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

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71 before their focal point. This facilitates overlapping of the beams. The nonlinear crystal is centered on the overlap of the two beams. I rotate the crystal about the normal to its face to max:imize the SHG from each individual beam. This procedure aligns the beams' polarizations in the proper plane for type I phase matching. I adjust the angle of incidence between the fundamental beams and the crystal normal to produce an equal amount of SHG from each of the fundamental beams; this can be verified visually. This ensures maximum SHG from the overlap of the beams. Finally, I place the PMT directly between the SHG from the fundamental beams. Phase matching ensures that the SHG from the overlap of the fundamental beams will propagate in this direction. The fundamental beams may be approximately temporally overlapped by constructing the arms of the interferometer to have equal distances. The overlap of the fundamental pulses is detected by observing the signal from the P~IT on an oscilloscope while the speaker is on. 3.5 Normalization There are three components required of any properly normalized spectral measurement: elimination of the effects of the temporal fluctuations of the source. compensation for the spectral variations of the source, and compensation or elimination of the inherent spectral response of the detection system. This section discusses the experimental techniques that address these issues. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
72 Unlike the linear spectroscopic measurements presented in chapter 4. nonlinear optical spectra are highly sensitive to a number of factors including • pulse duration • beam polarization • beam spot size or diameter • beam spatial profile • pulse energy During a spectral scan, the pulse duration may vary from 80-150 fs and the cw power may vary from 500-800 m W due to the position of the Brewster prisms and shutter and the frequency dependence of the Ti:Ah03 crystal. The influence of the uncertainties and variations in these parameters on the nonlinear response of our samples is eliminated by simultaneously measuring the nonlinear response of a y-cut quartz slab. Quartz has well measured linear optical properties as well as a secondorder susceptibility, Xxxx(2w = wo), that is spectrally flat [52]. vVe chose y-cut quartz because it is free of optical activity [41], which would confuse the interpretation of a polarized measurement. vVhile comparison of the nonlinear response of quartz to that of a sample eliminates the signal's dependence on the characteristics of the Ti:Ah03 pulse and any temporal fluctuations of the source, it does not eliminate any discrepancy in the spectral response of the detection apparatus. We minimized this discrepancy by us- 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
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: 70 780 800 820 840 860 880 900 920
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
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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!
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162 4 ""' ::J en Q) - -' .D 2L ·oJ
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164 approximation. The agreement be
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166 midgap state) could playa role
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168 r: b S ~ r b I rs ~ r b I 0)1 r
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170 in various bonding geometries w
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, 172 .----. ::l U'J Q) ttl 0 '-.,;
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Chapter 7 SHG Microscopy The majori
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176 7.1 Historical Context of Secon
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178 comPJter - - - - - - - - - ~ ,-
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180 second-harmonic light towards t
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182 ~ 20 _____ ~ ____ J -----f- ---
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184 wave at normal incidence is (7.
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186 polarization is negligible for
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chopper AGate B Gate Signal Figure
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190 E 4000 1 c: 0 3000 ~ rJl -' 0 c
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192 depend on two components: a hig
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194 nanorope ~ Figure 7.8: Carbon n
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196 of light reflected from the sam
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198 mean square deviation, of the p
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200 7.3 Calculated SHG Signal from
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202 parameter symbol value laser re
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204 parameter symbol value surface
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Chapter 8 Conclusion In this brief
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208 properties of carbon nanotubes.
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210 that propagate through quartz a
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Appendix B Theory of Nonlinear Resp
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214 Fourier transforming equation (
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216 and (CA) with f.b == t(.:.vo) a
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218 The polarization, et, of the po
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220 and (0.1.,1) respectively. Equa
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Appendix E Effect of Sapphire Miscu
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224 with cosO 0 - sin (} o 1 o (E.3
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226 Let us compare the light transm
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228 , .............................
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230 it ( (fp·top..,(arr (ll, M r "
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232 nal-2.00 tab'(:r[ihi]-:r[ila] )
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234 1 - 2500.0; III - xU]; 1/ ti. t
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Bibliography [1] R. K. Chang~ J. Du
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238 [12] J. QL "V. Angerer, M. S. Y
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240 Diamond, SiC and Wide Bandgap S
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242 [40] M. M. Choy and R. L. Byer,
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244 [55] \V. P. Lin, P. M. Lundquis
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246 [70] J. vV. Yang, J. N. Kunzia,
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248 [85] B. Monemar and O. Lagerste
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250 [99] R. C. Miller, Optical Seco
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252 [114] "V. de HeeL W. S. Bacsa,
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William Angerer - Department of Physics and Astronomy - University ...

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