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Optically pumped mirrorless lasing. 
A Review. 
Part II. Lasing in photonic crystals and microcavities

Dudok T. H. and Nastishin Yu. A.

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Abstract. This article is a second part of the review on optically pumped mirrorless lasing. Consideration of random lasing presented in the first part [Nastishin Yu A and Dudok T H, 2013. Ukr. J. Phys. Opt.] is now followed by analysis of the literature on the lasing in photonic structures, which is mainly focussed on dye-doped cholesteric liquid crystals and microcavities, including liquid-crystal microdroplets

Keywords: mirrorless lasing, mirrorless lasers, photonic bandgap edge lasing, dye-doped cholesteric liquid crystals, liquid crystal lasers, whispering-gallery modes, optical microcavities

PACS: 42.55.Mv, 42.55.Sa, 42.55.Tv, 42.70.Qs, 61.30.-v, 77.84.Nh, 78.60.Lc
UDC: 535.37+535.35+681.7.069.24+52-626
Ukr. J. Phys. Opt. 15 47-67
doi: 10.3116/16091833/15/2/47/2014
Received: 31.01.2014

Анотація. Ця стаття є другою частиною огляду про бездзеркальну лазерну генерацію з оптичним нагнітанням. Розгляд випадкової лазерної генерації, представлений у першій частині огляду [Nastishin Yu A and Dudok T H, 2013. Ukr. J. Phys. Opt.], тут продовжено аналізом літератури з генерації фотонними структурами, зокрема холестеричними рідкими кристалами з домішками барвника і мікрорезонаторами з включенням мікрокрапель рідких кристалів.

REFERENCES
  1. Purcell E M, 1946. Spontaneous emission probability at radio frequencies. Phys. Rev., Proc. Amer. Phys. Soc. Abstract B10. 69: 674–702.
  2. Nastishin Yu A and Dudok T H, 2013. Optically pumped mirrorless lasing. A review. Part I. Random lasing. Ukr. J. Phys. Opt. 14: 146–170. doi:10.3116/16091833/14/3/146/2013
  3. Stokes G G, 1885. On a remarkable phenomenon of crystalline reflection. Proc. Roy. Soc. 26: 174–186.
  4. Rayleigh J W S, 1888. On the remarkable phenomenon of crystalline reflexion described by Prof. Stokes. Phil. Mag. 26: 256265.
  5. Kleman M, Lavrentovich O D and Nastishin Yu A, Dislocation and disclination in mesomorphic phases, Vol. 12, in 'Dislocations in Solids', Ed. by F R N Nabarro and J P Hirth, Elsevier, 147–271 (2004). doi:10.1016/S1572-4859(05)80005-1
  6. Kleman M, Meyer C and Nastishin Yu A, 2006. Imperfections in focal conic domains: the role of dislocations. Phil. Mag. 86: 4439–4458. doi:10.1080/14786430600724496
  7. De Gennes P G and Prost J, The physics of liquid crystals, 2nd Ed. Oxford: Clarendon Press (1993).
  8. Kogelnik H and Shank C V, 1971. Stimulated emission in a periodic structure. Appl. Phys. Lett. 18: 152–154. doi:10.1063/1.1653605
  9. Shank C V, Bjorkholm J E and Kogelnik H, 1971. Tunable distributed feedback dye laser. Appl. Phys. Lett. 18: 395–396. doi:10.1063/1.1653714
  10. Kogelnik H and Shank C V, 1972. Coupled wave theory of distributed feedback lasers. J. Appl. Phys. 43: 2327–2335. doi:10.1063/1.1661499
  11. Yablonovitch E, 1987. Inhibited spontaneous emission in solid-state physics and electronics. Phys, Rev. Lett. 58: 2059–2062. doi:10.1103/PhysRevLett.58.2059
  12. John S, 1984. Electromagnetic absorption in a disordered medium near a photon mobility edge. Phys. Rev. Lett. 53: 2169–2172. doi:10.1103/PhysRevLett.53.2169
  13. John S, 1987. Strong localization of photons in certain disordered dielectric superlattices. Phys. Rev. Lett. 58: 2486–2489. doi:10.1103/PhysRevLett.58.2486
  14. John S, 1991. Localization of light. Phys. Today. 44: 32–40. doi:10.1063/1.881300
  15. Yablonovitch E, 2001. Photonic crystals: Semiconductors of light. Scientific American. 285: 47–55. doi:10.1038/scientificamerican1201-46
  16. Dowling J P, Scalora M, Bloemer M J and Bowden Ch M. 1994. The photonic band edge laser: A new approach to gain enhancement. J. Appl. Phys. 75: 1896–1899.
  17. John S and Quang T, 1991. Localization of superradiance near a photonic band gap. Phys. Rev. Lett. 74: 3419–3422. doi:10.1103/PhysRevLett.74.3419
  18. Baba T, 2008. Slow light in photonic crystals. Nature Photonics. 2: 465–473. doi:10.1038/nphoton.2008.146
  19. Megens M, Wijnhoven J E G J, Lagendijk Ad and Vos W L, 1999. Light sources inside photonic crystals. J. Opt. Soc. Amer. B. 16: 1403–1408. doi:10.1364/JOSAB.16.001403
  20. Bulu I, Caglayan H and Ozbay E, 2003. Radiation properties of sources inside photonic crystals. Phys. Rev. B. 67: 205103–7. doi:10.1103/PhysRevB.67.205103
  21. Wu S–T and Fuh A Y–G, 2005. Lasing in photonic crystals based on dye-doped holographic polymer-dispersed liquid crystal reflection gratings. Jpn. J. Appl. Phys. 44: 977–980. doi:10.1143/JJAP.44.977
  22. Woltman S J and Crawford G P, 2007. Patterned liquid-crystal laser film for multi-dimensional multi-color emissive film technology. J. SID. 15/8: 559–564.
  23. Jakubiak R, Natarajan L V, Tondiglia V, He G S, Prasad P N, Bunning T J and Vaia R A, 2004. Electrically switchable lasing from pyrromethene 597 embedded holographic-polymer dis-persed liquid crystals. Appl. Phys. Lett. 85: 6095–6097. doi:10.1063/1.1839282
  24. Strangi G, Barna V, Caputo R, De Luca A, Versace C, Scaramuzza N, Umeton C, Bartolino R and Price G N, 2005. Color-tunable organic microcavity laser array using distributed feedback. Phys. Rev. Lett. 94: 063903–4. doi:10.1103/PhysRevLett.94.063903
  25. Liu N, Guo H, Fu L, Kaiser S, Schweizer H and Giessen H, 2008. Three-dimensional photonic metamaterials at optical frequencies. Nature. 7: 31–37. doi:10.1038/nmat2072
  26. Kobayashi Ch, Yamamoto J and Takanishi Y, 2012. Photonic effect in a hyper-swollen lyo-tropic lamellar phase. J. Appl. Phys. 112: 013531. doi:10.1063/1.4734001
  27. de Vries Hl, 1951. Rotatory power and other optical properties of certain liquid crystals. Acta Cryst. 4: 219–226. doi:10.1107/S0365110X51000751
  28. Schmidtke J and Stille W, 2003. Fluorescence of a dye-doped cholesteric liquid crystal film in the region of the stop band: theory and experiment. Eur. Phys. J. B. 31: 179–194. doi:10.1140/epjb/e2003-00022-x
  29. Ozaki M, Kasano M, Ganzke D, Haase W and Yoshino K, 2002. Mirrorless lasing in dye-doped ferroelectric liquid crystal. Adv. Mater. 14: 306–309. doi:10.1002/1521-4095(20020219)14:4<306::AID-ADMA306>3.0.CO;2-1
  30. Cao W, Munoz A, Palffy-Muhoray P and Taheri B, 2002. Lasing in a three-dimensional photonic crystal of the liquid crystal blue phase II. Nature. 1: 111–113. doi:10.1038/nmat727
  31. Yokoyama S, Mashiko S, Kikuchi H, Uchida K and Nagamura T, 2006. Laser emission from a polymer-stabilized liquid crystal phase. Adv. Mater. 18: 48–51. doi:10.1002/adma.200501355
  32. Coles H J, Morris S M, Ford A D, Hands P J W and Wilkinson T D. Red-green-blue 2D tuneable liquid crystal laser devices. Proc. SPIE. 7414: 741402–21. doi:10.1117/12.831230
  33. Pansu B, Nastishin Y, Imperor-Clerc M, Veber M and Nguyen H T, 2004. New Investigations on the tetragonal liquid crystalline phase or SmQ. Eur. Phys. J. E. 15: 225–230. doi:10.1140/epje/i2004-10051-y
  34. Ruan L Z, Sambles J R and Stewart I W, 2003. Self-organized periodic photonic structure in a nonchiral liquid crystal. Phys. Rev. Lett. 91: 033901–4. doi:10.1103/PhysRevLett.91.033901
  35. Pishnyak O P, Nastishin Yu A and Lavrentovich O D, 2004. Comment on 'Self-organized periodic photonic structure in a nonchiral liquid crystal'. Phys. Rev. Lett. 93: 109401–1. doi:10.1103/PhysRevLett.93.109401
  36. Lydon J, 2011. Chromonic liquid crystalline phases. Liq. Cryst. 38: 16631681. doi:10.1080/02678292.2011.614720
  37. Nastishin Yu A, Liu H, Schneider T, Nazarenko V, Vasyuta R, Shiyanovskii S V and Lavrentovich O D, 2005. Optical characterization of the nematic lyotropic chromonic liquid crystals: light absorption, birefringence, and scalar order parameter. Phys. Rev. E. 72: 041711–14. doi:10.1103/PhysRevE.72.041711
  38. Kobayashi T, Ed., J-aggregates. Singapore: World Scientific (1996). doi:10.1142/3168
  39. Melnikau D, Savateeva D, Chuvilin A, Hillenbrand R and Rakovich Yu P, 2011. Whispering gallery mode resonators with J-aggregates. Opt. Express. 19: 22280–22291. doi:10.1364/OE.19.022280
  40. Fofang N T, Park T–H, Neumann O, Mirin N A, Nordlander P and Halas N J, 2008. Plexcitonic nanoparticles: plasmon-exciton coupling in nanoshell-J-aggregate complexes. Nano Lett. 8: 3481–3487. doi:10.1021/nl8024278
  41. Goldberg L S and Shnur J M, 1973. Tunable internal-feedback liquid. U.S. Pat. No 3,771,065.
  42. Kukhtarev N V, 1978. Cholesteric liquid crystal laser with distributed feedback. Sov. J. Quantum Electron. 8: 774–776. doi:10.1070/QE1978v008n06ABEH010397
  43. Il'chishin I P, Tikhonov E A, Tishchenko V G and Shpak T M, 1981. Generation of tunable radiation by impurity cholesteric liquid crystals. JETP Lett. 32: 24–27.
  44. Ilchishin I P and Vakhnin A Yu, 1995. Detecting of the structure distortion of cholesteric liquid crystal using the generation characteristics of the distributed feedback laser based on it. Mol. Cryst. Liq. Cryst. 265: 687–697. doi:10.1080/10587259508041736
  45. Kopp V I, Fan B, Vithana H K M and Genack A Z. 1998. Low-threshold lasing at the edge of a photonic stop band in cholesteric liquid crystals. Opt. Lett. 23: 1707–1709. doi:10.1364/OL.23.001707
  46. Taheri B, Munoz A F, Palffy-Muhoray P and Twieg R, 2001. Low threshold lasing in cholesteric liquid crystals. Mol. Cryst. Liq. Cryst. 358: 73–82. doi:10.1080/10587250108028271
  47. Munoz A F, Palffy-Muhoray P and Taheri B, 2001. Ultraviolet lasing in cholesteric liquid crystals. Opt. Lett. 26: 804–804. doi:10.1364/OL.26.000804
  48. Ford A D, Moris S M and Coles H J, 2006. Photonics and lasing in liquid crystals. Mater. Today. 9: 36–42. doi:10.1016/S1369-7021(06)71574-7
  49. Coles H and Morris S, 2010. Liquid-crystal lasers. Nature Photonics. 4: 676–685. doi:10.1038/nphoton.2010.184
  50. Palto S P, 2006. Lasing in liquid crystal thin films. JETP. 103: 472–479. doi:10.1134/S1063776106090172
  51. Kopp V I, Zhang Zh-Q and Genack A Z, 2003. Lasing in chiral photonic structures. Progr. Quant. Electron. 27: 369416. doi:10.1016/S0079-6727(03)00003-X
  52. Fuh A Y–G, Lin T–H, Liu J–H and Wu F–C, 2004. Lasing in chiral photonic liquid crystals and associated frequency tuning. Opt. Express. 12: 1857–1863. doi:10.1364/OPEX.12.001857
  53. Palto S P, Shtykov N M, Umansky B A, Barnik M I and Blinov L M, 2006. General properties of lasing effect in cholesteric liquid crystals. Opto-Electron. Rev. 14: 323–328. doi:10.2478/s11772-006-0044-7
  54. Lee C-R, Lin S-H, Yeh H-C, Ji T-D, Lin K-L, Mo T-S, Kuo C-T, Lo K-Y, Chang S-H, Fuh A Y-G and Huang S-Y, 2009. Color cone lasing emission in a dye-doped cholesteric liquid crystal with a single pitch. Opt. Express. 17: 12910–12921. doi:10.1364/OE.17.012910
  55. Lee C–R, Lin S–H, Yeh H–C and Ji T–D, 2009. Band-tunable color cone lasing emission based on dye-doped cholesteric liquid crystals with various pitches and a pitch gradient. Opt. Express. 17: 22616–22623. doi:10.1364/OE.17.022616
  56. Lee C–R, Lin S–H, Ku H–S, Liu J–H, Yang P–C, Huang S–Y, Yeh H–C, Ji T–D and Lin C–H, 2010. Spatially band-tunable color-cone lasing emission in a dye-doped cholesteric liquid crystal with a photoisomerizable chiral dopant. Opt. Lett. 35: 1398–1400. doi:10.1364/OL.35.001398
  57. Lin S–H and Lee C–R, 2011. Novel dye-doped cholesteric liquid crystal cone lasers with various birefringences and associated tunabilities of lasing feature and performance. Opt. Express. 19: 18199–18206. doi:10.1364/OE.19.018199
  58. Palto S P, Shtykov N M, Umanskii B A and Barnik M I, 2012. Multiwave out-of-normal band-edge lasing in cholesteric liquid crystals. J. Appl. Phys. 112: 013105–8. doi:10.1063/1.4723641
  59. Penninck L, Beeckman J, De Visschere P and Neyts K, 2012. Light emission from dye-doped cholesteric liquid crystals at oblique angles: Simulation and experiment. Phys. Rev. E. 85: 041702–7. doi:10.1103/PhysRevE.85.041702
  60. Blinov L M, Cipparrone G, Pagliusi P, Lazarev V V and Palto S P, 2006. Mirrorless lasing from nematic liquid crystals in the plane waveguide geometry without refractive index or gain modulation. Appl. Phys. Lett. 89: 0311114–3. doi:10.1063/1.2234316
  61. Blinov L M, Cipparrone G, Mazzulla A, Pagliusi P, Lazarev V V and Palto S P, 2008. Quasi-in-plane leaky modes in lasing cholesteric liquid crystal cells. J. Appl. Phys. 104: 103115–7. doi:10.1063/1.2975971
  62. Yoshida H, Inoue Y, Isomura T, Matsuhisa Y, Fujii A and Ozakib M, 2009. Position sensitive, continuous wavelength tunable laser based on photopolymerizable cholesteric liquid crystals with an in-plane helix alignment. Appl. Phys. Lett. 94: 093306–3. doi:10.1063/1.3089846
  63. Morris S M, Ford A D, Pivnenko M N and Coles H J. The effects of reorientation on the emission properties of a photonic band edge liquid crystal laser. J Opt. A: Pure Appl. Opt. 7: 215–223. doi:10.1088/1464-4258/7/5/002
  64. Cao W, Palffy-Muhoray P, Taheri B, Marino A and Abbate G, 2005. Lasing thresholds of cholesteric liquid crystals lasers. Mol. Cryst. Liq. Cryst. 429: 101–110. doi:10.1080/15421400590930782
  65. Morris S M, Ford A D, Gillespie C, M N Pivnenko, Hadeler O and Coles H J, 2006. The emission characteristics of liquid-crystal lasers. J. SID. 14: 565–573.
  66. Woon K L, O'Neill M, Richards G J, Aldred M P and Kelly S M, 2005. Stokes parameter studies of spontaneous emission from chiral nematic liquid crystals as a one-dimensional photonic stopband crystal: Experiment and theory. Phys. Rev. E. 71: 041706–8. doi:10.1103/PhysRevE.71.041706
  67. Watanabe Y, Uchimura M, Araoka F, Konishi G–I, Watanabe J and Takezoe H, 2009. Extremely low threshold in a pyrene-doped distributed feedback cholesteric liquid crystal laser. Appl. Phys. Express. 2: 102501–3. doi:10.1143/APEX.2.102501
  68. Dolgaleva K, Wei S K H, Lukishova S G, Chen S H, Schwertz K and Boyd R W, 2008. Enhanced laser performance of cholesteric liquid crystals doped with oligofluorene dye. J. Opt. Soc. Amer. B. 25:1496–1504. doi:10.1364/JOSAB.25.001496
  69. Förster T, 1959. Transfer mechanisms of electronic excitation. Disc. Faraday Soc. 27: 717 doi:10.1039/df9592700007
  70. Berggren M, Dodabalapur A, Slusher R E and Bao Z, 1997. Light amplification in organic thin films using cascade energy transfer. Nature. 389: 466–469. doi:10.1038/38979
  71. Alvarez E, He M, Munoz A F, Palffy-Muhoray P, Serak S V, Taheri B and Twieg R, 2001. Mirrorless lasing and energy transfer in cholesteric liquid crystals doped with laser dyes. Mol. Cryst. Liq. Cryst. 369: 75–82. doi:10.1080/10587250108030010
  72. Chambers M, Fox M and Grell M, 2002. Lasing from a Förster transfer fluorescent dye couple dissolved in a chiral nematic liquid crystal. Adv. Func. Mater. 12: 808–810. doi:10.1002/adfm.200290010
  73. Sonoyama K, Takanishi Y, Ishikawa K and Takezoe H, 2008. Lowering threshold by energy transfer between two dyes in cholesteric liquid crystal distributed feedback lasers. Appl. Phys. Express. 1: 032002–3. doi:10.1143/APEX.1.032002
  74. Morris S M, Ford A D, Pivnenko M N and Coles H J, 2005. Enhanced emission from liquidcrystal lasers. J. Appl. Phys. 97: 023103–9. doi:10.1063/1.1829144
  75. Morris S M, Ford A D, Pivnenko M N, Hadeler O and Coles H J, 2006. Correlations between the performance characteristics of a liquid crystal laser and the macroscopic material properties. Phys. Rev. E. 74: 061709–5. doi:10.1103/PhysRevE.74.061709
  76. Ford A D, Morris S M, Pivnenko M N, Gillespie C O and Coles H J, 2007. Emission characteristics of a homologous series of bimesogenic liquid-crystal lasers. Phys. Rev. E. 76: 051703–9. doi:10.1103/PhysRevE.76.051703
  77. Chee M G, Song M H, Kim D, Takezoe H and Chung I J, 2007. Lowering lasing threshold in chiral nematic liquid crystal structure with different anisotropies. Jpn. J. Appl. Phys. 18: L437–L439. doi:10.1143/JJAP.46.L437
  78. Huang Y, Zhou Y, Hong Q, Rapaport A, Bass M and Wu S–T, 2006. Incident angle and polarization effects on the dye-doped cholesteric liquid crystal laser. Opt. Commun. 261: 91–96. doi:10.1016/j.optcom.2005.11.049
  79. Huang Y, Lin T–H, Zhou Y and Wu S–T, 2006. Enhancing the laser power by stacking multiple dye-doped chiral polymer films. Opt. Express. 14: 11299–11303. doi:10.1364/OE.14.011299
  80. Shtykov N M, Barnik M I, Blinov L M, Umanskii B A and Palto S P, 2007. Amplification of the emission of a liquid-crystal microlaser by means of a uniform liquid-crystal layer. JETP Lett. 85: 602–604. doi:10.1134/S002136400712003X
  81. Wang Y, Manabe T, Takanishi Y, Ishikawa K, Shao G, Orita A, Otera J and Takezoe H, 2007. Dependence of lasing threshold power on excitation wavelength in dye-doped cholesteric liquid crystals. Opt. Commun. 280: 408–411. doi:10.1016/j.optcom.2007.08.027
  82. Mowatt C, Morris S M, Song M H, Wilkinson T D, Friend R H and Coles H J, 2010. Com-parison of the performance of photonic band-edge liquid crystal lasers using different dyes as the gain medium. J. Appl. Phys. 107: 043101–9. doi:10.1063/1.3284939
  83. Chanishvili A, Chilatya G, Petriashvili G, Barberi R, Bartolino R, Cipparone G, Mazzulla A and Oriol L, 2004. Lasing in dye-doped cholesteric liquid crystal: two new tuning strategies. Adv. Mater. 16: 791–795. doi:10.1002/adma.200306542
  84. Furumi S, Yokoyama S, Otomo A and Mashiko S, 2004. Phototunable photonic bandgap in a chiral liquid crystal laser device. Appl. Phys. Lett. 84: 2491–2493. doi:10.1063/1.1699445
  85. Bobrovsky A Yu, Boiko N I, Shibaev V P and Wendorf J H, 2003. Cholesteric mixtures with photochemically tunable circularly polarized fluorescence. Adv. Mater. 15: 282–287. doi:10.1002/adma.200390067
  86. Huang Y, Chen L–P, Doyle Ch, Zhou Y and Wu S–T, 2006. Spatially tunable laser emission in dye-doped cholesteric polymer films. Appl. Phys. Lett. 88: 011107. doi:10.1063/1.2161167
  87. Sonoyama K, Takanishi Y, Ishikawa K and Takezoe H, 2007. Position-sensitive cholesteric liquid crystal dye laser covering a full visible range. Jpn. J. Appl. Phys. 46: L874–L876. doi:10.1143/JJAP.46.L874
  88. Wang Ch–T and Lin T–H, 2008. Multi-wavelength laser emission in dye-doped photonic liquid crystals. Opt. Express. 16: 18334–18339. doi:10.1364/OE.16.018334
  89. Funamoto K, Ozaki M and Yoshino K, 2003. Discontinuous shift of lasing wavelength with temperature in cholesteric liquid crystal. Jpn. J. Appl. Phys. 42: L523–L525. doi:10.1143/JJAP.42.L1523
  90. Morris S M, Ford A D and Coles H J, 2009. Removing the discontinuous shifts in emission wavelength of a chiral nematic liquid crystal laser. J. Appl. Phys. 106: 023112–4. doi:10.1063/1.3177251
  91. De Gennes P G, 1968. Calcul de la distorsion d'une structure cholesterique par un champ magnetique. Solid State Commun. 6: 163–165. doi:10.1016/0038-1098(68)90024-0
  92. Kasano M, Ozaki M, Yoshino K, Ganzke D and Haase W, 2003. Electrically tunable waveguide laser based on ferroelectric liquid crystal. Appl. Phys. Lett. 82: 4026–4028. doi:10.1063/1.1580992
  93. Shirota K, Sun H–Bo and Kawata S, 2004. Two-photon lasing of dye-doped photonic crystal lasers. Appl. Phys. Lett. 84: 1632–1634.
  94. Chanishvili A, Chilaya G, Petriashvili G, Barberi R, Bartolino R, Cipparrone G and Mazzulla A, 2004. Laser emission from a dye-doped cholesteric liquid crystal pumped by another choles-teric liquid crystal laser. Appl. Phys. Lett. 85: 3378–3380. doi:10.1063/1.1806561
  95. Shibaev P V, Tang K, Genack A Z, Kopp V and Green M M, 2002. Lasing from a stiff chain polymeric lyotropic cholesteric liquid crystal. Macromolecules. 35: 3022–3025. doi:10.1021/ma011738j
  96. Schmidtke J, Stille W, Finkelman H and Kim S T, 2002. Laser emission in a dye doped cholesteric polymer network. Adv. Mater. 14: 746–749. doi:10.1002/1521-4095(20020517)14:10<746::AID-ADMA746>3.0.CO;2-5
  97. Finkelmann H, Kim S T, Munoz A, Palffy-Muhoray P and Taheri B, 2001. Tunable mirrorless lasing in cholesteric liquid crystalline elastomer. Adv. Mater. 13: 1069–1072. doi:10.1002/1521-4095(200107)13:14<1069::AID-ADMA1069>3.0.CO;2-6
  98. Matsui T, Ozaki R, Funamoto K, Ozaki M and Yoshino K, 2002. Flexible mirrorless laser based on a free-standing film of photopolymerized cholesteric liquid crystal. Appl. Phys Lett. 81: 3741–3743. doi:10.1063/1.1522498
  99. Araoka F, Shin K–Ch, Takanishi Y, Ishikawa K, Takezoe H, Zhu Zh and Swager T M, 2003. How doping a cholesteric liquid crystal with polymeric dye improves an order parameter and makes possible low threshold lasing. J. Appl. Phys. 94: 279–283. doi:10.1063/1.1578534
  100. Yablonovitch E, Gmitter T J, Meade R D, Rappe A M, Brommer K D and Joannopoulos J D, 1991. Donor and acceptor modes in photonic band structure. Phys. Rev. Lett. 67: 3380–3383. doi:10.1103/PhysRevLett.67.3380
  101. Stoytchev M and Genack A Z, 1997. Microwave transmission through a periodic three-dimensional metal-wire network containing random scatterers. Phys. Rev. B. 55: R8617–8621. doi:10.1103/PhysRevB.55.R8617
  102. Chabanov A A, Stoytchev M and Genack A Z, 2000. Statistical signatures of photon localization. Nature. 404: 850–853. doi:10.1038/35009055
  103. Yang Y–Ch, Kee Ch–S, Kim J–E and Park H Y, 1999. Photonic defect modes of cholesteric liquid crystals. Phys. Rev. E. 60: 6852–6854. doi:10.1103/PhysRevE.60.6852
  104. Barnik M I, Blinov L M, Lazarev V V, Palto S P, Umanskii B A and Shtykov N M, 2008. Lasing from photonic structure: Cholesteric-voltage controlled nematic-cholesteric liquid crystal. J. Appl. Phys. 103: 123113–7. doi:10.1063/1.2948937
  105. Song M H, Park B, Shin K–Ch, Ohta T, Tsunoda Y, Hoshi H, Takanishi Y, Ishikava K, Watanabe J, Nishimura S, Toyooka T, Zhu Zh, Swager T M and Takezoe H, 2004. Effect of phase retardation on defect mode lasing in polymeric cholesteric liquid crystals. Adv. Mater. 16: 779–783. doi:10.1002/adma.200306360
  106. Song M H, Park B, Toyooka T, Chung I J, Takanishi Y, Ishikava K and Takezoe H, 2006. Electrotunable non-reciprocal laser emission from a liquid-crystal photonic device. Adv. Func. Mater. 16: 1793–1798. doi:10.1002/adfm.200600107
  107. Kopp V I and Genack A Z, 2002. Twist defect in chiral photonic structures. Phys. Rev. Lett. 89: 033901–4. doi:10.1103/PhysRevLett.89.033901
  108. Schmidtke J, Stille W and Finkelman H, 2003. Defect mode emission of a dye doped cholesteric polymer network. Phys. Rev. Lett. 90: 083902–4. doi:10.1103/PhysRevLett.90.083902
  109. Schmidtke J and Stille W, 2003. Photonic defect modes of cholesteric liquid crystal films. Eur. Phys. J. E. 12: 553–564. doi:10.1140/epje/e2004-00027-2
  110. Becchi M, Ponti S, Reyes J A and Oldano C, 2004. Defect modes in helical photonic crystals: An analytic approach. Phys. Rev. B. 70: 033103–4. doi:10.1103/PhysRevB.70.033103
  111. Matsui T, Ozaki M and Yoshino K, 2004. Tunable photonic defect modes in a cholesteric liquid crystal induced by optical deformation of helix. Phys. Rev. E. 69: 061715–4. doi:10.1103/PhysRevE.69.061715
  112. Takanishi Y, Tomoe N, Ha N Y, Toyooka T, Nishimura S, Ishikava K and Takezoe H, 2007. Defect-mode lasing from a three-layered helical cholesteric liquid crystal structure. Jpn. J. Appl. Phys. 46: 3510–3513. doi:10.1143/JJAP.46.3510
  113. Song M H, Ha Y, Amemiya K, Park B, Takanishi Y, Ishikava K, Wu J W, Nishimura S, Toyooka T and Takezoe H, 2006. Defect-mode lasing with lowered threshold in three-layered hetero-cholesteric liquid-crystal structure. Adv. Mater. 18: 193–197. doi:10.1002/adma.200501438
  114. Takanishi Y, Ohtsuka Y, Suzaki G, Nishimura S and Takezoe H, 2010. Low threshold lasing from dye-doped cholesteric liquid crystal multi-layered structures. Opt. Express. 18: 12909–12914. doi:10.1364/OE.18.012909
  115. Ha N Y, Takanishi Y and Takezoe H, 2007. Simultaneous RGB reflections from single-pitched cholesteric liquid crystal films with Fibonaccian defects. Opt. Express. 15: 1024–1029. doi:10.1364/OE.15.001024
  116. Ha N Y, Ohtsuka Y, Jeong S M, Nishimura S, Suzaki G, Takanishi Y, Ishikava K and Takezoe H, 2008. Fabrication of a simultaneous red-green-blue reflector using single-pitched cho-lesteric liquid crystals. Nature. 7: 43–47. doi:10.1038/nmat2045
  117. Gellermann W, Kohmoto M, Sutherland B and Taylor P C, 1994. Localization of light waves in Fibonacci dielectric multilayers. Phys. Rev. Lett. 72: 633636. doi:10.1103/PhysRevLett.72.633
  118. Negro L D, Stolfi M, Yi Y, Michel J, Duan X, Kimerling L C, Le Blanc J and Haavisto J, 2004. Photon band gap properties and omnidirectional reflectance in Si/SiO2 Thue-Morse quasi-crystals. Appl. Phys. Lett. 84: 51865188.
  119. Vasconcelos M S and Albuquerque E L, 1999. Transmission fingerprints in quasiperiodic dielectric multilayers. Phys. Rev. B. 59: 11128–11131. doi:10.1103/PhysRevB.59.11128
  120. Ganic K, Gan X, Gu M, Hain M, Somalingam S, Stankovic S and Tschudi T, 2002. Generation of doughnut laser beams by use of a liquid-crystal cell with a conversion efficiency near 100%. Opt. Lett. 27: 13511353. doi:10.1364/OL.27.001351
  121. Voloschenko D and Lavrentovich O D, 2000. Optical vortices generated by dislocations in a cholesteric liquid crystal. Opt. Lett. 26: 317–319. doi:10.1364/OL.25.000317
  122. Matsko A B, Savchenkov A A, Strekalov D, Ilchenko V S and Maleki L, 2005. Review of applications of whispering-gallery mode resonators in photonics and nonlinear optics. 4, IPN Progress Rep. 15: 42–162.
  123. Lord Rayleigh, 1910. The problem of whispering gallery. Philos. Mag. 20: 1001–1004. doi:10.1080/14786441008636993
  124. Vahala K J, 2003. Optical microcavities. Nature. 424: 841–846. doi:10.1038/nature01939
  125. Chiasera A, Dumeige Y, F’ron P, Ferrari M, Jestin Y, Conti G N, Pelli S, Soria S and Righini G C, 2010. Spherical whispering-gallery-mode microresonators. Laser & Photon. Rev. 4: 457482. doi:10.1002/lpor.200910016
  126. Collot L, Lef`vre-Seguin V, Brune M, Raimond J M and Haroche S, 1993. Very high-Q whispering-gallery mode resonances observed on fused silica microspheres. Europhys. Lett. 23: 327–334. doi:10.1209/0295-5075/23/5/005
  127. Sandoghdar V, Treussart F, Hare J, Lef`vre-Seguin V, Raimond J M and Haroche S, 1996. Very low threshold whispering-gallery-mode microsphere laser. Phys. Rev. A. 54: R1777–R1780. doi:10.1103/PhysRevA.54.R1777
  128. Garret C G B, Kaiser W and Bond W L, 1961. Stimulated emission into optical whispering modes of spheres. Phys. Rev. 124: 1807–1809. doi:10.1103/PhysRev.124.1807 
  129. Cai M, Painter O and Vahala K J, 2000. Fiber-coupled microsphere laser. Opt. Lett. 25: 1430–1432. doi:10.1364/OL.25.001430
  130. Yang L and Vahala K J, 2003. Gain functionalization of silica microresonators. Opt. Lett. 28: 592–594. doi:10.1364/OL.28.000592
  131. Kuwata-Gonokami M and Takeda K, 1998. Polymer whispering gallery mode lasers. Opt. Mater. 9: 12–17. doi:10.1016/S0925-3467(97)00160-2
  132. Cha J N, Bartl M H, Wong M S, Popitsch A, Deming T J and Stucky G D, 2003. Microcavity lasing from block peptide hierarchically assembled quantum dot spherical resonators. Nano Lett. 3: 907–911. doi:10.1021/nl034206k
  133. Yamaguchi K, Niimi T, Haraguchi M, Ookamoto T and Fukui M, 2006. Fabrication and optical evaluation of silica microsphere coated with J-aggregates. Jpn. J. Appl. Phys. 45: 6750–6753. doi:10.1143/JJAP.45.6750
  134. Nöckel J U, Stone A D, Chen G, Grossman H L and Chang R K, 1996. Directional emission from asymmetric resonant cavities. Opt. Lett. 21: 1609–1611. doi:10.1364/OL.21.001609
  135. Gmachl C, Capasso F, Narimanov E E, Nöckel J U, Stone A D, Faist J, Sivco D L and Cho A Y, 1998. High-power directional emission from microlasers with chaotic resonators. Science. 280: 1556–1564. doi:10.1126/science.280.5369.1556
  136. Lacey S and Wang H, 2001. Directional emission from whispering-gallery modes in deformed fused-silica microspheres Opt. Lett. 26: 1943–1945. doi:10.1364/OL.26.001943
  137. Wang Q J, Yan C, Yu N, Unterhinninghofen J, Wiersig J, Pflügl C, Diehl L, Edamura T, Yamanishi M, Kan H and Capasso F, 2010. Whispering-gallery mode resonators for highly uni-directional laser action. Proc. Nat. Acad. Sci. U.S.A. 107: 22407–22412. doi:10.1073/pnas.1015386107
  138. Wiersig J, Unterhinninghofen J, Song Q, Cao H, Hentschel M and Shinohara S, 2011. Review on unidirectional light emission from ultralow-loss modes in deformed microdisks. Trends in Nano- and Micro-Cavities. 2011: 109–152.
  139. Psaltis D, Quake S R and Yang C, 2006. Developing optofluidic technology through the fusion of microfluidics and optics. Nature. 442: 381–386. doi:10.1038/nature05060
  140. Kou Q, Yesilyurt I and Chen Y, 2006. Collinear dual-color laser emission from a microfluidic dye laser. Appl. Phys. Lett. 88: 091101–3. doi:10.1063/1.2179609
  141. Li Z, Zhang Z, Scherer A and Psaltis D, 2006. Mechanically tunable optofluidic distributed feedback dye laser. Opt. Express. 14: 10494–10499. doi:10.1364/OE.14.010494
  142. Gersborg-Hansen M and Kristensen A, 2007. Tunability of optofluidic distributed feedback dye lasers. Opt. Express. 15: 137–142. doi:10.1364/OE.15.000137
  143. Song W, Vasdekis A E, Li Z and Psaltis D, 2009. Optofluidic evanescent dye laser based on a distributed feedback circular grating. Appl. Phys. Lett. 94: 161110–3. doi:10.1063/1.3124652
  144. Aubry G, Kou Q, Soto-Velasco J, Wang C, Meance S, He J J and Haghiri-Gosnet A M, 2011. A multicolor microfluidic droplet dye laser with single mode emission. Appl. Phys. Lett. 98: 111111–3. doi:10.1063/1.3565242
  145. Humar M and Muševič I, 2011. Surfactant sensing based on whispering-gallery-mode lasing in liquid-crystal microdroplets. Opt. Express. 19: 19836–19844. doi:10.1364/OE.19.019836
  146. Gottardo S, Cavalieri S, Yaroshchuk O and Wiersma D S, 2004. Quasi-two-dimensional diffusive random laser action. Phys. Rev. Lett. 93: 263901–4. doi:10.1103/PhysRevLett.93.263901
  147. Liu Y J, Suna X W, Elim H I and Ji W, 2006. Gain narrowing and random lasing from dye-doped polymer-dispersed liquid crystals with nanoscale liquid crystal droplets. Appl. Phys. Lett. 89: 011111–3. doi:10.1063/1.2219988
  148. Humar M and Muševič I, 2010. 3D microlasers from self-assembled cholesteric liquid-crystal microdroplets. Opt. Express. 18: 26995–27003. doi:10.1364/OE.18.026995
  149. Kurik M V and Lavrentovich O D, 1982. Negative-positive monopole transitions in cholesteric liquid crystals. JETP Lett. 35: 444–447.
  150. Nastishin Yu A, Kléman M, Malthête J and Nguyen H T, 2001. Identification of a TGBA liquid crystal phase via its defects. Eur. Phys. J. E. 5: 353–357. doi:10.1007/s101890170066
  151. Kléman M, Nastishin Yu A and Malthête J, 2002. Defects in a TGBA phase: A theoretical approach. Eur. Phys. J. E. 8: 67–78. doi:10.1140/epje/i2002-10009-1
  152. Lin J–D, Hsieh M–H, Wei G–J, Mo T–S, Huang S–Y and Lee C–R, 2013. Optically tun-able/switchable omnidirectionally spherical microlaser based on a dye-doped cholesteric liquid crystal microdroplet with an azo-chiral dopant. Opt. Express. 21: 15765–15776. doi:10.1364/OE.21.015765
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