Nonlinear Optical Probes and Processes in Polymers and Liquid ...

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Table of Contents Table of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xii 1 Introduction 1 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2 Photorefractive effect: Phenomenological considerations 10 2.1 Introduction to the photorefractive effect . . . . . . . . . . . . . . . . 10 2.1.1 History of the photorefractive effect . . . . . . . . . . . . . . . 10 2.1.2 Origin of photorefractivity in polymer composites . . . . . . . 14 2.1.3 Experimental methods for photorefractive studies . . . . . . . 20 Two-beam coupling . . . . . . . . . . . . . . . . . . . . . . . . 21 Four-wave mixing . . . . . . . . . . . . . . . . . . . . . . . . . 29 2.2 Molecular theory of the photorefractive effect . . . . . . . . . . . . . 35 2.2.1 Photogeneration . . . . . . . . . . . . . . . . . . . . . . . . . . 40 2.2.2 Charge transport . . . . . . . . . . . . . . . . . . . . . . . . . 44 2.2.3 Charge trapping and detrapping . . . . . . . . . . . . . . . . . 49 2.2.4 Recombination . . . . . . . . . . . . . . . . . . . . . . . . . . 51 2.3 Semi-empirical and numerical analysis of the photorefractive model . 53 2.3.1 Zeroth Order: Photoconductivity in photorefractive polymers 58 Trap-unlimited regime . . . . . . . . . . . . . . . . . . . . . . 61 Short time scale . . . . . . . . . . . . . . . . . . . . . . 61 Long time scale . . . . . . . . . . . . . . . . . . . . . . 69 Trap-limited regime . . . . . . . . . . . . . . . . . . . . . . . . 70 Time evolution of ionized acceptor density n i A0 . . . . . . . . . 72 2.3.2 First Order: Photorefraction . . . . . . . . . . . . . . . . . . . 75 Photorefractive rise . . . . . . . . . . . . . . . . . . . . . . . . 78 Photorefractive decay . . . . . . . . . . . . . . . . . . . . . . . 86 iv
Page 1: Nonlinear Optical Probes and Proces
Page 5 and 6: References . . . . . . . . . . . .
Page 7 and 8: List of Figures 2.1 Schematic exper
Page 9 and 10: 3.31 Time evolution of the diffract
Page 11 and 12: Nonlinear Optical Probes and Proces
Page 13 and 14: Chapter 1 Introduction From ancient
Page 15 and 16: of the polarization density is [2]
Page 17 and 18: degenerate four-wave mixing and the
Page 19 and 20: (Section 3.3) as well as photorefra
Page 21 and 22: References [1] R. Boyd. Nonlinear o
Page 23 and 24: the optics of nonlinear devices bas
Page 25 and 26: materials. The figure-of-merit may
Page 27 and 28: generation of charge carriers, tran
Page 29 and 30: after the interference pattern is c
Page 31 and 32: transport is mostly due to drift ra
Page 33 and 34: 2 1' 2' 1 1 Detector 2 d 2 E a 2
Page 35 and 36: coincide. However, due to refractio
Page 37 and 38: The equation to be solved is the wa
Page 39 and 40: It is obvious that the differential
Page 41 and 42: the symmetry group of the crystal a
Page 43 and 44: much weaker than the writing beams
Page 45 and 46: where d is the thickness of the sam
Page 47 and 48: ability to reorient in the space ch
Page 49 and 50: energy levels (ionization potential
Page 51 and 52: ficiency is the external applied fi
Page 53 and 54:
photogeneration efficiency φ then
Page 55 and 56:
where α is the absorption coeffici
Page 57 and 58:
Energy 0 g( ) i Figure 2.6: Schem
Page 59 and 60:
charge carrier mobility arises from
Page 61 and 62:
2.2.3 Charge trapping and detrappin
Page 63 and 64:
Eqs. 2.29 and so, we will assume be
Page 65 and 66:
However, Eq. 2.44 was derived under
Page 67 and 68:
So, in this case the form of the so
Page 69 and 70:
independent ζ0 [17]. We substitute
Page 71 and 72:
on the both photoconductivity and p
Page 73 and 74:
Trap-unlimited regime In this secti
Page 75 and 76:
m xa 1 0.8 0.6 0.4 0.2 1 -1 TMT1
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simplify these to: ˜ λ1 ≈ 1; ˜
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- 6 0 , 10 40 30 20 10 simulated d
Page 81 and 82:
and ˜γ, the correct estimate of i
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is no longer valid, so the followin
Page 85 and 86:
tion 2.3.2, we show how the ionized
Page 87 and 88:
numerical simulation of the dynamic
Page 89 and 90:
The first order system of equations
Page 91 and 92:
where C, ˜ C are constants determi
Page 93 and 94:
Diffr.eff. , arb.units 1 0.8 0.6 0.
Page 95 and 96:
Figure 2.15: PR speed ν calculated
Page 97 and 98:
a real system the effect from a cha
Page 99 and 100:
ρ0(t) ≈ ˜ρ0 and ionized accept
Page 101 and 102:
the PR performance, in particular d
Page 103 and 104:
2.4.1 “Simple” electro-optic ef
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Eq. 2.71 and compared to the measur
Page 107 and 108:
For one-dimensional molecules whose
Page 109 and 110:
applied electric field Ea, but also
Page 111 and 112:
or, in terms of microscopic quantit
Page 113 and 114:
The photoconductivity part of the P
Page 115 and 116:
[14] Y. Cui, B. Swedek, N. Cheng, J
Page 117 and 118:
[41] P. Gunter and J.-P. Huignard,
Page 119 and 120:
Next, in Section 3.4, we will discu
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a) NC O O C 60 NC O NC O NC PVK c)
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transport is only conducted through
Page 125 and 126:
NA of the C60 molecules (see Figure
Page 127 and 128:
3.3 Photoconductivity experiments I
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photogenerated in the bulk during a
Page 131 and 132:
voltage V , but the voltage V0 at w
Page 133 and 134:
Figure 3.4: Electric field dependen
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320nm Nd:YAG laser with Raman shift
Page 137 and 138:
zero. In these equations, q is the
Page 139 and 140:
non-Gaussian charge transport. In t
Page 141 and 142:
30 V/ m 30 C 0 40 C 0 50 C 0 Figure
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Figure 3.9: Dependence of the mobil
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a) b) Figure 3.10: Current transien
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Conventionally, in the DC photocond
Page 149 and 150:
a) b) 40 V/ m 100 mW/cm 2 Figure 3.
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1 0= 770 s -1 -1 = 4.35 s B = 1.66
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Figure 3.14: Trapping parameter γT
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Figure 3.15: Long time scale photoc
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Figure 3.16: Example of the photocu
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He-Ne laser Beam Splitter Polarizat
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Figure 2.3. Then, the ratio of the
Page 163 and 164:
to explore experimentally which mec
Page 165 and 166:
In most of the PR polymer composite
Page 167 and 168:
disappeared, we opened the other wr
Page 169 and 170:
Now we describe the general trends
Page 171 and 172:
ciency is an increasing function of
Page 173 and 174:
are defined in Eqs. 2.58). Eq. 3.23
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state diffraction efficiency was th
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Figure 3.26: Dependence of the fast
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E a) b) Applied electri
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Figure 3.28: Dependence of the fast
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(i) calculate the PR speed as deter
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h h C 60 (N A ) s T 1 E PVK PDCST
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ferences that affect dissociation r
Page 189 and 190:
serve that the addition of all chro
Page 191 and 192:
is simplified. Knowing the availabl
Page 193 and 194:
the free hole with the ionized acce
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Figure 3.30: Intensity dependence o
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3.5.2 Plasticized composites This c
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the recombination rate γ and the s
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h h h h h h C 60 (N (NA) A) s s s
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Figure 3.33: Concentration dependen
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mophore may contain a large error d
Page 207 and 208:
ather requires knowing trapping rat
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Figure 3.36: Time evolution of diff
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and for low concentrations of AODCS
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concentration x10 %. For the lower
Page 215 and 216:
3.6 Summary of Chapter 3 In Chapter
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References [1] W. E. Moerner and S.
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[27] J. Schildkraut and Y. Cui. Zer
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[51] A. Blythe. Electrical Properti
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E = 0 E 0 Fi
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chromophores are randomly oriented
Page 227 and 228:
where the local field factors are g
Page 229 and 230:
system, and k is Boltzmann’s cons
Page 231 and 232:
Ar Laser + Ti:Sapphire Laser Spectr
Page 233 and 234:
Figure 4.4: Typical data in the EFI
Page 235 and 236:
and the birefringence ∆n(t) is pr
Page 237 and 238:
experiment is the applied field. Ho
Page 239 and 240:
nature. For the transient shown in
Page 241 and 242:
Figure 4.7: Illustration of the HeN
Page 243 and 244:
the screening of the external elect
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is accompanied by the reduction in
Page 247 and 248:
References [1] W. E. Moerner, S. M.
Page 249 and 250:
Chapter 5 Second harmonic generatio
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2 d 2 0 L Figure 5.1: Schematic
Page 253 and 254:
of the nonlinear susceptibilities i
Page 255 and 256:
x z E p E s Figure 5.2:
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(a) (b) (c)
Page 259 and 260:
to βz ′ z ′ z ′ as follows [
Page 261 and 262:
d31 = N 2 〈cos θ sin2 θ〉〈co
Page 263 and 264:
Thus, SHG measurements of the azimu
Page 265 and 266:
a) b) 10 5 -10 -5 5 10 15 -5 -10 c)
Page 267 and 268:
Nd:YAG “Reference” PMT 2 F Quar
Page 269 and 270:
( ) ( ) H3C Si (CH2) 11 O NO2 H 3C
Page 271 and 272:
Figure 5.11: Maker fringes observed
Page 273 and 274:
We observed light-induced alignment
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polarized UV light. The intensity o
Page 277 and 278:
and then d31 = d sub 31 + N 4 cos
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The angular dependence of the secon
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= ⎛ ⎜ ⎝ sin Φ d25cos 2 Φ s
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S-input polarization The case of s-
Page 285 and 286:
pf,y = 0 pf,x = 1 ω nf bf,x = pf,
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References [1] M. B. Feller, W. Che
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Chapter 6 Summary In this, final, C
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anticipated from the theoretical mo
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Bibliography Abkowitz, M., Bassler,
Page 295 and 296:
Daubler, T. K., Bittner, R., Meerho
Page 297 and 298:
Kuzyk, M. G., and Dirk, C. W., Eds.
Page 299 and 300:
Reznikov, Y., Ostroverkhova, O., Si
Page 301:
Zilker, S. J., Grasruck, M., Wolff,
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