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

More documents

Recommendations

Info

211 vVe calculate the effect of GVD on our second harmonic pulse of the form equation (A.l) that propagates through a 3 mm piece of quartz. vVe used the dispersion relationship listed in equation (2.67) and Table 2.3. vVe assume the fundamental pulse has a pulse width of 130 fs. For the parameters stated above, the pulse broadens less than 2 x 10- 6 % for both the free and bound waves over a fundamental wavelength range of 740 nm to 1 J..lm for a film thickness of 3 mm. For GaN, the free wave pulse broadens by .43% and the bound wave pulse broadens by less than 10- 6 % for a film thickness of 5 J..lm over a wavelength range of 740 nm to 1 J..lm. These values were calculated using the Sell meier dispersion relation for GaN with the parameters listed in Table 4.2.2. This justifies our first order expansion of k with respect to..v. Xote. since the bound wave propagates with a wavevector twice that of the fundamental field. the broadening of the fundamental wave can be related to the broadening of the bound wave by fundamental"" 8rbound rout out . (A.8) Thus. the fundamental wave does not appreciably broaden during propagation through the Ga~ film or quartz crystal. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Appendix B Theory of Nonlinear Response Functions In this appendi.x, we formally derive the relationship between the nonlinear polarization. Pi(2'(w = WI + W2), the applied electric fields, Ej(wr) and Ek(W2). This relationship is applied to calculated SHG from the ultrafast Ti:Ah03 laser system. \Ve start with a generalized second order nonlinear response function in time [118] (B.1) p/2) (t) is the second order nonlinear polarization at time t resulting from the application of fields E j (Tr) and E k ( T2) at all times before t. Since the system cannot respond before the electric fields are applied, (B.2) This condition is known as causality. \Ve wish to solve the nonlinear wave equation and calculate the nonlinear fields from the nonlinear polarization in angular frequency space. The angular frequency 212 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Page 1 and 2:
SHG SPECTROSCOPY OF GALLIUM NITRIDE
Page 3 and 4:
COPYRIGHT vVilliam E. Angerer 1998
Page 5 and 6:
ACKNOWLEDGEMENTS I am most grateful
Page 7 and 8:
vi and support over the last three
Page 9 and 10:
viii and we report on photoluminesc
Page 11 and 12:
x 2.5 ~ovel Technique and Apparatus
Page 13 and 14:
Xll 7.3 7.2.3 Registering and Posit
Page 15 and 16:
xiv
Page 17 and 18:
xvi 2.10 Device for measuring ultra
Page 19 and 20:
xviii 6.5 Polarization and propagat
Page 21 and 22:
2 scopies as a probe of these featu
Page 23 and 24:
4 tionallinear microscopy is unable
Page 25 and 26:
6 interference by group velocity mi
Page 27 and 28:
Chapter 2 Introduction to Nonlinear
Page 29 and 30:
10 the electric fields as In this t
Page 31 and 32:
12 SHG is a virtual process, Le. th
Page 33 and 34:
14 2.3 (2) Xijk and Symmetry In gen
Page 35 and 36:
16 X (2) zxx = ,\.zyy v(2) (2) = v(
Page 37 and 38:
18 X~}k(W = 2wo) of our GaN samples
Page 39 and 40:
20 nonlinear element of quartz, X~~
Page 41 and 42:
22 the transmitted wave, E:t'°, Th
Page 43 and 44:
24 150 I I "1 I :) ~ >- -. iii c v
Page 45 and 46:
26 Quartz fundamental Figure 2.5: I
Page 47 and 48:
28 The bound wave, which propagates
Page 49 and 50:
30 1/e 2 its ma.'{imum value. This
Page 51 and 52:
32 Here, x~;!Aw = 2wo) is a constan
Page 53 and 54:
34 simplifications (2.39) and (2.40
Page 55 and 56:
36 nonlinear waves. This model assu
Page 57 and 58:
38 Fourier transform to E /2 (r, w)
Page 59 and 60:
40 3 mm and with the parameters dis
Page 61 and 62:
42 I " i iii iii iii iii iii iii ii
Page 63 and 64:
44 parameter value Bl 2.35728 B2 -0
Page 65 and 66:
46 is measured as a function of tra
Page 67 and 68:
48 send pulse into device \11 input
Page 69 and 70:
50 2.6 Conclusion In this brief sec
Page 71 and 72:
52 LOCK-IN AMPLIAER LOCK-IN AMPLIAE
Page 73 and 74:
54 After polarization, the beam was
Page 75 and 76:
56 PO HR !l o IV team BP Figure 3.3
Page 77 and 78:
58 .. ........... • / ~ '" ~ r --
Page 79 and 80:
60 The production of ultrafast, hig
Page 81 and 82:
62 800 ~ 0 0 J 0 0 0 0 J ~ 0 600~ 0
Page 83 and 84:
64 measurements. Typically, I incre
Page 85 and 86:
66 described below. Note that laser
Page 87 and 88:
68 sentiallya nonlinear optical int
Page 89 and 90:
70 780 800 820 840 860 880 900 920
Page 91 and 92:
72 Unlike the linear spectroscopic
Page 93 and 94:
74 fore, the ratio of these two qua
Page 95 and 96:
76 of :UN is deposited on the Ah03
Page 97 and 98:
78 computer HeNe Las polarizer chop
Page 99 and 100:
80 ~------".... GaN A12a3 index flu
Page 101 and 102:
82 + d I , GaN A12a3 Figure 4.3: Co
Page 103 and 104:
84 4.2 Measurement of Indices of Re
Page 105 and 106:
86 fields at the lh interface to th
Page 107 and 108:
88 traveling wave, i.e. (-1.7) wher
Page 109 and 110:
90 Note that the additional subscri
Page 111 and 112:
92 £b, are defined only at the int
Page 113 and 114:
94 Equations (4.30) and (4.32) are
Page 115 and 116:
96 the calculation of the transmitt
Page 117 and 118:
98 '- -0 OJ N 0.4 o E ~ o Z 0.2 o 2
Page 119 and 120:
100 2.0 "'"" "I 1.5 E ::t ~ --c 0 -
Page 121 and 122:
102 4.3 Photoluminescence of GaN To
Page 123 and 124:
104 a photoluminescence measurement
Page 125 and 126:
106 :J 0.01 0 ~ L ~ 0.008 r- :n :v
Page 127 and 128:
108 0.08 ~. j -i ,-... I I ""I :::l
Page 129 and 130:
Chapter 5 Properties of GaN In rece
Page 131 and 132:
112 5.1 Crystal Structure :\ crucia
Page 133 and 134:
114 PJO'tI [{fall Figure 5.1: \Vurz
Page 135 and 136:
116 e 4 r .1 It Figure 5.2: Calcula
Page 137 and 138:
118 Parameter Symbol Value electron
Page 139 and 140:
120 high intrinsic electron concent
Page 141 and 142:
122 equation (5.2), is represented
Page 143 and 144:
124 C6v E E £l. 2C3 2C 3 2C6 2C 6
Page 145 and 146:
126 gap, the nonlinear susceptibili
Page 147 and 148:
128 rrb 10.0 eV -------- 5 9.0 eV r
Page 149 and 150:
130 In> 1m> 1m>
Page 151 and 152:
132 Emission of a photon on the bra
Page 153 and 154:
134 5.5 MOCVD Growth of GaN Our GaN
Page 155 and 156:
136 # dopant thickness mobility car
Page 157 and 158:
138 6.1 Nonlinear Optical Spectrosc
Page 159 and 160:
140 y lab X)lSlaJ / 2m Figure 6.1:
Page 161 and 162:
142 Fig. 6.2 displays the azimuthal
Page 163 and 164:
144 includes the effects of pulse p
Page 165 and 166:
146 6.3 Theory of Nonlinear Optical
Page 167 and 168:
148 L x i d 1 E( 00) air GaN sapphi
Page 169 and 170:
150 wavevector components. The free
Page 171 and 172:
152 z y x E( ro) air GaN Figure 6.5
Page 173 and 174:
154 various free waves and summing
Page 175 and 176:
156 factors are: the nonlinearity o
Page 177 and 178:
158 where v /2 is the group velocit
Page 179 and 180: 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: 210 that propagate through quartz a
Page 233 and 234: 214 Fourier transforming equation (
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,
show all

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

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?