William Angerer - Department of Physics and Astronomy - University ...

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213 space representation allows the simplification of the nonlinear wave equation from a partial differential equation to an algebraic equation. Therefore. we must derive the generalized second order nonlinear response function in angular frequency space. This may be effected by Fourier transforming equation (B.1). The Fourier transforms are defined in the usual way as (B.3) and E(w) = -. 1 100 27r -00 E(t)eiwtdt (B..1) with (B.5) The frequency space representation of X(2) (t - T1, t - T2) follows as y(2) (t _ T t _ To ) = 100 100 y(2) (w ., )e-iW1(t-TI )e-iW2(t-T2)dl.J;' d' " ''-Ilk 1, 2 ''-Ilk 1,w2 1 ""'1, -00 -00 (B.6) Therefore. the time representation of the nonlinear polarization may be written explicitly as (B.7) Using the Fourier transform equations, equation (B.7) can be expressed as Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
214 Fourier transforming equation (8.8) from time to frequency yields Equation (8.9) represents a general expression that determines p?)(w) as a function of the incident fields. Ej{wd and Ek(W2). For monochromatic fields, i.e. .( ) _ 6(Wl - wo ) E J Wl - 27r ' (B.lO) Equation (8.9) reduces to the usual expression (8.11) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
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SHG SPECTROSCOPY OF GALLIUM NITRIDE
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COPYRIGHT vVilliam E. Angerer 1998
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ACKNOWLEDGEMENTS I am most grateful
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vi and support over the last three
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viii and we report on photoluminesc
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x 2.5 ~ovel Technique and Apparatus
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Xll 7.3 7.2.3 Registering and Posit
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xiv
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xvi 2.10 Device for measuring ultra
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xviii 6.5 Polarization and propagat
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2 scopies as a probe of these featu
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4 tionallinear microscopy is unable
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6 interference by group velocity mi
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Chapter 2 Introduction to Nonlinear
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10 the electric fields as In this t
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12 SHG is a virtual process, Le. th
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14 2.3 (2) Xijk and Symmetry In gen
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16 X (2) zxx = ,\.zyy v(2) (2) = v(
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18 X~}k(W = 2wo) of our GaN samples
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20 nonlinear element of quartz, X~~
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22 the transmitted wave, E:t'°, Th
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24 150 I I "1 I :) ~ >- -. iii c v
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26 Quartz fundamental Figure 2.5: I
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28 The bound wave, which propagates
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30 1/e 2 its ma.'{imum value. This
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32 Here, x~;!Aw = 2wo) is a constan
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34 simplifications (2.39) and (2.40
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36 nonlinear waves. This model assu
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38 Fourier transform to E /2 (r, w)
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40 3 mm and with the parameters dis
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42 I " i iii iii iii iii iii iii ii
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44 parameter value Bl 2.35728 B2 -0
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46 is measured as a function of tra
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48 send pulse into device \11 input
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50 2.6 Conclusion In this brief sec
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52 LOCK-IN AMPLIAER LOCK-IN AMPLIAE
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54 After polarization, the beam was
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56 PO HR !l o IV team BP Figure 3.3
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58 .. ........... • / ~ '" ~ r --
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60 The production of ultrafast, hig
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62 800 ~ 0 0 J 0 0 0 0 J ~ 0 600~ 0
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64 measurements. Typically, I incre
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66 described below. Note that laser
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68 sentiallya nonlinear optical int
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70 780 800 820 840 860 880 900 920
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72 Unlike the linear spectroscopic
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74 fore, the ratio of these two qua
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76 of :UN is deposited on the Ah03
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78 computer HeNe Las polarizer chop
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80 ~------".... GaN A12a3 index flu
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82 + d I , GaN A12a3 Figure 4.3: Co
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84 4.2 Measurement of Indices of Re
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86 fields at the lh interface to th
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88 traveling wave, i.e. (-1.7) wher
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90 Note that the additional subscri
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92 £b, are defined only at the int
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94 Equations (4.30) and (4.32) are
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96 the calculation of the transmitt
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98 '- -0 OJ N 0.4 o E ~ o Z 0.2 o 2
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100 2.0 "'"" "I 1.5 E ::t ~ --c 0 -
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102 4.3 Photoluminescence of GaN To
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104 a photoluminescence measurement
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106 :J 0.01 0 ~ L ~ 0.008 r- :n :v
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108 0.08 ~. j -i ,-... I I ""I :::l
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Chapter 5 Properties of GaN In rece
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112 5.1 Crystal Structure :\ crucia
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114 PJO'tI [{fall Figure 5.1: \Vurz
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116 e 4 r .1 It Figure 5.2: Calcula
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118 Parameter Symbol Value electron
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120 high intrinsic electron concent
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122 equation (5.2), is represented
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124 C6v E E £l. 2C3 2C 3 2C6 2C 6
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126 gap, the nonlinear susceptibili
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128 rrb 10.0 eV -------- 5 9.0 eV r
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130 In> 1m> 1m>
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132 Emission of a photon on the bra
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134 5.5 MOCVD Growth of GaN Our GaN
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136 # dopant thickness mobility car
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138 6.1 Nonlinear Optical Spectrosc
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140 y lab X)lSlaJ / 2m Figure 6.1:
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142 Fig. 6.2 displays the azimuthal
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144 includes the effects of pulse p
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146 6.3 Theory of Nonlinear Optical
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148 L x i d 1 E( 00) air GaN sapphi
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150 wavevector components. The free
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152 z y x E( ro) air GaN Figure 6.5
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154 various free waves and summing
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156 factors are: the nonlinearity o
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158 where v /2 is the group velocit
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160 i N -' '- 0 ::J a 0 o.sf fiftH!
Page 181 and 182: 162 4 ""' ::J en Q) - -' .D 2L ·oJ
Page 183 and 184: 164 approximation. The agreement be
Page 185 and 186: 166 midgap state) could playa role
Page 187 and 188: 168 r: b S ~ r b I rs ~ r b I 0)1 r
Page 189 and 190: 170 in various bonding geometries w
Page 191 and 192: , 172 .----. ::l U'J Q) ttl 0 '-.,;
Page 193 and 194: Chapter 7 SHG Microscopy The majori
Page 195 and 196: 176 7.1 Historical Context of Secon
Page 197 and 198: 178 comPJter - - - - - - - - - ~ ,-
Page 199 and 200: 180 second-harmonic light towards t
Page 201 and 202: 182 ~ 20 _____ ~ ____ J -----f- ---
Page 203 and 204: 184 wave at normal incidence is (7.
Page 205 and 206: 186 polarization is negligible for
Page 207 and 208: chopper AGate B Gate Signal Figure
Page 209 and 210: 190 E 4000 1 c: 0 3000 ~ rJl -' 0 c
Page 211 and 212: 192 depend on two components: a hig
Page 213 and 214: 194 nanorope ~ Figure 7.8: Carbon n
Page 215 and 216: 196 of light reflected from the sam
Page 217 and 218: 198 mean square deviation, of the p
Page 219 and 220: 200 7.3 Calculated SHG Signal from
Page 221 and 222: 202 parameter symbol value laser re
Page 223 and 224: 204 parameter symbol value surface
Page 225 and 226: Chapter 8 Conclusion In this brief
Page 227 and 228: 208 properties of carbon nanotubes.
Page 229 and 230: 210 that propagate through quartz a
Page 231: Appendix B Theory of Nonlinear Resp
Page 235 and 236: 216 and (CA) with f.b == t(.:.vo) a
Page 237 and 238: 218 The polarization, et, of the po
Page 239 and 240: 220 and (0.1.,1) respectively. Equa
Page 241 and 242: Appendix E Effect of Sapphire Miscu
Page 243 and 244: 224 with cosO 0 - sin (} o 1 o (E.3
Page 245 and 246: 226 Let us compare the light transm
Page 247 and 248: 228 , .............................
Page 249 and 250: 230 it ( (fp·top..,(arr (ll, M r "
Page 251 and 252: 232 nal-2.00 tab'(:r[ihi]-:r[ila] )
Page 253 and 254: 234 1 - 2500.0; III - xU]; 1/ ti. t
Page 255 and 256: Bibliography [1] R. K. Chang~ J. Du
Page 257 and 258: 238 [12] J. QL "V. Angerer, M. S. Y
Page 259 and 260: 240 Diamond, SiC and Wide Bandgap S
Page 261 and 262: 242 [40] M. M. Choy and R. L. Byer,
Page 263 and 264: 244 [55] \V. P. Lin, P. M. Lundquis
Page 265 and 266: 246 [70] J. vV. Yang, J. N. Kunzia,
Page 267 and 268: 248 [85] B. Monemar and O. Lagerste
Page 269 and 270: 250 [99] R. C. Miller, Optical Seco
Page 271 and 272: 252 [114] "V. de HeeL W. S. Bacsa,
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William Angerer - Department of Physics and Astronomy - University ...

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