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

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38 Here ρ is the free charge (hole) density, NA the total density of acceptors, N i A the density of ionized acceptors, M1, M2, MT 1, MT 2 the densities of filled shallow traps, filled deep traps, and total shallow and deep trapping sites, respectively, E the electric field, and I the incident light intensity. J is the current density, µ the charge carrier drift mobility, ξ is the diffusion coefficient given by ξ = kBT/e. The quantity s is the cross-section of photogeneration, γT , β1, β2 the trapping rate and detrapping rates for shallow and deep traps, respectively, γ the recombination rate, and ε the dielectric constant. Since the creation of a photorefractive hologram assumes a non-uniform light intensity pattern created by the interfering beams, the incident light intensity can be expressed as a periodic function of x : I = I0 + I1 cos Kx (2.30) where K is the grating vector chosen to be parallel to x -direction. We consider the parameters s, µ, γT and γ to be electric field dependent assuming the following dependencies [17]: s = s(Eref)(E/Eref) p , µ = µ(Eref)e βµ(E1/2 −E 1/2 ref ) γ = γ(Eref)e βµ(E1/2 −E 1/2 ref ) , γT = γT (Eref)e βγ(E1/2 −E 1/2 ref ) (2.31) Here Eref is the relevant reference electric field for each of the parameters. During photorefractive grating formation, the reference electric field for photogeneration ef-
ficiency is the external applied field, while for mobility, trapping and recombination rates the reference electric field is the projection of the applied field on the grating vector. Electric field dependencies given by Eqs. 2.31 are derived from the photogeneration and charge transport theories for polymers [18]. The most commonly used theories leading to Eqs. 2.31 will be summarized later in this section. The molecular theory of the PR effect presented by Eqs. 2.29, 2.31 takes into account only the photoconductivity part of the PR performance (Step 1 through Step 3 as introduced in Section 2.1.2). As it can be seen from Figure 2.5 and Eqs. 2.29, the photoconductivity part of the PR effect involves a number of parameters. One of the goals of my work with PR materials was to investigate what parameters are the most crucial for the PR performance, in particular PR speed. Further, we wanted to study whether it is possible to predict the PR speed of a PR polymer composite based on its photoconductive properties. Then, the next step would be to study the photoconductive and PR properties of different materials, observe how good the theoretical prediction was and design an “ideal” PR polymer composite. This is what we actually did and what I am going to describe in the next sections. We start from the brief theoretical description of the relevant PR processes that are characterized by the parameters shown in Figure 2.5. 39
Page 1 and 2: Nonlinear Optical Probes and Proces
Page 3 and 4: Table of Contents Table of Contents
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: energy levels (ionization potential
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
Page 77 and 78: simplify these to: ˜ λ1 ≈ 1; ˜
Page 79 and 80: - 6 0 , 10 40 30 20 10 simulated d
Page 81 and 82: and ˜γ, the correct estimate of i
Page 83 and 84: 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
Page 105 and 106:
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
Page 121 and 122:
a) NC O O C 60 NC O NC O NC PVK c)
Page 123 and 124:
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
Page 129 and 130:
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
Page 135 and 136:
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
Page 143 and 144:
Figure 3.9: Dependence of the mobil
Page 145 and 146:
a) b) Figure 3.10: Current transien
Page 147 and 148:
Conventionally, in the DC photocond
Page 149 and 150:
a) b) 40 V/ m 100 mW/cm 2 Figure 3.
Page 151 and 152:
1 0= 770 s -1 -1 = 4.35 s B = 1.66
Page 153 and 154:
Figure 3.14: Trapping parameter γT
Page 155 and 156:
Figure 3.15: Long time scale photoc
Page 157 and 158:
Figure 3.16: Example of the photocu
Page 159 and 160:
He-Ne laser Beam Splitter Polarizat
Page 161 and 162:
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
Page 175 and 176:
state diffraction efficiency was th
Page 177 and 178:
Figure 3.26: Dependence of the fast
Page 179 and 180:
E a) b) Applied electri
Page 181 and 182:
Figure 3.28: Dependence of the fast
Page 183 and 184:
(i) calculate the PR speed as deter
Page 185 and 186:
h h C 60 (N A ) s T 1 E PVK PDCST
Page 187 and 188:
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
Page 195 and 196:
Figure 3.30: Intensity dependence o
Page 197 and 198:
3.5.2 Plasticized composites This c
Page 199 and 200:
the recombination rate γ and the s
Page 201 and 202:
h h h h h h C 60 (N (NA) A) s s s
Page 203 and 204:
Figure 3.33: Concentration dependen
Page 205 and 206:
mophore may contain a large error d
Page 207 and 208:
ather requires knowing trapping rat
Page 209 and 210:
Figure 3.36: Time evolution of diff
Page 211 and 212:
and for low concentrations of AODCS
Page 213 and 214:
concentration x10 %. For the lower
Page 215 and 216:
3.6 Summary of Chapter 3 In Chapter
Page 217 and 218:
References [1] W. E. Moerner and S.
Page 219 and 220:
[27] J. Schildkraut and Y. Cui. Zer
Page 221 and 222:
[51] A. Blythe. Electrical Properti
Page 223 and 224:
E = 0 E 0 Fi
Page 225 and 226:
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
Page 245 and 246:
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
Page 251 and 252:
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:
Page 257 and 258:
(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
Page 275 and 276:
polarized UV light. The intensity o
Page 277 and 278:
and then d31 = d sub 31 + N 4 cos
Page 279 and 280:
The angular dependence of the secon
Page 281 and 282:
= ⎛ ⎜ ⎝ sin Φ d25cos 2 Φ s
Page 283 and 284:
S-input polarization The case of s-
Page 285 and 286:
pf,y = 0 pf,x = 1 ω nf bf,x = pf,
Page 287 and 288:
References [1] M. B. Feller, W. Che
Page 289 and 290:
Chapter 6 Summary In this, final, C
Page 291 and 292:
anticipated from the theoretical mo
Page 293 and 294:
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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