Integrated optics nano-opto-fluidic sensor based on whispering gallery modes for picoliter volume refractometry This article has been downloaded from IOPscience. Please scroll down to see the full text article. 2013 J. Phys. D: Appl. Phys. 46 105104 (http://iopscience.iop.org/0022-3727/46/10/105104) Download details: IP Address: 130.194.20.173 The article was downloaded on 18/03/2013 at 05:33 Please note that terms and conditions apply. View the table of contents for this issue, or go to the journal homepage for more Home Search Collections Journals About Contact us My IOPscience
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Integrated optics nano-opto-fluidic sensor based on whispering gallery modes for picoliter
volume refractometry
This article has been downloaded from IOPscience. Please scroll down to see the full text article.
Received 9 October 2012, in final form 16 January 2013Published 13 February 2013Online at stacks.iop.org/JPhysD/46/105104
AbstractWe propose and numerically investigate an integrated optics refractometric nano-opto-fluidicsensor based on whispering gallery modes in sapphire microspheres. A measurand fluid isinjected in a micromachined reservoir defined in between the microsphere and an opticalwaveguide. The wavelength shift due to changes in the refractive index of the measurand fluidare studied for a set of different configurations by the finite element method and a highsensitivity versus fluid volume is found. The proposed device can be tailored to work with aminimum fluid volume of 1 pl and a sensitivity up of 2000 nm/(RIU·nl). We introduce a figureof merit which quantifies the amplifying effect on the sensitivity of high quality factorresonators and allows us to compare different devices.
S Online supplementary data available from stacks.iop.org/JPhysD/46/105104/mmedia
(Some figures may appear in colour only in the online journal)
1. Introduction
Micro- and nano-optofluidics is being explored for developingfunctional lab-on-a chip systems and sensors [1, 2]. Integrationof these systems offers significant advantages includingminimized consumption of reagents, portability, increasedautomation, reduced costs and shorter time constants ascompared with their macroscopic counterparts. Identificationand quantification of the analyte can be accomplished byevaluation of the refractive index. This can be measuredby several techniques, such as evanescent waves in liquidwaveguides [3], surface plasmon resonance [4–6], long periodgratings [7], photonic crystals [8–10], interference at theliquid–solid interface [11], Fabry–Perot cavities [12], Mach–Zehnder interferometry [13] ring resonators [14] and capillary-based optofluidic ring resonator [15].
Reducing the liquid volume is a crucial requirement formany applications involving traces of substances. In suchcases, detection techniques with high sensitivity to refractiveindex variations in extremely small volumes of fluids areneeded. The smallest volume measured claimed up to date wasin the order of 10 fl, though without apparent confinement [16].However, as the volume shrinks, so does the light-analyte
interaction volume with the probing light. This problem canbe circumvented by increasing either the effective interactiondepth or the effective interaction length. The former can beincreased by confining the resonant optical field close to theliquid sample. The latter can be increased using resonanttechniques based on multi-pass interaction. However, multi-pass interaction demands resonant cavities with long photonlifetimes or, in other words, a high quality factor Q =E/E = ωRτ = 2πcτ/λR [17], where c is the speed of light,E is the energy stored in the resonator, E is the energy lost perunit cycle associated with the considered resonance, τ, ωR andλR are the ring down time, circular frequency and wavelengthat resonance, respectively. An equivalent definition is oftengiven as Q = λR/λ where λ is the line width. The formerdefinition allows us to measure the Q-factor with a ring downtechnique in the time domain [18], while the latter requires atunable source or filtering element with a linewidth narrowerthan λ.
For a resonator uniformly covered by a measurandsubstance, the effective length Leff is related to the Q-factorby Leff = QλR/2πnmicrosphere [19], i.e. a high Q-factor ofthe resonator increases the capability to detect tiny variationsof the refractive index of the analyte, provided the Q-factor
J. Phys. D: Appl. Phys. 46 (2013) 105104 G Gilardi and R Beccherelli
Figure 1. Device structure and definition of the geometrical parameters.
is not limited by absorption losses in the fluid [20]. Whenthe analyte is in shortage, it may cover only a fraction ofthe resonator. Thus, the effective length is reduced by asuitable cover factor (and so are losses due to absorption inthe fluid). The photonics devices showing the highest Q-factors operate in the whispering gallery mode (WGM) regime.Recent reviews are given in [21–27].
Ring resonators optically coupled by integrated opticswaveguides and a microfluidic chamber are amenable tointegration [28]. However, the highest value of Q-factorreported to date for ring resonators is Q = 1.2 × 106
[29] in air with much lower values in denser fluids. Thecapillary-based optofluidic ring resonators (OFRR) is alsoa very interesting approach, though the demonstrated Q-factor is still moderate (1.2 × 105) [30]. The highest Q-factor reported to date for unloaded WGM resonators is 108
in air and 106 in water for microtoroids [31] and 1011 formicrospheres [32]. However, in most cases, in- and out-coupling to microtoroids and microspheres are performed bya fragile suspended tapered fibre optics which is accuratelypositioned using bulky and expensive 3-axis nano-positioningstages. Recently, a more robust technique based on anglepolished waveguides has shown to reduce the hassle ofhandling thinned suspended fibres [33]. However, while thesecoupling techniques are effective to show the proof of principleon bulky vibration-free optical benches, none are amenable tointegration and large scale deployment in lab-on-chips nor forconfining tiny quantities of measurand liquid analyte. On theother hand, coupling to microspheres by means of integratedoptical waveguides has been recently shown [34–36]. In thiscontext, the integration of WGM spherical resonators in micro-optofluidic filters [37] and sensors has been proposed by us [38]but not systematically studied yet.
In WGM sensors, estimation of the refractive index isperformed by measuring the frequency shift of the resonancepeak. A perturbation model was developed to predict thebehaviour in a uniform surrounding medium [39]. However,numerical techniques are needed to correlate the sensor’sresponse to the refractive index of a fluid confined in a micro-optofluid device. An authoritative review on the performance
quantification of resonant refractive index sensors is providedin [40].
In this paper, we present and numerically investigatean integrated optics nano-opto-fluidic refractometric sensorwhich exploits the very high Q-factor of crystal microsphereresonators. Lossless fluids only are assumed to better elucidatethe performances as a purely refractometric sensor. Thestudy is performed in the 1550 nm telecom window, whereequipment and NIST-traceable calibration fluids are broadlyavailable, and in the 1.3–1.53 refractive index range, whichincludes many organic fluids [41] as well as water solutions.Water does show some losses at this wavelength, but these aresignificantly reduced using heavy water [42]. Nevertheless,the analysis carried out in the following easily scales withwavelength and this study can be extended to other wavelengthswhere targeted fluids are transparent. We define a figure ofmerit for comparing different configurations of the deviceand optimize it. This parameter can be effectively usedin comparing different types of microfluidic refractometricsensors.
2. Device structure
The proposed device, illustrated in figure 1, is designed withthe explicit objective to benefit from the very high Q-factorof microspheres, while removing difficulties in their in- andout-coupling to fibre optics. In its general concept, it consistsof (i) a microsphere positioned over (ii) a channel waveguideand (iii) a low refractive index micromachined cladding witha recessed feature, preferably a cylindrical aperture. Themicromachined cladding provides both accurate positioning ofthe microsphere and confinement of the measurand fluid. Thechannel waveguide is precisely aligned once for all with respectto the microsphere at fabrication stage and is butt-coupledto external fibre optics in a compact integrated assembly,thus removing the need for bulky nano-positioning stagesat measurement time as used so far in the literature. Thethickness h of the cladding layer is easily controlled at thedeposition stage with extreme precision, virtually down to the
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J. Phys. D: Appl. Phys. 46 (2013) 105104 G Gilardi and R Beccherelli
atomic/molecular scale for suitable materials and depositiontechniques. The radius r of the cylindrical aperture and itsrelative position with respect to the waveguide is defined bya lithographic process, with potential accuracy down to afew nm.
The cylindrical aperture supports the microsphere andcontrols its distance D from the waveguide and, at thesame time, defines the confining cavity and the inlets andoutlets for the injection of the measurand fluid. Underlaboratory conditions, the microsphere is positioned over thecylindrical aperture by means of a mechanical tool under astereomicroscope. For better control, we prefer to use a suctioncapillary to hold the microsphere and move the glass substrateon a xyz stage until the sphere is positioned in place. Themicrosphere is then glued by means of a suitably dispensedUV epoxy (for instance a needle tip with ≈10 µm radius). Theepoxy glue is dispensed preferably at ±π/4 and ±3π/4 fromthe waveguide axis to prevent the glues infiltrating the fluidinlet and outlet or perturbing the optical field. The viscosityof the glue is critical, as this may penetrate the cylindricalaperture. However, viscosity can be optimized by pre-curing.Finally, vacuum is removed and the microsphere is released.For batch manufacturing, a suitably designed jig that promotesself-positioning of one or several microspheres at a time maybe used. Gluing provides a stable vibration-free arrangement.D is related to the cladding thickness (h) and the cylindricalaperture radius (r). Hence, while the approach followed in [35]makes use of uniformly deposited low refractive index claddingto control the distance only, our patterned cladding controlssimultaneously both distance and position at fabrication stage,thus relieving the operator from tedious alignment.
In this work, we study a low cost implementationwith rather relaxed fabrication constraints, based on asapphire microsphere, a glass double-ion exchange waveguidefabricated as in [43–47] and a polydimethylsiloxane (PDMS)cladding. Features defined with UV photolithography by ushave proven perfectly adequate to pattern batches of singlemode waveguides showing a mode profile that well matchesthat of single mode fibre optics (≈10.4 ± 0.8 nm) [44]. Thesame process provides alignment of the microsphere equatorwith respect to the waveguide to better than 1/10 of the modewaist. Thickness of PDMS (h) is controlled by spin-coatingspeed. PDMS is one of the preferred materials for optofluidics[48] due to its elasticity, optical transparency, compatibilitywith several fluids [49], biocompatible surface chemistry [50]and low-cost processability by several techniques, includingsoft lithography [51], lift-off [52, 53] and wet or dry etching[54] or their optimized combination [55]. A simple O2 plasmaactivates its surface [50], allowing adhesion to other materialsthus resulting in sealed devices. Furthermore, its low refractiveindex (1.406@1550 nm) makes it an excellent optical claddingfor glass waveguides. For our common fabrication process,once covered by PDMS, our double-ion exchange waveguides[44] show an effective refractive index of neff ≈ 1.5089 forthe fundamental TE mode, as computed using a mode solver.These glass waveguides are easy to couple to standard fibreoptics by means of index-matching UV epoxy.
The dispensing of the measurand fluid is schematicallyexemplified in figure 1 by a syringe, though microfluidic
systems made with PDMS and capable of dispensing sub-nanoliter volumes have been demonstrated [56]. Picoliter havebeen dispensed by us with commercial inkjet printer [57, 58].Here, the measurand fluid flows in under Couette conditions.We anticipate that the inlet and outlet can provide the Poiseuilleflow at the cost of some technological optimization by fullyencapsulating the device by PDMS. Negligible differencesare expected with respect to the optical analyses with themicrosphere surrounded by air because PDMS is a low lossand low refractive index material.
Small variations of the effective refractive index of thewaveguide occur for a set of relevant covering liquids withrefractive index nfluid in the 1.3–1.53 range, but as a generalrule, guided propagation in the waveguide results only formeasurand fluids with nfluid < neff . Excellent resonantcoupling (i.e. critical coupling) into the sphere and low lossfor non-resonant wavelengths (i.e. under-coupling) is obtainedwhen nfluid < neff < nsphere. When nfluid exceeds neff ,optical modes leak out of the waveguide show poor couplingto the spherical resonator and high optical losses whichlimit the effective interaction length. Hence, to be ableto measure a broader range of fluids, we focus this studyto commercially available sapphire microspheres (nsphere =1.7@1550 nm, minor birefringence of crystalline sapphire isneglected) instead of the more common silica spheres whichhave a lower refractive index.
We also anticipate that a similar device concept basedon silicon resonators [59] coupled to silicon-on-insulator(SOI) waveguide [60] could be effective in measuring fluidswith refractive indices larger than those considered here.Similarly, high refractive index chalcogenide and fluorideglass waveguides and microspheres can also be used at largerwavelengths up to the mid-IR [61, 66].
The phase matching coupling condition for a lightbeam propagating in the waveguide and the WGMs in themicrosphere depends on the refractive index of the fluid. Whenthe phase matching condition holds, light is evanescentlycoupled into the microsphere and travels near the internalsurface of the microsphere due to total internal reflection witha path ≈2πR in one lap. If one lap is equal to l wavelengthsin the medium (l is an integer), a stationary wave is excited inthe microsphere. This resonance condition may be writtenas 2πR ≈ l(λR/nsphere). The number of wavelengths inthe microsphere is identified as the angular momentum. Theinjection of an isotropic fluid with nfluid > 1 in the cavityresults in an apparent increase in the effective size of themicrosphere. Hence, the propagation pathway of the photonsinside the microsphere increases. This increase is measuredin the spectrum transmitted by the waveguide as a shift in theresonance peak wavelength to longer wavelengths.
We consider a microsphere described by the equation:
(x + x0)2 + y2 + z2 = R2. (1)
The centre of the microsphere is raised above the glass substrateby x0 = R + D, where R is the microsphere radius and D isthe distance from the substrate to the edge of the microsphere.Thus, the radius of the cylindrical aperture is
r =√
2[D(h − R) + hR] − h2 − D2. (2)
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J. Phys. D: Appl. Phys. 46 (2013) 105104 G Gilardi and R Beccherelli
(a) (b)
Figure 2. (a) Percentage of microsphere circumference (C%) and surface (S%) in contact with the isotropic fluid which affects the effectiveinteraction length, and (b) total fluid volume inside the cavity. C% and S% affect the effective interaction length Leff = (Qλr)/2πnmicrosphere.Data are calculated for the case T = h.
We consider a choice of values for the PDMS thickness andlimit our study in the case of D = 0, i.e. T = h, where T isthe height of the spherical cap as this condition determines theminimum fluid volume for any combination of R, r and h. Itwas experimentally found that WGM resonance peaks almostmaintain their wavelengths, when the separation between thewaveguide and microsphere increases to 70 nm or a lateralmisalignment occurs to within 2 µm and that only a minorincrease in the Q-factor is found due to the reduced couplingstrength at separations beyond critical coupling [35].
In the present design the condition T = h implies thatthe sphere is in physical contact with the waveguide whichmakes the sensor less sensitive to vibrations that strongly limitpractical usability of WGM resonators coupled by taperedfibres. Hence, equation (2) becomes
r =√
2hR − h2. (3)
The surface (S) of the microsphere in contact with the isotropicfluid is
S = 2πRT (4)
and the fluid volume trapped in the cylindrical aperture underthe microsphere:
V = πr2h − πT3r2 + T 2
6. (5)
The effect of the fluid on the optical properties of the structureis defined at design stage by geometrical overlap of the opticalmode in the waveguide and in the sphere and by the lengthof interaction. This overlap is dynamically varied by theinjected measurand fluid which somehow behaves as an opticalmatching fluid.
As the fluid covers only a fraction of the microsphere,we have two options for defining a cover factor to helpcomparing different geometries. In figure 2(a) we plot theeffect of the radius and the PDMS thickness on the fraction ofcircumference (C%)
C% = 2 cos−1(
R−TR
)π
× 100% (6)
and fraction of area (S%)
S% = 2πRT
4πR2× 100% = T
2R× 100% (7)
of the sphere and fluid volume. The corresponding volumeoccupied by the measurand fluid is shown in figure 2(b),where it can be remarked that volumes as low as 1 pl, a yetunprecedented value for a microfluidic sensor, are possible. Inthe following we systematically study the effect of the fluidvolume on the performance of the sensor.
3. Numerical result and discussion
The behaviour of the device is studied by the finite elementmethod (FEM) implemented in a commercial software [67]as a function of nfluid for microspheres with R = 75 andR = 150 µm to elucidate the effect of their radius. Theanalysis is carried out in the frequency domain by sweepingthe wavelength of a Gaussian optical field with TE polarizationwhich is coupled to the diffused waveguide, thus mimickingbutt-coupling from an optical fibre used exited by a tuneablelaser under real experimental conditions. We have optedfor a frequency domain analysis, as this allows us to finelyand adaptively follow the narrowband resonances of WGM.Conversely, time domain analyses would have required tocompute fields over a lapse a few times the ring down timeof the resonator, an unacceptably long simulation time forhigh-Q resonators. Our 2D numerical model solves Maxwell’sequations in the frequency domain and correctly describes theexcitation of modes of the resonator having l = m, where l andm are the angular and polar mode numbers, respectively. Thesemodes lie in the equatorial plane bisecting the waveguide.In order to study the excitation of power at higher latitude,an extremely computational intensive 3D analysis would berequired. However, Panitchob et al [34] found that, in asimilar waveguide-coupled geometry, the strongest couplingis shown for the fundamental modes with radial number n = 1and l = m and that these modes correspond to the deepestresonances.
In figure 3 we plot the computed normalized transmission,focused on the deepest and highest Q-factor mode, for seven
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J. Phys. D: Appl. Phys. 46 (2013) 105104 G Gilardi and R Beccherelli
Figure 3. Computed normalized transmission for seven values of refractive index for (a) R = 75 µm and h = 2 µm and (b) R = 150 µmand h = 4 µm. Focus is on the deepest and highest Q-factor mode.
Figure 4. Computed electric field intensity in the microsphere for (a) off-resonance and (b) on-resonance cases. In the linear scale, blue andred represent zero and maximum intensity, respectively. The multimedia file (stacks.iop.org/JPhysD/46/105104/mmedia) shows thepropagation of light inside the microsphere as a function of wavelength for a fluid refractive index 1.48.
values of refractive index for two cases scenarios, (a) R =75 µm, h = 2 µm and (b) R = 150 µm, h = 4 µm asthis combination results in the same exposed surface S% (seefigure 2(a)). We have produced full data set for h = 4 µm,h = 8 µm, h = 15 µm for both R = 75 µm and R = 150 µm,and we have obtained similar resonant curves. When nfluid
is comparable to or larger than neff = neff(nfluid), opticalpower is progressively transferred to the liquid and scattered,which results in a decrease in the Q-factor. This makes theidentification of the peak shift less precise.
In figure 4, we show the computed electric fielddistribution in the y = 0 plane for R = 150 µm and nfluid =1.48 under the conditions off-resonance at λ = 1550.9320 nmand on-resonance at λ = 1550.9052 nm. The input light isa Gaussian optical field with TE polarization, which travelsfrom left to right, a few micrometres under the PDMS–glass substrate interface. Figure 4 demonstrates that the
electromagnetic field resonantly coupled to the microsphere(for D = 0 µm) is confined in a few micrometres below thesurface, thus clearly showing that the highest Q mode is theone with the lowest radial number.
From the full data sets, in figure 5 we summarize thecomputed shift of the peak when fluids with larger refractiveindices are injected for different geometries and fluid volumes.
Our results in figure 5 follow the trend described byequations (3) and (4) in [68]. Those equations indicate thatthe resonance shift strongly depends on the field intensity atthe microsphere surface. The increase in the refractive indexof the fluid inside the cavity enhances the amplitude of theevanescent field that senses the fluid. As expected, figure 5shows that the larger the surface of the microsphere in contactwith the fluid, the larger the peak shift. However, this alsoimplies an increase in the measurand fluid’s volume. Whilesensitivity is often defined as S = ∂λ/∂n [65], this does
J. Phys. D: Appl. Phys. 46 (2013) 105104 G Gilardi and R Beccherelli
(a) (b)
Figure 5. Computed peak shift as a function of refractive index values of measurand fluid. For R = 75 µm (a) and R = 150 µm (b). Alarger cavity determines larger shifts, but at the expense of larger fluid volumes.
(a) (b)
Figure 6. Sensitivity SV curves for (a) 75 µm and (b) 150 µm radius. In all cases, sensitivity slightly increases with the refractive index dueto better phase matching of optical power inside the resonator.
not take into any account any constraint that may exist onthe volume of the measurand fluid. Biological measurandmaterials are often found in traces in forensic science [69].Hence, to study quantitatively this behaviour of our device,we define its sensitivity per unit volume S = (1/V )(∂λ/∂n),here approximated for our discrete data set as the normalizedcentred difference
SV = 1
V
(λk+1 − λk−1
2n
)(8)
and plot it in figure 6.From figure 6 one would be tempted to conclude that
smaller spheres are more sensitive. However, one must alsokeep into account the resolution and limit of detection inthe measurement of the resonant wavelength λR . This isdone in the frequency domain by ‘sampling’ the transmittancecurve versus wavelength with a stable tuneable laser witha bandwidth much narrower the one of the resonator.Commercially available tunable lasers in the near 1.55 µmtelecom window have a bandwidth of ≈100 kHz (0.8 fm at1550 nm) and a comparable resolution δλ in the tuning. Themeasure of the peak shift is ultimately carried out by measuringvariations in the transmitted power. This is also affectedby intrinsic noise in the measurement chain. Variations inpower are measured with a resolution normalized by Pmin, thetransmitted power at the resonant wavelength. To estimatethe minimum detectable power variation δP measureable at
the output of the device, we write the transmittance versuswavelength as the simplest parabolic approximation of theLorentzian shape dip as P = a(λ−λR)2+Pmin. The coefficienta is found by imposing that the parabola joins the vertex (λR ,Pmin) and the ‘3 dB’ points (λR−λ/2, 2Pmin) and (λR+λ/2,2Pmin). By differentiating P versus λ, we find that δP /Pmin
is directly related to Q = λR/λ through the relationshipδP/Pmin = 8Q2 · δλ/λR . As one would expect, largervalues of Q-factor, typical of larger spheres, ease the detectionof small wavelength changes as the Q-factor ‘amplifies’ thepower variation in the detector. However, for the same valueof the cladding thickness h, smaller spheres expose a largerpercentage of circumference and surface to the measurand fluid(see figure 2(a)), thus somehow counterbalancing the smallerQ-factor.
Smaller values of Q-factor also result in easier shift ofthe resonant frequency, thus in a more sensitive readout.To quantify these opposing effects in small and largermicrospheres and optimize the design of the microfluidicsensor, there is a need for detailed information aboutexperimental conditions such as temperature variation andlinewidth and spectral resolution of the tuneable laser usedto perform the measurements experimental noise in themeasurement chain. For instance, it was shown that a highQ-factor is advantageous in reducing the spectral noise ofthe sensor, because resonant modes with narrower linewidthfilter the spectral noise more effectively and that high-Q-factor RI sensors are typically limited in performance by
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J. Phys. D: Appl. Phys. 46 (2013) 105104 G Gilardi and R Beccherelli
(b)(a)
Figure 7. Amplified sensitivity SQ versus refractive index of the mesurand fluid nfluid for 75 µm (a) and 150 µm (b) radius.
Figure 8. Amplified sensitivity SQ versus measurand fluid volume nfluid for (a) R = 75 µm and (b) R = 150 µm.
temperature stabilization, while low Q-factor RI sensors aretypically limited by amplitude noise and spectral resolution.We here focus on critical experimental constraints such asavailable fluid volume not adequately addressed in previousworks and on the refractive index range. Hence, we here definean ‘amplified’ sensitivity per unit volume as a figure of meritSQ = 8 × Q2 × SV . This takes into account the sensitivityas ‘amplified’ by the resonant multi-pass effect. We plot thisas a function of refractive index in figure 7. This figure ofmerit provides a quantitative way to identify the best designparameters of the microfluidic resonator for a range of valuesof the refractive index of the measurand fluid.
From figure 7, we see that small volumes of low refractiveindex fluids should be measured using smaller microspheres,as these have larger SQ. For instance, SQ 1015 nm/(RIU*nl)are obtained with nfluid 1.42 with h = 2 µm or h =4 µm. For nfluid 1.48 the amplified sensitivity drops below1015 nm/(RIU*nl), whatever the configuration defined by thePDMS height (h). Conversely, larger refractive indices shouldbe measured using larger microspheres with R = 150 µmfor which there exist some configurations with SQ 1014
or even SQ 1015 for nfluid = 1.48. To get insight into theoptimal configuration when a measurand fluid volume is theruling parameter, we replot in figure 8 the same data versusfluid volume. We see that smaller spheres provide larger SQ
for small values of nfluid, while larger sphere are generallypreferable in all other cases.
4. Conclusions
In this paper, we have presented what is, to the best of ourknowledge, the first integrated optics refractometric nano-opto-fluidic sensor based on whispering gallery modes inmicrospheres. Thanks to the nanofluidic design this sensorcould operate with a tiny and well controlled volume ofmeasuring fluid, down to 1 pl, which to the best of ourknowledge, appears to be among the smallest, while benefitingfrom the high quality factors of microsphere. Such smallvolumes are relevant to deoxyribonucleic acid microarraytechnology chips [56], especially in forensic science [69]. Wehave systematically studied the performance of the sensor witha numerical model and put this in direct relationship withthe measuring set-up in the 1550 nm telecom window. Thesystematic numerical study shows sensitivity S = ∂λ/∂n upto 2 nm/RIU (top curve in figure 6(a), for h = 2 µm and0.925 pl). We have identified figures of merit SV and SQ, whichclarifies the effect of high quality factor resonators and allowsus to compare different geometries of the device, choosing theoptimal one according to the range of the refractive index of themeasurand fluid and the volume available for the measurement.The study clearly shows that smaller spheres present a largersensitivity for smaller values of the refractive index and smallervolumes of measurand fluids, while larger ones provide largerquality factors and are generally preferable in all othercases.
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J. Phys. D: Appl. Phys. 46 (2013) 105104 G Gilardi and R Beccherelli
When our design is compared with the state of the art,as recently reviewed by White and Fan [40] and by Soriaet al [71], it is observed that some devices in the literaturedo show larger sensitivity S. However, most works do notmention overall volume required. For instance, it was foundas high as 30 nm/RIU for a 55 µm radius microsphere fullyimmersed in water/ethanol solution [72], 160 ± 25 nm/RIUfor grated silicon wire [73], 570 nm in a OFRR with a radius≈35 µm and an unspecified though apparently much longerpath which increases the volume of measurand fluid [30], in700 nm/RIU for an optical microfibre coil with the sensingpart fully immersed in the fluid [72, 73]. We hope that inthe future, performances of refractometric sensors will not begiven only in terms of sensitivity as measured in nm/RIU, butin the proposed amplified sensitivity per unit volume.
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