Symposium on Applications of Sum Rules and Scaling in Nonlinear Optics

Linear spring

Nonlinew spring expansion


Washington State University, Pullman, WA, August 12-13, 2014


The origin of the nonlinear-optical response resides in the redistribution of chargers in a material due to an externally-applied electric field. When the charge density is quantified by a series in the the spherical harmonic functions, the tensor coefficients are the moments, which together fully characterize the charge distribution. Click here for a nonlinear optics tutorial.

The moments are observables that are determined from the wave functions of the quantum system in the presence of the applied electric field using expectation values. When the applied electric field is weak compared with the internal fields that hold a molecule together, the expectation values of the moments can be expanded in a power series of the electric field. The coefficients of the fields are tensors that are called the nonlinear susceptibilities.

When the fields are small, perturbation theory can be used to calculate the nonlinear susceptibilities, which are found to be expressed in terms of the dipole matrix and the energy eigenvalues. The sum rules, which are a direct consequence of the Schrodinger equation, are an infinite set of equations that relate the dipole matrix elements and the energies. As such, they are a powerful tool for simplifying complex calculations; and, since all quantum systems must obey the sum rules, they can be used to assess the accuracy of quantum models. Note that while all solutions of the schrodinger Equation must obey the sum rules, there exist transition moments and energies that obey the sum rules but are not a solution of the Schrodinger equation.

Both the Schrodinger equation and the sum rules scale in the same way, as follows. The Schrodinger Equation is invariant when the energy is re-scaled in inverse proportion to the square of the re-scaled length. This is referred to as simple scaling. Every wave functions is stretched upon simple scaling, but otherwise, its shape remains the same.

The purpose of this meeting is to bring together top researchers in the field to discuss developments in nonlinear optics with sum rules and scaling as the unifying theme.

The Symposium

The symposium is intended to be informal, with no timers or tight schedule. Speakers are asked to present talks in the form of a classroom lecture, and aimed at the level of a graduate student with only a basic knowledge of nonlinear optics. Interruptions for questions are encouraged, as are heated discussions. Invited speakers will be allotted 60 minutes, which includes time for interruptions, discussions, and a long winded introduction of the topic by the moderator.

Each speaker is asked to provide one or two pdf files (maximum of three if needed) of papers on the topic that will be presented. Please email them to the organizers at least one week before the meeting. These can include the presenter's own papers, preprints, introductory materials, or the literature at large. Presenters are encouraged to submit half-baked ideas and rough versions of manuscripts in preparation. It is understood that symposium attendees will treat these documents as confidential. The symposium organizers will prepare a single pdf document that will be shared with attendees at least 3 days before the meeting. Keep in mind that the purpose of the pdf files is to provide the audience with the background needed to understand the talks. Click here for a nonlinear optics tutorial.

We hope that the meeting will be stimulating, informative, and lots of fun.


The meeting will be held in the Department of Physics, Webster Physical Science Building Room B11, at Washington State University, August 12-13, 2014.


On average, each talk is allotted 60 minutes, including time for questions, speaker introductions, etc. The "teachers" have been asked to prepare a pedagogical talk that introduces each topic in the form of a classroom lecture to bring the audience member up to speed. A packet of background materials are available and should be downloaded here and read before the meetins.

To keep the meeting informal and focused on learning, there are no shcedules, time tables or timers. Only the order of the talks will be specified, which are arranged from basics to applications and grouped by topic area. Click here to DOWNLOAD THE PROGRAM.

Background Materials

A book of materials has been prepared. All attendees are encourged to preapre for the lectures by reading at least the introductory parts of the articles and skimming over the results.


List of Confirmed Invited Speakers

"What features of a potential yield a large nonlinear response," Timothy Atherton, Tufts University, MA

"Using a GPU for ultrafast solutions to the Schrodinger Equation," Jared Aurentz, Washington State University, WA

"Optimized intrinsic and specific polarizabilities for large third-order susceptibilities in high optical quality single-component materials," Ivan Biaggio, Lehigh University, PA

"Design engineering of organic non-linear optical molecules ," Jacqueline M. Cole, Cavendish Laboratory, University of Cambridge, UK

"Relativistic corrections to sum rules and effects near the fundamental limits in one dimension," Nathan Dawson, Case Western University, OH

"FeyPy: A Python package for visualizing and calculating nonlinear optical properties," Adam Goler, Washington State University, WA

"Using Monte Carlo sampling and sum rules to study the nature of the hyperpolarizability," Mark C. Kuzyk, University of Oregon, OR

"Topological and geometrical scaling of Quantum Graphs in a nutshell," Rick Lytel, First Degree Innovation, CA

"Photophysics of organic semiconductors: from single molecules to optoelectronic devices," Oksana Ostroverkhova, Oregon State University, OR

"Quantitative 2-photon spectroscopy: what the measurements can tell us," Aleks Rebane, Montana State University, MT

"Using a Dyson Series approach for calculating the cascading response with virtual intermediate photons ," Sean Mossman, Washington State University, WA

"Universal scaling in nonlinear optical molecules," Xavier Perez-Moreno, Skidmore College, NY

"Cross-Conjugation as a Design Motif for Non-Linear Optical Molecules," Meghana Rawal, University of Washington, WA

"The Finite-difference Time-domain Simulation of the Schroedinger Equation," Dennis Sullivan, University of Idaho, ID

"Multi-scale modeling of ONLO chromophores," Andreas F Tillack, University of Washington, WA

"Optimizing the nonlinear susceptibility by variations of the potential energy function in the Schrodinger Equation," David S. Watkins, Washington State University, WA


The Holiday Inn Express and Suites Pullman is the recommended hotel. They offer free shuttle service to any Pullman location, including the airport and campus.


There are three airport choices for the area.

1. The Pullman airport (PUW) is 5 minutes from campus and very convenient but is only serviced by Alaska Airlines, who partners with several airlines.

2. The Lewiston airport (LWS) is 40 minutes from Pullman and offers a picturesque drive up an 800 foot grade. The two carriers flying into Lewiston are Delta and Alaska.

3. The Spokane airport (GEG) is a 90 minute drive from Pullman but is serviced by all major carriers. Almost the whole trip is on one highway that takes you straight into Pullman.


To register, please send an email to Mark Kuzyk with the following information:

Full Name:


email address:

There is no registration fee.

More Information

Contact Mark Kuzyk