We demonstrate efficient coupling to the optical whispering gallery modes (WGMs) of nematic liquid crystal (NLC) microdroplets immersed in an immiscible aqueous environment. An individual NLC microdroplet, confined at the tip of a microcapillary, was coupled via a tapered optical fiber waveguide positioned correctly within its vicinity. Critical coupling of the taper-microdroplet system was facilitated by adjusting the gap between the taper and the microdroplet to change the overlap of the evanescent electromagnetic fields; efficient and controlled power transfer from the taper waveguide to the NLC microdroplet is indeed possible via the proposed technique. We also found that NLC microdroplets can function as highly sensitive thermal sensors: A maximum temperature sensitivity of 267.6 pm/°C and resolution of 7.5 × 10−2 °C were achieved in a 78-μm-diameter NLC microdroplet.
© 2017 Optical Society of America
By virtue of their high optical quality, enhanced optical field, and small modal volume, optical resonators supporting whispering gallery modes (WGMs) have garnered considerable research interest over recent decades [1–4]. They have shown potential application as microlasers as well as biological and chemical sensors [5–11]. The liquid microdroplet represents a unique type of optical resonator that is capable of hosting resonant modes with ultra-high quality (Q) factors . Liquid microdroplets were first explored as optical resonators some 40 years ago and have been researched extensively since then . The lasing emission from microdroplets with various gain media surrounded by air or other immiscible liquids has been explored at length [14–17], suggesting that microdroplets have promising potential application in microbiology [18,19], optical communications , and optofluidics  fields.
Liquid microdroplets are naturally formed resonant cavities which are perfectly spherical in shape and possess exceptionally smooth surfaces . There are two main obstacles preventing the practical utilization of microdroplets: The instability of their position and size during the measurement, and the inability to efficiently couple probe light into them . Many previous researchers have attempted to resolve these problems. Typically, immersing the microdroplet into a liquid medium can prevent it from evaporating and protect it from external contaminants, enhancing its spectral stability. The scattering loss is greatly reduced due to the smoothness of the liquid-liquid interface. Nevertheless, immiscibility in tandem with sufficient refractive index contrast between the microdroplet and the host medium are necessary to ensure optical resonance. In addition, the tapered optical fiber waveguide allows selective phase-matched excitation of individual WGMs and extensive overlap of evanescent electromagnetic fields between the waveguide and the resonator, offering opportunities for efficient coupling . Evanescent coupling from a tapered optical fiber was initially used to couple WGMs inside silica microspheres [23,24] and was first utilized to couple the droplet WGMs ten years ago . It has been shown that the taper-droplet coupling efficiency is boosted by many orders compared to free-space methods.
Microdroplets composed of liquid crystals (LCs), which have large tunability and are readily manufacturable, are commonly exploited as optical microlasers and sensors [17,26,27]. Resonant spectrum shift is detectable with changes in orientational structures within the LC microdroplets, which can be easily regulated by external stimuli such as electric field and temperature. In this paper, we report efficient coupling to the optical WGMs of the LC microdroplets via a tapered optical fiber waveguide. The LC microdroplets were embedded into an immiscible cladding liquid of lower refractive index to support WGM resonance, then the tapered fiber coupler was positioned next to the microdroplets to efficiently couple them. The proposed taper-microdroplet coupling system was also utilized to establish a thermal sensor with a maximum temperature sensitivity up to 267.6 pm/°C, which represents significant potential in regards to future integrated photonic devices.
2. Experimental setups
A tapered optical fiber was used to couple to the microdroplet resonator, as the input beam can be directly launched into the non-tapered portion of the fiber without necessitating a complex setup , as well as the collection of output beam. In addition, the propagation constant in the core of an optical fiber will always be closest to that of the lowest radial mode number of WGMs, which is the most desirable due to the smallest mode volume . Figure 1 shows a schematic diagram of the experimental setup used for detecting the coupling between the tapered optical fiber waveguide and the NLC microdroplet. The tapered fiber was prepared by heat-pull method and had a taper diameter ranging from 1 to 2 μm, as Fig. 2(a) shown the micrographs of the fabricated tapered fiber in different regions. The tapered fiber was glued onto two glass carriers and mounted onto a glass slide with ultraviolet adhesive. The input port of the tapered fiber was connected to a broadband amplified spontaneous emission (ASE) light source (A-0002, wavelength range 1525 to 1570 nm; Hoyatek Co., Ltd.), while the output port connects with an optical spectrum analyzer (OSA) with 0.02 nm resolution for transmission spectrum analysis.
Because adhesion to a stable object is the simplest way to trap a microdroplet, we used a glass capillary microtube [Fig. 2(b)] connected to a pump-controlled microchannel to generate and manipulate the NLC (BHR33200, Bayi Space, China) droplet with the desired size in an immiscible water environment. The microtube was prepared by a technique similar to that used in a previous study . Scanning electron microscope image (Fig. 2(b) inset) revealed that the microtube diameter was approximately 8 μm. To avoid the influence of microtube-microdroplet joint to circulation of WGM inside the microdroplet, we experimentally adjusted the inclination angle of the microtube along the z-axis (see the reference system in Fig. 2(c)) so that the joint was non-coplanar with the coupling plane between the tapered fiber and the microdroplet. The NLC microdroplet as-formed was hung from the microtube’s end instead of connected to it, so changes in microdroplet size caused by small pressure fluctuations in the microtube can be ignored. In short, the proposed technique maintains the symmetrical microdroplet shape required to support WGM resonance.
To induce evanescent coupling between the tapered fiber and the microdroplet, we brought the microtube towards the tapered fiber (negative x-axis direction) as shown in Fig. 2(d); the gap between the microdroplet and taper was controlled by electromechanical 3D X-Y-Z stages with 10 nm resolution. We recorded the transmission spectra and stopped the approach upon observing resonant transmission dips. The micro-manipulation process was observed under a polarizing optical microscope (POM) connected to a CCD camera. For the purposes of our thermal experiments, a heating stage (minimum regulation value 0.1 °C) was placed under the glass slide to provide the required environment for the NLC microdroplet. A thermocouple probe (resolution 0.1 °C) connected to a temperature meter was injected into the deionized water droplet to monitor the environmental temperature.
3. Results and discussion
Micrographs of NLC microdroplets in water are shown in non-polarized light and between crossed polarizers in Figs. 3(a) and 3(b), respectively. The polarized image indicates the radial director configuration within the NLC microdroplet, where the NLC molecules were perpendicularly aligned from the surface to the center of the droplet [27,28]. WGM resonances were clearly observed in the transmission spectrum as the NLC microdroplet approached the tapered fiber waveguide, as shown in the upper portion of Fig. 3(c). The sharp transmission dips indicate the excitation of WGMs inside the NLC microdroplet, at which the light source wavelengths matched the optical modes in the cavity. When the measured free spectral range (FSR) was 10.49 nm, the diameter of the microdroplet was calculated via Chylek’s asymptotic formula  to be 50.8 μm, which is well agreement with the observed diameter of 50 μm.
A close-up image of the spectrum near 1547.6 nm is presented in the lower portion of Fig. 3(c) for Q-factor analysis. The measured full width at half maximum (FWHM) was 0.55 nm, resulting in a Q-factor of 2.8 × 103 for the selected WGM. The optical modes can be characterized by the radial (q), polar (l), and azimuthal (m) mode numbers; we did not observe high order modes (q > 1) in the spectrum but did identify a fundamental mode (q = 1). The mode number l can be simply expressed as l = 2πnr/λ, where n is the refractive index of the microdroplet, r is the radius of the microdroplet, and λ is the resonant wavelength. The wavelengths of the calculated TM modes fit well with the wavelengths of experimental peaks and l counts from 174 to 177, as marked in Fig. 3(c). In addition, by tuning the polarization state of the incident light, the TM and TE polarized WGMs can appear simultaneously in the transmission spectrum, corresponding to different polarization state of the WGMs circulating within the microdroplet.
For a perfect sphere, all the planes in which the light circulates are equivalent, so the modes are degenerated in regards to azimuthal mode number m . Sphere deformation can lead to the lifting of the azimuthal mode degeneracy, however. In any given experiment, the generated microdroplets are never perfect spheres but can be considered spheroids (oblate or prolate). Spheroid deformation was manifested in our transmission spectrum [Fig. 3(c)] as a slight splitting of mode lines.
To further investigate the relationship between azimuthal mode degeneracy and microdroplet deformation, we select two NLC microdroplets coupled by the same tapered fiber waveguide for transmission spectra analysis. Figures 4(a) and 4(b) show the transmission spectra of NLC microdroplets with equal diameters of 103 μm (measured via micrographs). The diameters of the two microdroplets calculated by FSR are 102.6 and 103.9 μm, respectively. We clearly observed splitting of the azimuthal m-modes in reverse directions in the spectra. The positive wavelength shift indicates that the microdroplet is prolate [Fig. 4(c)], while the negative wavelength shift corresponds to an oblate microdroplet [Fig. 4(d)] .
Here, we use eccentricity (e) to characterize the deformation degree of the microdroplet :Fig. 4(c)] and oblate microdroplet [Fig. 4(d)] were 1.12 and 1.16 nm, respectively. Assuming a perfect alignment between the taper and the microdroplet (i.e., where the tapered fiber aligns perfectly to the equatorial plane of the microdroplet), only the even azimuthal modes were excited; therefore, the measured mode separations were actually equal to 2Δλ [12,25]. Using n = 1.657 for the extraordinary index of the NLC (with TM-polarized modes); r1 = 51.3 μm (prolate microdroplet) and r2 = 51.95 μm (oblate microdroplet); Δλ1 = 0.56 nm and Δλ2 = 0.58 nm for mode splitting separations; and λ1 = 1538.08 nm and λ2 = 1546.16 nm for resonant wavelengths, we estimated that the eccentricities of the prolate and oblate microdroplets are e1 = 0.126 and e2 = 0.131.
In a taper-microdroplet coupling system, overlap of the evanescent electromagnetic fields and phase matching are two key factors in realizing efficient coupling [25,31]. The evanescent fields emanated from both the microdroplet resonator and the tapered optical fiber waveguide decrease exponentially into the surrounding medium. Therefore, the gap between the taper and the microdroplet must be precisely controlled to ensure the evanescent fields overlap, which is on the order of the penetration depth d = λ / (2π (n2 D – n2 W)1/2) , where nD and nw are the refractive indices of the microdroplet and water, respectively. Under our experimental conditions, the calculated d was about 250 nm.
The critical coupling of taper-microsphere takes place at an optimum taper-microsphere distance, where the resulting transmission at the output of the waveguide has zero resonance . To determine this critical point accurately, we experimentally measured the transmitted optical power for fundamental WGM (q = 1, l = m) in the NLC microdroplets at various tapered fiber positions in the vicinity of the microdroplet. The results indicated that the coupling between the taper and the microdroplet can be divided into three regimes, which are discussed separately below.
Figure 5(a) shows normalized transmitted optical power as a function of taper-microdroplet distance; the transmission without coupling between the tapered fiber and the microdroplet is about –15 dB, and all transmission intensities with coupling are less than –35 dB and thus normalized in the range from –15 to –35 dB. The minimum transmission (nearly zero) was observed at a distance of about 200 nm, corresponding to the critical-coupled regime of the taper-microdroplet system. At this critical point, there was intrinsic loss of the microdroplet resonator equal to the waveguide coupling loss; power in the waveguide nearly completely transferred into the microdroplet. By comparison, the experimental value for critical coupling distance (200 nm) was close to the calculated penetration depth (250 nm) of the evanescent field. At distances smaller than the critical coupling distance (< 200 nm, Fig. 5(a)), the transmission exceeded zero; at distance of zero, the transmission was nearly 20%. This indicates that the taper-microdroplet system was pushed into the over-coupled regime where light coupled out of the microdroplet was returned to the waveguide . In another NLC microdroplet with a different diameter [Fig. 5(b)], over-coupled transmission of nearly 40% was observed and the critical point was identified at a distance of about 250 nm. At distances greater than that of the critical coupling (200 ~500 nm, Fig. 5(a)), overlapping between the evanescent fields of the taper and the microdroplet was relatively weak and the coupling system was in an under-coupled regime . In this regime, the coupling efficiency (or coupling coefficient) increased as taper-microdroplet distance decreased, thus decreasing the transmission. The transmission spectra of the coupling system in the above three regimes are shown in the insets of Fig. 5. In a word, the results shown in Fig. 5 indicate that efficient and controlled power transfer between the tapered fiber waveguide and the NLC microdroplet is possible via the proposed technique.
The refractive index of the LC is well known for its significant response to temperature , making the NLC microdroplets promising for thermal sensing applications. In this study, we demonstrated the feasibility and effectiveness of NLC microdroplets coupled by tapered fiber waveguide as thermal sensors. An increasing temperature was applied to individual NLC microdroplet with a diameter of 78 μm and the change in transmission spectrum was recorded as shown in Fig. 6(a). Clearly, the resonance dip (corresponds to TM1 264 mode) exhibited a blue-shift as temperature increased from 33 to 39 °C in 2°C steps. This was expected, as the extraordinary refractive index of the NLC decreases with increasing temperature . The modes correspond to TM polarization which is associated with extraordinary refractive index (i.e., the electric field of light is perpendicular to the microdroplet’s surface, so along the director and experiences extraordinary refractive index) . Since this index decreases with increasing temperature, the wavelength also decreases to preserve the condition for WGM resonance (the resonant condition 2πnr = lλ).
The undisturbed spectral profiles (Q-factor) with increasing temperature signified the robustness of the proposed microdroplet-based sensor. Figure 6(b) shows the resonant wavelengths of full four resonance dips (all TM modes with radial mode number 1 and polar mode numbers 261-264) as a function of temperature from 31 to 41°C. The resonance wavelengths linearly decreased as temperature increased; the maximum temperature sensitivity reached 267.6 pm/°C. Under a resonant mode with Q of 3 × 103, we can easily locate the resonance to Δλ / 20 , corresponding to the spectral resolution of our system, which is about 0.02 nm. We estimated the resolution of the NLC microdroplet-based temperature sensor to be 7.5 × 10−2 °C accordingly. This temperature resolution is slightly lower than other resonance-based solid temperature micro-sensors [35,36], while the sensitivity is comparable with (or better than) most reported temperature micro-sensors [37–39]. Absorption and scattering in the NLC microdroplets as well as surface roughness of the microdroplets can substantially reduce the Q-factor and thus enlarge the temperature resolution. In view of practical application of the proposed thermal sensor, nonresonant insertion loss was measured by comparing the transmission with and without the tapered fiber coupling to the microdroplet. The minimum insertion loss (reduction in transmission intensity) was observed to be 1.31 dB.
In conclusion, we presented an efficient technique for coupling to the optical WGMs of the NLC microdroplets embedded in water. The microdroplet was coupled by a tapered optical fiber waveguide, which enable efficient coupling to the WGMs by controlling overlap of the evanescent fields and phase matching between the taper and the microdroplet. The natural spheroid deformation of the NLC microdroplets was carefully analyzed by calculating the eccentricity. We found that the coupling regimes of the taper-microdroplet system could be changed by adjusting the coupling gap. This means that efficient and controlled power transfer from the taper waveguide to the NLC microdroplet is possible. We also demonstrated the practicability of the proposed, taper-coupled NLC microdroplet as a novel thermal sensor. A maximum temperature sensitivity of 267.6 pm/°C and resolution of 7.5 × 10−2 °C were achieved in a 78-μm-diameter NLC microdroplet. The high sensitivity, facile fabrication, and low cost of these materials make the NLC microdroplet a promising candidate for thermal sensing applications in future integrated photonic devices.
National Natural Science Foundation of China (Grants No. 61605031, 61422505, 61635007). Program for New Century Excellent Talents in University (NCET-12-0623). National Key Scientific Instrument and Equipment Development Project (No. 2013YQ040815). Postdoctoral Science Foundation of China (No. 2016M591511). Joint Research Fund in Astronomy Under Cooperative Agreement Between the National Natural Science Foundation of China (NSFC) and Chinese Academy of Sciences (CAS) (No. U1531102). Fundamental Research Funds for the Central Universities.
References and links
2. H. Li, S. Hao, L. Qiang, J. Li, and Y. Zhang, “Observation of whispering gallery modes in microtube-microspheres system,” Appl. Phys. Lett. 102(23), 231908 (2013). [CrossRef]
8. A. M. Armani, R. P. Kulkarni, S. E. Fraser, R. C. Flagan, and K. J. Vahala, “Label-free, single-molecule detection with optical microcavities,” Science 317(5839), 783–787 (2007). [CrossRef] [PubMed]
9. M. A. Santiago-Cordoba, S. V. Boriskina, F. Vollmer, and M. C. Demirel, “Nanoparticle-based protein detection by optical shift of a resonant microcavity,” Appl. Phys. Lett. 99(7), 073701 (2011). [CrossRef]
12. A. Jonáš, Y. Karadag, M. Mestre, and A. Kiraz, “Probing of ultrahigh optical Q-factors of individual liquid microdroplets on superhydrophobic surfaces using tapered optical fiber waveguides,” J. Opt. Soc. Am. B 29(12), 3240–3247 (2012). [CrossRef]
13. A. Ashkin and J. M. Dziedzic, “Observation of resonances in the radiation pressure on dielectric spheres,” Phys. Rev. Lett. 38(23), 1351–1354 (1977). [CrossRef]
14. H.-M. Tzeng, K. F. Wall, M. B. Long, and R. K. Chang, “Laser emission from individual droplets at wavelengths corresponding to morphology-dependent resonances,” Opt. Lett. 9(11), 499–501 (1984). [CrossRef] [PubMed]
19. A. Jonáš, M. Aas, Y. Karadag, S. Manioğlu, S. Anand, D. McGloin, H. Bayraktar, and A. Kiraz, “In vitro and in vivo biolasing of fluorescent proteins suspended in liquid microdroplet cavities,” Lab Chip 14(16), 3093–3100 (2014). [CrossRef] [PubMed]
20. A. Kiraz, A. Sennaroglu, S. Doğanay, M. A. Dündar, A. Kurt, H. Kalaycıoğlu, and A. L. Demirel, “Lasing from single, stationary, dye-doped glycerol/water microdroplets located on a superhydrophobic surface,” Opt. Commun. 276(1), 145–148 (2007). [CrossRef]
21. S. K. Y. Tang, Z. Li, A. R. Abate, J. J. Agresti, D. A. Weitz, D. Psaltis, and G. M. Whitesides, “A multi-color fast-switching microfluidic droplet dye laser,” Lab Chip 9(19), 2767–2771 (2009). [CrossRef] [PubMed]
22. J. C. Knight, G. Cheung, F. Jacques, and T. A. Birks, “Phase-matched excitation of whispering-gallery-mode,” Opt. Lett. 22(15), 1129-1131 (1997).
24. M. Cai, O. Painter, and K. J. Vahala, “Observation of critical coupling in a fiber taper to a silica-microsphere whispering-gallery mode system,” Phys. Rev. Lett. 85(1), 74–77 (2000). [CrossRef] [PubMed]
25. M. Hossein-Zadeh and K. J. Vahala, “Fiber-taper coupling to Whispering-Gallery modes of fluidic resonators embedded in a liquid medium,” Opt. Express 14(22), 10800–10810 (2006). [CrossRef] [PubMed]
27. M. Humar, M. Ravnik, S. Pajk, and I. Muševič, “Electrically tunable liquid crystal optical microresonators,” Nat. Photonics 3(10), 595–600 (2009). [CrossRef]
28. V. S. R. Jampani, M. Humar, and I. Muševič, “Resonant transport of light from planar polymer waveguide into liquid-crystal microcavity,” Opt. Express 21(18), 20506–20516 (2013). [CrossRef] [PubMed]
29. P. Chýlek, “Partial wave resonances and ripple structure in Mie normalized extinction cross section,” J. Opt. Soc. Am. 66(3), 285–287 (1976). [CrossRef]
30. M. Humar, “Liquid-crystal-droplet optical microcavities,” Liq. Cryst. (to be published).
31. M. J. Humphrey, E. Dale, A. T. Rosenberger, and D. K. Bandy, “Calculation of optimal fiber radius and whispering-gallery mode spectra for a fiber-coupled microsphere,” Opt. Commun. 271(1), 124–131 (2007). [CrossRef]
32. J. Li and S.-T. Wu, “Extended Cauchy equations for the refractive indices of liquid crystals,” J. Appl. Phys. 95(3), 896–901 (2004). [CrossRef]
33. J. Li, S. Gauza, and S.-T. Wu, “Temperature effect on liquid crystal refractive indices,” J. Appl. Phys. 96(1), 19–24 (2004). [CrossRef]
34. N. M. Hanumegowda, C. J. Stica, B. C. Patel, I. M. White, and X. Fan, “Refractometric sensors based on microsphere resonators,” Appl. Phys. Lett. 87(20), 201107 (2005). [CrossRef]
35. C.-H. Dong, L. He, Y.-F. Xiao, V. R. Gaddam, S. K. Ozdemir, Z.-F. Han, G.-C. Guo, and L. Yang, “Fabrication of high-Q polydimethylsiloxane optical microspheres for thermal sensing,” Appl. Phys. Lett. 94(23), 231119 (2009). [CrossRef]
36. B.-B. Li, Q.-Y. Wang, Y.-F. Xiao, X.-F. Jiang, Y. Li, L. Xiao, and Q. Gong, “On chip, high-sensitivity thermal sensor based on high-Q polydimethylsiloxane-coated microresonator,” Appl. Phys. Lett. 96(25), 251109 (2010). [CrossRef]
37. S. H. Nam and S. Yin, “High-temperature sensing using whispering gallery mode resonance in bent optical fibers,” IEEE Photonics Technol. Lett. 17(11), 2391–2393 (2005). [CrossRef]
38. M. S. Nawrocka, T. Liu, X. Wang, and R. R. Panepucci, “Tunable silicon microring resonator with wide spectral range,” Appl. Phys. Lett. 89(7), 071110 (2006). [CrossRef]
39. L. L. Martín, C. Pérez-Rodríguez, P. Haro-González, and I. R. Martín, “Whispering gallery modes in a glass microsphere as a function of temperature,” Opt. Express 19(25), 25792–25798 (2011). [CrossRef] [PubMed]