We propose the use of an optically trapped, dye doped polystyrene microsphere
for spatial probing of the refractive index at any position in a fluid. We
demonstrate the use of the dye embedded in the microsphere as an internal
broadband excitation source, thus eliminating the need for a tunable excitation
source. We measured the full width at half maximum of the TE and TM resonances,
and their frequency spacing as a function of the refractive index of the
immersion fluid. From these relations we obtained an absolute sensitivity of
5e-4 in local refractive index, even when the exact size of the microsphere was
not a priori known.Comment: 3 pages, 3 figure

Mosk, Allard

van der Molen, K.L.

Zijlstra, P.

Zijlstra, Peter

English

arXiv

The authors propose the use of an optically trapped, dye doped polystyrene microsphere for spatial probing of the refractive index at any position in a fluid. Using the dye embedded in the microsphere as an internal broadband excitation source the authors eliminated the need for a tunable excitation source. They measured the full width at half maximum and frequency spacing of the transverse electric and transverse magnetic resonances as a function of the refractive index of the immersion fluid. The authors achieved a sensitivity of 5×10−4 in refractive index, even when the exact size of the microsphere was not known

NARCIS 

Spatial refractive index sensor using whispering gallery modes in an optically trapped microsphere

Peter Zijlstra

Karen L. van der Molen

Allard P. Mosk

Crossref

University of Twente Research Information

Spatial refractive index sensor using whispering gallery modesin an optically trapped microspherePeter Zijlstra,a Karen L. van der Molen, and Allard P. MoskbComplex Photonic Systems, MESA Institute for Nanotechnology and Department of Scienceand Technology, University of Twente, P.O. Box 217, 7500 AE Enschede, The NetherlandsReceived 4 December 2006; accepted 14 March 2007; published online 16 April 2007The authors propose the use of an optically trapped, dye doped polystyrene microsphere for spatialprobing of the refractive index at any position in a fluid. Using the dye embedded in the microsphereas an internal broadband excitation source the authors eliminated the need for a tunable excitationsource. They measured the full width at half maximum and frequency spacing of the transverseelectric and transverse magnetic resonances as a function of the refractive index of the immersionfluid. The authors achieved a sensitivity of 510−4 in refractive index, even when the exact size ofthe microsphere was not known. © 2007 American Institute of Physics. DOI: 10.1063/1.2722695Microspheres can act as high Q resonators in the opticalregime1,2 and can store electromagnetic waves by repeatedtotal internal reflection. Constructive interference results inan enhanced internal field which is called a whispering gal-lery mode WGM. Because of the evanescent interactionbetween the WGM and the surrounding medium the WGM’sresonance frequency is sensitive to changes in the refractiveindex of the sphere’s surroundings. This sensitivity makesmicrospheres a useful tool in sensory applications. RecentlyHanumegowda et al. demonstrated the use of microspheresin refractometric sensing.3 Moreover Vollmer et al.4 andWhite et al.5 demonstrated protein detection using micro-spheres. In all these studies3–5 narrowband light from a tun-able diode laser was evanescently coupled to the microspherevia an optical fiber. Spatial mapping of the refractive indexwas not possible because the microsphere could not be freelymoved through the sample.In this letter we demonstrate the use of a dye dopedpolystyrene microsphere as a refractometric sensor. Thepolystyrene microsphere was trapped with optical tweezers,by which it could be positioned anywhere within the fluid. Itcan therefore be used to sense the refractive index in spa-tially inhomogeneous media, for example, near interfaces orin mixing flows. In this system we did not need a tunablelaser to excite WGMs, instead we used the dye embedded inthe microsphere itself as a broadband excitation source. Themicrospheres used in this study were synthesized in bulk andconsequently showed a considerable size polydispersity. Theabsolute frequency of the WGM, which was used to probethe refractive index in previous studies,3–5 is very sensitive tothe size of the sphere. Measurements of the absolute reso-nance frequency of a particle that has not been individuallycalibrated does not provide information about the refractiveindex of the medium. In contrast, we show that both the fullwidth at half maximum FWHM of the emission peaks andthe frequency spacing between adjacent transverse electricTE and transverse magnetic TM modes are sensitive androbust probes of the refractive index of the sphere’s sur-roundings. We show that our method works over the wholerange of the microsphere size distribution without the needfor individual calibration.The FWHM of a WGM is determined by the loss upontotal internal reflection at the curved surface of the micro-sphere. These losses depend on the mode number l and therefractive index contrast m=m0 /mI, where m0 and mI are therefractive indices of the immersion medium and the micro-sphere, respectively. The FWHM of a WGM can be ex-pressed as62= Nx2nlx2−1, 1with nl the spherical Neumann function, x=m0ka the sizeparameter at which the WGM occurs, where k is the wavevector in vacuum and a the radius of the microsphere, andN = m2 − 1 for TE modesm2 − 12 + 2/m2 − 1 for TM modes, 2where = /x, with = l+1/2.The frequency spacing between a TE and TM mode ofthe same mode number is due to a difference in phase shift ofs and p polarized light upon reflection at the sphere surface.The absolute frequency at which a WGM occurs is defined asthe real part of the pole of the scattering coefficient,7 and wecalculated the frequency spacing by numerically calculatingthe poles for TE and TM modes.In our experiments we used dye doped polystyrene mi-crospheres, suspended in water G1000, Duke Scientific Cor-poration. We measured the size distribution of the spheresby determining the absolute resonance frequencies of 24 mi-crospheres in a reference fluid water and found a meanradius of 5.30 m with a maximum deviation of only 0.5%.Taking into account a conservative error margin, we assumedthat the size of any sphere we trap was 5.30±0.05 m. Thissize distribution is much narrower than the specifications ofthe manufacturer 5.0±0.3 m. Although with our methodit is not necessary to know the exact size of any individualsphere, the size distribution must be measured in advance.The microspheres were doped with 2% dye which emits inthe green part of the spectrum =480–540 nm. Thesample holder was borosilicate glass capillary with inner di-mensions 0.1240 mm3.aPresent address: Centre for Micro-Photonics, Swinburne University ofTechnology, Melbourne, Australia.bElectronic mail: a.p.mosk@utwente.nlAPPLIED PHYSICS LETTERS 90, 161101 20070003-6951/2007/9016/161101/3/$23.00 © 2007 American Institute of Physics90, 161101-1Downloaded 01 Dec 2010 to 130.89.112.86. Redistribution subject to AIP license or copyright; see http://apl.aip.org/about/rights_and_permissionsWith optical tweezers operating at 1064 nm we held asingle microsphere far away from any surface. The lateraltrap stiffness measured using a quadrant photo diode8 was190±40 pN/m using 1 W of laser power on the sample.The excitation light source was a continuous wave argonlaser Spectra Physics Satellite 2016 emitting at 488 nmwith a maximum output power of 30 mW, attenuated to500 W on the sample. We expect that similar results couldbe obtained with thermal illumination. The light of the exci-tation source was slightly defocused on the sphere, so thatthe whole sphere was illuminated. The emission of the dyewas collected through a water immersed objective numeri-cal aperture of 1.2 and detected by an intensified charge-coupled device camera Princeton Instruments ICCD 576,connected to a spectrograph Oriel Instruments, MS257which has a Gaussian response function with a width of4.5 cm−1.Tuning of the refractive index of the immersion fluid m0was achieved by mixing water with ethylene glycolm0=1.4317 at 293 K and 589 nm in various fractions. Eth-ylene glycol does not chemically affect polystyrene and ismiscible with water in all volume fractions. Refractive indi-ces of the mixtures were measured with an Abbe refractome-ter type 1 T which is temperature stabilized and has an ac-curacy of 210−4 in refractive index.We compared our experimental emission spectra to anelaboration of Mie theory EMT developed by Chew9,10 de-scribing the emission of dipoles inside a spherical cavity. Theonly parameters were the refractive index of the sphere mI,the refractive index of the immersion medium m0, and thesphere radius a. The refractive index of the sphere wasmeasured11 to be mI=1.586−1.510−5i. The refractive in-dex of the immersion fluid m0 was measured with the refrac-tometer. The only free parameter in our system was the ra-dius of the sphere a. The theoretical emission spectra werecorrected for the response function of the spectrograph.In Fig. 1 we show the emission spectra obtained from asingle dye doped polystyrene microsphere immersed in awater m0=1.3325 and b a mixture of water and ethyleneglycol m0=1.3978. Sharp peaks were observed in the spec-trum due to WGMs. The dashed lines show the radiationrates normalized to the rate in bulk polystyrene as predictedby EMT for a a=5.33 m and b a=5.319 m. Compar-ing the spectra in a and b we observe that the decrease inrefractive index contrast induced an increase in FWHM ofthe WGMs and a decrease in the spacing between the adja-cent TE and TM modes.As we have shown in Fig. 1 it is possible to obtain m0and a by fitting the experimental spectra with a theoreticalemission spectrum. However, the initial values for the pa-rameters must be chosen rather carefully. The same param-eters can be obtained in a more straightforward way by com-paring only the FWHM and the TE96-TM96 mode spacing topredictions from EMT. Both the FWHM and the mode spac-ing were determined by fitting a Voigt profile12 to an indi-vidual WGM in the measured emission spectrum. The Voigtprofile models the convolution of the Lorentzian width of theresonance and the Gaussian response function of the spec-trograph. To accurately fit the resonance shape, we sub-tracted a quadratic fit of the background intensity.In Fig. 2 we show the Lorentzian FWHM as a functionof m0 for the TE96 mode. The size of the error bars was takenfrom the error in the Lorentzian width of the fits. The largeerror at m0=1.41 was due to a low signal to noise ratioresulting from a low refractive index contrast. The theoreti-cal FWHMs solid lines were calculated for the biggest andsmallest spheres in the measured size distribution and werecalculated from Eq. 1. It can be seen that the FWHM isvery insensitive to the sphere size as the calculated curvesare almost identical.In Fig. 3 we show the experimental TE96-TM96 modespacing, obtained from the central frequency of the fittedVoigt line shapes. The error bars are the uncertainty in thecentral frequency of the Lorentzian fits. The theoretical modespacing is again calculated for the biggest and smallestspheres in the measured size distribution, and the result isshown as a gray area. It can be seen that the TE96-TM96mode spacing is slightly more sensitive to sphere size thanthe FWHM Fig. 2.Figures 2 and 3 show that our measurements correspondvery well to the theoretical model, even though the size ofthe trapped microsphere varies between measurements due toFIG. 1. Measured emission intensity solid lines of single dye doped poly-styrene microspheres immersed in a water m0=1.3325 and b a mixtureof water and ethylene glycol m0=1.3978. The dashed lines show the nor-malized radiation rates as predicted by EMT for a a=5.33 m and ba=5.319 m.FIG. 2. Measured Lorentzian FWHM vs m0 for the TE96 mode. The solidlines show the theoretical FWHM Eq. 1 for the biggest and the smallestspheres in the measured size distribution.161101-2 Zijlstra, van der Molen, and Mosk Appl. Phys. Lett. 90, 161101 2007Downloaded 01 Dec 2010 to 130.89.112.86. Redistribution subject to AIP license or copyright; see http://apl.aip.org/about/rights_and_permissionssize polydispersity. The polydispersity in the sphere size in-troduced an inaccuracy in the theoretical values for theFWHM and TE-TM mode spacing of 1%.One can use either the FWHM or the mode spacing tomeasure the refractive index of the medium. However, thesensitivity and robustness of these methods is not the same.The TE96-TM96 mode spacing is nearly linear in our refrac-tive index range with a slope of 385 cm−1 per refractive in-dex unit. An accuracy in width of 2 cm−1 was easilyachieved for refractive indices below 1.39, resulting in a sen-sitivity of nearly 510−3 in refractive index. When measur-ing the FWHM of a WGM the sensitivity of the sensor ishigher and varies throughout our refractive index domain.From the slope of the curve in Fig. 2 we obtained a sensitiv-ity of 510−4 in refractive index around m0=1.41.The FWHM method leads to the most precise measure-ments in the ideal case. However, this method is very sensi-tive to line broadening due to contamination at the surface ofthe sphere. When contamination is suspected, both theTE-TM mode frequency spacing and the FWHM should bemeasured. If both methods lead to the same value of therefractive index, contamination can be excluded.In conclusion we demonstrated a spatial probe for therefractive index comprising an optically trapped dye dopedmicrosphere. The use of optical tweezers gives us the free-dom to measure the refractive index anywhere in the fluid.This freedom allows for spatial mapping of refractive indexgradients or inhomogeneities caused by, for example, flow inmicrofluidic devices or chemical processes. The emission ofan embedded dye acted as the internal excitation source. Wemeasured the FWHM and the frequency spacing between TEand TM modes as a function of refractive index of the im-mersion fluid. The measured values showed excellent agree-ment with theoretical predictions, confirming the suitabilityof the system for spatial probing of the refractive index. In-dividual calibration of the sphere size was not necessary be-cause the measured parameters are practically insensitive tosphere size within the size distribution found in commer-cially available microspheres. Very recently, Knöner et al.8have demonstrated a method to determine the refractive in-dex of a trapped microsphere by measuring the trappingforce. Their method and ours are complimentary and couldeasily be combined, providing a versatile system for sensoryapplications.The authors thank Ad Lagendijk for useful discussionsand support and Léon Woldering for his help with the samplepreparation. This work is part of the research program of theStichting voor Fundamenteel Onderzoek der Materie FOM,which is financially supported by the NederlandseOrganisatie voor Wetenschappelijk Onderzoek NWO.1K. J. Vahala, Nature London 424, 839 2003.2J. Kalkman, A. Polman, T. J. Kippenberg, K. J. Vahala, and M. L. Brong-ersma, Nucl. Instrum. Methods Phys. Res. B 242, 182 2006.3N. M. Hanumegowda, C. J. Stica, B. C. Patel, I. White, and X. Fan,Appl. Phys. Lett. 87, 201107 2005.4F. Vollmer, D. Braun, A. Libchaber, M. Khoshsima, I. Teraoka, and S.Arnold, Appl. Phys. Lett. 80, 4057 2002.5I. M. White, N. M. Hanumegowda, and X. Fan, Opt. Lett. 30, 31892005.6C. C. Lam, P. T. Leung, and K. Young, J. Opt. Soc. Am. B 9, 1585 1992.7C. F. Bohren, and D. R. Huffman, Absorption and Scattering of Light bySmall Particles Wiley-VCH, Weinheim, 2004, 99–101.8G. Knöner, S. Parkin, T. A. Nieminen, N. R. Heckenberg, and H.Rubinsztein-Dunlop, Phys. Rev. Lett. 97, 157402 2006.9H. Chew, J. Chem. Phys. 87, 1355 1987.10H. Chew, Phys. Rev. A 38, 3410 1988.11K. L. van der Molen, P. Zijlstra, A. Lagendijk, and A. P. Mosk, Opt. Lett.31, 1432 2006.12R. Loudon, The Quantum Theory of Light, 3rd ed. Oxford UniversityPress, New York, 2000, 65–68.FIG. 3. Measured TE96-TM96 mode spacing vs m0. The gray area shows thetheoretical mode spacing calculated for the biggest and smallest spheres inthe measured size distribution.161101-3 Zijlstra, van der Molen, and Mosk Appl. Phys. Lett. 90, 161101 2007Downloaded 01 Dec 2010 to 130.89.112.86. Redistribution subject to AIP license or copyright; see http://apl.aip.org/about/rights_and_permissions