Surface plasmon based thermo-optic and temperature sensor for microfluidic thermometry
aa r X i v : . [ phy s i c s . op ti c s ] S e p Surface plasmon based thermo-optic and temperature sensor formicrofluidic thermometry
L.J. Davis III and M. Deutsch
Department of Physics, 1274 University of Oregon, Eugene, OR 97403
Abstract
We report on a non-interacting technique for thermal characterization of fluids based on surfaceplasmon resonance interrogation. Using liquid volumes less than 20 µ L we have determined thematerials’ thermo-optic coefficients with an accuracy of better than 1 × − ◦ C − and demon-strated temperature sensing with an accuracy of 0 . ◦ C. The apparatus employs a low-powerprobe laser, requiring only a single wavelength, polarization and interrogation angle for accuratecharacterization. The device is particularly suited for precise diagnostics of liquids and gases withinmicrofluidic systems, and may also be readily integrated into a variety of lab-on-chip platforms,providing rapid and accurate temperature diagnostics. . INTRODUCTION Accurate and precise knowledge of temperature conditions inside microfluidic systemsis crucial for a variety of devices and applications, such as chemical microreactors [1] andbiofluidic devices [2]. From the control of micro processor temperature [3], microfluid mo-tion [4], and biophysical processes [5] to in situ [6] sensing for lab-on-chip technologies [7–9]the needs for non-invasive micro-scale temperature sensing are widespread and growing.However, measurement of temperature on the microliter to nanoliter scale is challenging be-cause standard techniques normally require exchange of heat to achieve thermal equilibriumbetween probe and sample [10]. This leads to the restriction that sample heat capacity bemuch larger than that of the probe for accurate temperature measurements. While nanoscalemetal thermocouples have been recently demonstrated [11], their novel architectures maynot always be compatible with temperature sensing of fluids either confined to nanolitervolumes or under flow conditions.Alternatively, using an electromagnetic (EM) field to probe a temperature dependentrefractive index allows for highly accurate and non-invasive temperature sensing [10]. Thethermo-optic (TO) effect, where the refractive index n of a material exhibits dependence onthe temperature T , is characterized by the thermo-optic coefficient dn/dT and is the originof thermally induced optical signals. Thus, proper optical monitoring of temperature-relatedchanges in the refractive index of a material with a known TO coefficient enables preciseknowledge of a system’s temperature. Recently it has been shown that thermo-opticalmonitoring may be applied to detect the binding of proteins at metal-liquid interfaces [12].Accurate measurement of the TO coefficient requires simultaneous knowledge of a mate-rial’s refractive index and temperature. Various optical methods, such as thermoreflectancemeasurements [13] and the minimal deviation method [14] have been used for measuring theTO coefficient of liquids. However, due to limitations of many experimental setups, mea-surements of n and T in bulk do not always overlap in space or time. Due to this separation,existing temperature gradients may hinder accurate determination of TO coefficients andadditional modeling of thermal transport processes is often necessary in order to correct forthis. These additional sources of error may contribute to the spread in reported TO values,which is often greater than 10%, even for well characterized and commonly used materialssuch as ethanol [13]. 2e report on the development of an optical reflectance method which employs surfaceplasmon resonance (SPR) monitoring for accurate determination of the TO coefficients offluids. This method relies on optical interrogation using a surface-propagating EM wavewhich is exponentially sensitive to changes in the dielectric properties of its environment.Use of SPR monitoring as a sensitive and accurate optical thermometry technique has beenstudied both theoretically [15, 16] and experimentally [17, 18]. Albeit, the potential of anintegrated optical SPR-based sensor for real-time, microfluidic thermal characterization hasnot yet been realized. We present here a SPR-based system which is capable of TO coef-ficient determination as well as optical microthermometry. When measuring temperature,the system is readily integrable with lab-on-chip platforms. The apparatus and procedurereported here are specifically designed to mitigate the technical challenges and limitations ofTO measurement mentioned above. In particular, by utilizing fluid sample volumes in themicro liter range and embedding the system in a thermal reservoir, thermal gradients areeliminated and equilibration times are significantly reduced, minimizing spatial separationbetween refractive index and temperature measurements during TO coefficient determina-tion. This allows highly precise measurement of TO coefficients with accuracy better than1 × − ◦ C − . Such accuracy in TO measurement is becoming increasingly necessary insensing applications where the TO effect is often a primary source of noise. For example,SPR-based refractive index sensors have recently been shown to have resolution of 1 × − refractive index units (RIU)[19], making it necessary to control the temperature to within1 × − ◦ C − . However, with the accurate measurement of TO coefficients and temperatureenabled by this setup it is possible to correct for the TO-induced noise and eliminate theneed for such accurate temperature control.Once the TO coefficient of the fluid has been determined, the same setup can be used forcontinuous determination of the sample temperature. This is accomplished by continuousmonitoring of the reflectance from the sample at a fixed interrogation angle and a singlewavelength. This new reflectance interrogation method [20] is significantly faster than bothangular and wavelength interrogation techniques, which have been usually applied in SPRsensing. Moreover, this now enables SPR-based real-time thermometry in a range of mi-crofluidic systems with only a slight modification to the current setup.3 I. SPR-BASED THERMO-OPTIC CHARACTERIZATIONA. Optical Temperature Sensing Using Surface Plasmon Resonance Interrogation
Surface plasmon polaritons (SPPs) are surface bound EM waves which only propagatewhen guided along a well-defined metal-dielectric interface. These modes are primarilycharacterized by a sub-wavelength evanescent confinement of their electric field in directionsnormal to the interface, resulting in a large EM field enhancement at the interface, asshown in Fig. 1. In particular, the electric field component extending into the dielectricmedium decays exponentially with a decay coefficient γ d = ωǫ d p − / ( ǫ d + ǫ m ) /c , where ω is the angular frequency of the incident EM field, ǫ d and ǫ m are the permittivities ofthe bounding dielectric and metal, respectively, and c is the speed of light in vacuum.In the visible and infrared EM frequency range the permittivities of metals suitable forthe applications discussed here (e.g. gold, silver) are negative and fairly large in absolutevalue [21], ensuring the exponential decay of the field into the two bounding media. Thisdecay profile leads to SPPs being highly sensitive to the nanoscale structure and compositionof the metal-dielectric interface, thus rendering them excellent probes for surface sensingapplications [22]. Typical sensing setups utilizing SPR monitoring rely either on angular orwavelength interrogation of the reflectance in vicinity of the resonance. The best sensors todate are capable of detecting changes of 10 − RIU in the test dielectric [19].In all our studies detailed here we utilize the Kretschmann configuration [23], shownin the inset to Fig. 1. In this configuration a metal film of the order of the optical skindepth in thickness is sandwiched between a dielectric prism and a test dielectric mediumwith refractive index less than that of the prism. To excite SPPs at the interface betweenthe metal and the test medium, a p -polarized, collimated and monochromatic light beamimpinges on the metal at an angle greater than the angle for total internal reflection, asshown in Fig. 1 [23]. Figure 2 shows the signature of SPP excitation, evident as a largedip in the reflectance and measured by angular interrogation of the reflected intensity. Theangle at which minimal reflectance is observed is known as the surface plasmon resonanceangle . The SPR angle and corresponding reflectance line shape and width are functions ofthe permittivities of the metal and test dielectric, as well as the thickness of the metal film,and therefore depend also on the ambient temperature through thermal effects.4 hin Metal FilmTest Dielectric Glass PrismSPPIncident Light ReflectedLight FIG. 1: Normalized amplitude of the SPP electric field, plotted against the distance from theinterface normalized to the wavelength, λ = 632 . p -polarized laser light. In this geometry the SPP is excited at the interface of the thin metal filmwhich is not adjacent to the coupling prism, and is thus used to probe the adjoining test dielectric.The dashed lines in the metal film indicate evanescent beams. N o r m a li z ed R e f l e c t an c e Incident Angle (deg)
FIG. 2: Reflectance measured as function of incident angle in the Kretschmann configuration, using p -polarized light of wavelength 632.8nm and silver films with various thicknesses as stated in thelegend. The test dielectric is air at room temperature. The width, magnitude and resonance angleof the reflectance are seen to depend strongly on film thickness, with maximal contrast obtainedfor film thickness of ≈ . Calculated Thermo-Optic Signal The origin of the TO effect in most non-conducting dielectrics is due primarily to volu-metric thermal expansion. In metals, electron-phonon as well as electron-electron scatteringprocesses also contribute to the variation of the index of refraction with temperature [16].The optical reflectance of a monochromatic light beam with vacuum wavelength λ incidentat angle θ at a prism-metal interface as shown in Fig. 1 can be expressed in terms of theFresnel reflection coefficients at the prism-metal and metal-dielectric interfaces, r pm ( θ, T )and r md ( θ, T ), respectively, as R ( θ, T ) = (cid:12)(cid:12)(cid:12)(cid:12) r pm + r md e i k m h ( T ) r pm r md e i k m h ( T ) (cid:12)(cid:12)(cid:12)(cid:12) (1)Here h ( T ) is the temperature dependent thickness of the metal film. The wave vectorcomponent, normal to the interface, of the light field in the metal layer is given by k m =2 π p ǫ m ( T ) − ǫ p sin θ/λ and is a function of both θ and T . The arguments in the right-hand-side of Eq. 1 have been omitted for brevity. For simplicity, the permittivity of thecoupling prism ǫ p is assumed to be independent of temperature. While it is straightforwardto account for the TO effect in the glass prism, our experimental results indicate that toleading order this is not necessary, since the TO coefficient of the glass used in this setupis more than two orders of magnitude less than that of the test dielectrics used [24]. Wefurther justify this approximation below.In the linear approximation the temperature dependent refractive index of any non-magnetic medium with permittivity ǫ ( T ) is given by n ( T ) ≡ p ǫ ( T ) = n + ( T − T ) dn/dT where n is the material-specific refractive index at temperature T and dn/dT is the mate-rial’s thermo-optic coefficient. The linearized temperature-dependent thickness of the metalfilm is written as h ( T ) = h [1 + α ′ ( T − T )]. Here h is the film thickness at temperature T ,and α ′ ≡ α (1 + µ ) / (1 − µ ) is a geometric correction to the thermal expansion coefficient ofthe metal which comes to account for expansion of the metal film mostly in direction normalto the interface, with α and µ being the metal thermal expansion coefficient and Poissonnumber, respectively [15].Using the linearized expressions for n ( T ) and h ( T ) we obtain an expression for the tem-perature dependence of the reflectance written as6 RdT = ∂R∂ǫ d ∂ǫ d ∂T | ǫ m ,h + ∂R∂ǫ m ∂ǫ m ∂T | ǫ d ,h + ∂R∂h ∂h∂T | ǫ d ,ǫ m (2)where the left-most term in the right hand side of Eq. (2) denotes the TO contributionfrom the test dielectric and the remaining terms describe the contributions of the metalfilm to the measured signal. Figure 3 shows dR/dT at room temperature ( T = 22 ◦ C)calculated for a 50nm thick silver thin film and liquid ethanol as the test dielectric. Theinset to Fig. 3 shows the calculated contribution from the silver film. We find that theTO contribution from the metal itself is three orders of magnitude smaller than the liquidcontribution, therefore allowing us to neglect any TO effects in the metal sensing film inour current experiments. We also calculate the contribution of the glass prism to the TO-induced change in reflectance (using reported values for BK7 glass) and find that it is anorder of magnitude less than the contribution from the silver film. Hence the notation inEq. 2 becomes dR/dT ≈ ( ∂R/∂ǫ d ) ( ∂ǫ d /∂T ) | ǫ m ,h .
66 68 70 72 74 76 78 80-0.04-0.03-0.02-0.010.000.010.020.03 d R / d T ( / C ) Incident Angle (deg.) x10 -5
66 69 72 75 78 012345
FIG. 3: Temperature derivative of the reflectance plotted against angle of incidence, calculatedat room temperature using λ = 632 . h = 50nm and liquid ethanol as the test dielectric.Inset: Calculated contribution of the metal to dR ( θ, T ) /dT | T =22 ◦ C . Previously published valuesfor the permittivity of silver, µ , α and the TO coefficients of silver and ethanol were used in thecalculations [13, 15, 21]. We see from Eq. (2) that test dielectrics with large TO coefficients will result in greatertemperature sensitivity of the device. It is also desirable to utilize test dielectrics with lowrefractive indices since the SPR reflectance dip broadens with increasing values of the di-electric refractive index, thus leading to overall lower sensitivity. Previous demonstrations7f SPR temperature sensors have employed metal-semiconductor junctions exploiting thelarge TO coefficients of materials such as amorphous silicon. However, most semiconduc-tors exhibit relatively high losses in the optical frequency range as well as large values fortheir refractive indices, both of which lead to broadening of the SPR and reduced sensitiv-ity [17, 18]. This leads us to conclude that transparent fluids with relatively low refractiveindices and large TO coefficients constitute ideal candidates for accurate SPR-based tem-perature sensing, rendering the latter particularly suitable for applications discussed in theIntroduction. Such materials, comprising a large range of liquids and gases also satisfy theapproximation discussed above, rendering this setup applicable for accurate thermal charac-terization in microfluidic lab-on-chip environments. As examples we exploit these propertiesin ethanol and water to realize a microfluidic, SPR-sensitive TO and temperature sensor.
III. EXPERIMENTAL SYSTEMA. Experimental Setup
The experimental apparatus for determining TO coefficients consists of a temperature-controlled micro-volume liquid reservoir coupled to an optical monitoring system, shownschematically in Fig. 4. A 0.4mm deep reservoir 6.3mm in diameter was drilled into a 1kgbrass block which served as the thermal bath. Either water or ethanol were used to overfillthe reservoir to a total fluid volume of ≥ . µ L. To form the optical probing window a 50nmthick silver film 1cm in diameter was thermally deposited onto one side of a glass microscopeslide (Corning Glass Works soda lime glass, n = 1 . . ◦ C resolution was also embedded inside thebrass at a distance of 250 µm from the base of the liquid reservoir, and was used to read thetemperature of the test dielectric. A collimated, 1mW HeNe laser probe beam ( λ =632.8nm)with 2mm diameter was incident on the silver window through the prism. The brass-prismsystem was affixed to a rotation stage mounted on a translation stage, allowing for rotationwhile maintaining the beam spot position centered on the optical interrogation region. Amechanical chopper provided a 911Hz signal modulation of the incoming probe beam, andthe reflected signal was detected using a silicon photo diode and a lock-in amplifier. ProbeBeam DetectorBK7 PrismTeflon SpacerThermometerGlassSlideMetal Foil Heater ResistorO-RingSilver Liquid Brass
FIG. 4: Diagram of the experimental setup excluding the stages to which the brass-prism systemis mounted. The diagram is not to scale.
B. Thermo-Optic Sensor Calibration
In order to apply the model discussed in Section II B to our experimental results andmeasure the liquid TO coefficient it is necessary to have an accurate determination of therefractive index of the silver film. Since the material properties of thin metal films generallydepend on parameters such as deposition conditions and ambient environment, we firstdetermine the sample-specific relevant optical constants of our deposited silver films. Usinga probe wavelength of 632.8nm we measure R c ( θ, T c ) – the reflectance of the silver film asfunction of incident angle at a known, constant temperature T c . The real and imaginaryvalues of the refractive index, along with the thickness of the film are determined usinga least-squares fit of the theoretical reflectance to measured values of R c ( θ, T c ). We use aDekTak profilometer calibrated to a 3nm height resolution to independently verify the filmthickness obtained by the fitting procedure. (While determination of the film’s refractive9ndex can also be done using standard ellipsometry, the high sensitivity of the SPR to thepolarization of the probe beam eliminates the need for any such additional instrumentation,resulting in comparably accurate values for the optical constants.) The values providedby this procedure are then used to calibrate the sensor. Figure 5 compares the calculatedreflectance for a sample film using measured film thickness and previously reported valuesfor the optical constants of silver [21] with the measured reflectance R c ( θ, T c ) as well as thecorresponding fitted values, illustrating the need for this calibration.
66 67 68 69 70 71 72 73 74 75 760.00.20.40.60.81.0 N o r m a li z ed R e f l e c t an c e Incident Angle (deg.)
66 67 68 69 70 71-1.0-0.50.00.5 d R / d ( deg . ) - FIG. 5: Reflectance as function of incident angle. The probe wavelength is 632.8nm, silver filmthickness is 50nm and the test dielectric is ultra-pure water (18.2MΩ-cm resistivity) at T = 21 . ◦ C.Measured values are indicated by dots. The solid curve is the reflectance function obtained by aleast-squares fit to the data. The dashed line denotes the calculated reflectance obtained usingtabulated values for the refractive index of silver [21]. Inset: Angular derivative of the reflectancecalculated using the fitted function, plotted against θ . C. Experimental Procedure and Measurement of the Thermo-Optic Coefficient
Our first demonstration is of measurements of the TO coefficients of water and ethanol.The rotation stage was initially positioned to produce the desired probe beam-silver filmincident angle, θ . For maximal sensitivity θ was chosen near the extremal value of | dR ( θ, T ) /dT | as obtained from Fig. 3. The temperature of the system was then increased byapplying 4 volts across the embedded resistor. When the desired temperature was reached(as determined by reading the embedded thermometer) the heating power was turned off10nd the system was allowed to relax for 30 seconds. This guarantees that the thermometerreadings are consistent with temperature changes of the liquid reservoir, and also serves toeliminate any thermal gradients in the liquid as well as between the liquid and the brassmass. Following this initial relaxation, data acquisition software was used to record thetime, temperature, and reflected optical probe signal as the system was cooling, at intervalsof 0 . ◦ C. We note that fixed temperature intervals, equal in magnitude to the resolutionof the thermometer were used instead of fixed time intervals when recording data. This isto avoid over-sampling the reflectance and temperature at longer times as the rate of tem-perature change decreases exponentially during the cooling process. The resulting data setis used to obtain the measured reflectance, expressed as R m ( θ , T ( t )) with t denoting time.Figure 6 shows R m ( θ , T ) obtained for water (main figure) and ethanol (bottom inset).Each data point represents an average of ten successive values measured using the lock-inamplifier, with their computed standard deviation used as the measurement error for eachaveraged point. These errors range in value between 1 × − and 4 × − , and are notresolved on the scale used in Fig. 6.To model R m ( θ , T ) it is necessary to know θ accurately. We see from Fig. 5 and itsinset that the reflectance varies strongly with incident angle in vicinity of the SPR. Infact, ∂R ( θ, T ) /∂θ | T is large enough near the incident angles of interest that an error in θ of order (1 × − ) ◦ , well below the angular resolution of standard rotational stages, willintroduce a measurable reflectance error of the order of 10 − . This is a common problem inoptical sensors employing angular interrogation, and various subpixelling algorithms havebeen developed to address it [25]. To enable a more accurate determination of θ in our setupwe conduct an iterative least-squares fit of the reflectance, with the TO coefficient and θ asadjustable parameters. Since the reflectance depends strongly on θ we are able to reduce theeffective number of fitting parameters from two to one. We find that best fits are obtainedwhen the incidence angle is held fixed at a chosen value and the TO coefficient is varied.Several iterations of this fitting procedure are required, each with a newly adjusted value of θ until a value of the TO coefficient which faithfully reproduces R m ( θ , T ) is obtained, forsome final value of θ (which is always within the angular measurement error of our system.)The solid lines in Fig. 6 demonstrate the result of this iterative fitting procedure for bothfluids used. We measure the TO coefficients of ethanol and water to be (4 . ± . × − RIU / ◦ C and (1 . ± . × − RIU / ◦ C, respectively. These agree very well with the11
Water N o r m a li z ed R e f l e c t an c e Temperature ( C)
Ethanol
FIG. 6: Reflectance as function of temperature for water (main figure) and ethanol (inset). Mea-sured values are denoted by dots and solid traces indicate the fitted functions. reported values of (4 . ± . × − RIU / ◦ C for ethanol [13] and (1 . ± . × − RIU / ◦ C for water [14, 26].
IV. EXPERIMENTS AND DISCUSSIONA. Temperature Sensing
Once R m ( θ , T ( t )) has been determined for a specific fluid and the TO coefficient is known,it is possible to utilize the same interrogation method for use as an optical temperature sen-sor. To demonstrate this we apply a linear fit to the data in Fig. 6, which we invert to obtainthe temperature as function of reflectance and time. Figure 7 compares T ( t ), the calculatedtemperature plotted against time, with temperature values measured by the thermometerduring the experiment, demonstrating the accuracy of our method. To determine the mea-surement error, ∆ T , of this temperature sensor we compute ∆ T = σ ( ∂R m ( θ , T ( t )) /∂T ) − where σ = 4 × − is the measured error in the reflectance. We find ∆ T to range between0 . − . ◦ C, depending on the sample-specific reflectance line shape and the choice of θ .While we have demonstrated here temperature sensing of a confined and stationary fluidin thermal equilibrium, the system may be easily modified to enable temperature sensing offluids with known TO coefficients in practical microfluidic systems. In this case the thermalbrass mass used for determining the TO coefficient in our setup is not necessary, since the12emperature of the fluid is determined by the specific conditions in the flow system. Insteadof abutting the fluid reservoir as described previously the prism mounted silver film should bedirectly contacting the flowing fluid. This can be made possible through a small diagnosticswindow which may be incorporated into many microfluidic systems [27].As mentioned previously, large errors in measuring the reflectance exist mostly when thesystem is far from thermal equilibrium and is undergoing rapid cooling or heating. Whilethe signal averaging technique described above is acceptable in near-equilibrium situationswhen the temperature is varying slowly, it is not practical in cases where rapid changes intemperature are taking place. The calibrated setup used here, however, is accurate enoughto allow meaningful temperature measurement in real time using only lock-in detection. Theinset to Fig. 7 shows the non-averaged temperature values plotted against time for rapidcooling of deionized water. The data were obtained by recording the reflectance every 130msand then converting the data to temperature values using a linear fit of R m ( θ , T ( t )) datameasured according to the procedure in Section III C. We see that even with the existingnoise the exponential cooling behavior is still evident, allowing us to extract meaningfultemperature values.It can be seen from Fig. 3 that the magnitude of | dR ( θ, T ) /dT | is significant only over alimited and rather narrow angular range, spanning either side of the resonance angle. The T e m pe r a t u r e ( C ) Time (s)
FIG. 7: Temperature plotted against time showing calculated values (black dots) and values mea-sured using the thermometer (red triangles). The blue solid curve denotes a fitted exponentialcooling law, with a coefficient of determination R = 0 . θ to be near the extremal value of | dR ( θ, T ) /dT | guaranteesmaximal sensitivity for the detection technique used here since it measures changes to thereflectance at the point where its slope is the steepest. However, a large enough change influid temperature will shift the SPP resonance angle too far away from the initially optimizedvalue of θ , into a lower sensitivity range and potentially even away from the calibrationcurve of the instrument. The high sensitivity as well as accuracy of this setup are thereforelimited to a finite range of temperatures. To verify this we measured the temperature-dependent reflectance over a range of 10 ◦ C, as shown in Fig. 8. The inset to Fig. 8 comparesthe temperature derivative of the reflectance calculated using our model (solid line) with thedata shown in the main figure (dots). We find that | dR ( θ, T ) /dT | drops to half its extremalvalue over a range of ∼ ◦ C in either direction, and hence set the operational range of thissetup to be 10 ◦ C. Since the slope and width of the SPR depend on the permittivity of thedielectric layer, this range will vary with the sensing fluid used.
24 26 28 30 320.200.250.300.350.40 N o r m a li z ed R e f l e c t an c e Temperature ( C) d R / d T ( / C ) Temperture ( C)
FIG. 8: Reflectance values (raw data) plotted against temperature measured using ethanol as thetest dielectric. Inset: Temperature derivative of the reflectance calculated using the theoreticalmodel (solid line) and measured reflectance values from main figure (dots).
B. Probe Induced Heating
Generally the excitation of SPPs in metals is accompanied by damping of the surface-propagating electromagnetic wave, leading to heating of the metal. This heat will be trans-ferred to the liquid reservoir and cause a TO response. It is therefore important to use14he lowest probe-laser powers possible while still maintaining sufficiently detectable re-flected light powers. Probe-induced heating can be estimated using the steady-state relation P = α ∆ T ss where P denotes the heat transferred into the system from SPP dissipation,∆ T ss is the temperature difference across the reservoir in steady state and 1 /α is the char-acteristic thermal resistance of the system for heat flow across the reservoir (for simplicitywe assume one dimensional heat flow and ignore the thickness of the silver film comparedto that of the fluid reservoir.) In a standard temperature sensing experiment using wateras the test fluid (thermal conductivity = 0.6W/m · K) and probe reflectance of about 0.5 wefind that the 0.5mW of probe power dissipated in the metal film will result in an increasein steady state temperature of no more than 0 . ◦ . This temperature increase is below theoperational resolution of the instrument and will therefore not be measurable under the op-erating conditions described here. Taking into consideration also the thermal conductivityof the coupling prism, which is typically higher than that of many practical fluids, the risein temperature in the fluid is guaranteed to remain well below the detection limit. In fact,when using test fluids with lower heat capacity or greater thermal resistance (e.g. ethanol,methanol) it is advantageous to use coupling prisms with large thermal conductivities andlow TO coefficients as here. The latter will often have relatively high refractive indices (e.g.BK7 and SF10 glasses,) thus facilitating SPP excitation while minimizing any probe-inducedheating effects in the sample. C. Minimal Fluid Volume
The minimal fluid volume necessary for the SPP-based measurement of TO coefficientsand temperature is set by the following two constraints: (i) The liquid-metal interfacecontact area must be larger than the optical beam spot, and (ii) the fluid thickness (i.e.reservoir depth in our case) must be significantly larger than the decay length of the SPPelectric field inside the dielectric medium. In our setup the beam spot at the interfacemeasured less than 6mm in length along its longer axis. Exponential decay lengths of theSPP field depend on the fluid’s refractive index, and are typically in the range of 100-300nm.These conditions render nanoliter liquid volumes accessible to this type of temperaturemeasurement. However, such small fluid volumes may be susceptible to probe inducedheating and will require proper thermal management as discussed above.15 . SUMMARY
We have developed a minimally-invasive SPR-based temperature sensor with temper-ature resolution of 0 . ◦ C. This sensor and outlined calibration procedure may also beused to obtain the TO coefficients of fluids while addressing typical sources of error in TOcoefficient measurement. The apparatus utilizes the exponential sensitivity of surface plas-mon polaritons, excited at the interface between a thin silver film and a confined fluid, toextract accurate values of the temperature or the TO coefficient of the fluid. The charac-terization employs reflectance interrogation, utilizing a low-power probe laser and requiringonly a single wavelength, polarization and interrogation angle for accurate determination oftemperature. Due to the low refractive indices and high TO coefficients that many fluidspossess, this device is particularly suited for precise diagnostics within opto-fluidic systems.Requiring only micro-liter fluid volumes to operate, the setup may be readily integrated intoa variety of lab-on-chip platforms, providing rapid and accurate temperature diagnostics.This work was supported by NSF grant No. DMR-0804433 and ONAMI ONR Grant No.N00014-07-10457. The data in Fig. 2 were acquired separately by A. Chen.16 eferences [1] R. Kikkeri, P. Laurino and A. Odedra and P.H. Seeberger, Angew. Chem. Int. Ed. , 2054(2010).[2] F.E. Anglie, H. Duan, J.J. Agresti, A. Wintner, C. Schmitz, A.C. Rowat, C.A. Merten, D.Pisignano and A.D. Griffiths, Lab Chip , 1110 (2008).[3] G. Maltezos, A. Rajagopal and A. Scherer, Appl. Phys. Lett. , 074107 (2006).[4] F.M. Weinert, J.A. Kraus, T. Franosch and D. Braun, Phys. Rev. Lett. , 164501 (2008).[5] M.U. Kopp, A.J. de Mello, and A. Manz, Science , 1064 (1998).[6] J.P. Valentino, S.M. Troian and S. Wagner, Appl. Phys. Lett. , 184101 (2005).[7] D.S. Peterson, T. Rohr, F. Svec and J.M.J. Frechet, Anal. Chem. , 469 (2002).[8] H.A. Stone, A.D. Stroock and A. Ajdari, Annu. Rev. Fluid Mech. , 381 (2004).[9] J.D. Suter, I.M. White, H.Y. Zhu and X.D. Fan, J. Appl. Opt. , 389 (2007).[10] P.R.N. Childs, J.R. Greenwood and C.A. Long, Rev. Sci. Instrum. , 2959 (2000).[11] E. Shapira, D. Marchak, A. Tsukernik and Y. Selzer, Nanotechnology , 833 (2008).[12] S. Brantzen, F. V¨olklein, W. Knoll and B. Menges, Sens. Actuators, A. , 492 (2007).[13] C.H. Fan, and J.P. Longtin, J. Heat Transfer , 757 (2000).[14] M. Daimon and A. Masumura, Appl. Opt. , 3811 (2007).[15] A.K. Sharma and B.D. Gupta, Appl. Opt. , 151 (2006).[16] K.Q. Lin, L.M. Wei, D.G. Zhang, R.S. Zheng, P. Want, Y.H. Lu and H. Ming, Chin. Phys.Lett. , 3081 (2007).[17] B. Chadwick and M. Gal, Jpn. J. Appl. Phys., Part 1 , 2716 (1993).[18] H.P. Chiang, C.W. Chen, J.J. Wu, H.L. Li, T.Y. Lin, E.J. Sanchez and P.T. Leung, ThinSolid Films , 6953 (2007).[19] J. Homola, Chem. Rev. , 462 (2008).[20] C.-W.Chen, C.-H. Lin, H.-P. Chiang, Y.-C., Liu, P.T. Leung, and W.S. Tse, Appl. Phys.A-Mater. , 377 (2007).[21] E.D. Palik, J. Opt. Soc. Am. A: Mater. , 1297 (1984).[22] J. Homola, Surface Plasmon Resonance-based Sensors (Springer-Verlag, Berlin Heidelberg,2006).
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