Whispering gallery mode pressure sensing

T. Weigel, C. Esen, G. Schweiger and A. Ostendorf

Ruhr-Universitat Bochum, Universitatsstr. 150, 44780 Bochum,Germany

ABSTRACT

Optical resonances of microresonators, also known as whispering gallery modes, are attracting considerableinterest as highly sensitive measuring devices with a variety of applications. Such resonators can be used forpressure, force or strain measurement. Droplets, embedded in an appropriate substrate, form perfect spheresdue to their surface tension and can be used as optical resonators with high quality factors. The resonancefrequencies of these droplets depend sensitively on their size and shape. Pressure changes affect the dropletshape. Therefore, pressure change can be measured with high sensitivity. In the work presented here, ethanoldroplets embedded in a silicone matrix are considered. The shift of the resonance frequencies of microdropletsembedded in silicone as function of the applied pressure is investigated.

Keywords: Whispering gallery modes, microdroplet, pressure sensing

1. INTRODUCTION

Due to its high sensitivity to a variety of parameters, optical resonances on microparticles are of high interestin a wide range of applications.1 Especially, these resonances are very sensitive to deformations of the surfaceor changes of the particle size. For this reason whispering gallery modes (WGMs) are predestinated for sensingtemperature,2 pressure and force with high accuracy. Ioppolo and Otugen3 investigated the influence of theathmospheric pressure on the WGMs excited in hollow PMMA-particles. Klitzing et al.4 investigated the tuningcapability of silica particles. Pressure sensitivity can be enhanced by using droplets instead of solid particles.Therefore, inspired by the work of Saito et al.,5 we also used droplets embedded in a silicone matrix. Saitoconsidered optical resonances in the fluorescence signal (output resonances). In this case, a spectral devices hasto be used which limits the spectral resolution of the measurement. In contrast to this work, we consideredthe resonances at the laser wavelength (input resonances) by scanning the wavelength of the incident light witha tunable diode laser with a small linewidth (<300kHz). Here, the spectral resolution is only limited by theresonator properties and the laser line width.

2. WHISPERING GALLERY MODES IN GEOMETRICAL OPTICS

Before describing experimental details, a short overview in the theory of optical resonances in spherical particlesis given. Here the geometrical optics (GO) model is used, since GO is more descriptive than wave optics. UsingGO is justified because the droplets are large compared to the applied wavelength.Within this picture resonancescan be interpreted as surface waves, which are created by constructively interfering rays as can be seen in Fig. 1.In contrast to the often cited resonance condition, that the ray has to hit its tail in phase after one roundtrip, itis sufficient that the ray crosses its path in phase. As a consequence of this condition, the phase fronts illustratedin Fig.1. Since a ray inside a spherical object never leaves the plane of incidence, the creation of resonances isa two dimensional problem and hence the resonance can be described by two independent resonance conditions.It can be easily understood from Fig.1 that the difference between the phase progress of a ray travelling from Ato C over B

∆ϕABC = 2npk0

√r2p − r2ci −

π

2− δϕrefl. (1)

and the phase progress along the inner caustic

∆ϕAC = 2npk0rci arccosrcirp

(2)

Further author information: (Send correspondence to T .Weigel)T. Weigel: E-mail: weigel@lat.rub.de, Telephone: +49 (0)234 32-23455

Optical Sensing and Detection II, edited by Francis Berghmans, Anna Grazia Mignani, Piet De Moor, Proc. of SPIE Vol. 8439, 84390T · © 2012 SPIE · CCC code: 0277-786X/12/$18 · doi: 10.1117/12.921759

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Figure 1. Coupling and generation of optical resonances

must be zero or an integer multiple of 2π. This leads to the first resonance condition:

2npk0

(√r2p − r2ci − arccos

rcirp

)− π

2− δϕrefl. = (n− 1) · 2π n = 1, 2, 3, . . . mode order (3)

With the vacuum wavenumber k0 = 2πλ0, the mode order m describes the number of maxima in radial direction.

For reflections at the outer surface an additional phase shift δrefl. has to be considered, the subtrahend π2 comes

from focusing at the inner caustic. rci, np and np are the refractive index and radius of the particle. Thesecond resonance condition can be derived from the fact, that the phase progress along the inner caustic afterone roundtrip must be an integer multiple of 2π. Here we have to consider phaseshifts due to focusing at theaxis of incidence (2×−π

2 )

∆ϕ = 2πk0nprci − 2 · π2= l · 2π

⇒ k0nprci = l +1

2l = 1, 2, 3, . . . mode number (4)

The mode number l gives the number of maxima in one half of the particle. One can see, that the inner causticradius rci is independent of the particle radius. For this reason, high values of the mode number l leads toresonant rays which travel inside the particle with a high reflection angle, i.e. with small losses. For this reasonresonances with high l are sharper than those with small l values. Obviously the inner caustic must be insidethe particle and therefore sharp resonances can only be excited in large particles. Until now, only the creation ofresonances is described. Another important point is the coupling of resonant rays from outside into the particle.Usually rays enter the particle by refraction. Such rays undergo high damping when travelling inside the particleand can therefore excite weak resonances. In contrast, sharp resonances are created by rays which are totallyreflected on the surface of the particle. This is only possible if the refractive index of the particle is higher thanthat of the surrounding medium. As we will see, such resonances can only be excited by rays passing the particlein some distance. The coupling mechanism of such rays can be described by considering the angular momentum,which is conserved in the special case of spherical particles. Especially the angular momentum at Point P1,L1 = hk0nsb equals the angular momentum at point A, LA = hk0nprci, this leads to

rci =ns

npb. (5)

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Camera

Laser

1...4c

V.

(a) Experimental setup for the measurement process (b) Typical image of droplet with laser

Figure 2. Experimental setup for the measurement process and image of an excited droplet (postprocessed)

Since rci ≤ rp the tunneling distance b must be smaller than

bmax = rpns

np. (6)

The above, more heuristic, explanations are based on detailed descriptions of the optical resonances with geo-metrical optics given by Roll and Schweiger.6

3. DROPLET PREPARATION AND MEASUREMENT SETUP

The droplet consists of DDI (Lambdachrome) solved in ethanol. The droplet was inserted into the silicone (Shin-Etsu Chemicals KE-103) 2 hours after the start of the curing process with help of a microliter syringe (Hamilton7000.5, 0.5µl volume). The silicone was prepared in a cuvette (4.5 × 10 × 23mm), i.e. a cross sectional areaof 45mm2). The refractive index of ethanol (nethanol = 1.36) is much smaller than the refractive index of thesurrounding silicone (nsilicone = 1.41), therefore another part of a surfactant, Tween 20 (Merck Chemicals), withan refractive index nTween = 1.46 was added to enable sharp resonances. Since the volume of the syringe wasmuch larger than the droplet volume (≈0.5nl) a micrometer screw was used for proper droplet generation. Withthis setup, droplets from 100-120µm are generated. Because of the hydrophilic character of ethanol in contrastto the hydrophobic silicone, the droplets form a perfect sphere. After an additional curing time of about 8hthe silicone is ready for pressure measurements. Closer investigations by Raman spectroscopy showed, that theethanol diffuses out of the droplet. Therefore, at the end of the preparation process, the droplet consists only ofdye (with a concentration in the range of a few µM) and Tween 20. The experimental setup of the measurementprocess is shown in Fig.2(a).

The resonances are excited by focused laser beam (10× microscope objective, NA 0.18) with focus diameter ofabout 2µm. As stated before, sharp resonances are excited by rays that pass the particle surface in some distancebut not more than the maximal tunnel distance bmax. With Eqn. 6 this is in our case ≈ 3.5% of the particleradius. For this reason the laser beam must be placed at a small distance of a few microns from the surface ofthe droplet. Spectra are achieved by scanning the laser (NewFocus Velocity 6309) with a velocity of 0.1nm/s. At

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λ / nm

d / µ

m

682 682.5 683 683.5 684 684.5 685−4

−2

0

2

4

6

8

10

12

Figure 3. Resonance intensity as function of the wavelength and the distance d, between the laser beam and the particlesurface.

the same time, pictures are captured from above through an objective by a standard CMOS-camera (VRMagicVRmC-3+/bw) with a frame rate of about 60fps through an objective. This leads to a spectral resolution ofapprox. 2pm. Fig. 2(b) shows a typical image of an illuminated droplet. The image is postprocessed to beable to see the particle as well as the laser beam. Here, bright islands at the surface of the droplet are visible.We assume that this is crystallized dye after diffusion of the ethanol solvent, since the solubility of the dye inethanol is higher than in Tween. However, these defects act as additional scatterers inside the droplet. Since thefield inside the particle is deeply enhanced in resonance, the scattering on these points is also very high in thecase of resonance. Therefore these points are utilized within the evaluation process. The intensity at the brightpoints along the central axis of the droplet—parallel to the direction of the laser beam—is nearly independentof the wavelength and can be explained by backreflections from the surface of the silicone and are therefore notconsidered. The intensity dependence on the wavelength at all other bright points along the surface is similar.

4. RESULTS

The distance of the laser beam from the surface of the droplet is of high interest since it affects deeply thecoupling efficiency of the resonances. Therefore we first investigated the dependence of the resonances on thecoupling distance. The results are shown in Fig. 3. Here, the distance between the laser beam and the particlesurface is varied. Within the uncertainty, given by the thickness of the laser beam and the determination of thedroplet surface, the measured results agree well with the above theoretical considerations.

With the right distance, high, sharp resonances can be excited. Fig. 4 shows a typical spectrum of a droplet.The free spectral range is about 1nm, which is usual for objects around 100µm. The sharpness of the resonances,described by the quality factor Q = λ

∆λ , is larger than 104. When pressure is applied over the micrometerscrew, the droplet will be deformed and therefore the resonance position shifts. In Fig. 5 the dependence ofthe resonance position for three different resonances on the screw displacement ∆l is shown. With the Young’smodulus E=0.7MPa (according to the manufacturer) this leads to a pressure dependence on ∆l:

p ≈ 30Pa

µm·∆l (7)

and hence to a pressure change of about 4.5kPa. The dependence is almost linear and equal for all resonances.The sensitivity is about 0.01 nm

µm (3 · 10−4 nmPa ). With a spectral resolution of 2pm this leads to minimal pressure

resolution of about 6Pa.

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682 682.5 683 683.5 684 684.5 6850

2000

4000

6000

8000

10000

12000

14000

16000

18000

λ / nm

inte

nsity

/ a.

u.

683.9 683.95 684 684.05 684.1 684.150

2000

4000

6000

8000

10000

12000

14000

16000

λ / nm

inte

nsity

/ a.

u.Figure 4. right: typical spectrum of a droplet, left: zoomed resonance with Q≈ 104

0 10 20 30 40 500

0.1

0.2

0.3

0.4

0.5

0.6

0.7

∆l / µm

∆λ /

nm

Resonance 1Resonance 2Resonance 3

Figure 5. Dependence of the shift of the resonance wavelength for three consecutive resonances on ∆l, the feed of themicrometer screw generating the pressure. It is assumed that the pressure is linearly proportional to ∆l.

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5. CONCLUSION

The aim of this work was to investigate the influence of pressure on the optical resonances of droplets embeddedin a silicone matrix. We found sharp resonances whose frequency shifts nearly linearly with pressure. This makesit an useful tool for pressure and strain measurements in not easily accessible surroundings.

ACKNOWLEDGMENTS

The work presented in this paper was supported by the Deutsche Forschungsgemeinschaft (DFG, grant ES182/3-2).

REFERENCES

[1] Chiasera, A., Dumeige, Y., Feron, P., Ferrari, M., Jestin, Y., Conti, N. G., Pelli, S., Soria, S., and Righini,G., “Spherical whispering-gallery-mode microresonators,” Laser & Photonics Reviews 4(3), 457–482 (2010).

[2] Ozel, B., Nett, R., Weigel, T., Schweiger, G., and Ostendorf, A., “Temperature sensing by using whisperinggallery modes with hollow core fibers,” Meas. Sci. Technol. 21(9), 094015 (2010).

[3] Ioppolo, T. and Otugen, M., “Pressure tuning of whispering gallery mode resonators,” J. Opt. Soc. Am.B 24(10), 2721–2726 (2007).

[4] Klitzing, W. v., Long, R., Ilchenko, V. S., Hare, J., and Lefevre-Seguin, V., “Tunable whispering gallerymodes for spectroscopy and CQED experiments,” Opt. Lett. 26(3), 166–168 (2001).

[5] Saito, M., Shimatani, H., and Naruhashi, H., “Tunable whispering gallery mode emission from a microdropletin elastomer,” Opt. Express 16(16), 11915–11919 (2008).

[6] Roll, G. and Schweiger, G., “Geometrical optics model of mie resonances,” J. Opt. Soc. Am. B 17(7), 1301–1311 (2000).

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