Imaging studies of photodegradation and self-healing in anthraquinone derivative dye-doped PMMA.

We study photodegradation and self-healing of nine different anthraquinone-derivatives doped into PMMA using transmission imaging microscopy in search of structure-property relationships of the underlying mechanisms. We find that seven of the nine anthraquinone derivatives display partially reversible photodegradation, with 1,8-dihydroxyanthraquinone (Dantron/Chrysazin) having the best photostability and recovery characteristics of all dyes tested in this study. Based on these measurements we predict that a sample of 1,8-dihydroxyanthraquinone doped into PMMA with a concentration of 9 g l-1 will have a record setting irreversible inverse quantum efficiency of Bε = 4.56 × 109. Additionally, by considering the performance of the different anthraquinone derivatives and their structures, we develop three rules-of-thumb to qualitatively predict the photostability and recovery characteristics of anthraquinone derivatives. These rules-of-thumb will help guide future experiments and molecular modeling in discerning the underlying mechanisms of reversible photodegradation. Finally, we compare our results for disperse orange 11 dye-doped PMMA to the extended Correlated Chromophore Domain Model (eCCDM). While the eCCDM correctly predicts the behavior of the reversible decay component, it fails to correctly predict the behavior of the irreversible degradation component. This implies further modifications to the eCCDM are required.

Using a proxy state to improve the accuracy of truncated hyperpolarizability calculations.

We present a simple algorithm for defining a single proxy state that accounts for state truncation in the sum-over-states calculations of the dispersion of the molecular hyperpolarizabilities. The transition strengths between the proxy state and the truncated set of states are determined using the Thomas-Reiche-Kuhn sum rules further constrained by the zero-frequency linear polarizability. This proxy state method can augment experimentally determined parameters or finite-state theories to allow for a more accurate prediction of the nonlinear optical properties of molecular systems. We benchmark this approach by comparison to exact perturbation calculations of one-dimensional power law potentials.

Exact Fundamental Limits of the First and Second Hyperpolarizabilities.

Nonlinear optical interactions of light with materials originate in the microscopic response of the molecular constituents to excitation by an optical field, and are expressed by the first (ß) and second (γ) hyperpolarizabilities. Upper bounds to these quantities were derived seventeen years ago using approximate, truncated state models that violated completeness and unitarity, and far exceed those achieved by potential optimization of analytical systems. This Letter determines the fundamental limits of the first and second hyperpolarizability tensors using Monte Carlo sampling of energy spectra and transition moments constrained by the diagonal Thomas-Reiche-Kuhn (TRK) sum rules and filtered by the off-diagonal TRK sum rules. The upper bounds of ß and γ are determined from these quantities by applying error-refined extrapolation to perfect compliance with the sum rules. The method yields the largest diagonal component of the hyperpolarizabilities for an arbitrary number of interacting electrons in any number of dimensions. The new method provides design insight to the synthetic chemist and nanophysicist for approaching the limits. This analysis also reveals that the special cases which lead to divergent nonlinearities in the many-state catastrophe are not physically realizable.

Imaging studies of temperature dependent photodegradation and self-healing in disperse orange 11 dye-doped polymers.

Using confocal transmission imaging microscopy, we measure the temperature dependence of photodegradation and self-healing in disperse orange 11 (DO11) dye-doped (poly)methyl-methacrylate (PMMA) and polystyrene (PS). In both dye-doped polymers, an increase in sample temperature results in a greater photodegradation rate and degree of degradation, while also resulting in a slower recovery rate and larger recovery fraction. These results confirm the temperature dependence predictions of the modified correlated chromophore domain model (mCCDM) [B. R. Anderson and M. G. Kuzyk, Phys. Rev. E 89, 032601 (2014)]. Additionally, using quantitative fitting of the imaging data for DO11/PMMA, we determine the domain density parameter to be ρ = 1.19 (±0.25) × 10(-2) and the domain free energy advantage to be λ = 0.282 ± 0.015 eV, which are within the uncertainty of the values previously determined using amplified spontaneous emission as the probe method [S. K. Ramini et al., Polym. Chem. 4, 4948 (2013)]. Finally, while we find photodegradation and self-healing of DO11/PS to be qualitatively consistent with the mCCDM, we find that it is quantitatively incompatible with the mCCDM as recovery in DO11/PS is found to behave as a stretched (or double) exponential as a function of time.

Time-Domain Simulation of Three Dimensional Quantum Wires.

A method is presented to calculate the eigenenergies and eigenfunctions of quantum wires. This is a true three-dimensional method based on a direct implementation of the time-dependent Schrödinger equation. It makes no approximations to the Schrödinger equation other than the finite-difference approximation of the space and time derivatives. The accuracy of our method is tested by comparing it to analytical results in a cylindrical wire.

Spectroscopic studies of the mechanism of reversible photodegradation of 1-substituted aminoanthraquinone-doped polymers.

The mechanism of reversible photodegradation of 1-substituted aminoanthraquinones doped into poly(methyl methacrylate) and polystyrene is investigated. Time-dependent density functional theory is employed to predict the transition energies and corresponding oscillator strengths of the proposed reversibly and irreversibly damaged dye species. Ultraviolet-visible and Fourier transform infrared (FTIR) spectroscopy are used to characterize which species are present. FTIR spectroscopy indicates that both dye and polymer undergo reversible photodegradation when irradiated with a visible laser. These findings suggest that photodegradation of 1-substituted aminoanthraquinones doped in polymers originates from interactions between dyes and photoinduced thermally degraded polymers, and the metastable product may recover or further degrade irreversibly.

Phase disruption as a new design paradigm for optimizing the nonlinear-optical response.

The intrinsic optical nonlinearities of linear structures, including conjugated chain polymers and nanowires, are shown to be dramatically enhanced by the judicious placement of a charge-diverting path sufficiently short to create a large phase disruption in the dominant eigenfunctions along the main path of the probability current. Phase disruption is proposed as a new general principle for the design of molecules, nanowires, and any quasi-1D quantum system with large intrinsic response and does not require charge donor-acceptors at the ends.

Generalizing the correlated chromophore domain model of reversible photodegradation to include the effects of an applied electric field.

All observations of photodegradation and self-healing follow the predictions of the correlated chromophore domain model [Ramini et al., Polym. Chem. 4, 4948 (2013)]. In the present work, we generalize the domain model to describe the effects of an electric field by including induced dipole interactions between molecules in a domain by means of a self-consistent field approach. This electric field correction is added to the statistical mechanical model to calculate the distribution of domains that are central to healing. Also included in the model are the dynamics due to the formation of an irreversibly damaged species, which we propose involves damage to the polymer mediated through energy transfer from a dopant molecule after absorbing a photon. As in previous studies, the model with one-dimensional domains best explains all experimental data of the population as a function of time, temperature, intensity, concentration, and now applied electric field. Though the precise nature of a domain is yet to be determined, the fact that only one-dimensional domain models are consistent with observations suggests that they might be made of correlated dye molecules along polymer chains. Furthermore, the voltage-dependent measurements suggest that the largest polarizability axis of the molecules are oriented perpendicular to the chain.

A self healing model based on polymer-mediated chromophore correlations.

Here we present a model of self healing in which correlations between chromophores, as mediated by the polymer, are key to the recovery process. Our model determines the size distribution of the correlation volume using a grand canonical ensemble through a free energy advantage parameter. Choosing a healing rate that is proportional to the number of undamaged molecules in a correlated region, and a decay rate proportional to the intensity normalized to the correlation volume, the ensemble average is shown to correctly predict decay and recovery of the population of disperse orange 11-DO11 (1-amino-2-methylanthraquinone) molecules doped in PMMA polymer as a function of time and concentration as measured with amplified spontaneous emission and linear absorption spectroscopy using only three parameters that apply to the full set of data. Our model also predicts the temperature dependence of the process. One set of parameters should be characteristic of a particular polymer and dopant chromophore combination. Thus, the use of the model in determining these parameters for various materials systems should provide the data needed to test fundamental models of the underlying mechanism responsible for self healing.

Off-resonance and non-resonant dispersion of Kerr nonlinearity for symmetric molecules [Invited].

The exact formula is derived from the "sum over states" (SOS) quantum mechanical model for the frequency dispersion of the nonlinear refractive index coefficient n2 for centrosymmetric molecules in the off-resonance and non-resonant regimes. This expression is characterized by interference between terms from two-photon transitions from the ground state to the even-symmetry excited states and one-photon transitions between the ground state and odd-symmetry excited states. When contributions from the two-photon terms exceed those from the one-photon terms, the non-resonant intensity-dependent refractive index n2>0, and vice versa. Examples of the frequency dispersion for the three-level SOS model are given. Comparison is made with other existing theories.

The effect of electron interactions on the universal properties of systems with optimized off-resonant intrinsic hyperpolarizability.

Because of the potentially large number of important applications of nonlinear optics, researchers have expended a great deal of effort to optimize the second-order molecular nonlinear-optical response, called the hyperpolarizability. The focus of our present studies is the intrinsic hyperpolarizability, which is a scale-invariant quantity that removes the effects of simple scaling, thus being the relevant quantity for comparing molecules of varying sizes. Past theoretical studies have focused on structural properties that optimize the intrinsic hyperpolarizability, which have characterized the structure of the quantum system based on the potential energy function, placement of nuclei, geometry, and the effects of external electric and magnetic fields. Those previous studies focused on single-electron models under the influence of an average potential. In the present studies, we generalize our calculations to two-electron systems and include electron interactions. As with the single-electron studies, universal properties are found that are common to all systems-be they molecules, nanoparticles, or quantum gases-when the hyperpolarizability is near the fundamental limit.

Optimizing the hyperpolarizability tensor using external electromagnetic fields and nuclear placement.

We investigate the effects of an external electric and magnetic field on the first hyperpolarizability tensor of a quantum system, such as a molecule or nanoparticle, whose nonlinear response is well below the fundamental limit. We find that the intrinsic hyperpolarizability is optimized when the applied electric and magnetic fields are comparable to the internal molecular fields. Indeed, the nonlinear response is just as large for an electron in the presence of the external field without the nuclei as it is for an electron bound to a molecule and in the presence of the applied field. We find that all combinations of fields and molecular structures that optimize the largest diagonal component of the intrinsic hyperpolarizability share the same universal properties: The three-level ansatz is obeyed, the normalized transition moment to the dominant state is about 0.76, the ratio of the two dominant excited state energies is about 0.48, the electron density tends toward being one-dimensional, and the intrinsic hyperpolarizability is less than 0.71. Thus, strategies for optimizing the hyperpolarizability should focus on ways to achieve these universal properties. On the other hand, when beta(xxy) is optimized, the three level ansatz appears to hold for a pair of degenerate states. In this case, the energy ratio between the pairs of degenerate states is 0.42 and the normalized transition moment to the pair of dominant states is 0.87. Most importantly, the intrinsic hyperpolarizability is 0.9, the largest ever calculated for a system described by a potential energy function.

Modulated conjugation as a means of improving the intrinsic hyperpolarizability.

A new strategy for optimizing the first hyperpolarizability based on the concept of a modulated conjugated path in linear molecules is investigated. A series of seven novel chromophores with different types of conjugated paths were synthesized and characterized. Hyper-Rayleigh scattering experiments confirmed that modulated conjugation paths that include benzene, thiophene, and/or thiazole rings in combination with azo and/or ethenyl linkages between dihydroxyethylamino donor groups and various acceptor groups result in enhanced intrinsic hyperpolarizabilities that exceed the long-standing apparent limit for two of the chromophores. The experimental results are analyzed and interpreted in the context of quantum limits, which show that conjugation modulation of the bridge in donor/acceptor molecules simultaneously optimizes the transition moments and the energy-level spacing.

Femtosecond bulk transparent material processing and recovery.

Femtosecond lasers have a unique ability of processing bulk transparent materials for various applications such as micromachining, waveguide manufacturing, and photonic bandgap structures, just to name a few. These applications depend on the formation of micron or submicron size features are known to be index modifications to the bulk substrate [2, 11], which were thought to persist indefinitely. However, it has been observed that some of these bulk transparent materials recover or "heal" with time. This "healing" process is studied and quantified using Nomarski Differential Interference Contrast optical microscopy and diffraction efficiency measurements of micro-machined gratings. We find healing to be accelerated in dye doped polymers.

Mechanisms of reversible photodegradation in disperse orange 11 dye doped in PMMA polymer.

We use amplified spontaneous emission (ASE) and linear absorption spectroscopy to study the mechanisms of reversible photodegradation of 1-amino-2-methylanthraquinone (disperse orange 11-DO11) in solid poly(methyl methacrylate). Measurements as a function of intensity, concentration, and time suggest that ASE originates in a state (be it a tautomer or a vibronic level) that can form a dimer or some other aggregate upon relaxation, which through fluorescence quenching leads to degradation of the ASE signal. Whatever the degradation route, a high concentration of DO11 is required and the polymer plays a key role in the process of opening a new reversible degradation pathway that is not available at lower concentrations or in liquid solutions. We construct an energy level diagram that describes all measured quantities in the decay and recovery processes and propose a hypothesis of the nature of the associated states.

A new dipole-free sum-over-states expression for the second hyperpolarizability.

The generalized Thomas-Kuhn sum rules are used to eliminate the explicit dependence on dipolar terms in the traditional sum-over-states (SOS) expression for the second hyperpolarizability to derive a new, yet equivalent, SOS expression. This new dipole-free expression may be better suited to study the second hyperpolarizability of nondipolar systems such as quadrupolar, octupolar, and dodecapolar structures. The two expressions lead to the same fundamental limits of the off-resonance second hyperpolarizability; and when applied to a particle in a box and a clipped harmonic oscillator, have the same frequency dependence. We propose that the new dipole-free equation, when used in conjunction with the standard SOS expression, can be used to develop a three-state model of the dispersion of the third-order susceptibility that can be applied to molecules in cases where normally many more states would have been required. Furthermore, a comparison between the two expressions can be used as a convergence test of molecular orbital calculations when applied to the second hyperpolarizability.

Combined molecular and supramolecular bottom-up nanoengineering for enhanced nonlinear optical response: experiments, modeling, and approaching the fundamental limit.

The authors study the combination of two independent strategies that enhance the hyperpolarizability of ionic organic chromophores. The first molecular-level strategy is the extension of the conjugation path in the active chromophore. The second supramolecular-level strategy is the bottom-up nanoengineering of an inclusion complex of the chromophore in an amylose helix by self-assembly. The authors study a series of five (dimethylamino)stilbazolium-type chromophores with increasing conjugation length between the (dimethylamino)phenyl donor ring and the pyridinium acceptor ring in conjunction with four amylose helices of differing molecular weights. The first hyperpolarizabilities of the self-assembled inclusion complexes, as determined with frequency-resolved femtosecond hyper-Rayleigh scattering at 800 and 1300 nm, are compared with experimental values for the free chromophores in solution and with theoretical values. While the experimental values for the hyperpolarizability in solution are lower than the theoretically predicted values, an enhancement upon inclusion is observed, with the longest chromophore in the best amylose helix showing an enhancement by one order of magnitude. Molecular modeling of the inclusion of the chromophore suggests that the coplanarity of the two rings is more important than all-trans configuration in the conjugation path. The fundamental limit analysis indicates that the inclusion inside the amylose helix results in an optimal excited-level energy spacing that is responsible for breaching the apparent limit.

Two-photon fluorescence measurements of reversible photodegradation in a dye-doped polymer.

We report on the dynamics of photodegradation and subsequent recovery of two-photon fluorescence in a dye-doped polymer. The energy dependence suggests that photodegradation is a linear process, while recovery is entropic. Such recovery could be useful to high-intensity devices such as two-photon absorbers, which can be used in many applications.

Modulated conjugation as a means for attaining a record high intrinsic hyperpolarizability.

We report on a series of chromophores that have been synthesized with a modulated conjugation path between donor and acceptor. Hyper-Rayleigh scattering measurements of the best molecule show an enhanced intrinsic hyperpolarizability that breaches the apparent limit of all previously studied molecules.