatig a silica (o dopat) microtoroid resoator with Yb 3+ - doped sol-gel followed by CO laser aealig. The details of fabricatio process ca be foud i Ref. 16 of the mai text. Fabricated microtoroids had optical Q factors i the rage of 5x We have also fabricated passive microspheres by meltig the ed of tapered fibers usig fusio splicer (Ericsso FSU 995FA) or CO laser pulses. Active microspheres were made by dipcoatig passive oes ito the sol-gel solutio cotaiig Yb 3+ (io cocetratio x1 18 /cm 3 to x1 19 /cm 3 ) followed by high temperature aealig. The resultig passive ad active microspheres had Q factors betwee 1 7 ad 1 8. Tapered fibers 1, used to extract light from microresoators were fabricated by pullig sigle mode fibers o a hydroge flame. I order to couple the pump light (free space light coupled ito the resoator via the proposed aocouplers) ad the geerated laser light (from the rare-earth ios doped ito the silica resoators) out from the WGMs of the resoators, we fabricated fiber tapers of varyig sizes ad selected the oes which achieved optimal or close-to-optimal couplig efficiecy. It is worth otig that, due to the wavelegth differece betwee the pump ad lasig modes, optimal couplig for the pump (lasig) mode does t esure optimal coditio for the lasig (pump) mode. To sed laser light from free space to the microresoator, we fabricated a lesed fiber by cleavig a sigle mode fiber followed by partially reflowig the ed usig a fusio splicer (Ericsso FSU 995FA). The resultig lesed-fibers (Fig. S1c) had focusig distaces i the rage of -1 m ad beam spot diameters of 5-1 m i 155 m wavelegth bad. Naoparticles of kow sizes ad materials were delivered oto the surface of a resoator by usig a system similar to that described i Ref. 4 ad 5 i the mai text. We used polystyree aospheres with radii of -75 m (Thermo Scietific 3 Series Naosphere Size

4 Stadards) as aocouplers i our experimets. Naospheres were dispersed i water ad set through the aerosol particle classificatio system ad fially carried out by ultra-high purity itroge ad blow oto the resoator usig a glass ozzle with ed diameter of about 1 m. The ozzle allows targetig of ay microtoroid chose for depositio. The distributio of particles o the resoator is govered by the ozzle agle ad positio. Deposited aoparticles were verified usig SEM (Fig. S1d). We probed the WGMs of the resoators usig tuable diode lasers (New focus Velocity, TLB- 63-LN cotroller) i 155 m or 98 m bads. The tuable laser was tued to match with the resoace modes ad the its wavelegth was modulated with a triagle wave sigal to perform fie-scaig of.8 m aroud the resoace. The out-coupled light from the fiber taper was moitored with photodetectors (New Focus 1811-FC Photoreceiver, 9-17 m, 15 MHz) ad data was acquired to a computer through a oscilloscope. The fiber les was mouted o a 3D traslatioal stage ad poited at the microtoroid at a agle of about 15 degrees with respect to the plae of the silico chip. We adjusted the distace betwee the les ad the resoators usig a 3D traslatioal stage to allow maximal coverage of the microtoroid, or, a miimal beam spot o the microtoroid.

5 Supplemetary Note 1 Free space couplig through a sigle aoparticle For a WGM cavity with quality factor Q ad effective circumferece L, we have: where Pcav Q (S1) cav P L fs deotes the power scattered ito the cavity mode i both the clockwise (CW) ad the couter-clockwise (CCW) directios uder free-space coditio (whe cavity is ot preset) ad P cav cav P fs represets the power scattered ito the cavity mode, whe the cavity is preset, which should be equal to the power dissipated by the cavity. Due to Purcell ehacemet 33-35, ad takig ito accout the ormalized field distributio f (r) at the particle locatio r, we fid P dip P cav f 3 3Q P (S) (r) 4 V where P dip desigates total power scattered ito the dipole mode i free space, deotes the effective wavelegth of the WGM mode ad V is the mode volume defied as: (r) E(r) dv V V (S3) max( (r) E(r) ) Thus, we have: P P P Q L cav cav 3 fs fs cav L 3 3 f (r) f dip Pcav Pdip Q 4 V 8V P (r) (S4) Sice P dip ca be evaluated by multiplyig the iput itesity I i (or E i ) ad the particle crosssectio, we ca calculate s cav P fs usig: P 3L 8V cav fs f (r) Ii s (S5)

6 This relatio ca also be obtaied by evaluatig the overlap itegral betwee dipole radiatio mode ad a Hermite-Gaussia cavity mode i a mirror cavity 33. Next, we ca write the cavity rate equatios with oe particle of radius r : de dt CW de dt CCW i 3L I 1 (( i g) ) ECW ( ig ) ECCW f (r) 16V i 3L (( i 1 g) ) ECCW ( ig ) ECW f ( r) 16V Ii s i s where f (r) 6 V 4 c 3 a ie (S6) fiber CW 1 f (r) c, g, ad V. Defie 3 4r ( p 1)/( p ) E ( E E )/ as the symmetric eigemode (the asymmetric eigemode does't sym CW CCW receive ay iput power because the particle is situated at its ode). From the above differetial equatios, we fid the rate equatio for the symmetric mode as: de sym dt i 3L 1 (( i g) ) Esym f (r) Ii (S7) s 8V At resoace coditio g, we fid the steady state solutio of Esym as E sym 3 3L 3L 8 3 f (r) I (r) i s f I i I i V V f (r) c 1 ( ) V Here we used 8 /3 ad f (r) / (6 V ). If or is the oly variable, s whe 1, the itesity of the symmetric mode c Esym (S8) is maximized (Cauchy Schwarz iequality). This meas that for a sigle scatterer whe the particle iduced loss equals to the sum of the all other cavity losses, the itra-cavity power is maximized. Calculatios i Fig. S1 ad experimet results i Fig. of mai text verify this coclusio. It is worth otig that this coclusio is also correct for multiple particle case, as suggested i Fig. of the mai text ad Fig. S11.

7 O the other had, for the fiber taper output, we have: 3 a ie ie I fiber CW 1 1 sym 1 / i 8 ( 1 ) (S9) If fiber taper couplig 1 is the oly variable parameter, the we fid that settig it as (critical couplig coditio) maximizes the fiber output (Fig. S). This coclusio is 1 cosistet with the experimetal results give i Fig. of the mai text. Supplemetary Figure S Fiber taper coupled power a fiber versus ormalized cavity loss (ormalized to ) with varyig 1. Free space couplig through multiple aoparticles Whe there are multiple scatterig ceters o the resoator, the scatterig light from each scatterer eeds to be take ito cosideratio. Assumig there are N particles, ad the light field icidet o particle is i Ee, the rate equatios ca be expressed as: i de dt CW de dt CCW + - (( i g + g ) ) E (( i g - g ) ) E i E N 1 sym asym sym asym sym asym CW sym asym CCW CWi (( i g + g ) ) E (( i g - g ) ) E i E N 1 sym asym sym asym sym asym CCW sym asym CW CCWi 1 (S1)

8 3L 3L where ECWi f (r), ( r) s Ei e ECCW i f E e 16 V 16 V i( N ) i( N ) s i [, ) is the spatial phase positio of the -th particle 36,37 assumig that the distace betwee the odes of stadig wave mode (SWM) correspods to, [, ) is the phase of light icidet o the -th particle ad [, ) is the phase positio of the ati-ode of the symmetric SWM 36,37. The scatterig ad dampig terms are defied as 36,37 :, sym sym N N 1 N asym 1 N g g cos ( ), g g si ( ) N N 1 N asym 1 N = cos ( ), si ( ) (S11) where g ad are the scatterig ad dampig coefficiets of th particle. The phase positio of stadig wave modes ca be calculated by 37 : ta( ) N N 1 N 1 g g si( ) cos( ) (S1)

9 Supplemetary Note Fiite-elemet Simulatios To verify our theoretical model ad experimetal results, we performed fiite-elemet simulatios usig Comsol Multiphysics. A D model is preseted to demostrate the fudametal priciples of the aocoupler scheme. We also calculated the couplig of light ito a microtoroid via a aosphere by usig a full 3D model 43. Free space excitatio with ad without a sigle aoparticle We performed the simulatio with a D WGM resoator with diameter 3 m ad refractive idex i, surrouded by air (refractive idex of 1). The small imagiary part i the refractive idex is itroduced to accout for the absorptio ad scatterig losses experieced i the experimets. The Q factor of this resoator is 7.375x1 7. The ceter of the resoator (outside WGM area) is set to have strog absorptio (refractive idex of 1-.5i) to miimize the lesig effect by the curvature of resoator-air iterface. A free space light port with 3 m width is placed to the left of the resoator. Supplemetary Figure S3 Simulated electrical field distributio whe free space light is illumiated o a bare resoator (without aoparticles). WGM is ot efficietly excited.

10 First, we performed eigemode aalysis to fid the resoace frequecy ad Q factor of the system. Next, we set the frequecy of the free space light equal to the resoace frequecy of the resoator ad coducted harmoic statioary aalysis. Figure S3 shows the simulatio result. We calculated the average electrical field stregth i the resoator to be 1.19 (a.u.). Although WGM patter exists i the resoator, the electrical field stregth iside the resoator is comparable to that of the iput light i free space. I other words, WGM is ot efficietly excited. By efficiet excitatio we mea that there is a sigificat discrepacy betwee the electric field stregths i the resoator ad i the surroudig, i.e., the former beig much larger tha the latter due to resoace-ehacemet of the field iside the resoator. Supplemetary Figure S4 Simulated electrical field distributio whe free space light is illumiated o a resoator with a sigle aoparticle. a, Symmetric mode, which has maximal overlap with the aoparticle, is efficietly excited. b, Asymmetric mode, which has miimal overlap with the aoparticle, is ot efficietly excited. Fially, we added a aoparticle oto the resoator surface ad repeated the simulatio. The aoparticle had a radius of m ad refractive idex of 1.3. As expected the eigefrequecy of the resoator-particle system showed mode splittig. The Q factor of the symmetric mode (mode whose atiode overlapped with the aoparticle) decreased to.94x1 7 whereas the Q factor of the asymmetric mode (mode whose ode overlapped with the aoparticle) was uchaged (7.375x1 7 ) compared to the case without the aoparticle coupler. The, we performed harmoic statioary aalysis with the frequecy of the free space light set to the

11 frequecies of each of the split modes. Figure S4 shows the simulatio results. For the symmetric mode, the light scattered from aoparticle is efficietly collected ito the mode due to optimal overlap betwee the mode ad the particle, ad the WGM is efficietly excited. O the other had, the asymmetric mode receives very little scattered light due to miimal overlap betwee the mode ad the aoparticle. The average field stregth i the resoator was calculated to be ad 1.86 for the symmetric ad asymmetric mode, respectively. Accordig to these umbers, a sigle aoparticle icreases the itra-cavity power by a factor of about 5. To obtai the frequecy respose of the resoator-particle system, we performed parametric aalysis where the frequecy of the free-space light was scaed ad the average field stregth i the resoator was calculated. Figure S5 shows the relatio betwee the itra-cavity field ad the frequecy of the free-space light. The domiat resoace peak at the frequecy of symmetric mode implies the efficiecy of the proposed aocoupler scheme to couple free-space light ito the cavity ad the resoace-ehacemet of the itra-cavity field. Supplemetary Figure S5 Simulated itra-cavity field stregth versus the frequecy of the freespace light. A domiat resoace peak at the frequecy of symmetric mode ad a weak resoace peak at the frequecy of asymmetric mode are clearly visible. I order to study the effect of aoparticle polarizability o the itracavity field, we varied the refractive idex of the particle from 1 to 3, ad keep the particle size uchaged to use the same mesh i the simulatios. To compare with experimetal results, we obtaied the liewidth ad Q factor of the symmetric mode whe aoparticle refractive idex was icreased. Figure S6

12 shows the relatio betwee the itracavity power ad the total liewidth or total Q factor. Simulatio shows that whe the particle-iduced loss equals to the sum of all other cavity losses, the itra-cavity field is maximized, which agrees well with theory ad our experimetal results show i the mai text (Fig. ). Supplemetary Figure S6 Simulated itra-cavity field stregth whe aoparticle iduced loss is icreased. a, Itra-cavity field versus total liewidth. b, Itra-cavity field versus total Q factor (ormalized by Q ). The itra-cavity field stregth reaches maximum whe particle iduced loss equals cavity itrisic loss, or Q load =.5Q. Free space excitatio with two aoparticles Whe there are multiple aoparticles o the resoator, the eigemodes (stadig wave modes, SWMs) iside the resoator o loger locate their ode or atiode at the positio of aoparticles. The distributios of SWMs (split modes) are determied by the particle esembles accordig to their relative spatial phase positios i the azimuthal directio o the resoator ad

13 their overlap f (r) with WGM 36. As discussed i Sec., itracavity power depeds ot oly o the positios of the particles ad their overlap with WGM, but also o the itesity ad phase of the free-space icidet light o each particle. To study this pheomeo, we performed simulatios o the simplest case of two particles o the resoator. Similar to the simulatio model i the sigle particle case, we added aother particle of the same size o the resoator; the two particles are arraged symmetrically (vertically mirrored) with respect to the axis of the resoator alog the directio of the icidet light (Fig. S7). The phase of the icidet light o these two particles was kept the same, ad the particles had the same distace to the resoator surface (same overlap f (r) with WGM). The itesity of light icidet o the first particle was decreased to about half of that o the secod particle by atteuatig the icidet light. Note that if the itesity of light icidet o two particles is the same, oly the symmetric mode ca be excited because the system becomes symmetric aroud horizotal ceter lie. The aoparticles had radii of m ad refractive idex of i. The purpose of havig a complex refractive idex for the aoparticles is to icrease the particle iduced loss to compesate the differece i particle scatterig properties betwee D ad 3D cases. I D simulatio, aoparticles scale differetly from 3D case, ad with the same diameter ad refractive idex usually give larger mode splittig but smaller particle- iduced liewidth broadeig compared to the 3D simulatio. Supplemetary Figure S7 Fiite-elemet simulatio model with two particles o a resoator. Two aoparticles (too small to be see i the figure) are positioed symmetrically with respect to the horizotal axis of the resoator ad light port. A atteuator with refractive idex of 1-

14 .1i is placed i frot of particle 1 to decrease the light itesity icidet o the particle. The resoator has diameter of 3 m ad refractive idex of i ad the aoparticles have radii of m ad refractive idex of i. Supplemetary Figure S8 Itracavity power with two aoparticles o a resoator. The spectra are vertically shifted for clarity. From bottom to top: phase distace betwee the two particles is icreased from /8 to with /8 iterval. a, Optical spectra of itra-cavity power calculated usig the theoretical model. The aoparticles have radii of 1 m ad refractive idex of Itrisic Q factor of the resoator is 7x1 7. b, Optical spectra of itra-cavity power calculated usig D fiite-elemet simulatios. We the varied the relative spatial phase distace betwee the two particles from /8 to at itervals of /8, ad calculated the relatio betwee average itesity iside the resoator ad wavelegth usig harmoic parametric simulatio. Figure S8 shows the simulatio results ad compares them with theoretical calculatios. Both theoretical ad simulatio results show mode crossig patter which is due to the chages i the relative positio of aoparticles 31. The

15 simulatio results for eigemode positio ad field stregth agree well with the calculated results from the theoretical model preseted i Sectio. Note that the sice the theoretical model cosiders a 3D model, there is a slight differece with the umerical simulatios based o a D model: As see i Fig. S8, the Q of the mode with shorter wavelegth is higher i the simulatio (Fig. S8b) tha i the aalytical model (Fig. S8a) ad thus has a higher itracavity power. This ca be attributed to the differece i the particle-iduced scatterig loss i D ad 3D models. This differece leads to higher Q factor i D simulatios as the optical mode experieces less loss whe the correspodig stadig wave mode does ot strogly overlap with the particles (Fig S8b). Cosequetly, a higher itracavity circulatig power is predicted. Noetheless, the simulatios provide a verificatio of our theoretical model. 3D model of a microtoroid-aoparticle system We also calculated the couplig of light ito a microtoroid via a aoparticle usig a fully 3D model 43. The toroid is represeted by a slice spaig 1.5 wavelegths alog the circumferece. As expected, with o aosphere (Figure S9a, right) the field is miimally coupled to the surroudig 44. O the cotrary, whe a aosphere is attached to the toroid (Figure S9a, left) we see a quasi-spherical wavefrot spreadig aroud the aosphere. I previous studies 8-9,45 this spherical wave represets light that is scattered out of the toroid by the aoparticle. Here, o the cotrary, this spherical wave represets light that is comig from the surroudig ad coupled ito the toroid. Both of the above iterpretatios are valid sice this optical system is reciprocal 46. Though the icomig field i our experimet is ot idetical with the oe calculated, it was sufficietly similar to explai couplig of light ito the toroid. Usig the same umerical calculatio 43, we check the couplig rate as a fuctio of the aoparticle size for various modes. This calculatio shows a large differece betwee the couplig rates for various modes ad allows, i priciple, a critical couplig coditio for the pump mode, while beig uder coupled for the laser mode i accordace with what is eeded for low-threshold lasers.

16 Supplemetary Figure S9 Simulatio results from a 3D model for light couplig from free space to WGMs by a aoparticle. a, The form of the electric field exhibits a quasi-spherical wave with origi at the aoparticle. A test case with o aoparticle preset is also show for compariso. b, Parametric study of the couplig rate as a fuctio of the aoparticle size. The toroid major ad mior diameters are 5 ad 5 um. The microtoroid ad the aosphere are made of silica ( = 1.45) ad polystyree ( = 1.555) ad the vacuum optical wavelegth is ear 1.55 μm. I a, the electric field outside the resoator has bee scaled up by a factor of 1 to be visible, the aoparticle radius is m ad the optical polarizatio is horizotal. I b, the white lies represet polarizatio directio.

17 Supplemetary Note 3 Couplig efficiecy ad Q degradatio with a sigle scatterer With a sigle scatterer o the resoator, from Eq. (S8) we have E cw 3 Eccw Ii 8 1 /( ) (S13) To obtai the maximum itracavity power, we eed to set 1 ad, implyig that there is o fiber taper couplig to extract power from the cavity, ad that the scatterer-iduced loss is equal to itrisic cavity loss (i.e., critical couplig). Uder this coditio, we have cw max ccw 3 /( 3 max i ) E E I, where is the cavity roudtrip time, ad is the effective wavelegth of the cavity mode. We see that the maximum itracavity power is proportioal to 1/ (i.e., the itrisic cavity Q factor.) Also, smaller resoator with smaller produces higher itra-cavity power tha larger oes, but the total eergy iside the cavity ( E ) is the same. Whe the fiber taper is preset (i.e., fiber taper to extract power from the cavity), we keep fiber taper at critical couplig coditio ( 1 ), which allows maximum power extractio from the resoator to the fiber taper. Uder this coditio, whe, we obtai the maximum itracavity power as smaller tha the case without fiber taper. cw max ccw 3 /( 18 max i ) E E I. Note that it is 4 times The power extracted from fiber taper at critical couplig coditio ( 1 ) is give by: 3 afiber iec W 1 ies ym 1/ Ii 3 (S14) Whe the couplig stregth of the scatterer is very large or (i.e., 1 ), we fid the maximum power coupled ito the fiber taper as idepedet of the cavity-specific parameters. fiber max Ii a 3 /3, which is ot

18 To cosider the tradeoff betwee couplig efficiecy ad Q degradatio, we plot the relatio betwee itracavity power ad total liewidth. The chage i liewidth was achieved by chagig the size of the sigle particle deposited o the resoator (Fig. S1). I Fig. S1, we keep the fiber taper at critical couplig ( 1 ). It is clearly see that the itracavity power reaches maximum whe the total liewidth is broadeed to about twice of the origial liewidth. With a high Q resoator (Q=5x1 7 ) ad 1mW of free space iput light, oe ca achieve a itracavity power of 1 mw with a fiber taper at critical couplig, or 488mW without the fiber taper, with a sigle aoparticle of optimal size. The maximum power coupled ito the fiber taper is about 3.1 W with a large scatterer ( 1 ). These umbers are cosistet (at the same level) with our experimetal observatio. If oe uses the maximum power coupled ito the fiber taper as the idicatio for the efficiecy of free space couplig, we fid that the couplig efficiecy is about.31% for a sigle particle. Supplemetary Figure S1 a, b. The relatio betwee the power extracted by the fiber taper ad total system liewidth (solid lie), ad the relatio betwee total itracavity circulatio power ad total system liewidth (dashed lie) for a sigle spherical aoparticle. c, d. The relatio betwee fiber extracted power ad aoparticle diameter (solid lie), ad total itracavity circulatio power ad aoparticle diameter (dashed lie). The refractive idex of

19 the aoparticle is 1.5, ad the ormalized overlap betwee the particle ad cavity mode is.3. The free space beam spot size is 4 m, with total power of 1 mw. Resoator diameter is 4 m, with itrisic Q factor of 5x1 7 (a,c) or 5x1 6 (b,d). Wavelegth is 155 m. Couplig efficiecy ad Q degradatio with multiple scatterers To estimate the couplig efficiecy ad Q degradatio as a result of multiple scatterers i the mode volume, we ra simulatios accordig to Eq. (S1-S1). Sice i the experimets, aoparticles were deposited o the resoator surface radomly, we assumed radom placemet of aoparticles i the simulatios. The results are show i Fig. S11, which are averaged results of 5 simulatios. I each simulatio, particles were radomly placed o the resoator. I simulatios, the aoparticles were radomly placed o the resoator, thus, a large portio of the particles are deposited outside of the sesitive area of the resoator (f(r)<.5), ad do ot have a sigificat cotributio to the results. We estimate the umber of particles that have sigificat cotributio to the couplig of free space light is less tha 1. This is also true i experimets, as a large portio of particles are deposited at isesitive area of the resoator ad do ot affect the experimetal results sigificatly. As see i Fig. S11, the itracavity power reaches maximum whe the total system liewidth is about doubled, correspodig to the critical couplig coditio for scatterer-couplig. The power extracted ito the fiber taper mootoically icreases whe the scatterer-iduced liewidth broadeig is larger. These results are expected ad are very similar to the case of a sigle scatterer (Fig. S1). Note that the results i Fig. S11 are the average of 5 simulatios. For each sigle simulatio, there could be sigificat deviatio from the averaged lie which maifests as fluctuatios, because of the radom placemet of the particles. We see a good agreemet betwee these results ad our experimetal results show i Fig. d of the mai text. The tred is the same despite the fluctuatios.

20 Supplemetary Figure S11 a. The relatio betwee circulatio power ad total liewidth (lie with triagles, ad the relatio betwee fiber taper extracted power ad total liewidth (lie with squares), whe multiple particles are placed o a microtoroid. The poits are obtaied by averagig the results of 5 simulatios. I each simulatio, aoparticles with diameter of 15 m are radomly deposited o the resoator surface. The free space beam spot diameter is 6 m, with total power of 1 mw. The resoator i simulatio has a diameter of 6 m, ad itrisic Q factor of 5x1 7. Wavelegth is 155 m. The fiber taper is always at critical couplig coditio. b. Example of idividual simulatio result showig radom fluctuatios due to radom aoparticle positios. The result is sampled by 5 poits.

21 Supplemetary Refereces 43. Kapla, A. et al. Fiite elemet simulatio of a perturbed axial-symmetric whisperiggallery mode ad its use for itesity ehacemet with a aoparticle coupled to a microtoroid. Optics Express 1, (13). 44. Tomes, M., Vahala, K.J. & Carmo, T. Direct imagig of tuelig from a potetial well. Optics Express 17, (9). 45. Liu, Y.C. et al. Cavity-QED treatmet of scatterig-iduced free-space excitatio ad collectio i high-q whisperig-gallery microcavities. Phys Rev A 85 (1). 46. Potto, R.J. Reciprocity i optics. Rep Prog Phys 67, (4).