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Liquid-Crystal Microdroplets As Optical Microresonators and Lasers

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Liquid-Crystal Microdroplets As Optical Microresonators and Lasers LIQUID-CRYSTAL MICRODROPLETS AS OPTICAL MICRORESONATORS AND LASERS MatjaˇzHumar Doctoral Dissertation JoˇzefStefan International Postgraduate School Ljubljana, Slovenia, February 2012 Evaluation Board: Prof. Boˇstjan Zalar, Chairman, Joˇzef Stefan Institute, Ljubljana, Slovenia Asst. Prof. Miha Skarabotˇ , Member, Joˇzef Stefan Institute, Ljubljana, Slovenia Prof. Slobodan Zumerˇ , Member, University of Ljubljana, Ljubljana, Slovenia MatjaˇzHumar LIQUID-CRYSTAL MICRODROPLETS AS OPTICAL MICRORESONATORS AND LASERS Doctoral Dissertation TEKOCEKRISTALNEˇ MIKROKAPLJICE KOT OPTICNIˇ MIKRORESONATORJI IN LASERJI Doktorska disertacija Supervisor: Prof. Igor Muˇseviˇc Ljubljana, Slovenia, February 2012 Poets say science takes away from the beauty of the stars - mere globs of gas atoms. I, too, can see the stars on a desert night, and feel them. But do I see less or more? Richard P. Feynman VII Index Abstract XI Povzetek XII Abbreviations XIII 1 Introduction 1 1.1 Whispering-gallery modes . 1 1.1.1 Tunable WGMs . 2 1.1.2 WGM microcavities for biosensing . 3 1.1.3 WGM microcavities for filters and optical communications . 4 1.1.4 WGM ultralow-threshold microlasers . 4 1.1.5 Coupled WGM cavities . 4 1.2 Circular and spherical Bragg microcavities . 5 1.3 Liquid crystals . 6 1.3.1 Polymer dispersed liquid crystals . 6 1.3.2 Lasing in cholesteric liquid crystals . 7 1.3.3 Liquid crystal biosensors . 8 1.4 Goal of the thesis . 10 2 Theoretical background 13 2.1 Optical microcavities . 13 2.1.1 Quality factor . 13 2.1.2 Purcell effect . 14 2.2 Theory of WGMs . 15 2.2.1 WGM frequencies in an isotropic sphere . 15 2.2.2 Approximate solutions . 18 2.2.3 Non-spherical whispering-gallery cavity . 19 2.2.4 WGM frequencies in an anisotropic sphere . 20 2.2.5 Excitation of WGMs . 21 2.2.5.1 Evanescent field coupling . 21 2.2.5.2 Fluorescence . 21 2.3 Theory of lasing . 21 2.4 Bragg microcavities . 23 2.5 Liquid crystals . 25 2.5.1 Introduction to liquid crystals . 25 2.5.1.1 Nematic liquid crystals . 25 2.5.1.2 Order parameter . 26 2.5.1.3 Elastic properties of liquid crystals . 26 2.5.1.4 Electric field effect in liquid crystals . 26 2.5.1.5 Change of the refractive indices of liquid crystals by temper- ature . 27 VIII INDEX 2.5.2 Surface anchoring of liquid crystals . 28 2.5.2.1 Anchoring on a anisotropic surface . 28 2.5.2.2 Anchoring on an isotropic surface . 29 2.5.3 Cholesteric liquid crystals . 29 2.5.3.1 Position and width of the photonic bandgap . 30 3 Materials and methods 31 3.1 Liquid crystals . 31 3.2 Dyes . 31 3.3 Carrying medium . 32 3.4 Making dispersion of LC droplets . 33 3.5 Optical setup . 34 3.6 Microfluidic setup for chemical sensing . 37 3.7 Setup for angular measurements of the 3D laser emission . 38 3.8 Setup for 3D laser polarization measurements . 39 3.9 Sample preparation and setup for strain tuning . 40 3.10 Sample preparation for electric field tuning . 41 3.11 Preparation of cholesteric 3D lasers . 41 4 Experimental results and discussion 43 4.1 Dispersion of liquid-crystal droplets . 43 4.2 Whispering-gallery modes in nematic liquid-crystal droplets . 46 4.2.1 Polarization properties . 48 4.2.2 Fitting the WGMs . 51 4.2.3 Q-factor . 51 4.3 Electric field tuning of WGMs in nematic droplets . 53 4.3.1 Director distortion under electric field . 53 4.3.2 WGMs under electric field . 53 4.3.3 Tuning of multiple droplets . 57 4.3.4 In-plane electric field . 57 4.3.5 Electric field with droplets containing particles . 58 4.4 Temperature tuning . 61 4.5 Optical tuning . 65 4.6 Strain tuning . 69 4.7 Chemical sensors based on WGMs in LC droplets . 71 4.7.1 LC droplets at different surfactant concentrations . 71 4.7.2 Lasing in LC droplets . 72 4.7.3 Sensing characteristics . 74 4.7.4 Sensing in non-lasing regime . 76 4.8 3D laser . 77 4.8.1 Cholesteric liquid-crystal droplets . 77 4.8.2 Simulation of the CLC droplet configuration . 78 4.8.3 Lasing characterization . 81 4.8.4 Polarization . 85 4.8.5 Angle dependance . 86 4.8.6 Tunability . 86 4.8.7 Lasing of higher Bragg modes . 87 4.8.8 Polymerizable 3D laser . 90 4.8.9 Particles incorporated into a CLC droplet . 93 5 Conclusions 95 6 Acknowledgements 99 INDEX IX 7 Zahvala 101 8 References 103 Index of Figures 111 Index of Tables 113 Appendix A: Further observations 115 Lasing and switching in ferroelectric LCs . 115 Photonic molecules . 117 Measuring spectral width of WGMs using a Fabriy-Perot interferometer . 117 Pulse length of the 3D laser . 118 Appendix B: Bibliography 121 X INDEX XI Abstract This thesis investigates the use of single liquid-crystal droplets as optical microresonators and lasers. We have shown that liquid-crystal droplets can support a number of different optical modes that can be excited by introducing a fluorescent dye in the liquid crystal material and using an external excitation source of light. These optical modes are in general different from the ones in isotropic materials, because of birefringence of the liquid crystals and specific configurations of the director field within the droplet. The droplets were prepared just by mechanical mixing of a liquid crystal material and another non-miscible fluid. The director structure in the droplets self assembles to minimize the elastic energy. To measure the optical properties of the microresonators an optical setup was built that includes a pulsed laser for excitation and a spectrophotometer for spectral analysis. Regarding the type of liquid crystalline material used for the droplets and the type of optical modes supported in the droplets, the thesis is basically divided into two parts. In the first part, nematic liquid crystal is used to make the droplets. It has been shown that the nematic droplets confine light by total internal reflection and therefore support whispering-gallery modes. At higher peak intensities of the pump laser, low threshold mul- timode lasing has been achieved. The optical modes were tuned by electric field, temperature and mechanical deformation. In the case of applying electric field, the nematic director ori- entation changes locally, so that the circulating light sees a change in the refractive index. On the other hand, by changing the temperature only the order parameter is altered, which results in the change of both ordinary and extraordinary refractive indices. In the case of mechanical deformation, only geometrical path length is changed with the applied strain, like it would happen also in an isotropic droplet. It has been shown that the response to electric field and temperature is much larger than reported before in the literature for other materials. By applying just an electric field of few V=µm or changing the temperature by few ◦C, the modes shift by more than 10 nm in visible light. By using a nematic droplet floating in water, also a chemical sensor was demonstrated. The surfactant molecules, which concentration we want to measure, adsorp to the surface of the liquid-crystal droplet and change the anchoring and therefore also the director configuration in the droplet. This re- sults in a change of the optical properties of the droplet and therefore the frequencies of the optical modes. The spectrum of light captured from such a droplet serves as an indicator of the presence of the surfactant in the surrounding water. In the second part of the thesis, cholesteric liquid crystals with selective reflection in visible light were used to make the droplets. The cholesteric liquid crystal in the droplet self assembles so that the helical axis is pointing from the center in all the directions to the surface of the droplet. The structure is acting as a spherical Bragg onion microcavity with periodic modulation of the refractive index that confines the light into the center of the droplet. By having a fluorescent dye in the LC and illuminating the droplet by an external pulsed laser, the droplet starts to emit laser light in all the directions. In this way we have made a 3D laser, a coherent isotropic point source of light. The spherical cholesteric laser is one of the first lasers emitting in all the directions and also one of the easiest lasers to make in general. The laser is also highly tunable by changing the temperature. XII Povzetek Doktorsko delo obravnava uporabo posameznih tekoˇcekristalnih kapljic za optiˇcne mikrore- sonatorje in laserje. Pokazali smo, da so v tekoˇcekristalnih kapljicah moˇzni ˇstevilni optiˇcni nihajni naˇcini, ki jih vzbudimo s pomoˇcjo zunanjega vira svetlobe in fluorescentnega barvila razporejenega v tekoˇcem kristalu. Optiˇcni nihajni naˇcini v kapljicah tekoˇcega kristala so v sploˇsnem drugaˇcni od tistih v izotropnih snoveh. Razlog je dvolomnost tekoˇcih kristalov in posebne ureditve tekoˇcekrstalnega direktorja znotraj kapljice. Kapljice smo pripravili z enostavnim mehanskim meˇsanjem tekoˇcega kristala in druge tekoˇcine v kateri tekoˇcikristal ni topen. Struktura direktorja se v posameznih kapljicah uredi tako, da minimizira elastiˇcno energijo. Za namene prouˇcevanja optiˇcnih lastnosti kapljic, smo sestavili optiˇcni sistem, ki vkljuˇcuje pulzni laser za vzbujanje kapljic in spektrofotometer za spektralno analizo. Glede na uporabljeno vrsto tekoˇcega kristala in na tip optiˇcnih naˇcinov v kapljicah, je doktorska disertacija razdeljena na dva dela. V prvem delu smo kot material za pripravo kapljic uporabili nematski tekoˇcikristal. Pokazali smo, da zaradi totalnega notranjega odboja, nematske kapljice zadrˇzujejo v svoji notranjosti svetlobo in zato v njih obstajajo tako imenovani whispering gallery nihajni na- ˇcini. Pokazali smo tudi, da ob vzbujanju z viˇsjo intenziteto, ˇzepri zelo nizkem pragu, kapljice priˇcnejo oddajati veˇcrodovno lasersko svetlobo.
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