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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 18 — Aug. 30, 2010
  • pp: 18793–18804
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Second–harmonic generation in poled polymers: pre–poling history paradigm

G. Pawlik, I. Rau, F. Kajzar, and A. C. Mitus  »View Author Affiliations


Optics Express, Vol. 18, Issue 18, pp. 18793-18804 (2010)
http://dx.doi.org/10.1364/OE.18.018793


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Abstract

Experimental studies of second harmonic generation (SHG) from electric-field poled PMMA - DR1 system show occurrence of a maximum in diagonal and off diagonal tensor components χ(2)(−2ω; ω, ω) at 15 mol % concentration and a rapid decrease above, with a stabilization. The origin of the observed concentration dependence is studied using the Monte Carlo (MC) modeling. We find that presence of maximum is conditioned by the pre-poling history of the sample, when entanglement of linear dipolar structures takes place. Length of the pre-poling interval is an important kinetic parameter which differentiates between various non-exponential kinetics of build-up of polar phase responsible for strong/weak SHG susceptibility.

© 2010 Optical Society of America

1. Introduction

Efficiency of the second harmonic generation (SHG) in poled thin films of functionalized polymers, consisting of quasi 1D charge transfer (CT) chromophores in a polymer matrix depends on degree of polar order of CT molecules, induced by electric field corona poling, photo-assisted electric field poling or all optical poling methods [1

1. Z. Sekkat and W. Knoll, Photoreactive Organic Thin Films (Academic Press, 2002).

]. The second order nonlinear optical (NLO) susceptibility is characterized in this case by two tensor components (for details see e.g., Ref. [2

2. I. Rau and F. Kajzar, “Second harmonic generation and its applications,” Nonl. Opt. Quant. Opt. 38, 99–140 (2008).

]): the diagonal

χZZZ(2)(2ω;ω,ω)=NFβzzz(2ω;ω,ω)cos3θ,
(1)

and the off diagonal one

χXXZ(2)(2ω;ω,ω)=12NFβzzz(2ω;ω,ω)sin2θcosθ,
(2)

where Z is the poling field direction (perpendicular to the thin film surface) and X is perpendicular to it. θ is angle which makes the molecular axis z with Z direction. N denotes the number density of the chromophores (dipoles), βzzz – molecular first hyperpolarizability of CT chromophores, F – the local field factor. In Eqs. (1) and (2) brackets 〈…〉 denote configurational average over all chromophore orientations.

Load parameter defined as 𝓛 = N < cos3 θ >, which is proportional to χ (2) ZZZ, plays the central role in our study. Formula (1) predicts a linear dependence of χ (2) ZZZ on N. Departure from linear law is known since the last decade [3

3. Y-Ch. Lee, “Role of Carbohydrates in Oxidative Modification of Fibrinogen and Other Plasma Proteins” in Photoactive Organic Materials: Science and Application, F. Kajzar, V. M. Agranovich, and C. Y.-C. Lee, Eds. (NATO ASI Series High Technology Vol. 9, Kluwer, Dordrecht, 1995), pp. 175–181.

, 4

4. L. R. Dalton, “Nonlinear Optical Polymeric Materials: From Chromophore Design to Commercial Applications” in Polymers for Photonics Applications I, Advances in Polymer Science, K. S. Lee, Ed., Vol. 158 (Springer Berlin/Heidelberg Publisher, 2002), pp. 1–86.

]. Linear behaviour is reported at small concentration only, say, for N < 1020/cc. For higher concentrations saturation and, occasionally, subsequent falloff of SHG susceptibility are observed in guest–host [5

5. L. R. Dalton, B. H. Robinson, A. K.-Y. Jen, W. H. Steier, and R. Nielsen, “Systematic Development of High Bandwidth, Low Drive Voltage Organic Electrooptic Devices and Their Applications,” Opt. Mater. 21, 19–28 (2003). [CrossRef]

, 6

6. M. Rutkis, A. Jurgis, V. Kampars, A. Vembris, A. Tokmakovs, and V. Kokars, “New Figure of Merit for Tailoring Optimal Structure of the Second Order NLO Chromophore for Guest-Host Polymers,” Mol. Cryst. Liq. Cryst. 485, 903–914 (2008). [CrossRef]

, 7

7. A. W. Harper, S. S. Sun, L. R. Dalton, S. M. Garner, A. Chen, S. Kalluri, W. H. Steier, and B. H. Robinson, “Translating Microscopic Optical Nonlinearity to Macroscopic Optical Nonlinearity: The Role of Chromophore-Chromophore Electrostatic Interactions,” J. Opt. Soc. Am. B 15, 329–337 (1998). [CrossRef]

, 8

8. B. H. Robinson, L. R. Dalton, A. W. Harper, A. S. Ren, F. Wang, C. Zhang, G. Todorova, M. S. Lee, R. Aniszfeld, S. M. Garner, A. Chen, W. H. Steier, S. Houbrecht, A. Persoons, I. Ledoux, J. Zyss, and A. K. Y. Jen, “The Molecular and Supramolecular Engineering of Polymeric Electrooptic Materials,” Chem. Phys. 245, 35–50 (1999). [CrossRef]

] chromophore – polymer systems. Those effects are caused by a few competing mechanisms which become more or less pronounced depending on the system [9

9. I. Rau, P. Armatys, P.-A. Chollet, F. Kajzar, Y. Bretonniere, and C. Andraud, “Aggregation: A new mechanism of relaxation of polar order in electro-optic polymers,” Chem. Phys. Lett. 442, 329–333 (2007). [CrossRef]

]. On microscopic/mesoscopic scales the diminution of SHG susceptibility is due to spatial and orientational local and global correlations of chromophores, ascribed to hypothetical aggregation of dipoles into antiparallel pairs, which diminishes acentric order parameter < cos3 θ > (see Refs. [10

10. G. Pawlik, A. C. Mitus, I. Rau, and F. Kajzar, “Poling of Electro-Optic Materials: Paradigms and Concepts,” Nonl. Opt. Quant. Opt. 40, 57–63 (2010).

, 11

11. A. C. Mitus, G. Pawlik, I. Rau, and F. Kajzar, “Computer Simulations of Poled Guest-Host Systems,” Nonl. Opt. Quant. Opt. 38, 141–162 (2008).

] and references cited therein).

Theoretical statistical mechanics and MC studies were originated by Dalton and co–workers [12

12. L. R. Dalton, W. H. Steier, B. H. Robinson, C. Zhang, A. S. Ren, S. M. Garner, A. Chen, T. M. Londergan, L. Irwin, B. Carlson, L. Fifield, G. Phelan, C. Kincaid, J. Amend, and A. K.-J. Jen, “From Molecules to Opto-Chips: Organic Electrooptic Materials,” J. Chem. Mater. 9, 1905–1920 (1999). [CrossRef]

, 13

13. B. H. Robinson and L. R. Dalton, “Monte Carlo Statistical Mechanical Simulations of the Competition of Intermolecular Electrostatic and Poling Field Interactions in Defining Macroscopic Electrooptic Activity for Organic Chromophore/Polymer Materials,” J. Phys. Chem. A 104, 4785–4795 (2000). [CrossRef]

]. Subsequent lattice [14

14. L. R. Dalton, “Rational Design of Organic Electrooptic Materials,” J. Phys.: Condens. Matter 15, R897–R934 (2003). [CrossRef]

] and off–lattice [15

15. H.L. Rommel and B.H. Robinson, “Orientation of Electro-optic Chromophores under Poling Conditions: A Spheroidal Model,” J. Phys. Chem. C 111, 18765–18777 (2007). [CrossRef]

, 16

16. G. Pawlik, A.C. Mitus, I. Rau, and F. Kajzar, “Monte Carlo Modeling of Chosen Non-Linear Optical Effects for Systems of Guest Molecules in Polymeric and Liquid-Crystal Matrices,” Nonl. Opt. Quant. Opt. 38, 227–244 (2009).

] MC simulations, Molecular Dynamics simulations [17

17. M. Makowska-Janusik, H. Reis, M.G. Papadopoulos, I. Economou, and N.J. Zacharopoulos, “Molecular Dynamics Simulations of Electric Field Poled Nonlinear Optical Chromophores Incorporated in a Polymer Matrix,” J. Phys. Chem. B 108, 588–596 (2004). [CrossRef]

, 18

18. M. R. Leahy-Hoppa, P. D. Cunningham, J. A. French, and L. M. Hayden, “Atomistic Molecular Modeling of the Effect of Chromophore Concentration on the Electro-optic Coefficient in Nonlinear Optical Polymers,” J. Phys. Chem. A 110, 5792–5797 (2006). [CrossRef] [PubMed]

], density functional theories [19

19. H. Reis H., M. Makowska-Janusik, and M.G. Papadopoulos, “Nonlinear optical susceptibilities of poled guest–host systems: A computational study,” J. Phys. Chem. B 108, 8931 – 8940 (2004). [CrossRef]

], mean field theories [20

20. Y.V. Pereverzev and O.V. Prezhdo, “Mean-field theory of acentric order of dipolar chromophores in polymeric electro-optic materials,” Phys. Rev. E 62, 8324–8334 (2000). [CrossRef]

, 21

21. Y.V. Pereverzev, O.V. Prezhdo, and L.R. Dalton, “Mean-field theory of acentric order of chromophores with displaced dipoles,” Chem. Phys. Lett. 340, 328–335 (2001). [CrossRef]

], fully atomistic modeling [22

22. K. Won-Kook and L.M. Hayden, “Fully atomistic modeling of an electric field poled guest–host nonlinear optical polymer,” J. Chem. Phys. 111, 5212–5222 (1999). [CrossRef]

, 23

23. Y. Tu, Y. Luo, and H. Agren, “Molecular Dynamics Simulations Applied to Electric Field Induced Second Harmonic Generation in Dipolar Chromophore Solutions,” J. Phys. Chem. B 110, 8971–8977 (2006). [CrossRef] [PubMed]

, 24

24. Y. Tu, Q. Zhang, and H. Agren, “Electric field poled polymeric nonlinear optical systems: molecular dynamics simulations of poly(methyl methacrylate) doped with disperse red chromophores,” J. Phys. Chem. B 111, 3591–3598 (2007). [CrossRef] [PubMed]

], extended dipole models [25

25. G. Pawlik, A.C. Mitus, I. Rau, and F. Kajzar, “Monte Carlo kinetic study of chromophore distribution in poled guest–host systems,” Proc. SPIE 6891, 68910A-1 – 68910A-7 (2008).

], or inclusion of matrix into MC simulations [26

26. G. Pawlik, D. Wronski, A.C. Mitus, I. Rau, C. Andraud, and F. Kajzar, “A new mechanism of relaxation in poled guest–host systems: Monte Carlo analysis of aggregation scenario,” Proc. SPIE 6653, 66530J-1 – 66530J-7 (2007).

] have substantially deepened our understanding of the underlying physical processes, summarized in terms of various paradigms [10

10. G. Pawlik, A. C. Mitus, I. Rau, and F. Kajzar, “Poling of Electro-Optic Materials: Paradigms and Concepts,” Nonl. Opt. Quant. Opt. 40, 57–63 (2010).

, 11

11. A. C. Mitus, G. Pawlik, I. Rau, and F. Kajzar, “Computer Simulations of Poled Guest-Host Systems,” Nonl. Opt. Quant. Opt. 38, 141–162 (2008).

]. On the other hand, they have led to contradictory results concerning aggregation hypothesis and existence/nonexistence of SHG susceptibility maximum on concentration curve [11

11. A. C. Mitus, G. Pawlik, I. Rau, and F. Kajzar, “Computer Simulations of Poled Guest-Host Systems,” Nonl. Opt. Quant. Opt. 38, 141–162 (2008).

].

Recently, optical polarization microscopy studies have revealed the importance of temporal aspects of aggregation–driven poling [9

9. I. Rau, P. Armatys, P.-A. Chollet, F. Kajzar, Y. Bretonniere, and C. Andraud, “Aggregation: A new mechanism of relaxation of polar order in electro-optic polymers,” Chem. Phys. Lett. 442, 329–333 (2007). [CrossRef]

], emphasizing the role of so far completely disregarded aspect of poling – the pre–poling history of the sample.

The aim of this paper is to elucidate the role of pre–poling history in build–up of polar phase and SHG signal strength for electric field poled system of dipoles in a polymer matrix, using MC modeling. The importance of pre–poling history of the sample was first formulated quantitatively, to the best of our knowledge, in Ref. [11

11. A. C. Mitus, G. Pawlik, I. Rau, and F. Kajzar, “Computer Simulations of Poled Guest-Host Systems,” Nonl. Opt. Quant. Opt. 38, 141–162 (2008).

].

2. Maximum of SHG susceptibility: experimental studies

SHG signal was measured from electric–field poled polymethyl methacrylate - Disperse Red 1 (PMMA-DR1) side–chain polymer system. Side chain polymers are superior compared to guest–host systems in terms of stability and film quality [27

27. C.A. Walsh, D.M. Burland, V.Y. Lee, R.D. Miller, B.A. Smith, R.J. Twieg, and W. Volksen, “Orientational Relaxation in Electric Field Poled Guest – Host and Side – Chain Polymers below Tg,” Macromol. 26, 3720–3722 (1993). [CrossRef]

, 28

28. R.R. Barto, C.W. Frank, P.V. Bedworth, R.E. Taylor, W.W. Anderson, S. Ermer, A. K.-Y. Jen, J.D. Luo, H. Ma, H. - Z. Tang, M. Lee, and A.S. Ren, “Bonding and Molecular Environment Effects on Near – Infrared Optical Absorption Behavior in Nonlinear Optical Monoazo Chromophore – Polymer Materials,” Macromol. 39, 7566 – 7577 (2006). [CrossRef]

]. Moreover, the use of side-chain polymers secures more reliable experimental data, as the relaxation of the polar order is much faster in guest–host system because of a faster chromophore diffusion.

Immediately after the poling the films were mounted on a goniometer for NLO characterization by the optical SHG technique [2

2. I. Rau and F. Kajzar, “Second harmonic generation and its applications,” Nonl. Opt. Quant. Opt. 38, 99–140 (2008).

], performed at 1064.2 nm fundamental wavelength with a Q switched Nd:YAG laser. The data were calibrated with SHG measurements on an y-cut α-quartz single crystal, performed at the same condition, and screened using the formalism described in [2

2. I. Rau and F. Kajzar, “Second harmonic generation and its applications,” Nonl. Opt. Quant. Opt. 38, 99–140 (2008).

], which takes account of the harmonic wave reabsorption. More details can be found in [29

29. F. Kajzar, O. Krupka, G. Pawlik, A. Mitus, and I. Rau, “Concentration Variation of Quadratic NLO Susceptibility in PMMA-DR1 Side Chain Polymer,” Mol. Cryst. Liq. Cryst. 522, 180–190 (2010). [CrossRef]

].

The optical absorption of thin films was measured with a Perkins-Elmer UV-VIS-IR spectrometer. The measured absorption spectra for different concentrations are compared in Fig. 1. The optical densities of the thin films were not normalized for film thickness and thus do not scale linearly with concentration. A small blue shift of the maximum absorption wavelength λmax is observed. However it is significantly smaller than observed for the same molecule in other matrices [31

31. A. Priimagi, S. Cattaneo, R.H.A. Ras, S. Valkama, O. Ikkala, and M. Kauranen, “Polymer – Dye Complexes: A Facile Method for High Doping Level and Aggregation Control of Dye Molecules,” Chem. Mater. 17, 5798–5802 (2005). [CrossRef]

, 32

32. J. Reyes-Esqueda, B. Darracq, J. Garcia-Macedo, M. Canva, M. Blanchard-Desce, F. Chaput, K. Lahlil, J.P. Boilot, A. Brun, and Y. Levy, “Effect of chromophore – chromophore electrostatic interactions in the NLO response of functionalized organic – inorganic sol – gel materials,” Opt. Commun. 198, 207–215 (2001). [CrossRef]

]. But usually the polarity of molecule environment plays an important role in the position of excited levels, not only the aggregation. The values of λmax for different concentrations are listed in Table 1.

The measured values of χ (2) ZZZ/2 and χ (2) XXZ/2 tensor components for the studied thin films as function of the chromophore molar content expressed in percents, are shown in Fig. 2 for both tensor components, expressed in the commonly used notation: dsp = χ (2) XXZ/2 and dpp = χ (2) ZZZ/2. In both cases the maximum of SHG susceptibility is present.

Fig. 1. Absorption spectra of thin films of PMMA–DR1 with different chromophore concentrations. The optical densities of the thin films were not normalized for film thickness and thus do not scale linearly with concentration.

Table 1. Maximum absorption wavelength for studied thin films for different DR1 concentrations.

table-icon
View This Table
Fig. 2. Molar chromophore concentration (in percents) dependence of dsp = χ (2) XXZ/2 and dpp = χ (2) ZZZ/2 for the studied thin films. The error bar (not shown) is 10%.

In nonlinear optics and in the aggregation process important is the density of dipole moments which corresponds to the density of active molecules (cf. Eqs. (1) – (2)). This is why we preferred to use description in term of molar concentration. This follows directly from the usually used chemical formula for such polymers which in present case reads: MMA1−xDR1x, where MMA is monomer unit and x, multiplied by 100, gives directly the mol concentration in percents. The transformation to weight concentration is given by the following equation:

Cw=NsegMdyeNsegMseg+NmonMmon,
(3)

where Nseg and Nmon denote the number of substituents with dye polymer repetition units and the number of monomers, respectively. Mdye, Mseg and Mmon are, respectively, molecular masses of dye, substituted segment and monomer molecules, respectively. In the present case Mseg = 382.42 g/mol, Mmon = 100.12 g/mol and Mdye = 313.33 g/mol (314.34-1.008 because of substitution). The molar concentration refers also directly to the density of interacting dipoles, as used in MC stimulation.

Within the experimental accuracy we observe an almost linear increase of the both dsp and dpp tensor components up to 15 mol % of DR1 and a decrease at higher concentrations. For concentrations starting from 35 mol % both tensor components stabilize and remain almost constant. Although there are only two measurements points on the rising part of experimental data (8 mol % and 15 mol %), de facto there is another one corresponding to the origin (zeroth concentration) at which the SHG susceptibility is equal to zero. We note here that both tensor components exhibit similar concentration dependence. Also the ratio dpp/dsp ≈ 3 remains almost constant within the experimental accuracy which is roughly of ±20% for each concentration (the 20% relative error originates from adding 10% error on dsp and dpp determinations). It doesn’t take account of a possible effect of error in dsp determination on the deduced value of dpp. In fact the dpp value depends on the value of dsp injected in calculations (for details see Refs. [2

2. I. Rau and F. Kajzar, “Second harmonic generation and its applications,” Nonl. Opt. Quant. Opt. 38, 99–140 (2008).

, 33

33. L. Favaretto, G. Barbarella, I. Rau, F. Kajzar, S. Caria, M. Murgia, and R. Zamboni, “Efficient second harmonic generation from thin films of V-shaped benzo[b]thiophene based molecules,” Opt. Express 17, 2557–2564 (2009). [CrossRef] [PubMed]

]).

The same polymer system was studied also by Robinson and Dalton [13

13. B. H. Robinson and L. R. Dalton, “Monte Carlo Statistical Mechanical Simulations of the Competition of Intermolecular Electrostatic and Poling Field Interactions in Defining Macroscopic Electrooptic Activity for Organic Chromophore/Polymer Materials,” J. Phys. Chem. A 104, 4785–4795 (2000). [CrossRef]

] and the authors report a continuous increase of SHG susceptibility up to the concentration of 30 wt %, without reaching the maximum, with a tendency to saturate. Because of large molecular mass of DR1 molecules as compared to that of monomer it corresponds to a small substitution level of about 13.2 mol %. So their data lie on the increasing part of our experimental concentration dependence. Intriguing is a fast decrease of χ (2) susceptibility and its stabilization for concentrations starting from 35 mol %. A similar behaviour is observed in the case of solution of lyotropic liquid crystals (LC) in water [34

34. P. Oswald and P. Pieranski, Les cristaix liquides: Concepts et proprits physiques illustrs par des expriences, Vol. 1, p. 51 (Gordon and Breach Science Publishers, Paris, 2000).

]. At low concentration only monomers are present. Their concentration increases linearly with LC concentration. At higher concentration micelles (a kind of aggregates) appear and their concentration is increasing rapidly, while the monomer concentration stabilizes and remains constant when increasing LC concentration. It means that all introduced LC molecules either attach to micelles or form new ones. The mechanism behind this behaviour, similarly as in the present case, is the strong dipole-dipole interaction.

3. Monte Carlo study of guest–host system

The potential energy of the system consists of three parts: point dipole–dipole interaction, interaction of dipoles with poling field and repulsive soft–sphere interaction:

U=ij14πε0ε1rij3[μi·μj3(μi·r̂ij)(μj·r̂ij)]iE·μi+εLJij(σrij)12,
(4)

where E⃗ denotes electric poling field, µ⃗ii-th dipole moment, rij and ij – respectively distance and unit vector between dipoles i and j, ε – dielectric constant of the host, and σ – characteristic scale for soft–sphere interactions. The parameters were µ = 26 D, σ = 7 Å, εLJ/(kBT) = 0.1, ε = 4, E = 150 V/µm, T = 350 K. Cutoff for soft core and electrostatic interactions was 5 nm. The reaction field method was also used; both approaches yield similar results.

This specific set of parameters was taken after a seminal paper on poling [15

15. H.L. Rommel and B.H. Robinson, “Orientation of Electro-optic Chromophores under Poling Conditions: A Spheroidal Model,” J. Phys. Chem. C 111, 18765–18777 (2007). [CrossRef]

]. The dipole moment is larger than the dipole moment of individual DR1 molecule (≈ 7.5 D). It is well–known [13

13. B. H. Robinson and L. R. Dalton, “Monte Carlo Statistical Mechanical Simulations of the Competition of Intermolecular Electrostatic and Poling Field Interactions in Defining Macroscopic Electrooptic Activity for Organic Chromophore/Polymer Materials,” J. Phys. Chem. A 104, 4785–4795 (2000). [CrossRef]

] that in lattice models sufficiently large values of µ are necessary to get the maximum on the susceptibility curve. We note that PMMA is a polar medium. Its microscopic effective dielectric constant is of 22–30 as reported in Ref. [35

35. A. K. Hamanoue, S. Hirayama, M. Amano, K. Nakajima, T. Nakayama, and H. Teranishi, “Spectroscopic Study of 10-Benzoyl-9-anthrol and Its Anion in Basic Media. An Estimation of Microscopic Polarity of PMMA,” Bull. Chem. Soc. Jpn. 55, 3104–3108 (1982). [CrossRef]

]. Functionalizing PMMA with DR1 molecules will create a more polar environment because of large dipole moment of DR1. For this reason the dipole moment of DR1 molecule in PMMA-DR1 system may be larger (“dressed” dipole) than reported in literature for individual molecule. The observed blue shift (Fig. 1) may be due to the increasing polarity of the medium, as observed when poling PMMA-DR1 system [36

36. D. Morichere, M. Dumont, Y. Levy, G. Gadret, and F. Kajzar, “Nonlinear properties of poled polymer films: SHG and electrooptic measurements,” Proc. SPIE 1560, 214–225 (1991). [CrossRef]

], counterbalancing the expected red shift due to the aggregation process [9

9. I. Rau, P. Armatys, P.-A. Chollet, F. Kajzar, Y. Bretonniere, and C. Andraud, “Aggregation: A new mechanism of relaxation of polar order in electro-optic polymers,” Chem. Phys. Lett. 442, 329–333 (2007). [CrossRef]

]. Specific choice of µ is not critical since our main goal is to reproduce rather qualitatively than quantitatively the effect of maximum of χ (2).

We study the MC evolution of SHG susceptibility χ (2) ZZZ𝓛 in two cases. In the first one, referred to as the case with pre–poling history, the poling field is switched on following an interval of electric field–free evolution during which the pre–poling processes take place. In the second case, without pre–poling history, the poling field is switched on immediately after preparing of the sample. The dependence of the amplitude E of the poling field on number of MC Steps (MCS) is shown in Fig. 3. In this case the length of the pre–poling interval 𝒫 is 105 MCS.

Fig. 3. Poling electric field as function of number of MC steps: system with pre–poling phase (thin solid line) and without pre–poling phase (dashed line).

4. Pre–poling history and build–up of SHG susceptibility

Fig. 4. Plot of load parameter N < cos3 θ > ∝ χ (2) ZZZ as a function of number density N: with pre–poling history (left) and without pre–poling history (right) (note different scales on vertical axes).
Fig. 5. MC kinetics of acentric order parameter < cos3 θ > for N = 2.16 × 1020/cc. System with pre–poling history (left) and without pre–poling history (right). Solid lines: stretched–exponential fits.

Fig. 6. Configuration of dipoles: initial configuration (a); after 8 × 105 MCS, without pre–poling history (b); after 105 MCS without electric field (pre–poling period) (c); after 8 × 105 MCS for poling started after 105 MCS (d). Polymeric chains are not shown.

5. Discussion

Fig. 7. Plot of normalized susceptibility χ (2)/χ (2) max against normalized concentration of dipoles (see text). 〇: experiment, ×: MC simulations, thick solid line: after Ref. [8], thin solid line: after Ref. [6].

Direct comparison of Fig. 2 and Fig. 4 clearly shows that experimentally observed behaviour corresponds to that of a system with pre–poling history. The measured versus predicted SHG coefficients are shown in Fig. 7, where additionally the data from earlier studies of guest–host [6

6. M. Rutkis, A. Jurgis, V. Kampars, A. Vembris, A. Tokmakovs, and V. Kokars, “New Figure of Merit for Tailoring Optimal Structure of the Second Order NLO Chromophore for Guest-Host Polymers,” Mol. Cryst. Liq. Cryst. 485, 903–914 (2008). [CrossRef]

, 8

8. B. H. Robinson, L. R. Dalton, A. W. Harper, A. S. Ren, F. Wang, C. Zhang, G. Todorova, M. S. Lee, R. Aniszfeld, S. M. Garner, A. Chen, W. H. Steier, S. Houbrecht, A. Persoons, I. Ledoux, J. Zyss, and A. K. Y. Jen, “The Molecular and Supramolecular Engineering of Polymeric Electrooptic Materials,” Chem. Phys. 245, 35–50 (1999). [CrossRef]

] systems are shown. We use normalized concentrations defined as ratio of concentration to the concentration at maximum of χ (2). Susceptibilities were normalized to the maximum of χ (2): χ (2) norm = χ (2)/χ (2) max. Solid lines are fits to the experimental data. In the interval of normalized concentrations where the data are available in all four cases in Fig. 7 the curves are close to each other. This indicates some kind of universality in poling of thin films of guest–host and side–chain functionalized polymers for those concentrations. MC modeling offers a reasonable description of maximum on χ (2) curves. For larger values of normalized concentration (> 1.5) experimental data are lower than MC predictions. This implies that for those concentrations the model does not account for some unknown physical processes responsible for spatial and orientational ordering of the dipoles in the matrix.

The plots shown in Fig. 4 indicate that the length 𝒫 of pre–poling interval is an important kinetic parameter which determines the quality of emerging polar phase in the course of poling. To investigate this topic quantitatively we have studied the dependence of equilibrium load parameter 𝓛 on 𝒫 for two reduced densities: N = 3.43 × 1020/cc and N = 5.12 × 1020/cc, both larger then Nm = 1.7 × 1020/cc. The results for N = 5.12 × 1020/cc are shown in Fig. 8. We find a strong impact of pre–poling interval length 𝒫 on value of load parameter for short pre–poling intervals. With increasing value of 𝒫 the dependence becomes weaker and the load parameter levels off after (3 − 5) × 104 MCS. Similar results were found for lower number density N = 3.43 × 1020/cc. We conclude that the value 𝒫 = 105 MCS used in Section 4 is sufficient to account for important rearrangement processes in the pre–poling phase.

Another interesting topic is how the kinetics of the build–up process of polar phase depends on the dipole density. For reduced density N = 2.16 × 1020/cc the system with pre–poling interval length 𝒫 = 105 MCS follows stretched exponential kinetics with exponent α ≃ 0.5 (Section 4). Preliminary analysis shows that the kinetics for the systems with the same 𝒫 remains stretched exponential for all reduced densities studied in this paper. More specifically, the exponent α becomes dependent on the reduced density. For N < Nm = 1.7 × 1020/cc α is density independent: α ≃ 0.5, while for N > Nm a slow decrease of α is observed. For N = 5.12 × 1020/cc we have found α ≃ 0.35.

Fig. 8. Equilibrium load parameter 𝓛 = N < cos3 θ > as function of pre–poling interval length 𝒫 for reduced density N = 5.12 × 1020/cc.

Finally, let us comment briefly on the influence polymer chain length on the susceptibilities. We expect some weak dependency when the polymer chain length increases a few times, say up to 100 monomers (Kuhn elements), in a distant analogy with a weak dependence found in the case of diffraction gratings inscription in two-dimensional chromophore – polymer matrix guest–host system [37

37. G. Pawlik, A.C. Mitus, A. Miniewicz, and F. Kajzar, “Monte Carlo simulations of temperature dependence of the kinetics of diffraction gratings formation in a polymer matrix containing azobenzene chromophores,” J. Nonl. Opt. Phys. Mat. 13, 481–489 (2004). [CrossRef]

].

6. Conclusions

SHG from electric–field poled PMMA – DR1 side–chain system displays an undesirable effect: a maximum and a subsequent fall–off of SHG susceptibility as function of number density of DR1 dipoles. This effect was studied using MC modeling. We have found that presence (or absence) of maximum is conditioned by the pre–poling history of the sample. Pre–poling effects result in (i) slow, stretched–exponential build–up of polar phase; (ii) low SHG signal; and (iii) presence of a maximum of χ (2) ZZZ as function of number density of dipoles. On the contrary, the build–up of polar phase in freshly prepared films without pre–poling history (i) occurs quickly and follows a more complicated non–exponential relaxation; (ii) yields larger SHG susceptibility; and (iii) results in a saturation rather than a maximum of χ (2) ZZZ. On the microscopic/mesoscopic scale the origin of different kinetics is due to the spatial entanglement of linear (and more complicated) structures of dipoles with head–to–tail order in the pre–poling interval which hinders the reorientation of the dipoles, the build–up of well–ordered polar phase, and of large SHG susceptibility; stretched–exponential kinetics was observed.

Polymers (with guest inclusions) belong to the class of complex systems [38

38. R. Metzler and J. Klafter, “The random walk’s guide to anomalous diffusion: A fractional dynamics approach,” Phys. Rep. 339, 1–77 (2000). [CrossRef]

]. Thus, it is reasonable to assume that the occurrence of maximum is driven not by a single fundamental mechanism but rather by a few different mechanisms promoting various patterns of dipolar aggregation like, e.g., parallel or antiparallel aggregates. These mechanisms become more or less pronounced depending on the details of the system [9

9. I. Rau, P. Armatys, P.-A. Chollet, F. Kajzar, Y. Bretonniere, and C. Andraud, “Aggregation: A new mechanism of relaxation of polar order in electro-optic polymers,” Chem. Phys. Lett. 442, 329–333 (2007). [CrossRef]

]; in particular, the tendency of the molecules to aggregate can be reduced when intermolecular interactions between a polymer host and guest dye molecules are controlled [31

31. A. Priimagi, S. Cattaneo, R.H.A. Ras, S. Valkama, O. Ikkala, and M. Kauranen, “Polymer – Dye Complexes: A Facile Method for High Doping Level and Aggregation Control of Dye Molecules,” Chem. Mater. 17, 5798–5802 (2005). [CrossRef]

]. If parallel, antiparallel and more complex types of aggregates are present on various spatial scales then UV-Vis absorption spectra may display more complex features than a blue or a red shift.

Spatial inhomogeneities of any origin (kinetic or equilibrium) on sufficiently large scale can cause similar effects. The sample storage and processing conditions can have a profound effect on bulk material SHG response. The pre–poling time interval which can strongly influence (decrease) the SHG susceptibility can be relatively short. MC kinetics (Fig. 5, left) shows that the pre–poling interval constituting approximately 10% of the poling interval results in a strong decrease of SHG susceptibility. In our experiment poling took three minutes which implies that important spatial/orientational dipolar reorganization can take place in less than one minute close to Tg. The presence of dipolar aggregates in freshly obtained thin films reported in [9

9. I. Rau, P. Armatys, P.-A. Chollet, F. Kajzar, Y. Bretonniere, and C. Andraud, “Aggregation: A new mechanism of relaxation of polar order in electro-optic polymers,” Chem. Phys. Lett. 442, 329–333 (2007). [CrossRef]

] may be due to similar effects in a more dense system, where linear organization is strongly suppressed.

Let us comment on MC simulations. The experimental data are for a side–chain polymer whereas the simulations, for the sake of simplicity, are performed for the guest–host system. The comparison of available experimental data for guest–host and side–chain systems in Fig. 7 shows, however, that the normalized susceptibilities are similar, and that guest–host MC modeling is acceptable. For higher normalized concentrations it is no more true and modifications of the model are necessary, including more sophisticated MC simulations and more realistic treatment of physical dipoles. This is, however not the central point of interest of our study, which is primarily oriented onto an explanation of maximum of SHG susceptibility in terms of pre–poling history of the sample.

Finally, we have shown that the maximum of SHG susceptibility depends on the pre–poling history of the sample using some set of parameters for guest–host system, like volume fraction of dipolar material and polymer chain length. Very important is also the point–dipole approximation for physical dipoles. A systematic study, including additionally extended–dipole paradigm [10

10. G. Pawlik, A. C. Mitus, I. Rau, and F. Kajzar, “Poling of Electro-Optic Materials: Paradigms and Concepts,” Nonl. Opt. Quant. Opt. 40, 57–63 (2010).

, 11

11. A. C. Mitus, G. Pawlik, I. Rau, and F. Kajzar, “Computer Simulations of Poled Guest-Host Systems,” Nonl. Opt. Quant. Opt. 38, 141–162 (2008).

] and interpretation of stretched exponential kinetics in terms of “microscopic” models [39

39. A. Z. Patashinski and M.A. Ratner, “Orientation relaxation in glassy polymers. II. Dipole-size spectroscopy and short-time kinetics,” J. Chem. Phys. 103, 10779–10789 (1995). [CrossRef]

] requires massive simulations and is at progress now; the results will be published elsewhere.

Acknowledgements

ACM and GP thank Wroclaw University of Technology (Poland) for financial support. FK and IR acknowledge financial funding through the project POSCCE nr 634/12575, code SMIS-CSNR 12575.

References and links

1.

Z. Sekkat and W. Knoll, Photoreactive Organic Thin Films (Academic Press, 2002).

2.

I. Rau and F. Kajzar, “Second harmonic generation and its applications,” Nonl. Opt. Quant. Opt. 38, 99–140 (2008).

3.

Y-Ch. Lee, “Role of Carbohydrates in Oxidative Modification of Fibrinogen and Other Plasma Proteins” in Photoactive Organic Materials: Science and Application, F. Kajzar, V. M. Agranovich, and C. Y.-C. Lee, Eds. (NATO ASI Series High Technology Vol. 9, Kluwer, Dordrecht, 1995), pp. 175–181.

4.

L. R. Dalton, “Nonlinear Optical Polymeric Materials: From Chromophore Design to Commercial Applications” in Polymers for Photonics Applications I, Advances in Polymer Science, K. S. Lee, Ed., Vol. 158 (Springer Berlin/Heidelberg Publisher, 2002), pp. 1–86.

5.

L. R. Dalton, B. H. Robinson, A. K.-Y. Jen, W. H. Steier, and R. Nielsen, “Systematic Development of High Bandwidth, Low Drive Voltage Organic Electrooptic Devices and Their Applications,” Opt. Mater. 21, 19–28 (2003). [CrossRef]

6.

M. Rutkis, A. Jurgis, V. Kampars, A. Vembris, A. Tokmakovs, and V. Kokars, “New Figure of Merit for Tailoring Optimal Structure of the Second Order NLO Chromophore for Guest-Host Polymers,” Mol. Cryst. Liq. Cryst. 485, 903–914 (2008). [CrossRef]

7.

A. W. Harper, S. S. Sun, L. R. Dalton, S. M. Garner, A. Chen, S. Kalluri, W. H. Steier, and B. H. Robinson, “Translating Microscopic Optical Nonlinearity to Macroscopic Optical Nonlinearity: The Role of Chromophore-Chromophore Electrostatic Interactions,” J. Opt. Soc. Am. B 15, 329–337 (1998). [CrossRef]

8.

B. H. Robinson, L. R. Dalton, A. W. Harper, A. S. Ren, F. Wang, C. Zhang, G. Todorova, M. S. Lee, R. Aniszfeld, S. M. Garner, A. Chen, W. H. Steier, S. Houbrecht, A. Persoons, I. Ledoux, J. Zyss, and A. K. Y. Jen, “The Molecular and Supramolecular Engineering of Polymeric Electrooptic Materials,” Chem. Phys. 245, 35–50 (1999). [CrossRef]

9.

I. Rau, P. Armatys, P.-A. Chollet, F. Kajzar, Y. Bretonniere, and C. Andraud, “Aggregation: A new mechanism of relaxation of polar order in electro-optic polymers,” Chem. Phys. Lett. 442, 329–333 (2007). [CrossRef]

10.

G. Pawlik, A. C. Mitus, I. Rau, and F. Kajzar, “Poling of Electro-Optic Materials: Paradigms and Concepts,” Nonl. Opt. Quant. Opt. 40, 57–63 (2010).

11.

A. C. Mitus, G. Pawlik, I. Rau, and F. Kajzar, “Computer Simulations of Poled Guest-Host Systems,” Nonl. Opt. Quant. Opt. 38, 141–162 (2008).

12.

L. R. Dalton, W. H. Steier, B. H. Robinson, C. Zhang, A. S. Ren, S. M. Garner, A. Chen, T. M. Londergan, L. Irwin, B. Carlson, L. Fifield, G. Phelan, C. Kincaid, J. Amend, and A. K.-J. Jen, “From Molecules to Opto-Chips: Organic Electrooptic Materials,” J. Chem. Mater. 9, 1905–1920 (1999). [CrossRef]

13.

B. H. Robinson and L. R. Dalton, “Monte Carlo Statistical Mechanical Simulations of the Competition of Intermolecular Electrostatic and Poling Field Interactions in Defining Macroscopic Electrooptic Activity for Organic Chromophore/Polymer Materials,” J. Phys. Chem. A 104, 4785–4795 (2000). [CrossRef]

14.

L. R. Dalton, “Rational Design of Organic Electrooptic Materials,” J. Phys.: Condens. Matter 15, R897–R934 (2003). [CrossRef]

15.

H.L. Rommel and B.H. Robinson, “Orientation of Electro-optic Chromophores under Poling Conditions: A Spheroidal Model,” J. Phys. Chem. C 111, 18765–18777 (2007). [CrossRef]

16.

G. Pawlik, A.C. Mitus, I. Rau, and F. Kajzar, “Monte Carlo Modeling of Chosen Non-Linear Optical Effects for Systems of Guest Molecules in Polymeric and Liquid-Crystal Matrices,” Nonl. Opt. Quant. Opt. 38, 227–244 (2009).

17.

M. Makowska-Janusik, H. Reis, M.G. Papadopoulos, I. Economou, and N.J. Zacharopoulos, “Molecular Dynamics Simulations of Electric Field Poled Nonlinear Optical Chromophores Incorporated in a Polymer Matrix,” J. Phys. Chem. B 108, 588–596 (2004). [CrossRef]

18.

M. R. Leahy-Hoppa, P. D. Cunningham, J. A. French, and L. M. Hayden, “Atomistic Molecular Modeling of the Effect of Chromophore Concentration on the Electro-optic Coefficient in Nonlinear Optical Polymers,” J. Phys. Chem. A 110, 5792–5797 (2006). [CrossRef] [PubMed]

19.

H. Reis H., M. Makowska-Janusik, and M.G. Papadopoulos, “Nonlinear optical susceptibilities of poled guest–host systems: A computational study,” J. Phys. Chem. B 108, 8931 – 8940 (2004). [CrossRef]

20.

Y.V. Pereverzev and O.V. Prezhdo, “Mean-field theory of acentric order of dipolar chromophores in polymeric electro-optic materials,” Phys. Rev. E 62, 8324–8334 (2000). [CrossRef]

21.

Y.V. Pereverzev, O.V. Prezhdo, and L.R. Dalton, “Mean-field theory of acentric order of chromophores with displaced dipoles,” Chem. Phys. Lett. 340, 328–335 (2001). [CrossRef]

22.

K. Won-Kook and L.M. Hayden, “Fully atomistic modeling of an electric field poled guest–host nonlinear optical polymer,” J. Chem. Phys. 111, 5212–5222 (1999). [CrossRef]

23.

Y. Tu, Y. Luo, and H. Agren, “Molecular Dynamics Simulations Applied to Electric Field Induced Second Harmonic Generation in Dipolar Chromophore Solutions,” J. Phys. Chem. B 110, 8971–8977 (2006). [CrossRef] [PubMed]

24.

Y. Tu, Q. Zhang, and H. Agren, “Electric field poled polymeric nonlinear optical systems: molecular dynamics simulations of poly(methyl methacrylate) doped with disperse red chromophores,” J. Phys. Chem. B 111, 3591–3598 (2007). [CrossRef] [PubMed]

25.

G. Pawlik, A.C. Mitus, I. Rau, and F. Kajzar, “Monte Carlo kinetic study of chromophore distribution in poled guest–host systems,” Proc. SPIE 6891, 68910A-1 – 68910A-7 (2008).

26.

G. Pawlik, D. Wronski, A.C. Mitus, I. Rau, C. Andraud, and F. Kajzar, “A new mechanism of relaxation in poled guest–host systems: Monte Carlo analysis of aggregation scenario,” Proc. SPIE 6653, 66530J-1 – 66530J-7 (2007).

27.

C.A. Walsh, D.M. Burland, V.Y. Lee, R.D. Miller, B.A. Smith, R.J. Twieg, and W. Volksen, “Orientational Relaxation in Electric Field Poled Guest – Host and Side – Chain Polymers below Tg,” Macromol. 26, 3720–3722 (1993). [CrossRef]

28.

R.R. Barto, C.W. Frank, P.V. Bedworth, R.E. Taylor, W.W. Anderson, S. Ermer, A. K.-Y. Jen, J.D. Luo, H. Ma, H. - Z. Tang, M. Lee, and A.S. Ren, “Bonding and Molecular Environment Effects on Near – Infrared Optical Absorption Behavior in Nonlinear Optical Monoazo Chromophore – Polymer Materials,” Macromol. 39, 7566 – 7577 (2006). [CrossRef]

29.

F. Kajzar, O. Krupka, G. Pawlik, A. Mitus, and I. Rau, “Concentration Variation of Quadratic NLO Susceptibility in PMMA-DR1 Side Chain Polymer,” Mol. Cryst. Liq. Cryst. 522, 180–190 (2010). [CrossRef]

30.

F. Kajzar, A. Jen, and K. S. Lee, “Polymeric Materials and Their Orientation Techniques for Second-Order Nonlinear Optics, Polymers for Photonics Applications II: Nonlinear Optical, Photorefractive and Two-Photon Absorption Polymers,” in Advances in Polymer Science, K. S. Lee and G. Wegner, Eds., Vol. 161 (Springer Verlag, 2003).

31.

A. Priimagi, S. Cattaneo, R.H.A. Ras, S. Valkama, O. Ikkala, and M. Kauranen, “Polymer – Dye Complexes: A Facile Method for High Doping Level and Aggregation Control of Dye Molecules,” Chem. Mater. 17, 5798–5802 (2005). [CrossRef]

32.

J. Reyes-Esqueda, B. Darracq, J. Garcia-Macedo, M. Canva, M. Blanchard-Desce, F. Chaput, K. Lahlil, J.P. Boilot, A. Brun, and Y. Levy, “Effect of chromophore – chromophore electrostatic interactions in the NLO response of functionalized organic – inorganic sol – gel materials,” Opt. Commun. 198, 207–215 (2001). [CrossRef]

33.

L. Favaretto, G. Barbarella, I. Rau, F. Kajzar, S. Caria, M. Murgia, and R. Zamboni, “Efficient second harmonic generation from thin films of V-shaped benzo[b]thiophene based molecules,” Opt. Express 17, 2557–2564 (2009). [CrossRef] [PubMed]

34.

P. Oswald and P. Pieranski, Les cristaix liquides: Concepts et proprits physiques illustrs par des expriences, Vol. 1, p. 51 (Gordon and Breach Science Publishers, Paris, 2000).

35.

A. K. Hamanoue, S. Hirayama, M. Amano, K. Nakajima, T. Nakayama, and H. Teranishi, “Spectroscopic Study of 10-Benzoyl-9-anthrol and Its Anion in Basic Media. An Estimation of Microscopic Polarity of PMMA,” Bull. Chem. Soc. Jpn. 55, 3104–3108 (1982). [CrossRef]

36.

D. Morichere, M. Dumont, Y. Levy, G. Gadret, and F. Kajzar, “Nonlinear properties of poled polymer films: SHG and electrooptic measurements,” Proc. SPIE 1560, 214–225 (1991). [CrossRef]

37.

G. Pawlik, A.C. Mitus, A. Miniewicz, and F. Kajzar, “Monte Carlo simulations of temperature dependence of the kinetics of diffraction gratings formation in a polymer matrix containing azobenzene chromophores,” J. Nonl. Opt. Phys. Mat. 13, 481–489 (2004). [CrossRef]

38.

R. Metzler and J. Klafter, “The random walk’s guide to anomalous diffusion: A fractional dynamics approach,” Phys. Rep. 339, 1–77 (2000). [CrossRef]

39.

A. Z. Patashinski and M.A. Ratner, “Orientation relaxation in glassy polymers. II. Dipole-size spectroscopy and short-time kinetics,” J. Chem. Phys. 103, 10779–10789 (1995). [CrossRef]

OCIS Codes
(000.6590) General : Statistical mechanics
(190.2620) Nonlinear optics : Harmonic generation and mixing
(310.3840) Thin films : Materials and process characterization

ToC Category:
Nonlinear Optics

History
Original Manuscript: June 24, 2010
Revised Manuscript: July 18, 2010
Manuscript Accepted: August 11, 2010
Published: August 18, 2010

Citation
G. Pawlik, I. Rau, F. Kajzar, and A. C. Mitus, "Second–harmonic generation in poled polymers: pre–poling history paradigm," Opt. Express 18, 18793-18804 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-18-18793


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References

  1. Z. Sekkat, and W. Knoll, Photoreactive Organic Thin Films (Academic Press, 2002).
  2. I. Rau, and F. Kajzar, “Second harmonic generation and its applications,” Nonl. Opt. Quant. Opt. 38, 99–140 (2008).
  3. Y.-Ch. Lee, “Role of Carbohydrates in Oxidative Modification of Fibrinogen and Other Plasma Proteins” in Photoactive Organic Materials: Science and Application, F. Kajzar, V. M. Agranovich and C. Y.-C. Lee, Eds. (NATO ASI Series High Technology Vol. 9, Kluwer, Dordrecht, 1995), pp. 175–181.
  4. L. R. Dalton, “Nonlinear Optical Polymeric Materials: From Chromophore Design to Commercial Applications” in Polymers for Photonics Applications I, Advances in Polymer Science, K. S. Lee, Ed., Vol. 158 (Springer Berlin/Heidelberg Publisher, 2002), pp. 1–86.
  5. L. R. Dalton, B. H. Robinson, A. K.-Y. Jen, W. H. Steier, and R. Nielsen, “Systematic Development of High Bandwidth, Low Drive Voltage Organic Electrooptic Devices and Their Applications,” Opt. Mater. 21, 19–28 (2003). [CrossRef]
  6. M. Rutkis, A. Jurgis, V. Kampars, A. Vembris, A. Tokmakovs, and V. Kokars, “New Figure of Merit for Tailoring Optimal Structure of the Second Order NLO Chromophore for Guest-Host Polymers,” Mol. Cryst. Liq. Cryst. (Phila. Pa.) 485, 903–914 (2008). [CrossRef]
  7. A. W. Harper, S. S. Sun, L. R. Dalton, S. M. Garner, A. Chen, S. Kalluri, W. H. Steier, and B. H. Robinson, “Translating Microscopic Optical Nonlinearity to Macroscopic Optical Nonlinearity: The Role of Chromophore-Chromophore Electrostatic Interactions,” J. Opt. Soc. Am. B 15, 329–337 (1998). [CrossRef]
  8. B. H. Robinson, L. R. Dalton, A. W. Harper, A. S. Ren, F. Wang, C. Zhang, G. Todorova, M. S. Lee, R. Aniszfeld, S. M. Garner, A. Chen, W. H. Steier, S. Houbrecht, A. Persoons, I. Ledoux, J. Zyss, and A. K. Y. Jen, “The Molecular and Supramolecular Engineering of Polymeric Electrooptic Materials,” Chem. Phys. 245, 35–50 (1999). [CrossRef]
  9. I. Rau, P. Armatys, P.-A. Chollet, F. Kajzar, Y. Bretonniere, and C. Andraud, “Aggregation: A new mechanism of relaxation of polar order in electro-optic polymers,” Chem. Phys. Lett. 442, 329–333 (2007). [CrossRef]
  10. G. Pawlik, A. C. Mitus, I. Rau, and F. Kajzar, “Poling of Electro-Optic Materials: Paradigms and Concepts,” Nonl. Opt. Quant. Opt. 40, 57–63 (2010).
  11. A. C. Mitus, G. Pawlik, I. Rau, and F. Kajzar, “Computer Simulations of Poled Guest-Host Systems,” Nonl. Opt. Quant. Opt. 38, 141–162 (2008).
  12. L. R. Dalton, W. H. Steier, B. H. Robinson, C. Zhang, A. S. Ren, S. M. Garner, A. Chen, T. M. Londergan, L. Irwin, B. Carlson, L. Fifield, G. Phelan, C. Kincaid, J. Amend, and A. K.-J. Jen, “From Molecules to Opto-Chips: Organic Electrooptic Materials,” J. Chem. Mater. 9, 1905–1920 (1999). [CrossRef]
  13. B. H. Robinson, and L. R. Dalton, “Monte Carlo Statistical Mechanical Simulations of the Competition of Intermolecular Electrostatic and Poling Field Interactions in Defining Macroscopic Electrooptic Activity for Organic Chromophore/Polymer Materials,” J. Phys. Chem. A 104, 4785–4795 (2000). [CrossRef]
  14. L. R. Dalton, “Rational Design of Organic Electrooptic Materials,” J. Phys. Condens. Matter 15, R897–R934 (2003). [CrossRef]
  15. H. L. Rommel, and B. H. Robinson, “Orientation of Electro-optic Chromophores under Poling Conditions: A Spheroidal Model,” J. Phys. Chem. C 111, 18765–18777 (2007). [CrossRef]
  16. G. Pawlik, A. C. Mitus, I. Rau, and F. Kajzar, “Monte Carlo Modeling of Chosen Non–Linear Optical Effects for Systems of Guest Molecules in Polymeric and Liquid–Crystal Matrices,” Nonl. Opt. Quant. Opt. 38, 227–244 (2009).
  17. M. Makowska-Janusik, H. Reis, M. G. Papadopoulos, I. Economou, and N. J. Zacharopoulos, “Molecular Dynamics Simulations of Electric Field Poled Nonlinear Optical Chromophores Incorporated in a Polymer Matrix,” J. Phys. Chem. B 108, 588–596 (2004). [CrossRef]
  18. M. R. Leahy-Hoppa, P. D. Cunningham, J. A. French, and L. M. Hayden, “Atomistic Molecular Modeling of the Effect of Chromophore Concentration on the Electro-optic Coefficient in Nonlinear Optical Polymers,” J. Phys. Chem. A 110, 5792–5797 (2006). [CrossRef] [PubMed]
  19. H. Reis H., “M. Makowska-Janusik, and M.G. Papadopoulos, “Nonlinear optical susceptibilities of poled guest–host systems: A computational study,” J. Phys. Chem. B 108, 8931–8940 (2004). [CrossRef]
  20. Y. V. Pereverzev, and O. V. Prezhdo, “Mean-field theory of acentric order of dipolar chromophores in polymeric electro-optic materials,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 62, 8324–8334 (2000). [CrossRef]
  21. Y. V. Pereverzev, O. V. Prezhdo, and L. R. Dalton, “Mean-field theory of acentric order of chromophores with displaced dipoles,” Chem. Phys. Lett. 340, 328–335 (2001). [CrossRef]
  22. K. Won-Kook, and L. M. Hayden, “Fully atomistic modeling of an electric field poled guest–host nonlinear optical polymer,” J. Chem. Phys. 111, 5212–5222 (1999). [CrossRef]
  23. Y. Tu, Y. Luo, and H. Agren, “Molecular Dynamics Simulations Applied to Electric Field Induced Second Harmonic Generation in Dipolar Chromophore Solutions,” J. Phys. Chem. B 110, 8971–8977 (2006). [CrossRef] [PubMed]
  24. Y. Tu, Q. Zhang, and H. Agren, “Electric field poled polymeric nonlinear optical systems: molecular dynamics simulations of poly(methyl methacrylate) doped with disperse red chromophores,” J. Phys. Chem. B 111, 3591–3598 (2007). [CrossRef] [PubMed]
  25. G. Pawlik, A. C. Mitus, I. Rau, and F. Kajzar, “Monte Carlo kinetic study of chromophore distribution in poled guest–host systems,” Proc. SPIE 6891, 68910A–1 – 68910A–7 (2008).
  26. G. Pawlik, D. Wronski, A. C. Mitus, I. Rau, C. Andraud, and F. Kajzar, “A new mechanism of relaxation in poled guest–host systems: Monte Carlo analysis of aggregation scenario,” Proc. SPIE 6653, 66530J–1 – 66530J–7 (2007).
  27. C. A. Walsh, D. M. Burland, V. Y. Lee, R. D. Miller, B. A. Smith, R. J. Twieg, and W. Volksen, “Orientational Relaxation in Electric Field Poled Guest – Host and Side – Chain Polymers below Tg,” Macromol. 26, 3720–3722 (1993). [CrossRef]
  28. R. R. Barto, C. W. Frank, P. V. Bedworth, R. E. Taylor, W. W. Anderson, S. Ermer, A. K.-Y. Jen, J. D. Luo, H. Ma, H.-Z. Tang, M. Lee, and A. S. Ren, “Bonding and Molecular Environment Effects on Near – Infrared Optical Absorption Behavior in Nonlinear Optical Monoazo Chromophore – Polymer Materials,” Macromol. 39, 7566–7577 (2006). [CrossRef]
  29. F. Kajzar, O. Krupka, G. Pawlik, A. Mitus, and I. Rau, “Concentration Variation of Quadratic NLO Susceptibility in PMMA-DR1 Side Chain Polymer,” Mol. Cryst. Liq. Cryst. (Phila. Pa.) 522, 180–190 (2010). [CrossRef]
  30. F. Kajzar, A. Jen, and K. S. Lee, “Polymeric Materials and Their Orientation Techniques for Second-Order Nonlinear Optics, Polymers for Photonics Applications II: Nonlinear Optical, Photorefractive and Two-Photon Absorption Polymers,” in Advances in Polymer Science, K. S. Lee, and G. Wegner, Eds., Vol. 161 (Springer Verlag, 2003).
  31. A. Priimagi, S. Cattaneo, R. H. A. Ras, S. Valkama, O. Ikkala, and M. Kauranen, “Polymer – Dye Complexes: A Facile Method for High Doping Level and Aggregation Control of Dye Molecules,” Chem. Mater. 17, 5798–5802 (2005). [CrossRef]
  32. J. Reyes–Esqueda, and B. Darracq, “J. Garcia – Macedo, M. Canva, M. Blanchard – Desce, F. Chaput, K. Lahlil, J.P. Boilot, A. Brun, and Y. Levy, “Effect of chromophore – chromophore electrostatic interactions in the NLO response of functionalized organic – inorganic sol – gel materials,” Opt. Commun. 198, 207–215 (2001). [CrossRef]
  33. L. Favaretto, G. Barbarella, I. Rau, F. Kajzar, S. Caria, M. Murgia, and R. Zamboni, “Efficient second harmonic generation from thin films of V-shaped benzo[b]thiophene based molecules,” Opt. Express 17, 2557–2564 (2009). [CrossRef] [PubMed]
  34. P. Oswald, and P. Pieranski, Les cristaix liquides: Concepts et proprits physiques illustrs par des expriences, Vol. 1, p. 51 (Gordon and Breach Science Publishers, Paris, 2000).
  35. A. K. Hamanoue, S. Hirayama, M. Amano, K. Nakajima, T. Nakayama, and H. Teranishi, “Spectroscopic Study of 10-Benzoyl-9-anthrol and Its Anion in Basic Media. An Estimation of Microscopic Polarity of PMMA,” Bull. Chem. Soc. Jpn. 55, 3104–3108 (1982). [CrossRef]
  36. D. Morichere, M. Dumont, Y. Levy, G. Gadret, and F. Kajzar, “Nonlinear properties of poled polymer films: SHG and electrooptic measurements,” Proc. SPIE 1560, 214–225 (1991). [CrossRef]
  37. G. Pawlik, A. C. Mitus, A. Miniewicz, and F. Kajzar, “Monte Carlo simulations of temperature dependence of the kinetics of diffraction gratings formation in a polymer matrix containing azobenzene chromophores,” J. Nonlinear Opt. Phys. Mater. 13, 481–489 (2004). [CrossRef]
  38. R. Metzler, and J. Klafter, “The random walk’s guide to anomalous diffusion: A fractional dynamics approach,” Phys. Rep. 339, 1–77 (2000). [CrossRef]
  39. A. Z. Patashinski, and M. A. Ratner, “Orientation relaxation in glassy polymers. II. Dipole-size spectroscopy and short-time kinetics,” J. Chem. Phys. 103, 10779–10789 (1995). [CrossRef]

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