optical characterisation of rare-earth doped fluoride and phosphate ...

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20eld (Eqn. 1.2) over a quantisation volume, V Q , and is given by [35]V eff =ZVQ(r; ; )E(r; ; ) 2 dV; (1.13)where the quantisation volume includes both real internal microsphere elds and theimaginary evanescent elds, and =(n2s ; r a1; r > a:(1.14)It can be shown that both TE modes and TM modes have dierent mode volumesdue to slight dierences in the conguration of the elds in the cavity (c.f. Fig. 1.5).TE modes are found deeper inside the sphere and, therefore, occupy a smaller volume(and an associated higher Q factor), as given by [36]V T E 1:02(2a) 11=6 (=n s ) 7=6V T M 1:08(2a) 11=6 (=n s ) 7=6 :(1.15)There is also an alternative denition of mode volume for nonlinear processes [37]V eff RVQ E(r; ; )2 dVRVQ E(r; ; )4 dV 2(1.16) 3:4 3=2 (=2n s ) 3 l 11=6p l m + 1 ; (1.17)where l 2an s =. In the case of both Eqns. 1.15 and 1.17, the volume scalesas a 11=6 . However, as can be seen from Fig. 1.5, which presents the quantum andnonlinear mode volumes, there are some dierences in the denitions.Another issue to note is the dierence in mode volume between the pump wavelengthfor Er 3+(980 nm) and the lasing wavelength (1.5 m): the volume scalesalmost linearly with wavelength. Therefore, the gain region in the 1.5 m mode issome 1.7 times larger than the excitation region.
21Figure 1.5: Mode volume for a doped microsphere with n s = 1:5 for = 1550 nm (squares)and 980 nm (diamonds). The TE modes have a slightly smaller mode volume. In contrast,the nonlinear mode volume (green markers) is at variance with the quantum mode volumes(red and blue markers).
Page 1 and 2: OPTICAL CHARACTERISATION OF RARE-EA
Page 3: Table of ContentsAcknowledgementsLi
Page 6 and 7: AcknowledgementsThe work in this th
Page 8 and 9: viiiList of Publications[1] J. Ward
Page 10 and 11: xTo the best of our knowledge, this
Page 12 and 13: xiiWDMWGMZBNAZBLALiPZBLANWavelength
Page 14 and 15: xiv1.6 Fundamental light-matter int
Page 16 and 17: xvi3.8 Gain coecient for dierent po
Page 18 and 19: xviii4.9 Fluorescence slopes and sp
Page 20 and 21: xxList of Tables1.1 Rigorous select
Page 22 and 23: 2device size (typically < 200 m dia
Page 24 and 25: 4a wider range of materials can exh
Page 26 and 27: 6in Chapter 2: angle-polished bres
Page 28 and 29: 81.2 Whispering Gallery ModesWhispe
Page 30 and 31: 10where j l (h (1)l) are spherical
Page 32 and 33: 12(a)(b)Figure 1.2: Calculated inte
Page 34 and 35: 14parameter, x nl , up to order =
Page 36 and 37: 16coecient of water. There is an a
Page 38 and 39: 18(a) Silica glass(b) ZBLALiP glass
Page 42 and 43: 221.7 Spectroscopy of Rare Earth Io
Page 44 and 45: 241.9 Radiative Emission RatesIn th
Page 46 and 47: 261.10 Material Loss Mechanisms in
Page 48 and 49: 28Chapter 2Fabrication of and Coupl
Page 50 and 51: 30Figure 2.1: Microsphere fabricati
Page 52 and 53: 32Figure 2.3:Schematic of (a) taper
Page 54 and 55: 34Figure 2.4: Calculated polish ang
Page 56 and 57: 36bre, the exact electric eld equat
Page 58 and 59: 38Figure 2.6: Poynting vector for a
Page 60 and 61: 40a few dozen tapered bres.As an al
Page 62 and 63: 42Figure 2.7: Schematic of the tape
Page 64 and 65: 44Figure 2.8: Taper prole for a 3 m
Page 66 and 67: 46taper angle, the light in the pro
Page 68 and 69: 48Figure 2.10: Optical micrograph o
Page 70 and 71: 50controlled. The discrete step-siz
Page 72 and 73: 52In recent years, much eort has be
Page 74 and 75: 543.2 ZBLALiP Material PropertiesWe
Page 76 and 77: 56Figure 3.3: Er 3+ energy level di
Page 78 and 79: 58(Avanex, 1998 PLM) with a spectra
Page 80 and 81: 60Figure 3.6: 66 m diameter microsp
Page 82 and 83: 62(a) C-band(b) Pump bandFigure 3.7
Page 84 and 85: 64as Judd-Ofelt (JO) analysis [72]-
Page 86 and 87: 66The total spontaneous radiative t
Page 88 and 89: 68Table 3.2: Predicted radiative tr
Page 90 and 91:
70Figure 3.9: Observed Er 3+ :ZBLAL
Page 92 and 93:
72pumping at 637 nm [77]. The same
Page 94 and 95:
74Figure 3.10: Calculated fraction
Page 96 and 97:
76Figure 3.11: Light in-Light out l
Page 98 and 99:
78representing the Q of the cavity.
Page 100 and 101:
80Figure 3.13: Quality factor measu
Page 102 and 103:
82Chapter 4Thermally Induced Optica
Page 104 and 105:
84especially benecial for C-band la
Page 106 and 107:
86note three distinct emission band
Page 108 and 109:
88therefore a combination of the in
Page 110 and 111:
90This is close to the value of 2.1
Page 112 and 113:
92Figure 4.4: Lasing spectrum for a
Page 114 and 115:
94Figure 4.6: Intensity bistability
Page 116 and 117:
96Figure 4.7: Chromatic switching f
Page 118 and 119:
98equation, given byl = 2n s d 1 +
Page 120 and 121:
100Figure 4.9: Fluorescence slopes
Page 122 and 123:
102and the Kerr eect immediately, b
Page 124 and 125:
104a precise setting for each spher
Page 126 and 127:
106Figure 4.11: Graphical descripti
Page 128 and 129:
108explanation for the peak in the
Page 130 and 131:
110and the associated wheatstone br
Page 132 and 133:
112performance have made them an in
Page 134 and 135:
114laser slightly above threshold.
Page 136 and 137:
116range is shown in Fig. 5.3(a). S
Page 138 and 139:
118Chapter 6ConclusionsThis project
Page 140 and 141:
120work. The reason for choosing 80
Page 142 and 143:
122Appendix ASpectral Characterisat
Page 144 and 145:
In this paper we will give an overv
Page 146 and 147:
1.:1.21.21.11.10.90.60.70.60.90.60.
Page 148 and 149:
⎥⎦2.2 Mode matching between a m
Page 150 and 151:
Puill lengtln (iuniuncurrents or ot
Page 152 and 153:
1.6x10 -71.4x10 -7IOG-2intensity (a
Page 154 and 155:
134Appendix BA Heat-and-Pull Rig fo
Page 156 and 157:
083105-2 Ward et al. Rev. Sci. Inst
Page 158 and 159:
083105-4 Ward et al. Rev. Sci. Inst
Page 160 and 161:
140Appendix CUpconversion Channels
Page 162 and 163:
2 The European Physical Journal App
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Page 166 and 167:
Page 168 and 169:
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150
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152
Page 174 and 175:
JOURNAL OF APPLIED PHYSICS 102, 023
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023104-3 Ward et al. J. Appl. Phys.
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162
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164
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166
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168
Page 190 and 191:
Figure F.1: Electrical wiring diagr
Page 192 and 193:
172[9] J. Z. Zhang and R. K. Chang.
Page 194 and 195:
174[28] C. C. Lam, P. T. Leung and
Page 196 and 197:
176[45] F. Le Kien, J. Q. Liang, K.
Page 198 and 199:
178[63] M.-F. Joubert. \Photon aval
Page 200 and 201:
180[81] A. Biswas, G. S. Maciel, C.
Page 202 and 203:
182[98] M. Ajroud, M. Haouari, H. B
Page 204:
184[116] L. Ricci, M. Weidemuller,
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