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

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Chapter 3 Experimental Ultrafast Nonlinear Optical Spectroscopy In this chapter we discuss the nonlinear optical spectroscopy experimental setup. A further discussion of our spectra normalization and the effects of an ultrafast laser pulse on our measured second-harmonic generation signals (see also section 2.4.2) is given. In addition, the characteristics of the fundamental light generating source. the Ti:AI 2 0 3 laser, are discussed at length. 3.1 Optical Setup Fig. 3.1 displays a schematic of the nonlinear optical setup. This setup is somewhat similar to the one used by M. S. Yeganeh and J. Qi [49, 41J, but with a different fundamental light source. The fundamental light source with frequency ....: was a Ti:AI 2 0 3 laser, the details of which will be more thoroughly discussed in section 3.3. Briefly, the Ti:AI 2 0 3 laser produces ultrashort near IR laser pulses (",,700-1000 nm) at rate of 76 MHz. The individual ultrashort pulses have sufficiently high peak powers (",,50 kvV) to produce measurable nonlinear optical effects. Polarization of both 51 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
52 LOCK-IN AMPLIAER LOCK-IN AMPLIAER PMT MONO- CaMP lITER QUARTZ '> WEDGE SAMPLE 1 MONO- CHROMETER optical chopper I t I TI:SAPPHlRE 700-1000 nm fE- Ar Ion 0 = lens I = spectral filter = Ins ~ = polarizer = beam splitter 0 =pnsm ~ Figure 3_1: Set-up for nonlinear spectroscopy measurements 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
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: 50 2.6 Conclusion In this brief sec
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 -
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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!
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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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