Sean Mossman

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.

Optimization of eigenstates and spectra for quasi-linear nonlinear optical systems

Quasi-one-dimensional quantum structures with spectra scaling faster than the square of the eigenmode number (superscaling) can generate intrinsic, off-resonant optical nonlinearities near the fundamental physical limits, independent of the details of the potential energy along the structure. The scaling of spectra is determined by the topology of the structure, while the magnitudes of the transition moments are set by the geometry of the structure. This paper presents a comprehensive study of the geometrical optimization of superscaling quasi-one-dimensional structures and provides heuristics for designing molecules to maximize intrinsic response. A main result is that designers of conjugated structures should attach short side groups at least a third of the way along the bridge, not near its end as is conventionally done. A second result is that once a side group is properly placed, additional side groups do not further enhance the response.

Fundamental limits on the electro-optic device figure of merit

Device figures of merit are commonly employed to assess bulk material properties for a particular device class, yet these properties ultimately originate in the linear and nonlinear susceptibilities of the material, which are not independent of each other. In this work, we calculate the electro-optic device figure of merit based on the half-wave voltage and linear loss, which is important for phase modulators and serves as the simplest example of the approach. This figure of merit is then related back to the microscopic properties in the context of a dye-doped polymer, and its fundamental limits are obtained to provide a target. Surprisingly, the largest figure of merit is not always associated with a large nonlinear optical response, the quantity that is most often the focus of optimization. An important lesson for materials design is that the figure of merit alone should be optimized. The best device materials can have low nonlinearity provided that the loss is low, or near resonance high loss may be desirable because it is accompanied by a resonantly enhanced, ultralarge nonlinear response, so device lengths are short. Our work shows which frequency range of operation is most promising for optimizing the material figure of merit for electro-optic devices.

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.

Optimizing hyperpolarizability through the configuration space of energy spectrum and transition strength spanned by power law potentials

While sophisticated numerical computational techniques can calculate the hyperpolarizabilities of complex molecules, it is not clear what scale invariant parameters determine a large nonlinear response. We investigate the first and second intrinsic hyperpolarizabilities of one-dimensional power-law potentials with a hybrid analytical semiclassical analysis of energy spectra and numerical calculations of eigenfunctions. By varying the exponent, we determine how key underlying properties drive the nonlinear response as the system smoothly varies from particle in a box, harmonic oscillator, point charge potential, to all multipolar Coulomb potentials. The role of the well-known pathology of the 1/x2 potential is also discussed.

Outreach at Washington State University: a case study in costs and attendance

Making effective and efficient use of outreach resources can be difficult for student groups in smaller rural communities. Washington State Universitys OSA/SPIE student chapter desires well attended yet cost-effective ways to educate and inform the public. We designed outreach activities focused on three different funding levels: low upfront cost, moderate continuing costs, and high upfront cost with low continuing costs. By featuring our activities at well attended events, such as a pre-football game event, or by advertising a headlining activity, such as a laser maze, we take advantage of large crowds to create a relaxed learning atmosphere. Moreover, participants enjoy casual learning while waiting for a main event. Choosing a particular funding level and associating with well-attended events makes outreach easier. While there are still many challenges to outreach, such as motivating volunteers or designing outreach programs, we hope overcoming two large obstacles will lead to future outreach success.

General solution to nonlinear optical quantum graphs using Dalgarno–Lewis summation techniques

We develop an algorithm to apply the Dalgarno–Lewis (DL) perturbation theory to quantum graphs with multiple connected edges. We use it to calculate the nonlinear optical hyperpolarizability tensors for graphs and show that it replicates the sum over states computations but executes 10 to 50 times faster. DL requires only knowledge of the ground state of the graph, eliminating the requirement to determine all possible degeneracies of a complex network. The algorithm is general and may be applied to any quantum graph.

Dalgarno–Lewis perturbation theory for nonlinear optics

We apply the quadrature-based perturbation method of Dalgarno and Lewis to the evaluation of the nonlinear optical response of quantum systems. This general operator method for perturbation theory allows us to derive exact expressions for the first three electronic polarizabilities, which requires only a good estimate of the ground state wave function, makes no explicit reference to the underlying potential, and avoids complexities arising from excited state degeneracies. We apply this method to simple examples in one-dimensional quantum mechanics for illustration, exploring the sensitivity of this method to variational solutions as well as poor numerical sampling. Finally, to the best of our knowledge, we extend the Dalgarno–Lewis method for the first time to time-harmonic perturbations, allowing dispersion characteristics to be determined from the unperturbed ground state wave function alone.

Hybrid quantum systems for enhanced nonlinear optical susceptibilities

Significant effort has been expended in the search for materials with ultrafast nonlinear optical susceptibilities, but most fall far below the fundamental limits. This work applies a theoretical materials development program that has identified a promising new hybrid made of a nanorod and a molecule. This system uses the electrostatic dipole moment of the molecule to break the symmetry of the metallic nanostructure that shifts the energy spectrum to make it optimal for a nonlinear optical response near the fundamental limit. The structural parameters are varied to determine the ideal configuration, providing guidelines for making the best structures.

Design rules for quasi-linear nonlinear optical structures

The maximization of the intrinsic optical nonlinearities of quantum structures for ultrafast applications requires a spectrum scaling as the square of the energy eigenstate number or faster. This is a necessary condition for an intrinsic response approaching the fundamental limits. A second condition is a design generating eigenstates whose ground and lowest excited state probability densities are spatially separated to produce large differences in dipole moments while maintaining a reasonable spatial overlap to produce large off-diagonal transition moments. A structure whose design meets both conditions will necessarily have large first or second hyperpolarizabilities. These two conditions are fundamental heuristics for the design of any nonlinear optical structure.