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Electrical and Computer Engineering, University of Toronto, Toronto, Canada.*Corresponding author. Email: a.helmy@utoronto.ca

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Record Purcell factors in ultracompact hybridplasmonic ring resonatorsY. Su, P. Chang, C. Lin, A. S. Helmy*

For integrated optical devices and traveling-wave resonators, realistic use of the superior wave-matter interac-tion offered by plasmonics is impeded by ohmic loss, which increases rapidly with mode volume reduction. Inthis work, we report composite hybrid plasmonic waveguides (CHPWs) that are not only capable of guidingsubwavelength optical mode with long-range propagation but also unrestricted by stringent requirements instructural, material, or modal symmetry. In these asymmetric CHPWs, the versatility afforded by coupling dis-similar plasmonic modes provides improved fabrication tolerance and more degrees of device design optimi-zation. Experimental realization of CHPWs demonstrates propagation loss and mode area of 0.03 dB/mm and0.002 mm2, corresponding to the smallest combination among long-range plasmonic structures reported todate. CHPW ring resonators with 2.5-mm radius were realized with record Purcell factor compared with existingplasmonic and dielectric resonators of similar radii.

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INTRODUCTIONOptical microcavities are key components for photonic integratedcircuits and important for many applications ranging from nonlinearoptics, quantum optics, signal processing, and sensing (1, 2). For theseapplications, desired attributes such as exaltation of optical nonlinearity,laser threshold reduction, or enhancement of detection sensitivity aregoverned by the Purcell factor, which is proportional to Q/Veff, whereQ is the cavity quality factor and Veff is the effective mode volume (3).To date, the optimization of Purcell factor, particularly within traveling-wave cavities that are compatiblewith planar integrated photonic circuits,hasmainly focused on increasingQ using low-loss dielectric structures(4–6). AlthoughQ > 108 can be obtained within these integrated opticalmicrocavities, their radii typically span over hundreds of micrometers.As a result, the tenable Q/Veff factors for ultrahigh-Q dielectric resona-tors tend to be smaller than their dielectric counterparts. This is becausethey offer orders ofmagnitude smallerQs, but can be implementedwithmicrometer-scale radii (7, 8).

An alternative approach to increase the Purcell factor is to reduceVeff. To this end, subwavelength plasmonic structures have emergedas potential platforms for implementing high Purcell factor cavities(9–15). In contrast to dielectricwaveguides that guide light through totalinternal reflection (TIR), electromagnetic waves are guided in the formof surface plasmon polaritons (SPPs) in plasmonic waveguides, whichare guided along metal-dielectric interfaces (16–19). As SPPs areinterface modes and not restricted by the diffraction limit, higher fieldconfinement and density of states can be obtained, the combination ofwhich allows smaller Veff as well as enhancements of linear and non-linear optical processes. Unfortunately, the high energy density nearthemetal region inevitably leads to substantial ohmic loss,whichbecomesincreasingly severe as mode volume decreases (18–20). Consequently,the experimental Q for micrometer-scale, traveling-wave plasmonicresonators is only in the few hundreds. For the light-matter interactionafforded by plasmonic waveguides to be effectively used, the wave-guide loss needs to be reducedwithout sacrificingmodal confinement.If achieved, the combination of modest Q-factor and subwavelengthmode volume can result in Purcell factors that are competitive againstdielectric resonators.

To date, numerous strategies have been proposed to alleviate theloss-confinement trade-off. In plasmonic structures designed fortraveling-wave applications, coupled modes are commonly used toobtain favorable trade-offs. For example, metal-insulator-metal (MIM)waveguide with an insulator width of tens of nanometers can providethe highest mode localization, but at the cost of extremely short prop-agation length (22, 23). While gain media can be incorporated for losscompensation, this approach has seen limited success due to the highcurrent densities required (24). Another approach is to form hybridplasmonic waveguide (HPW), where the coupling between the SPPand TIR modes leads to smaller field overlap at the metal region(25, 26). More recently, coupled HPWs have been proposed, which fur-ther reduces the field overlap via destructive interference (27–29). Al-though the design approach requires geometrically or modallysymmetrical structures, subwavelength supermode with propagationloss akin to that of loosely confined, long-range plasmonic structurescan be obtained.

In this work, we report a composite HPW(CPHW), which supportsa low-loss supermode that is formed due to the coupling of the SPP andHPW modes through a common metal layer. Contrary to previouscoupled-mode plasmonic structures where symmetry conditions areenforced, our asymmetrical structure provides additional degrees of de-sign freedom to simultaneously optimizemultiple waveguide attributes.By using the HPW side of the waveguide stack for modal confinementwhilemanipulating the dimension on the SPP side to lower the field fluxwithin the lossymetal layer, reduced loss and confinement can be simul-taneously achieved. CHPW microring resonators with record Purcellfactor are demonstrated and outperform existing plasmonic and di-electric counterparts of similar radii.

RESULTSTheoretical analysis of the CHPW structureThe proposed CHPW structure consists of Si-Al-SiO2-Si layers, asschematically shown in Fig. 1A. The top Si-Al interface supports asingle-interface SPP mode, while the bottom Al-SiO2-Si stack sup-ports an HPWmode. The two modes have prominently different fielddistributions, as the SPP mode decays exponentially away from theinterface, whereas the HPW mode is primarily confined within theSiO2 spacer region. However, for metal thickness less than the skin

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depth, the perturbation between the evanescent fields leads to theformation of transverse magnetic supermodes (Fig. 1B). The character-istics of these supermodes are primarily dictated by the interferencebetween the longitudinal field component of the SPP and HPWmodes(Ez) (30). In-phase coupling increases the field interaction with themetal layer and corresponds to a short-range supermode (TMSR), whilean out-of-phase coupling reduces the overlap and results in a long-range supermode (TMLR). Note that transverse electric supermodescan also be supported by the structure. However, they are guided

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through TIR and will be cut off for sufficiently narrow CHPW width.Thus, only the TM supermodes will be considered here.

The coupling between the SPP and HPW modes can be controlledby tuning the vertical dimension of the CHPW, which, in turn, candrastically alter the attributes of the supermodes. For example, thedispersion and loss of a one-dimensional (1D) CHPW structure areshown in Fig. 1 (C and D) as functions of the top Si layer thickness(h). The results are calculated using Lumerical MODE Solutions atl = 1550 nm. The properties of stand-alone SPP and HPW modes

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Fig. 1. Plasmonic supermodes and modal properties of one-dimensional (1D) CHPW. (A) The CHPW structure is formed by coupling a single-interface SPP mode toan HPW mode through a common metal layer with a thickness smaller than its skin depth. The multilayer stack consists of Si (e1), SiO2 (e2), and Al (e3) forming the HPWside, and Al (e3) and Si (e4) forming the SPP side. (B) The coupling gives rise to transverse magnetic short-range (TMSR) and long-range (TMLR) supermodes. TMSR modeis highly absorptive as a result of in-phase coupling, leading to increased field interaction with the metal, while out-of-phase coupling in TMLR reduces the overlap,allowing for long-range propagation. (C) Effective mode index and (D) propagation loss as the top-side Si layer thickness are varied, calculated at an operatingwavelength of 1550 nm. The stand-alone SPP and HPW modes are plotted for comparison. (E) The normalized 1D field profile of CHPW within the Al metal layer isplotted for the optimal field cancellation at h = 147 nm and when it deviates at h = 135 and 165 nm. The y axis is centered at the middle of the 10-nm-thick metal layer,while the x axis shows the antisymmetric field profile centered at the zero crossing. (F) Optimizing the top-side Si layer thickness can lead to a substantial decrease inenergy flux through the metal layer, while no notable changes are observed in the other waveguide layers. As a result, the modal loss can be decreased by two ordersof magnitude while modal area is relatively invariant.

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are also plotted for comparison. As h increases, it is observed that theSPP andHPWmodes will become phasematched and strongly coupledat h = 108 nm, after which the two effectively decouple despite a metalthickness of only 10 nm. Correspondingly, an anticrossing behavior isobserved in the dispersion curves of the TMSR and TMLR supermodes,which converge toward that of the SPP and HPW modes at larger h,respectively. However, because of the asymmetry of the CHPW struc-ture, the losses of the TMSR and TMLR are not maximized and mini-mized at the phase-matching point. Instead, the TMSR loss showssmall sensitivity to the variation in h, while the TMLR loss can be tunedby over two orders of magnitude within the same range.

The strong tunability in the loss of the TMLR supermode can beexplained by examining the Ez distribution within the waveguide. FromFig. 1E, it is observed that Ez is rendered antisymmetrically distributedacross the metal at h = 147 nm, with a zero-crossing point at the centerof the metal layer. As h deviates from 147 nm, the propagation lossbecomes substantially higher, even though the zero-crossing pointcan still remain within the metal layer. Hence, it can be deduced fromthe antisymmetric field distribution that the loss of the TMLR super-mode reaches a minimum when there is an equal amount of positive

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and negative modal fields within the metal. In a 1D CHPW, the fieldsymmetry can be quantified via the field flux

f ¼ ∫tImfEzg

Pzdl ð1Þ

where Pz is the Poynting vector in the propagation direction and t is thethickness of the waveguide layer of interest. As depicted in Fig. 1F, fwithin the metal layer shows strong dependence on h and approacheszero at h = 147 nm. As such, the loss of the TMLR supermode is reducedto 0.019 dB/mm, which is 17.5 and 85 times smaller compared with thatof stand-alone HPWand SPP, respectively. In previous designs of long-range, coupledplasmonicwaveguides, stringent geometrical,material, andmodal symmetries are enforced to maximize the destructive interferencebetween the coupled modes (27–29). However, as shown here, giventhat loss is only dictated by the field overlap in the metal region, alow-loss supermode can be engineered even within a highly asym-metrical structure by simply manipulating the structural parametersto reduce the net field flux.

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Fig. 2. Schematic and modal properties of 2D CHPW. (A) A schematic of the CHPW core cross section discussed in this work. This CHPW is a 200-nm-wide four-layerstack that consists of 220-nm bottom high-index Si (e1), 20-nm low-index SiO2 (e2), 10-nm Al (e3) metal, and 185-nm top high-index a-Si (e4) layers. The long-rangemode in this structure is primarily confined within the low-index layer e2, as shown in the overlaid modal E-field intensity profile. (B) The cross-sectional area around thee3 metal layer is expanded to plot the longitudinal Ez field profile. By varying the e4 thickness h, the longitudinal electric flux f (in V⋅m/W) can be minimized byengineering the Ez within the metal. (C) Calculated modal area and propagation loss of the long-range mode as function of the layer e4 thickness. The thicknessfor optimal propagation loss (h = 185 nm) corresponds to the minimum flux within the metal layer. Using this method, the propagation losses of modes in CHPWscan be drastically reduced for a wide range of structures, without any restrictions on symmetry, while maintaining an extremely localized effective mode area of 0.002 mm2.(D) Insertion loss calculations for 200-nm-wide CHPW 90° bend extracted via finite-difference time-domain (FDTD) simulations. The insertion losses are optimized betweenbend radii of 1.5 and 3 mm, as bend losses become presiding below 1.5 mm, while absorption losses start becoming dominant above 3 mm. (E) FDTD-simulated transmissionspectra for ring resonators in all-pass filter configuration constructed using 200-nm-wide CHPW and 2.5-mm bend radius. Critical coupling is achieved at a gap spacing of285 nm between the bus and the ring.

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FromFig. 1B, it can also be observed that themodal energy of the 1DTMLR supermode is asymmetrically distributed and primarily confinedwithin the bottom HPW stack. Specifically, for the continuity of thedisplacement field to be satisfied, strong field confinement is establishedinside the 20-nm low-index SiO2 region (25, 26). As a result, f in themetal region is orders of magnitude lower compared with those ofthe other waveguide layers (Fig. 1F). By only changing the param-eters of the top SPP stack to engineer the field antisymmetry,minimal disturbance to the modal confinement between samplescan be ensured. As such, energy distribution of the TMLR supermodewill remain nearly constant despite the substantial variation in themodal loss. This is in stark contrast to the low-loss supermode guidedby traditional long-range plasmonic waveguides, where destructive in-terference between the coupled modes increases the energy densitywithin the nonmetallic waveguide layers and results in an increasedmodal area (23).

When extending to 2D CHPW structures (Fig. 2A), the minimiza-tion of the total Ez field remains an effective strategy for loss reduction.The field distribution of the TMLR supermode supported by a 200-nm-wide CHPW is shown in Fig. 2B. Because of the finite waveguidewidth, the modal field varies in the lateral direction, and the locationwhere complete field cancellation (zero-crossing) occurs is not flatacross the entire width of the metal layer. Nonetheless, by extendingEq. 1 to a surface integral, it is found that f in the metal layer can bereduced to 0.003 V⋅m2/W at h = 185 nm, which corresponds to aminimal loss of 0.02 dB/mm that is 20 and 75 times smaller comparedwith the losses of stand-alone HPW and SPP modes, respectively(Fig. 2A). Moreover, the long-range propagation condition is shownto be robust, as the TMLR loss remains <0.05 dB/mmeven if h deviatesfrom the optimal thickness by 10%. Last, although optimization hasbeen carried out at l = 1550 nm, the propagation loss of the optimized

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CHPW can remain <0.05 dB/mm across a 200-nm optical bandwidth(fig. S1).

The effective mode area of the 200-nm-wide CHPW is shown inFig. 2C. Specifically, a phenomenological mode area definition relatedto the Purcell factor is used (21)

A ¼ 1maxfWðrÞg ∫A∞

WðrÞdA

WðrÞ ¼ 12Re

d½weðrÞ�dw

� �∣EðrÞ2∣þ 1

2m0∣HðrÞ2∣

ð2Þ

whereW(r) is themode energy density. It is observed thatAwill expandin the regimewhere h<150nmdue to field leaking into the air cladding.However, as expected from the 1D analysis, it remains relatively con-stantly close to the region where loss is minimized as themajority of thefield is localized within the low-index SiO2 layer. Specifically, subwave-lengthA of 0.002 mm2 is achieved at h = 185 nm, which changes by only5% even with 10% deviation in h.

With strongly reduced propagation loss, the subwavelength modalconfinement offered by plasmonic structures can now facilitate theenhancement of thePurcell factor.UsingLumerical 2.5D finite-differencetime-domain (FDTD) simulations, the insertion loss of the 200-nmCHPW bend is calculated and shown in Fig. 2D. The insertion loss is~0.25 dB for bend radius between 1.5 and 3 mm. For bend radius below1.5 mm, radiation losses become dominant. However, even at a radiusequal to the waveguide width, the insertion loss is still under 3 dB, thushighlighting the capability of the CHPW platform for designingcompact devices. The transmission spectra for all-pass filter imple-mented via the 200-nm-wideCHPWring and bus are shown in Fig. 2E.Under the critical coupling conditionwhen the gapwidth is 285 nm, the

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Fig. 3. Cutback measurement of CHPWs. (A) Scanning electron micrograph of a cleaved CHPW. (B) Scanning electron micrograph of the Si nanowire–CHPW end-buttcoupler. (C) Propagation loss for CHPWs with different a-Si thickness. For comparison, the theoretical values obtained via FDTD modeling (gray dashed line) and the measuredpropagation losses of a silver-air-silver plasmonic slot waveguide and single-sided HPW that does not have a top a-Si layer are also plotted. (D) Coupling efficiency betweena junction formed by an 800-nm-wide Si nanowire and a 200-nm-wide CHPW. The theoretical values obtained via FDTD modeling are also plotted (gray dashed line).

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theoretical extinction ratio and quality factor are calculated to be 30 and775 dB, respectively. With an effective mode volume of 0.032 mm3, theQ/Veff for the CHPW ring is calculated to be ~16,000.

Table S1 compares the attributes of Si waveguides and exiting plas-monic waveguides with those of the CHPWs. Bymanipulating the cou-pling of dissimilar plasmonic modes within the same waveguide, theCHPW structure can achieve mode confinements similar to thosefound in the MIM structure as well as propagation loss that is an orderof magnitude smaller than that of HPWs. Thus, the loss-confinementtrade-off is heavily alleviated. Note that the use of anHPWas part of thecoupled-mode structure enables highly efficient, instantaneous CHPWmode excitation without the need for taper structures. As shown infig. S2, nonresonant excitation of CHPWdevices can be obtained usingSi nanowires with coupling efficiency of 71% at l = 1550 nm.

Experimental realization of the CHPW structureFor proof of concept, 200-nm-wide CHPWwaveguides and rings havebeen fabricated (Fig. 3A). First, 20-nm SiO2 and 10-nm Al layers aredeposited onto silicon-on-insulator (SOI) wafer via plasma-enhancedchemical vapor deposition (PECVD) and sputtering, respectively.Next, a-Si is sputtered and partially etched down such that differentsamples have different a-Si thicknesses, ranging between 0 and 250 nm.Last, the waveguides are patterned usingmultiple electron beam lithog-raphy steps, and the dielectric and Al layers are etched via reactive ionetching and wet processing, respectively. CHPWs with lengths between10 and 400 mmhave been fabricated for cutbackmeasurement. Light iscoupled in and out of the CHPW devices via 800-nm-wide Si nano-wires (Fig. 3B).

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Themeasured CHPWpropagation loss at l = 1550 nm is plotted inFig. 3C. As predicted by the field-matching analysis, loss can be subs-tantially reduced with increasing h and a minimum of 0.03 dB/mm ismeasured at h=190nm.This is slightly higher than the theoretical valueof 0.02 dB/mm, and the deviation can be attributed to additional lossmechanisms such as sidewall roughness, layer interface roughness,and absorption from the a-Si layer. The experimental propagationlosses for the MIM and HPW waveguides are also shown in Fig. 3C,which are orders of magnitude higher than that of the CHPW. Thus,the benefit of a coupled mode–based design approach is demonstrated.To our knowledge, this is the first experimental demonstration of long-range coupled plasmonic waveguides. Moreover, the strong fabricationtolerance is also illustrated, as the CHPW loss only increases to 0.07 and0.09 dB/mm for h = 155 and 250 nm, respectively. On the basis of thecutbackmethod, CHPWexcitation efficiencies have also been extracted(Fig. 3D). The coupling efficiency is only 56% at h = 155 nm due tosample-specific fabrication imperfections such as trapezoidal sidewallprofile andmisalignment betweenCHPWs and Si nanowires. Nonethe-less, a coupling efficiency of ~70% is maintained over a large range ofh values.

The fabricated all-passCHPWring resonator is shown inFig. 4A.Thefree spectral range is determined to be ~44.8 nm due to the micrometer-scale radius, and the resonance canbe tuned across theC-bandby varyingthe radius (Fig. 4B). Once critical coupling is established at a gapwidth of270 nm, amaximumextinction ratio of 29 dB is observed at l = 1574 nm(Fig. 4C). In addition, the full width at half maximum is measured to be4.8 nm, which corresponds to aQ-factor of 320. Although the exper-imental Q is lower than the theoretical prediction of 775 because of

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Fig. 4. Experimental CHPW microring resonator results. (A) Scanning electron micrograph of an all-pass CHPW resonator with 2.5-mm radius. (B) Measured trans-mission spectra of CHPW ring resonators with 270-nm gap width and varying radii. (C) Measured transmission spectra of CHPW ring resonators with 2.5-mm radius forvarying gap widths. (D and E) Measured transmission spectra and resonant wavelengths of CHPW ring at different substrate temperatures (2.5-mm radius and 270-nmgap width). The spectra and resonance wavelengths have been fitted to Lorentzian and linear functions, respectively.

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additional losses incurred due to absorption and roughness from thesputtered a-Si layer, it is the highest for hybrid plasmonic ring resonatorsreported to date. Given a calculated A of 0.002 mm2, the 2.5-mm-radiusring resonator has Veff of only 0.032 mm

3. Therefore, our experimen-tal device can achieveQ/Veff as high as 6507, the highest reported fortraveling-wave plasmonic resonator to date. Last, the temperaturedependence of the CHPW ring resonators is shown in Fig. 4D. Ex-tinction ratio is maintained >20 dB for temperatures up to 75°C, andthe transmission minimum exhibits a linear shift of 0.052 nm/°C(Fig. 4E).

DISCUSSIONIn conclusion, we report a CHPW architecture where dissimilar plas-monic modes are coupled together at a single metal interface to simul-taneously reduce field overlap with lossy metal and confine powerwithin a subwavelength area. The waveguide platform does not requireany structural or modal symmetry, therefore allowing a much morerelaxed fabrication tolerance. As such, it enables the realization of long-range plasmonic modes in any platform with no material or structuralrestrictions. Experimental realization of the proposedCHPWstructureshas shown record-low propagation and record-high Q/Veff. Table 1compares the experimental attributes of the different traveling-waveoptical microcavities. Specifically, it can be seen how CHPW rings with2.5-mm radius outperform their plasmonic and dielectric counterpartsof similar radii and can enableQ/Veff and extinction ratio that are anorder of magnitude higher compared with ultrahigh-Q dielectric cav-

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ities. Thus, the adverse effect of the ohmic loss inherent to plasmonicwaveguides has been effectively alleviated. As a proof of concept, we haveonly examined how the thickness of the top Si layer can influence thesupermode attributes. It is expected that the optimization of otherwaveguide layers or an extension to whispering-gallery disk structuremay lead to additional performance enhancement (8).

The experimental demonstration of CHPW microring resona-tors with high Q/Veff ratio and, therefore, high Purcell factor opensthe door to many potential applications. First, the CHPW is suitablefor nanolaser application because (i) as reported in 28, the combina-tion of low modal loss and nanoscale modal area within coupled-plasmonic waveguides can enable lower threshold gain and enhancethe rates of spontaneous and stimulated emissions. (ii) The use of aring resonator instead of Fabry-Perot–like cavities can avoid un-desired loss due to imperfect reflection at end facets (31, 32). (iii) Anefficient method for collecting the output light from the resonator isalready in place. Second, the CHPW may be useful for cavity quan-tum electrodynamics, particularly in a coupling regime where thePurcell factor is still a limiting factor (33). Third, the CHPW canbe exploited for nonlinear plasmonics by depositing nonlinear ma-terials within the spacer layer where the energy density is the highest(13). Last, it is important to highlight that although the analysis herehas focused on minimizing the field overlap with the metal layer, thesame coupled-mode design approach can instead be used to maxi-mize the field overlap for efficient photodetection (34). Alternatively,the waveguide loss can be dynamically tuned after fabrication usingbias or current for optical modulation (35). Hence, CHPWs will nodoubt have an impact that extends from ultracompact interconnectsto integrated optical circuitry that is programmable and reconfigur-able (14, 36).

MATERIALS AND METHODSCHPW device simulationThe effective index and propagation loss of the CHPWmode were cal-culated via 2D finite element method simulation using the commercialLumericalMode Solutions software.Metallic boundary conditions wereused to terminate the 2 mm by 2 mm computational domain. Grid sizesof 0.1, 1, and 2.5 nmwere used tomesh the Al thin film, the SiO2 spacerlayer, and the rest of the waveguide structure, respectively. The top Silayer was taken to be crystalline in the simulations. The refractiveindices of the materials at l = 1.55 mm are as follows: nSi = 3.4784,nSiO2 = 1.44, and nAl = 1.44 + 16i.

CHPW device fabricationThe CHPWs were fabricated using standard 220-nm SOITEC wafer.Deposition of 20-nm-thick SiO2 was carried out using Oxford Instru-ments PlasmaLab System100 PECVD at a plasma temperature of400°C using SiH4 and N2O. Deposition of 10-nm-thick Al was doneusing AJA International ATC Orion 8 Sputter Deposition System atroom temperature in Ar plasma. Last, deposition of a-Si:H was per-formed using the MVSystems Multi-Chamber PECVD at a substratetemperature of 180°C using SiH4 plasma. Lithography to define etchingpatterns was carried out in Vistec EBPG 5000+ Electron Beam Li-thography System. As Si nanowires and CHPWwere built on the samesubstrate, multiple alignment steps were required. Waveguide pat-terning was realized using Oxford Instruments PlasmaPro Estrelas100deep reactive ion etching for silicon andoxide layers, and aluminumetchant type A for the metal layer.

Table 1. Normalized Purcell factor (Q/Veff) comparison of CHPW ringresonators against literature. The measured propagation loss, ringresonator extinction ratio, and normalized Purcell factor of the CHPW ringresonators are compared against representative, previously reportedplasmonic and silicon ring resonators. In typical plasmonic waveguides,highly localized plasmonic modes are afflicted by low-quality factors as aresult of losses, while subwavelength confinement is not attainable indiffraction-limited dielectric waveguides. In contrast, the CHPW canachieve record-low losses of 0.03 dB/mm through flux engineering whileconcurrently asserting a nanoscale modal confinement of only 0.002 mm2,leading to an effective mode volume of 0.032 mm3 for 2.5-mm ring radius.Through this combination, 6507 normalized Purcell factor can beachieved as the loss-confinement trade-off inherent in plasmonics isdrastically alleviated using our structure.

Ring radius (mm)

Extinction ratio (dB) Q/Veff

[4]

9650 5.6 107

[5]

4300 3 300

[6]

300 2.6 446

[7]

1.5 –* 3621

[8]

2.75 –* 5149

[11]

5.4 13 43.7

[12]

2.59 12.8 538

[14]

1.5 29.5 213

CHPW

2.5 29 6507

*Not reported.

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CHPW device characterizationTo perform cutback measurement, light from a C-band continuous-wave laser was first amplified using an erbium-doped fiber amplifier(EDFA). Next, the output fiber from the EDFA was wrapped througha Thorlabs paddle fiber polarization controller to ensure TM-polarizedinput. A single-mode lensed fiber that has a 2.5-mm spot diameter wasused to couple light into the input Si nanowires. On the output side, thetransmitted light from the output Si nanowire was collected with a 20×objective lens with 0.4 numerical aperture. Noise from the substrate waseliminated using an iris, and the output polarizationwas confirmedwitha polarization beam splitter. Last, a germanium photodetector was usedfor power measurement.

Thermal measurement was performed using a custom copper stagewith thermoelectric coolers, where temperature was controlled usingthe Keithley 2510-AT Autotuning TEC source meter through electricalfeedback from a 10k thermistor.

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SUPPLEMENTARY MATERIALSSupplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/5/8/eaav1790/DC1Section S1. Wavelength dependence of 2D CHPWSection S2. Silicon nanowire-CHPW couplerSection S3. Comparisons for various short-range and long-range waveguides againstthe CHPWFig. S1. The wavelength dependence of the CHPW supermode attributes.Fig. S2. Mode matching and broadband power transfer between silicon nanowires and CHPW.Table S1. Comparison of physical cross-sectional dimensions, propagation loss, and mode areaof various waveguide designs.Reference (37)

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AcknowledgmentsFunding: This project was funded by the Natural Sciences and Engineering Research Council(NSERC) of Canada. Author contributions: A.S.H., C.L., P.H.C., and Y.W.S. have designed thestructures. Y.W.S. and P.H.C. have electromagnetically modeled the structure. Y.W.S. hasfabricated the samples. Y.W.S. and C.L. have characterized the devices. A.S.H., C.L., P.H.C., andY.W.S. have analyzed the measurements and wrote the manuscript. Competing interests:The authors declare that they have no competing interests. Data and materials availability:All data needed to evaluate the conclusions in the paper are present in the paper and/orthe Supplementary Materials. Additional data related to this paper maybe requested from the authors.

Submitted 21 August 2018Accepted 25 June 2019Published 2 August 201910.1126/sciadv.aav1790

Citation: Y. Su, P. Chang, C. Lin, A. S. Helmy, Record Purcell factors in ultracompact hybridplasmonic ring resonators. Sci. Adv. 5, eaav1790 (2019).

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Record Purcell factors in ultracompact hybrid plasmonic ring resonatorsY. Su, P. Chang, C. Lin and A. S. Helmy

DOI: 10.1126/sciadv.aav1790 (8), eaav1790.5Sci Adv 

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