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.

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.

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 (β) 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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

Real-time holographic reflection gratings in volume media of azo-dye-doped poly(methyl methacrylate).

Real-time formation of holographic reflection gratings is experimentally demonstrated in thick media of Disperse Red 1- (DR-1) doped poly(methyl methacrylate) at a nonresonant wavelength (647 nm). Our diffraction efficiencies of 30% and 23% are achieved for reflection gratings inscribed by spatial modulation of intensity and polarization, respectively, and are believed to be the highest achieved for a dye-doped polymer. In addition to the recording of amplitude and phase, the polarization state is also recorded and reconstructed.

High-efficiency holographic volume index gratings in DR1-dye-doped poly(methyl methacrylate).

Holographic volume index gratings with high diffraction efficiency (greater than 80%) are recorded in a thick sample of Disperse Red 1-doped poly(methyl methacrylate) with red light (647 nm), which is far away from the absorption peak (488 nm) of the material. Measurements of photoinduced birefringence and polarization holography recording confirm that the azo-dye reorientation mechanism is responsible for the grating formation. Energy coupling between the two writing beams is observed even when the incident beams have equal intensity.

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.

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.

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.

Fundamental limits of all nonlinear-optical phenomena that are representable by a second-order nonlinear susceptibility.

Applying the three-level ansatz and the sum rules to the new dipole-free sum-over-states expression, we develop a rigorous method for calculating the fundamental limits of the dispersion of the real and imaginary parts of the second-order electronic nonlinear-optical susceptibilities. These results can be applied to all orders of nonlinearity, hence can be used to study any nonlinear-optical phenomena at any wavelength. The theory can be used to understand how strongly light interacts with matter and can be applied to optimizing a material's properties for applications.

Pushing the hyperpolarizability to the limit.

We use numerical optimization to find a one-dimensional potential energy function that yields the largest hyperpolarizability, which we find is within 30% of the fundamental limit. Our results reveal insights into the character of the potential energy functions and wave functions that lead to the largest hyperpolarizability. We suggest that donor-acceptor molecules with a conjugated bridge with many sites of reduced conjugation to impart conjugation modulation may be the best paradigm for making materials with huge hyperpolarizabilities that approach the fundamental limit.

The effects of geometry on the hyperpolarizability.

Extensive studies in the past have focused on precise calculations of the nonlinear-optical susceptibility of thousands of molecules. In this work, we use the broader approach of considering how geometry and symmetry alone play a role, irrespective of molecular constraints. We investigate the nonlinear optical response of potential energy functions that are given by a superposition of force centers (representing the nuclear charges) that lie in various planar geometrical arrangements.