Tuning a microsphere whispering-gallery-mode sensor for extreme thermal stabilityY. Zhi and A. Meldrum

Citation: Applied Physics Letters 105, 031902 (2014); doi: 10.1063/1.4890961 View online: http://dx.doi.org/10.1063/1.4890961 View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/105/3?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Whispering gallery mode selection in optical bottle microresonators Appl. Phys. Lett. 100, 081108 (2012); 10.1063/1.3688601 Whispering gallery modes of microspheres in the presence of a changing surrounding medium: A new ray-tracing analysis and sensor experiment J. Appl. Phys. 107, 103105 (2010); 10.1063/1.3425790 A monolithic optical sensor based on whispering-gallery modes in polystyrene microspheres Appl. Phys. Lett. 93, 151103 (2008); 10.1063/1.2998652 Optical biosensor based on whispering gallery mode excitations in clusters of microparticles Appl. Phys. Lett. 92, 141107 (2008); 10.1063/1.2907491 Spatial refractive index sensor using whispering gallery modes in an optically trapped microsphere Appl. Phys. Lett. 90, 161101 (2007); 10.1063/1.2722695

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Tuning a microsphere whispering-gallery-mode sensor for extremethermal stability

Y. Zhi and A. Meldruma)

Department of Physics, University of Alberta, Edmonton, Alberta, T6G2E1, Canada

(Received 10 June 2014; accepted 1 July 2014; published online 21 July 2014)

The reactive sensing application of optical microspheres can be plagued by local temperature

fluctuations. Fluctuations due to laser heating or ambient changes in the lab environment cause

resonance shifts that appear as noise or an underlying drift in the sensor data. Here, we show that

thermal fluctuations can be exactly compensated in virtually any local medium (i.e., “analyte”) by

the application of a high-index coating on the surface of the microsphere. The coating precisely

controls the extent of the field penetration into the surroundings in such a way that the thermal

shifts associated with the three layers (the glass sphere, the coating, and the exterior medium) can

be exactly balanced. The conditions required for thermal stability were investigated theoretically;

on the basis of these calculations a real sphere was then synthesized that showed excellent stability

for aqueous solutions. VC 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4890961]

Optical microspheres can be used to measure minute

changes in the properties of the surrounding medium. If the

refractive index of the sphere (typically composed of silica

or polystyrene) is higher than that of the surroundings, radia-

tion can be trapped inside the sphere by total internal reflec-

tion as it propagates around the circumference. This leads to

the development of resonances known as “whispering gallery

modes” or WGMs, which in microspheres typically have a

quality (Q) factor in the range of 105–109. Part of the electric

field of each mode extends outside of the sphere, thus sam-

pling the external medium.

The WGMs can provide a sensitive transduction mecha-

nism for a variety of different sensing applications. The reso-

nant frequency is sensitive to (i) pressure1 and force2 (via

pressure-induced stress and strain in the sphere material); (ii)

the complex refractive index of the surrounding medium;3,4

and (iii) the ambient temperature (via thermo-optic and ther-

mal expansion effects).5–9 The second application is particu-

larly attractive because of the extremely small effects that can

be detected in a microfluidic environment. In all three,

changes in the local index of either the medium or the sphere

itself (due to changing pressure, temperature, or composition)

are transduced via resonance wavelength shifts. This is some-

times referred to as the “reactive” sensing mechanism.10

Some of the most sensitive experiments are able to

detect single viruses,11 proteins,12 or other biomolecules

when they bind to the surface of a microsphere. These

experiments typically use a tapered fiber or waveguide to

evanescently couple WGMs to the sphere, and a tunable

laser to sweep through the mode. While incredibly sensitive,

the sensors are fragile and can be difficult to incorporate into

a robust transduction device. Fluorescent microspheres have

also been widely investigated for refractometric sensing

applications. These devices require a spectrometer to

measure the emission from dye-doped13–17 or quantum dot

(QD)-doped18–21 microspheres immersed in the analyte.

Regardless of the measurement method, thermal fluctua-

tions can ultimately limit the ability to detect refractometric

changes in the surroundings. For “reactive” sensing, one

therefore desires the microcavity to be insensitive to temper-

ature. The same is true for other WGM-type cavity structures

such as cylindrical capillaries, for which the thermal shifts

have been calculated.22,23 While microspheres have been

proposed as thermal sensors5–9,24,25 (in which, contrary to

the case for refractometric sensors, one wants a large thermal

response), the detection limit optimization for refractometric

sensing with a microsphere has not been widely investigated

until quite recently26 despite the fact that thermo-optic fluc-

tuations can be a dominant noise source in microsphere reso-

nators.27 While thermal perturbations induced by variations

in the optical pump power can be “self-compensated” under

certain conditions,28,29 an external “laboratory” temperature

drift cannot be compensated via optical coupling.28

The presence of a high-index coating on the surface of a

microsphere can have strong effects on the refractometric sen-

sitivity (S)30,31 and will affect the thermal sensitivity (Stherm)

as well. Both sensitivities are controlled by the overall profile

of the electric field, while the Stherm is also determined by the

thermo-optic and thermal expansion properties of the different

layers. Here, we will show theoretically and demonstrate

experimentally that a high-index coating can be tailored to

provide thermal stability for virtually any exterior medium.

Unlike a recent interesting example for a microdisk resona-

tor,32 here we do not require a negative thermo-refractive

coating—instead, the positive coating serves both as a fluores-

cent layer and a means to “lure” the mode field energy into

the surrounding fluid. The work also draws on ideas for pas-

sive temperature stabilization of one-dimensional photonic

cavities, in which alternating positive and negative thermo-

refractive layers could, in theory, completely cancel the ther-

mal response of the structure.33 Alternative methods such as

self-referencing, using oppositely polarized modes in a bire-

fringent cavity, have also been investigated.34

The thermal sensitivity of a coated microsphere can be

calculated based on the fraction of the WGM mode energy in

a)Author to whom correspondence should be addressed. Electronic mail:

ameldrum@ualberta.ca

0003-6951/2014/105(3)/031902/5/$30.00 VC 2014 AIP Publishing LLC105, 031902-1

APPLIED PHYSICS LETTERS 105, 031902 (2014)

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each layer. Starting from the simple relation in which the

fractional wavelength shift dk=k0 is proportional to the frac-

tional change in the effective refractive index (meff) and

radius (a) (i.e., dk=k0¼ dmeff/meffþ da/a), one obtains22

Stherm ¼dkdT¼ k0

dmef f

mef fþ da

a

� �1

dT

¼ k0

1

mef f

dmef f

dTþ 1

a

da

dT

� �

¼ k0

f1j1 þ f2j2 þ f3j3

f1m1 þ f2m2 þ f3m3

þ a1

� �; (1)

where meff can be approximated as f1m1þ f2m2þ f3m3, in

which fi corresponds to the energy fraction in the ith layer,

k0¼ 2p/k0 is the resonance wavelength, and the thermo-optic

coefficient is ji¼ dmi/dT. The subscripts refer to the layer

number: layer 1! glass microsphere; layer 2! high-index

coating; layer 3! external medium.

For reactive sensing applications one wants Stherm to be

as close as possible to zero. This can, in principle, be

achieved if the thermo-optic coefficient of layer 3 (the sur-

rounding medium) is negative, as is the case for many com-

mon solvents. If j3 is negative, it can potentially balance the

positive coefficients of the glass and the QD coating.22

Particularly desirable would be a zero thermal sensitivity for

water, which is the most common solvent for biosensing

applications.

The energy fractions in each layer depend on the

polarization

fi;TM ¼Ii

I1 þ I2 þ I3

; (2a)

fi;TE ¼m2

i Ii

m21I1 þ m2

2I2 þ m23I3

; (2b)

where I1, I2, and I3 represent the volume-integrated electric

field radial functions in each layer

I1 ¼ðb

0

A2L½wLðm1k0rÞ�2dr; (3a)

I2 ¼ða

b

½BL1Lðm2k0rÞ þ nLðm2k0rÞ�2dr; (3b)

I3 ¼ð1

a

D2L½nLðm3k0rÞ�2dr: (3c)

Here, AL, BL, and DL are proportionality factors, and w, n,

and 1 refer to the Riccati-Bessel, Riccati-Hankel (type 1),

and Riccati-Hankel (type 2) functions of order L. The thick-

ness of the layer is t¼ a� b, where b is the radius of the bare

microsphere and a is the radius including the coating.

We follow the methods derived in Refs. 30 and 31 to

solve for k0, S, and the various coefficients for both the TE

and TM polarizations. This is done by establishing the appro-

priate boundary conditions for each polarization,30,31 and

using a numerical root solver on the system of spherical

equations that describe the radial field functions in each

layer. These calculations also provide the electric field radial

profile for any desired mode.

Finally, the reactive detection limit due to thermal fluc-

tuations is given by

DLtherm TE;TMð Þ ¼dk TE;TMð Þ

dT� dT

STE;TM: (4)

This gives the detection limit for refractometric sensing as

imposed by thermal fluctuations only. The term dT/S is the

ratio of the thermal fluctuations in the experiment to the re-

fractometric sensitivity. One wants DLtherm as close as possi-

ble to zero, or at least to be well below the detection limit

imposed by the (noise-limited) wavelength shift resolution

of the measurement system (DLsensing¼R/S, where R is the

shift resolution and S is the refractometric sensitivity of the

structure).

To estimate the thermal sensitivity and DL of a layered

microsphere, we model a microsphere of radius a¼ 30 lm

immersed in water. The coating consists of a layer of silicon

QDs, which can be easily deposited on a glass microsphere

and has a refractive index high enough to strongly modify

the electric field profiles.21 The refractive indices and

thermo-optic coefficients used were m1¼ 1.45, j1¼ 11.9

� 10�6 K�1, a1¼ 0.55� 10�6 K�1 (silica); m2¼ 1.67,35

j2¼ 1.0� 10�5 K�1 (silicon QDs); m3¼ 1.33, j3¼�0.8

� 10�4 K�1 (water). The value j2 for the silicon quantum

dot layer36 was taken for a Si-QD film composition that

should be similar to the one employed in the experiments.37

We then solved for the first-order radial modes with angular

mode orders having wavelengths near 750 nm corresponding

to the emission wavelength of the fluorescent coating.38

By solving Eq. (1) over a range of QD coating thickness

and angular mode order, one can effectively plot a thermal

sensitivity “map” for a given microsphere (Fig. 1). There is

an optimal coating thickness near 80 nm at which the thermal

sensitivity is zero for TE modes (dashed line in Fig. 1(a)).

The thermal sensitivity is also small for the TM-polarized

WGMs, eventually reaching zero at the slightly greater film

thickness near 140 nm. This result implies that it should be

relatively easy to achieve a zero thermal shift for a coated

sphere immersed in water simply by controlling the layer

thickness, while avoiding the exceptional fragility of thin-

walled capillary structures. For a microsphere, the coating

thicknesses needed to cancel the effect of thermal fluctua-

tions appear easily achievable for virtually any radial order,

FIG. 1. Calculated thermal shift (in pm/K) for a 30 lm-radius microsphere

coated with a Si-QD film of thickness t, for the first-radial-order whispering

gallery modes with angular orders from 345 to 355 (wavelength range from

�750 to �790 nm. Both the (a) TE and (b) TM polarization are shown.

031902-2 Y. Zhi and A. Meldrum Appl. Phys. Lett. 105, 031902 (2014)

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including the first-order modes that naturally dominate the

fluorescence spectrum.

The effect of different solvents on the thermal sensitivity

of a microsphere sensor can be visualized by constructing

thermal shift maps for a single value of L and t, as functions

of j3 and m3. An example is shown in Fig. 2, which covers a

range of refractive indices from m3¼ 1.30 to 1.36 and j3

from 0 to �4.5� 10�4, for both polarizations (again, for a

30 lm-radius glass sphere with a t¼ 80 nm coating and

L¼ 350). These values cover a wide range of common sol-

vents for refractometric or biosensing experiments. For this

thickness, the thermal sensitivity for water is zero for the TE

polarization, but for other external media the thermal shift

can be either positive or negative (e.g., it is negative for etha-

nol owing mainly to its high refractive index, but would be

positive for air). The effects of thermal fluctuations can, in

principle, be tuned to zero for any desired external medium,

by controlling the layer thickness.

The detection limit imposed by thermal fluctuations can

also be mapped, by converting directly from the thermal sen-

sitivity in Figs. 2(a1) and 2(b1) to a detection limit via

Eq. (4) (Figs. 2(a2) and 2(b2)). The detection limit “maps”

illustrate the result for a local temperature fluctuation of 1 K.

A “valley” develops where the thermal contribution to the re-

fractometric detection limit is small or even approaches zero.

For this particular QD film thickness, water falls precisely

within this valley, while solvents such as ethanol and metha-

nol (plotted as dots in Fig. 2) cause significant thermal shifts

that contribute to the overall detection limit.

Guided by the theory above, we attempted to build a

thermally stable (for water) microsphere by melting the end

of a tapered fiber, using a CO2 laser. The microsphere was

then dipped into a solution of hydrogen silsesquioxane

(HSQ) in a methyl isobutyl ketone solution. The microsphere

(which is still attached to the taper) was then annealed at

1100 �C for 1 h in flowing N2þ 5%H2 forming gas. This pro-

cess evaporates the solvent and collapses the HSQ (nomi-

nally Si8O12H8) molecular structure, forming a layer of

silicon QDs encapsulated in a silica matrix.38 The film thick-

ness can be controlled by changing the HSQ concentration in

the solvent and by employing a multiple-dip procedure.

Films with a thickness on the order of 102 nm (close to the

“zero valley”) can be made with a single-dip fabrication pro-

cess in a mixture of �15% to 35% HSQ concentration in

weight.39

The resulting microsphere had a nominal radius of

32 lm and was characterized by a bright red fluorescence

and a clear WGM resonance structure in the emission spec-

trum (Fig. 3). We have previously characterized the mode

structure from similar spheres quite extensively;40 these

modes are the first-radial-order WGMs with the angular

order L ranging from �330 to 410. The microsphere was

then inserted into a square capillary with an inner side length

of 700 lm and various fluids were pumped in using a syringe

pump. The sensitivity was found to be 87 and 70 nm/RIU for

the TE and TM modes, respectively, obtained by linear fit-

ting to the WGM shifts as the solvent was changed from

methanol, to water, to ethanol.

For thermal shift measurements, once the sphere was

completely immersed the pumping was stopped. A small

resistive heater and thermocouple were placed within �1 mm

of the capillary surface. The microsphere fluorescence spec-

trum was excited with a 442 nm HeCd laser and was measured

as the temperature was ramped at �0.3 �C/min from 25 to

40 �C. The laser was kept at a relatively low power in order to

minimize secondary heating effects. The experiments were

repeated with air, water, methanol, and ethanol in the capillary

channel. The wavelength shift was measured using the Fourier

shift theorem41 to extract the average WGM shift over the

whole spectrum.

The observed shifts were �8.5 6 0.3 and �14.7 6 0.2

pm/K for methanol and ethanol, respectively (TE modes);

whereas for air the shift was þ3.5 6 0.2 pm/K (Fig. 4(a)). For

TM modes, the shifts were �6.3 6 0.2, �11.0 6 0.3, and

þ2.7 6 0.1 pm/K for methanol, ethanol, and air, respectively

(Fig. 4(b)). The sign of the shifts is in agreement with the

theory, but their magnitude is only about half of the value

predicted by Eq. (1) (for reasons discussed below). As

FIG. 2. (a1) and (b1): Contour plots showing the thermal sensitivity as a

function of the thermo-optic coefficient and refractive index of the surround-

ing medium, for the TE (top) and TM (bottom) polarizations, respectively.

Panels (a2) and (b2) show the detection limits calculated using Eq. (4),

assuming a 1 K fluctuation. Again, we observe that for these conditions,

water falls into a valley of low detection limits, as indicated by the white

arrows.

FIG. 3. Fluorescence spectrum of the Si-QD-coated microsphere. The inset

is a fluorescence image (with the black background converted to a white

one) from which one can estimate a microsphere diameter of �64 lm.

031902-3 Y. Zhi and A. Meldrum Appl. Phys. Lett. 105, 031902 (2014)

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predicted by theory, for the case of water the wavelength

shifts were almost independent of temperature, with a thermal

sensitivity of only þ0.6 6 0.3 pm/K and �0.3 6 0.1 pm/K for

TE and TM modes, respectively. These shifts correspond

to a detection limit of (7.3 6 4.2)� 10�6 RIU (TE) and

(4.9 6 3.6)� 10�6 RIU (TM) assuming a temperature fluctu-

ation of 1 K. Thus, a controllable high-index coating can be

employed to fine-tune a microsphere for exceptional thermal

stability, even down to virtually zero, for the most common

bio-solvent (water).

For the case of a water solvent, the results agree (but not

exactly) with the theoretical calculations shown above. The

reasons for the discrepancy are that the synthesized micro-

sphere is slightly larger than 30 lm, and the film thickness,

while likely close to 80 nm,21 cannot be determined pre-

cisely. As well, the Fourier method averages the shift over

the whole spectrum, and dispersion was not considered in

the calculations. Despite these approximations, the results

agree reasonably well with the theoretical ones, showing a

nearly perfect thermal stability for a water solvent.

The reason that the measured thermal shifts for ethanol,

methanol, and air were smaller than the theoretical values is

probably due to the delay in heating the microsphere to the

temperature indicated by the thermocouple. Since the micro-

sphere was inserted within a glass capillary, it was effec-

tively shielded from the heating element and would be slow

to achieve the ambient temperature. To evaluate this hypoth-

esis, an additional experiment was conducted in which the

microsphere was held directly beside the heater without

being inserted into a capillary. The thermal sensitivity was

found to be þ8.2 6 0.1 pm/K for the TE polarization (meas-

ured in air), which is much closer to the theoretical values.

This is consistent with the idea that the shifts measured in

Fig. 4 are smaller than they “should” be as a result of thermal

shielding of the microsphere inside the capillary.

To conclude, we showed that a coated microsphere can

be designed to have WGMs that are almost perfectly insensi-

tive to thermal fluctuations for virtually any specific local

medium. We then synthesized a microsphere that approxi-

mated the ideal condition for a water solvent (the most im-

portant solvent for biosensing applications) and measured

the thermal shift. For water, the temperature-induced shifts

were indeed very close to zero, indicating that microsphere

WGM-based sensors can be constructed to be insensitive to

local temperature fluctuations. In this device, the positive

thermo-optic coefficients of the glass sphere and the coating

layer almost exactly balanced the negative thermo-optic

coefficient of the water solvent for a first-radial-order WGM.

Thus, by layering a microsphere with a high-index coating

with a specific thickness, one can achieve robust structure,

tuned for virtually any analyte, in which local temperature

fluctuations do not adversely affect the sensing performance.

We thank NSERC and AITF IciNano for funding, and

the Veinot lab for assistance in the preparation of the coated

microsphere.

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031902-4 Y. Zhi and A. Meldrum Appl. Phys. Lett. 105, 031902 (2014)

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