LIQUID CRYSTALS
2019, VOL. 46, NO. 4, 629–639
https://doi.org/10.1080/02678292.2018.1515373

Stability of liquid crystal micro-droplets based optical microresonators
Junaid Ahmad Sofi and Surajit Dhara
School of Physics, University of Hyderabad, Hyderabad, India
ABSTRACTARTICLE HISTORY

Liquid crystal (LC) based tuneable optical microresonators are potential for being used as crucialcomponents in photonic devices. In this article, we report experimental studies on LC microdroplets dispersed in several dispersing media. We find that the size of the micro-droplets formed
in a low refractive index and optically transparent perfluoropolymer are most stable with timethan commonly used dispersing media. Using a negative dielectric anisotropy nematic liquid
crystal, we show that the whispering gallery mode optical resonance properties such as thequality factor and the free spectral range of stable micro-droplets are independent of thestrength of the applied electric field. The optical resonance properties under applied field are
significantly different than that of the liquid crystals with positive dielectric anisotropy and are
explained based on the elastic deformation of the micro-droplets.

Received 5 July 2018
Accepted 21 August 2018

1. Introduction
In polymer dispersed liquid crystals, appropriate amount ofpolymers and liquid crystals are mixed. In the immiscible
mixture, tiny droplets ranging from a few tens of nanometre to micrometre size liquid crystal droplets are phaseseparated from the polymer matrix [1–4]. These microdroplets highly scatter incident light giving the sample amilky appearance. The application of electric field reorientsthe director (the average direction of molecular long axis[5]) of the micro-droplets and, hence, changes the scattering intensity and, thus, have been used in many applications. The dispersed droplets exhibit variety of director
structure depending on the bulk elasticity, surface tension
and surface anchoring. It has been shown that for sufficiently large droplets, the surface anchoring prevails. As a
CONTACT Surajit Dhara

dharasurajit@gmail.com© 2018 Informa UK Limited, trading as Taylor & Francis GroupKEYWORDS

Liquid crystal microdroplets; optical resonanceresult, topological defects are stable at the equilibrium statesof the large droplets [6]. In addition to this, it has also beenreported that both flexoelectricity and order electricity has
significant effect on the equilibrium defect structure [7]. In
case of nematic, if the surface anchoring is strongly homeotropic, commonly a radial director structure with a hedgehog defect at the centre of the droplets is observed. In caseof strongly planar surface anchoring two boojums at theinterface are usually observed. A variety of other complex
structures can be observed in cholesteric and smectic-C
liquid crystal micro-droplets [8–11].
Liquid crystal micro-droplets can be used as optical
micro-cavities when the refractive index of the surrounding medium is lower [12–15]. The light insidethe droplet circulates due to the total internal reflection
and the resonance condition is achieved when the630

J. A. SOFI AND S. DHARA

Figure 1. (Colour online) (a) Schematic diagram showing the WGM resonance of a spherical microresonator using ray and wave optics. n1
and n2 are the refractive indices of the respective media. (b) Small ellipsoids represent the electric field distribution of resonant modes.

circulating light meets in-phase. This is known as
whispering-gallery-mode (WGM) resonance [16,17].
A schematic representation of WGM resonance using
ray-optics and wave optics is shown in Figure 1. It hascreated a lot of interest as these micro-cavities possess asmall mode volume and high quality factors (Q) andthey are promising for many applications such as laser
sources, active filtres and all-optical switches.
The Q-factor of a spherical micro-cavity strongly
depends on the morphology and the optical properties ofthe microsphere. In case of soft microresonators like liquid
crystals they can be changed easily by varying the temperature, external electric and magnetic fields. The evanescentfield that exists upto a few hundreds of nanometres and lies
outside the micro-cavity makes these tiny resonators efficient sensors. Any modulation in the evanescent fielddomain of these droplets is strongly reflected in their optical resonance. Based on this, surfactant sensing by nematic
micro-droplets was reported through boundary changemechanism by Humar et al. [18]. Detection of subtle
phase transition among liquid crystal mesophases has also
been demonstrated from the WGM study [19]. Yan Wanget al. have studied the dye doped cholesteric liquid crystals
micro-droplet based microcavities [20]. Recently, we haveshown temperature, magnetic and electric field tuning ofstructure and WGM resonance in nematic and ferromagnetic nematic droplets [21,22]. In most of the previous
studies either glycerol or polydimethylsiloxane (PDMS)
were used as supporting media. It was reported that the
micro-droplets in these dispersing media are not stable inthe sense that the diameter decreases slowly with time [22].
This is disadvantageous as far as the application point ofview is concerned and, hence, it is important to find asuitable supporting media with desired properties. In thisarticle, we report experimental studies on several polymer
and liquid crystal systems. We find that the size of liquid

crystal micro-droplets is most stable with time in a low
refractive index, highly transparent perfluoropolymer solution. The electric field creates a substantial elastic distortionin the micro-droplets of a negative dielectric anisotropy
nematic liquid crystal but the resonance properties remain
unaffected and this is in contrast to the results reported indroplets of positive dielectric anisotropy liquid crystals. We
report quality factor, Q ’ 1:2  104 in our system, which
is so far the highest reported value in liquid crystal based
microresonators.

2. Experimental
In the experiment, we have used two liquid crystals namely,
pentyl cyano biphenyl (5CB) and a negative dielectricanisotropy nematic liquid crystal mixture, MLC-6608.
5CB was obtained from Sigma-Aldrich and it exhibits
room temperature nematic phase. MLC-6608 was obtained
from Merck and it exhibits a wide temperature range ofnematic phase, extending from −30ºC to 90ºC. The dielectric anisotropy of MLC-6608 is negative, i.e. Δ ¼ 4:2
and the elastic constants at ambient temperature are;K11 ¼ 16:7  1012 N,
K22 ¼ 7:0  1012 N
and12
K33 ¼ 18:1  10 N, respectively [23,24]. Since both ofthem are room temperature nematic liquid crystals, all theexperiments are performed at ambient temperature. The
extraordinary and ordinary refractive indices of 5CB atroom temperature are given by ne ¼ 1:702 and no ¼
1:55 [25]. In case of MLC-6608, ne ¼ 1:56 and no ¼
1:477 [26]. We used three polymers as supporting media
namely, PDMS, a mixture of glycerol-lecithin and a perfluoropolymer, i.e. poly(perfluoro (4-vinyloxy-1-butene)),commonly known as CYTOP (CTX-809A). CYTOP was
obtained from Asahi Glass Co. Ltd, Japan. We prepared asolution with volumetric ratio 2:1 of CT-Sol.180 solvent

LIQUID CRYSTALS

and CTX-809A. The refractive index of PDMS and glycerol
are 1.38 and 1.47, respectively [27]. PDMS provides homeotropic whereas glycerol provides planar liquid crystal
anchoring. A small amount of lecithin (about 5 to 10 wt%) mixed with glycerol provides homeotropic anchoring.
The refractive index of CYTOP is 1.34 and is much smaller
than that of both PDMS and glycerol. CYTOP is highly
transparent over a wide wavelength range (200 nm to 2 µm)
and is used as an antireflective coating in organic lightemitting devices [28,29]. It has high solubility in perfluorinated solvents and is highly resistant to chemical andthermal stimuli [30]. It has been used as an alignment
layer for liquid crystals and several experiments showing
the discontinuous anchoring transition have been reported[30–39]. Micrometre size droplets were dispersed throughmicropipette injection in the supporting media. About 1 to
2 µL of liquid crystal was injected into 1000 µL of polymer
and the tip of the micropipette was moved in a circular
fashion while releasing in to the polymer. This protocol
provides well separated micro-droplets with definite structure dispersed in the polymer. The micro-droplets arehighly stationary inside the polymers and no sedimentation
is observed during the experiment. Prior to the droplet
formation, the liquid crystals were doped with 0.1 to 0.5%
of Nile red fluorescent dye. No curing agent was added tothe polymers because it often changes the surface anchoring of the liquid crystals. The wavelength of Argon-ion
laser (514 nm) falls in the excitation band of Nile red andthe fluorescence emission from the sample is observed
within a range of 540–700 nm.
In the electric field experiments, we placed the supporting media containing liquid crystal micro-droplets
between two indium-tin-oxide-coated (ITO) glass plateswith appropriate spacers. Micro-droplets with uniform
radial director structure were selected and excited with afocussed beam of Argon-ion laser (514 nm) through theobjective of the microscope. The light emitted by thedye-doped droplets is collected by the same objective
and is sent to the spectrometer (Andor 500i) which isconnected to the inverted polarising microscope(Nikon, Eclipse Ti-U) [22]. Sinusoidal voltage wasapplied across the cell with the help of a function generator (Tektronix-AFG 3102) fixed at 5 KHz frequency
and a voltage amplifier (TEGAM-2350).

3. Results and discussion
We studied the time dependent size of the micro-droplets using a polarising optical microscope (POM).
Figure 2 shows the time variation of diameters of afew 5CB micro-droplets in PDMS (Figure 2(a)) and inglycerol (90%) lecithin (10%) mixture (Figure 2(b)).
5CB in PDMS shows a radial anchoring whereas in

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pure glycerol it shows planar anchoring with a pair ofboojum defects situated diametrically opposite. We
find that a small amount of lecithin in glycerol induced
homeotropic anchoring with radial director structure.
In PDMS, the micro-droplet diameter decreases rapidly
in a nonlinear way. For example the diameter of 70 µm
droplet decreases nearly to 10 µm within 2 h (Figure 2(a)). In fact sometimes the micro-droplets disappear
completely over a long period of time. An empiricalequation; DðtÞ ¼ Dð0Þ þ Aet=τ , is fitted to get the
decay constant for a particular droplet, where A is aconstant. The decay constant τ ’ 50 min, suggesting
63% of the size is shrunken within 50 min after the
droplet formation. In case of glycerol-lecithin mixture,
the micro-droplet diameter decreases linearly but it ismuch slower than PDMS (Figure2(b)). For example,
the diameter of a 26 µm droplet decreases to about
21 µm after about 6 h. Beyond about 50 min the microdroplet size decreases by about 100 nm/min. For bigger
droplets (D>40µm), initially the decay is faster (about
350 nm/min) and there is a clear slope change at about
30 min. Therefore, glycerol lecithin mixture is comparatively better dispersing medium than PDMS for
WGM experiments. However, the glycerol-lecithin
mixture appears yellowish and the scattering as well
as absorption losses are relatively higher than PDMS.
These short-comings motivated us to look for an alternative supporting medium.
There are some studies reporting the alignment properties of liquid crystals on CYTOP solution [31–33]. We havechosen it as a supporting medium for studying the liquid
crystal micro-droplets. Figure 3(a) shows micro-droplets of
MLC-6608 liquid crystal dispersed in CYTOP solution. It
stabilises spherical micro-droplets with radial anchoring.
Four orthogonal dark brushes with concentric rings
around the centre suggest the director is orthogonal tothe interface and radially symmetric. A radial hedgehog
point defect is seen at the centre of the droplets. Figure 3(b)shows the variation of diameter of a few micro-dropletswith time at room temperature, measured using optical
microscope. It is observed that micro-droplet diameterdecreases very slowly with time and beyond about 3 h offormation, they are completely stabilised (time shown by
dotted line in Figure3(b)). Thus, CYTOP solution is muchbetter supporting medium than PDMS and glycerollecithin mixtures at ambient temperature. The CYTOP
has a large number of fluorine atoms. Fluorine has asmall atomic radius and the largest electronegativity
among the atoms, so that it forms a stable covalent bondwith carbon and is effective in lowering the surface energy.
Hence, liquid crystal molecules are not soluble in CYTOP
solution [37] owing to the high bonding energy of C-F(485 kJ mol-1) and C-C (360 kJ mol-1) bonds [40].

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J. A. SOFI AND S. DHARA

Figure 2. (Colour online) Variation of diameter of 5CB micro-droplets with time dispersed in (a) PDMS (b) glycerol (90%) lecithin (10%)
mixture. Different colours represent LC micro-droplets with different initial diameters and their time evolution. The continuous red line in(a) is a best fit to the equation; DðtÞ ¼ Dð0Þ þ Aet=τ . Continuous lines in (b) are linear best fits. The measurements are made directlyfrom the optical microscope at room temperature. (Inset) Polarising optical microscope images of micro-droplets with defects.

We selected a micro-droplet of MLC-6608 of diameter 10.6 µm for studying optical resonance. Figure 4(a) shows the polarising optical microscope image.
Figure 4(b) shows spherical micro-droplet with sharp
interface of the droplet-CYTOP solution. Figure 4(c)shows excitation of WGM in the dye doped micro-

droplet when illuminated by a tightly focussed
514 nm laser beam through a 60X objective. A light
strip running diametrically across the droplet suggests
the localisation of the modes around it. Figure 4(d)shows a typical WGM resonance spectrum. The resonance modes are observed on the overlay of theLIQUID CRYSTALS

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Figure 3. (Colour online) (a) Polarising optical microscope images (POM) of MLC-6608 micro-droplets of various size suspended in
CYTOP solution. Inset shows a schematic diagram of radial director structure (b) Variation of micro-droplet diameters with time atroom temperature measured by using optical microscope. Different colours represent LC micro-droplets with different initial
diameters and their time evolution. The vertical dotted line indicates the time beyond which the droplets are highly stable andused for optical resonance studies.

fluorescence intensity of the droplet. Liquid crystals arebirefringent and, hence, possess different refractive
indices for different polarisations. In transverse magnetic mode (TM), the electric field oscillates along thelonger molecular axes while as in transverse electricmode (TE), the electric field oscillates perpendicular
to it. In spherical micro-droplets, the refractive index
sensed by former polarisation is extraordinary index

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J. A. SOFI AND S. DHARA

Figure 4. (Colour online) (a) Optical polarising micrograph of an MLC-6608 micro-droplet dispersed in CYTOP solution at room
temperature. (b) Droplet as seen without polarisers. (c) A Nile-Red dye-doped micro-droplet illuminated by a focussed 514 nm laser
beam. The irradiation point is marked by green arrow. (d) Optical resonance spectrum recorded by the spectrometer from anilluminated micro-droplet with calculated TM modes.

(ne ) and the latter one experiences ordinary index (no ).
Using analytical solutions of Mie type theories, theresonant frequencies for spherical birefringent microresonators can be calculated [12]. It has been shownthat for the TE mode in the radial anisotropic microsphere is equivalent to the TE mode in an isotropic
microsphere with the ordinary refractive index,
whereas the TM mode couples to both the ordinaryand extraordinary refractive indices. However, for aspherical resonator with small radial mode numbers q
the resonant WGM frequencies can be obtained analytically [41]. For a droplet of diameter 10.6 μm, we findthat only TM modes with radial mode number q ¼ 1
are supported. The angular mode numbers (l) for thesame droplet are calculated using ns ¼ 1:557 [42] andna ¼ 1:34 [37]. In the wavelength range of
540–680 nm, l varies from 71 to 89, which is labelledin Figure 4(d).

The stability of the droplets was further studied bymeasuring the free spectral range (FSR). It isdefined as:
FSR ¼ δλSM ¼

λ2
ne f f πD(1)

where, 1=n2e f f ¼ sin2 θ=n2e þ cos2 θ=n2o and δλSM , D, ne ,no and θ are spacing between two successive modes, thediameter of the micro-droplets, extraordinary refractive
index, ordinary refractive index of the liquid crystal
and the angle between the optical axis and the lightpropagation direction, respectively [43]. Figure 5(a)shows the variation of FSR with time for a few microdroplets. The measurements were made after 3 h fromthe formation of the droplets. It is observed that the
FSR for all the micro-droplets is independent of time.
Figure 5(b) shows the variation of FSR for several

LIQUID CRYSTALS

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Figure 5. (Colour online) (a) Time dependence of FSR of different size microdroplets dispersed in CYTOP solution. (b) Variation of
FSR with droplet size. The red line is the best fit to FSR / 1/D. The error bar in (a) is almost equal to the point size. All themeasurements are made at room temperature.

micro-droplets with varying diameter from 7 to 45 µm.
The FSR is inversely proportional to the droplet diameter (D). The best fit to the data (FSR / 1=D) is also
shown in Figure 5(b).

The WGMs displayed by the micro-droplets are highlymorphology dependent. In case of liquid crystals the director inside the droplets is distorted by external electric andmagnetic fields and consequently WGM resonance

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J. A. SOFI AND S. DHARA

Figure 6. (Colour online) Optical polarising micrographs of elastic distortion of a microdroplet dispersed in CYTOP solution at (a)zero electric field (b-c) increasing electric field. Corresponding λ-plate images are shown underneath. (d) Representative WGM
spectra of a droplet below (0.12 V=μm) and above (0.56 V=μm) Freedericksz threshold field. The direction of electric field and theorientation of the slow axis of the λ-plate with respect to the crossed polarisers is shown on the left side.

properties are expected to get affected. In our previous
studies we showed the effect of electric field on the WGM
resonance properties of a liquid crystal exhibiting positive
dielectric anisotropy (Δ>0) [22]. In the present experiment the dielectric anisotropy of MLC-6608 is negative(Δ<0). The effect of electric field on the micro-dropletsand defects in liquid crystal micro-droplets with Δ<0 has
been studied [44], however, its subsequent effects on theresonance properties have not been studied so far. Figure 6(a-c) shows typical elastic distortion in a micro-droplet
when applied electric field is parallel to the direction oflight propagation (Ejjk). The director configuration ismostly radial with a slight azimuthal twist near the central
region that encompasses a radial hedgehog defect. The
structure becomes complex with increasing field and the
distortion from the central region expands towards theboundary (see λ-plate image). It has been suggested thatthe hedgehog defect undergoes a continuous transition into
an escape non-singular line defect with s ¼ 1 [44]. It
appears that the line defect is well within the central region
and no significant or noticeable distortion of the director isobserved very close to the inner boundary wall. The WGM
spectra of a 10.6 µm droplet at two representative fields
namely 0.12 V=μm and 0.56 V=μm are shown in Figure 6

LIQUID CRYSTALS

637

Figure 7. (Colour online) (a) Variation of Q-factor (λ=Δλ) of a few TM modes with applied electric field of an MLC-6608 microdroplet with diameter 10.7 µm dispersed in CYTOP solution. Grating used 300 lines/mm. (b) Variation of FSR with applied electricfield of a few TM modes. Vertically dotted line represents the Freedericksz threshold field.

(d). The resonance intensity decreases slightly with increasing field. The modes above 635 nm shift slightly towards
higher wavelength and below, they shift towards lower
wavelength side.
We measured the Q-factor and FSR at different
fields of a few modes. It is defined as: Q ¼ λ=Δλ,where Δλ is the full-width at half maxima of a mode.
Figure 7(a,b) shows field dependent Q-factor and FSR.
We used a grating of 300 lines/mm (spectral resolution
0.32 nm) to observe and analyse many modes over alarger wave length range. It is observed that Q-factor isabout 1:5  103 and remains almost unchanged withapplied electric field. This is in sharp contrast with theresonance properties of micro-droplets with Δ>0,
where a substantial decrease in Q was reported beyond
Freedericksz threshold field [22]. The Freedericksz
threshold field for MLC-6608 is about 0.3 V/µm. Thismeans that just inside the liquid crystal-CYTOP
boundary where the light is circulating there is noelastic deformation. In other words, the circulating
light is confined within the extrapolation length inside
the interface. This is consistent with the observation(see λ-plate images in Figure 6), where the elastic distortion is mostly confined near the central region.

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J. A. SOFI AND S. DHARA

Figure 8. (Colour online) Optical resonance spectrum recorded by the spectrometer using a high resolution grating of 2400 lines/
mm without any electric field of an MLC-6608 microdroplet in CYTOP solution. Droplet diameter 10.6 µm.

Figure 7(b) shows the variation of FSR with the applied
electric field. It is observed that FSR of the modes isabout 7 nm and is almost independent of the applied
electric field. FSR depends mainly on two parametersnamely; the diameter (D) and the effective refractive
index (neff ) of the droplet. Thus, both the droplet
diameter and the effective refractive index at the interface do not change with the applied electric field.
The CYTOP solution is highly transparent and hence
the absorption is very low [37] and in addition, it has
lower refractive index than PDMS or glycerol or otherpolymers reported so far in WGM resonance studies.
Hence quality factor is expected to be larger. We usedhigh resolution grating (2400 lines/mm) which gives aspectral resolution of 0.021 nm within a small wavelength
range. Figure 8 shows a few highly narrow TM modes of a
10.6 µm droplet. The estimated quality factor of thesemodes is about Q ’ 1:2  104 . It is the highest Q-factor
reported so far in case of liquid crystal micro-droplets andis larger by about 2000 than the previous report [12].

4. Conclusions
In summary, we find that CYTOP solution is one of thebest supporting media for forming stable liquid crystal
micro-droplets, which is very crucial for the successful
realisation of liquid crystal based microresonators. This is
the first optical resonance study on negative dielectricanisotropy liquid crystal micro-droplets. FSR is inversely
proportional to the diameter of the micro-droplets inaccordance with the prediction and, hence, smaller
micro-droplets are of greater importance. The circulating
light is confined within the extrapolation length at theboundary region where the resonant modes are located.
Consequently the quality factor remains unaffected inspiteof elastic distortion in the micro-droplets by the external
electric field. The highest quality factor is attributed to the
low refractive index and high transparency of the supporting medium CYTOP solution. Finally, we showed a new
application of CYTOP solution in liquid crystal based
microresonators with superior performance. The resonance properties, when the applied electric field parallelto the direction of exciting laser beam are not encouraging
for electrical tuning of the resonance. The in-plane electricfield, i.e. the field direction perpendicular to the director is
expected to be more effective but further studies are
required.

Acknowledgments
J.A.S acknowledges UGC for BSR fellowship.

Disclosure statement
No potential conflict of interest was reported by the authors.

Funding
We gratefully acknowledge the support from SERB [EMR/
2015/001566] and DST [DST/SJF/PSA-02/2014-2015].

ORCID
Surajit Dhara

http://orcid.org/0000-0003-3144-0300

References[1] Drzaic PS. Liquid crystals dispersion. Singapore: World
Scientific; 1995.
[2] Prasad PN, Mark JE, Fai TJ. Polymers and otheradvanced materials. Boston, MA: Springer; 1995.

LIQUID CRYSTALS[3] Coates D. Polymer-dispersed liquid crystals, J Mater
Chem. 1995;5:2063.
[4] Loudet JC, Barois P, Poulin P. Colloidal ordering fromphase separation in a liquid-crystalline continuous
phase. Nature. 2000;407:611.
[5] De Gennes PG, Prost J. The physics of liquid crystals.
New York: Oxford University; 1993.
[6] Lavrentovich OD. Topological defects in dispersed
words and worlds around liquid crystals, or liquid crystal drops. Liq Cryst. 1998;24:117.
[7] Porenta T, Ravnik M, Zumer S. Effect of flexoelectricity
and order electricity on defect cores in nematic droplets.
Soft Matter. 2011;7:132.
[8] Zhou Y, Bukusoglu E, Martínez-González JA, et al.
Structural transitions in cholesteric liquid crystal droplets. ACS Nano. 2016;10:6484.
[9] Urbanski M, Reyes CG, Noh J, et al. Liquid crystals in
micron-scale droplets, shells and fibers. J Phys Condens
Matter. 2017;29:133003.
[10] Posnjak G. Copar S and Musevic I.Hidden topologicalconstellations and polyvalent charges in chiral nematic
droplets. Nat Commun. 2017;8:14594.
[11] Yoshioka J, Araoka F. Topology-dependent self-structure
mediation and efficient energy conversion in heat-flux-driven rotors of cholesteric droplets. Nat Commun. 2018;9:432.
[12] Humar M, Ravnik M, Pajk S, et al. Electrically tunable liquid
crystal optical microresonators. Nat Photon. 2009;3:595.
[13] Humar M, Musevic I. 3D microlasers from selfassembled cholesteric liquid-crystal microdroplets. Opt
Express. 2010;18:26995.
[14] Humar M. Liquid-crystal-droplet optical microcavities.
Liq Cryst. 2016;43:1937.
[15] Yang S, Ta VD, Wang Y, et al. Reconfigurable liquid whispering gallery mode microlasers. Sci Rep. 2016;6:27200.
[16] Vahala K. Optical microcavities. Singapore: World
Scientific; 2004.
[17] Arnold S, Holler S, Druger SD. Optical processes in
micro-cavities. In: editors, Chang RK, Campillo AJ.
Advanced series in applied physics. Vol. 3. Singapore:
World Scientfic; 1996.
[18] Humar M, Musevic I. Surfactant sensing based on whispering-gallery-mode lasing in liquid-crystal microdroplets. Opt Express. 2011;19:19836.
[19] Kumar TA, Mohiddon MA, Dutta N, et al. Detection ofphase transitions from the study of whispering gallery
mode resonance in liquid crystal droplets. Appl Phys
Lett. 2015;106:051101.
[20] Zhao L, Wang Y, Li H, et al. Tunable whispering gallery
modes lasing in dye-doped cholesteric liquid crystal
microdroplets. Appl Phys Lett. 2016;109:231906.
[21] Marusa M, Sofi JA, Kvasić I, et al. Magnetic-field tuning ofwhispering gallery mode lasing from ferromagnetic nematic
liquid crystal microdroplets. Opt Express. 2017;25:1073.
[22] Sofi JA, Mohiddon MA, Dutta N, et al. Electrical andthermal tuning of quality factor and free spectral range
of optical resonance of nematic liquid crystal microdroplets. Phys Rev E. 2017;96:022702.
[23] Nie X, Lin YH, Wu ST. Polar anchoring energy measurement of vertically aligned liquid-crystal cells. J Appl
Phys. 2005;98:013516.
[24] Li Jun. Refractive Indices Of Liquid Crystals And Their
Applications In Display And Photonic Devices. 2005.

639

Electronic Theses and Dissertations. 4460. University ofCentral Florida. http://stars.library.ucf.edu/etd/4460[25] Horn RG. Refractive indices and order parameters of
two liquid crystals. J De Physique. 1978;39:105–109.
[26] Li J, CbH W, Gauza S, et al. Refractive Indices of liquid
crystals for display applications. J Disp Technol. 2005;1:1.
[27] Hoyt LF, Buffalo NY . New table of the refractive index
of pure glycerol at 20C. J Ind Eeg Chem. 1934;26:329.
[28] Yamamoto K, Ogawa G. Structure determination of theamorphous perfluorinated homopolymer: poly[perfluoro(4-vinyloxyl-1-butene)]. J Fluorine Chem.
2005;126:1403.
[29] Jeong SM, Araoka F, Machida Y, et al. Enhancement of
normally directed light outcoupling from organic lightemitting diodes using nanoimprinted low-refractiveindex layer. Appl Phys Lett. 2008;92:083307.
[30] Kim JK, Jeong SM, Dhara S, et al. Bistable device using
anchoring transition of nematic liquid crystals. Appl
Phys Lett. 2009;95:063505.
[31] Kumar TA, Takezoe H, Dhara S. Perfluoropolymer as
planar alignment layer for liquid crystal mixtures. Jpn J
Appl Phys. 2011;750:040203.
[32] Kumar TA, Sastry VSS, Ishikawa K, et al. Effect of anelectric field on defects in a nematic liquid crystal withvariable surface anchoring Liq Cryst. 2011;38:971.
[33] Kumar TA, Le KV, Aya S. Anchoring transition in anematic liquid crystal doped with chiral agents. Phase
Transitions. 2012;85:888.
[34] Jampani VSR, Skarabot M, Takezoe H, et al. Laserdriven microflow-induced bistable orientation of anematic liquid crystal in perfluoropolymer-treatedunrubbed cells. Opt Express. 2013;21:724.
[35] Rasna MV, Zuhail KP, Manda R, et al. Discontinuous
anchoring transition and photothermal switching incomposites of liquid crystals and conducting polymer
nanofibers. Phys Rev E. 2014;89: 052503.
[36] Dhara S, Kim JK, Jeong SM, et al. Anchoring transitionsof transversely polar liquid-crystal molecules on perfluoropolymer surfaces. Phys Rev E. 2009;79:060701.
[37] Jeong SM, Shimbo Y, Araoka F, et al. Perfluoropolymer
surface for shock-free homeotropic alignment of smectic liquid crystals. Adv Mater. 2010;22:34.
[38] Sai DV, Kumar TA, Haase W, et al. Effect of smectic shortrange order on the discontinuous anchoring transition innematic liquid crystals. J Chem Phys. 2014;141:044706.
[39] Kumar TA, Sathyanarayana P, Sastry VSS, et al.
Temperature- and electric-field-induced inverse
Freedericksz transition in a nematogen with weak surface anchoring. Phys Rev E. 2010;82:011701.
[40] Arcella V, Colaianna P, Maccone P, et al. A study on a
perfluoropolymer purification and its application tomembrane formation. J Membr Sci. 1999;163:203–209.
[41] Lam CC. Leung PT and Young K. Explicit asymptotic
formulas for the positions, widths, and strengths of resonances in Mie scattering. J Opt Soc Am B. 1992;9:1585.
[42] Scharf T. Polarized light in liquid crystals. New Jersey:
Wiley Online Library; 2006 April.
[43] Si G, Zhao Y, Leong E, et al. Liquid-crystal-enabled active
plasmonics: a review. Materials. 2014;7(2):1296–1317.
[44] Xu F, Kitzerow H-S, Crooker PP. Electric-field effects
on nematic droplets with negative dielectric anisotropy.
Phys Rev A. 1992;46:6535–6540.