2 February 2015

Volume 106 Number 5

Applied Physics
Lettersapl.aip.org

APPLIED PHYSICS LETTERS 106, 051101 (2015)

Detection of phase transitions from the study of whispering gallery moderesonance in liquid crystal droplets
T. Arun Kumar,a) M. A. Mohiddon, N. Dutta, Nirmal K. Viswanathan, and Surajit Dharab)
School of Physics, University of Hyderabad, Hyderabad, India(Received 15 November 2014; accepted 14 December 2014; published online 2 February 2015)
We report studies on the whispering gallery mode (WGM) resonance of liquid crystal (LC)droplets across the smectic-A (SmA) to nematic phase transition. The quality factor (Q) in theSmA phase decreases rapidly with a characteristic slope change at the SmA-N transition. In theSmA phase, Q-factor is linearly proportional to the birefringence (Dn). We discuss the effect oftopological defect transformation on the WGM resonance. The study of WGM resonance isC 2015
expected to be very useful for detecting subtle phase transitions among LC mesophases. VAIP Publishing LLC. [http://dx.doi.org/10.1063/1.4906615]

Optical microresonators are very important from boththe technological and fundamental points of view. Becauseof their small mode volume and high Q-factors optical
microresonators are widely used as laser sources, active filters, and all-optical switches.1 The high Q associated withthe resonant modes in the microresonators has inspired various experiments. For example, the high energy density in thecavities facilitate the observation of various low threshold
nonlinear processes such as switching of coherent light, lowthreshold lasing, stimulated Raman scattering,1–4 and highsensitivity biological and chemical sensors.5–13 In the spherical microresonator, the light is confined inside the sphere
due to the total internal reflection, as the refractive index of
the sphere is larger than that of the surrounding medium.
The resonance condition is achieved when the circulating
light completes one cycle with in-phase, known as thewhispering-gallery-modes (WGMs). Mostly solid dielectricmaterials are used for making WGMs based microresonators.
There are also some reports on the investigation of microresonators based on the isotropic liquids such as CCl4,14CS2,15 water,16,17 and glycerol.18,19 Efforts were also madeto prepare polymer20–26 and single crystal based microresonators.27–29 However, the tuning of modes in the liquid orsolid microresonators is not easy in the sense that their resonance mode frequencies cannot be changed easily. In thiscontext, the recent studies on the microresonators based onnematic liquid crystals are very promising for designing tunable microresonators, which are useful for lasing and biosensors. In this letter, we report studies on the WGM resonanceof 8CB liquid crystal droplets with temperature. Our study
shows the potential application of WGM resonance of liquid
crystal droplets for detecting subtle phase transitions in liquid crystals.
We have used 4-octyl-40 -cyanobiphenyl (8CB) liquid
crystal, obtained from Sigma-Aldrich for the experiment. It
has the following phase transitions: Cr 21.5  C, SmA
33.5  C, and N 40.5  C I. We used 4-dicyanomethylene-2a)

Present address: Department of Electro-Optic Engineering, Ilse Katz
Institute for Nanoscale Science and Technology, Ben-Gurion University ofthe Negev, Israelb)
Electronic mail: sdsp@uohyd.ernet.in0003-6951/2015/106(5)/051101/4/$30.00

methyl-6–(p-dimethylaminostyryl)–4H-pyran (DCM) dye
as fluorescent material and Polydimethylsiloxane (PDMS)(Sylgard 184, Dow corning) as polymer matrix. In the present experiment no curing agent was added with PDMS. The
droplets are prepared in PDMS, which is confined between
two glass plates with spacers. The liquid crystal and DCM(<1 wt. %) dye are mixed together to make the microdroplets. The dispersed microdroplets are excited with a tightly
focused laser light of wavelength 532 nm (Nd: YAG secondharmonic). The absorption peak of DCM matches with thelaser wavelength and gives fluorescence in the visiblerange (540–650 nm). The resonance properties were studied
by a scanning near-field optical microscope (WiTec, alpha200) equipped with a spectrometer. A schematic diagram ofthe experimental setup is shown in Fig. 1. The evolution of
the defect structure was studied as a function of temperature
with the help of an optical polarizing microscope (Nikon,LV100 POL). The temperature of the sample was varied by atemperature controller (Instec Inc., mK1000).
We prepared several micron size SmA droplets of 8CB
in PDMS by using a micropipette. Typical photomicrographsof a SmA and a nematic microdroplet under optical polarizing microscope are shown in Figs. 2(a) and 2(c), respectively. A sharp spherical boundary with refractive index
difference can be seen in Fig. 2(b). Four extinction branchesoriginating from the center and oriented along the polarizer
axes suggests that the director distribution is radial and theSmA layers are concentric inside the microcavity. A schematic diagram of concentric SmA layers in the droplet isshown in Fig. 2(d). A point defect is also seen at the centersof the droplets. When the interfacial boundary of dye doped
LC microdroplets are illuminated (“þ” symbol in Fig. 2(e))
with a tightly focused laser beam (k ¼ 532 nm), a thin lightring along the circumference of the droplet and a brighter
spot on the other side of the droplet is seen (Fig. 2(e)). Thisis due to the excitation of WGMs resonance in the droplet.
The fluorescence is observed only inside the droplets suggesting that the dye has not diffused into the surrounding
PDMS.
The emitted light is collected with the same objective(20, NA ¼ 0.4) and fed to a spectrometer. The minimum
resolution of the spectrometer used for this experiment is106, 051101-1

C 2015 AIP Publishing LLC
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Kumar et al.

Appl. Phys. Lett. 106, 051101 (2015)

FIG. 1. Schematic diagram of the experimental setup.

limited to 0.09 nm. Usually, the WGMs are characterized by
two types of polarizations, namely, transverse electric (TE)and transverse magnetic (TM) modes where the electric fieldoscillates parallel and perpendicular to the surface of thesphere, respectively. Since LC droplets are birefringent, different polarizations sense different refractive indices. As thedroplet exhibits radial structure, the optic axis points in theradial direction. Therefore, the TE mode senses the ordinary(no) and the TM mode senses the extraordinary (ne) refractive indices. We systematically studied WGMs of LC droplets by varying temperature across the SmA-N phasetransition. Figure 3(a) shows the WGM resonances of a11 lm LC droplet at some representative temperatures. The
characteristic resonance spectra from a droplet are observed
overlaying the fluorescence background. The line width(¼ Dk) corresponding to the resonance peak (at k ¼ 600 nm)

FIG. 3. (a) A set of whispering gallery modes of a liquid crystal droplet atvarious temperatures. Various mode numbers corresponding with lowest radial modes (q ¼ 1) with TM polarization. The line width for the TM189 isapproximately 0.78 nm, and the LC cavity Q-factor is around 770. The droplet diameter is 11 lm. (b) Simulated resonant frequencies of a LC droplet
with corresponding radial mode and TM polarization.

for 26  C is 0.78 nm and the Q factor (k/Dk) is ’ 770. It isalmost one order of magnitude less than that reported previously in room temperature nematic droplets.30 This is due toour instrumental limitation of minimum spectral resolution,in particular, the spectral resolution of our spectrometer isone order of magnitude less than that used in Ref. 30. As thetemperature is increased (28  C), the fluorescence background decreases and more importantly the resonance width(Dk) increases and consequently the Q-factor decreases. AFIG. 2. (a) Photomicrograph of a SmA droplet obtained using optical polarizing microscope. (b) Without polarizers. (c) A nematic droplet between crossedpolarizers. (d) Schematic diagram of the SmA layer orientation. (e) Dark-field image of an illuminated SmA droplet. “þ” symbol indicates the illumination
region with focused laser beam of k ¼ 532 nm. (Inset) Bright-field image of the same SmA droplet.

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Appl. Phys. Lett. 106, 051101 (2015)

typical spectra in the nematic phase (34  C) is also presentedin Fig. 3(a). The resonant WGM frequencies for a sphericalresonator with small radial mode numbers q can be simulatedusing the asymptotic expansion in powers of (l/2)1=3 (Ref.
31)
 1=3 
3a2q l 1=3lvnr
 pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ þns ka ¼ l  aq
2n2r  1 20 2
 2
 2=3aq nr v 2v  3n2rl
þ Oðl1 Þ;
3=2
2
6 n2  1(1)rwhere a is the radius of the sphere, k is the wavenumber, l 1, q ¼ 1, 2, 3…. are mode numbers, and v ¼ 1=n2r for TM
modes. aq are negative q-th zeros of the Airy function, andnr ¼ ns/na is the relative refractive index, where ns is the refractive index of the sphere and na is the index of the surrounding medium. In the present experiment, for the dropletof diameter 11 lm, we found that only TM modes with radialmode number q ¼ 1 is supported. The experimental resonance peaks for the same droplet are labelled based on thesimulated spectra (Fig. 3(b)) using ns ¼ 1.67,32 na ¼ 1.37.33
The angular mode numbers l ranges from 79 to 98.
Figure 4 shows the temperature variation of Q-factor ofmode corresponding to k ¼ 600 nm across the SmA-N phasetransition. For the sake of comparison, we have plotted withshifted temperature T-TNS, where TNS is the SmA-N phasetransition temperature. We observe that the Q-factor
decreases rapidly with increasing temperature in the SmA
phase and tends to saturate in the N phase. For example, it
decreases from around 770 to 135 when the temperature isincreased from 6  C below to 4  C above the transition. We
collected the temperature dependence of the birefringence(Dn ¼ ne – no, where ne and no refers to the extraordinary andordinary indices) of the SmA phase from the Ref. 32 andplotted the variation of Q-factor with Dn in the inset of Fig.
4. We found that Q-factor is linearly proportional to Dn.
Since Dn / S, where S is the orientational order parameter,
the temperature variation of Q-factor truly reflects theFIG. 4. Temperature (T-TNS) variation of Q-factor of the mode corresponding to k ¼ 600 nm. Dotted line is drawn as guides to the eye. The verticalarrow indicates SmA-N phase transition. (Inset) Variation of Q-factor withbirefringence (Dn). The red line is a linear best fit with slope 83850. The
droplet diameter is 11 lm.

variation of order parameter. Thus phase transitions among
LC mesophases specially the transitions in ferroelectric LCs(SmC*) subphases namely, SmCa ; SmCb , etc, where thechange in Dn is very small could be detected easily by studying the WGM resonances.
Finally, we discuss the possible reason behind the low
Q-factor in the nematic phase compared to the SmA phase.
Apart from the lower birefringence of the nematic phase, thethermal fluctuations of the director could contribute to thelow Q value. In the SmA phase, the director is homeotropic
and the layers are concentric (Fig. 2(d)). In the nematic
phase the homeotropic boundary condition is retained but inthe central region the extinction branches are twisted in theanticlockwise direction (Fig. 2(c)). Similar phenomenon has
been observed previously by Lavrentovich and Terent’ev, inother compounds showing SmA to nematic transition.34
They showed both theoretically and experimentally that radial hedgehog defects in SmA droplets are transformed tohyperbolic hedgehog defects at the SmA-N phase transition
keeping the homeotropic boundary condition of the director
at the droplet interface. This is due to the critical divergenceof the bend elastic constant (K33). This transformation isaccompanied by a simultaneous formation of nonsingularring disclination in the nematic phase. A schematic diagramof a singular ring disclination is shown in Fig. 5(a). The transition between them occurs because the core of the droplet
surrounded by a nonsingular disclination ring (strengthm ¼ 1) is leaked away (Fig. 5(b)) and consequently the loss
in the cavity increases significantly.
In conclusion, we have studied the whispering gallery
mode resonance in 8CB liquid crystal droplets across theSmA to nematic phase transition. We found that the quality
factor of the resonance decreases rapidly as the temperature
is increased across the SmA-N phase transition. The temperature dependence of Q-factor reflects the temperature dependence of orientational order parameter of the SmA phase.
Apart from the director fluctuations in the nematic phase, theenergy loss in the nematic phase could partly be due to thechange of symmetry of the topological point defect, i.e.,from radial hedgehog to hyperbolic hedgehog inside thedroplets. The measured Q-factor in the SmA phase is comparatively lower due to the instrumental limitation; nevertheless, the essential features of the WGMs of the droplets

FIG. 5. The schematic diagrams of the director (the average direction of molecular orientation) orientation in a droplet (a) with nonsingular disinclination (dotted red line). (b) General appearance with leaked core in thenematic phase.

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Kumar et al.

across the SmA-N transition are revealed. Since the WGMs
resonances are very sensitive to the small change in birefringence they can be used for detecting subtle phase transitions
such as transitions among the ferroelectric LC subphases.
We gratefully acknowledge support from the DST (SR/NM/NS-134/2010) and CSIR (03(1207)/12/EMR-II), DSTPURSE, and UPE-II. We also acknowledge the facilities ofCenter for Nanotechnology.
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