Nonlinear Optics

Nonlinear optical materials are key to a variety of important optics applications in communications, defense, intelligence, lasers, photonics, imaging, and many other fields. These materials enable otherwise impossible transformations and optical phenomena, like two-photon absorption, second-harmonic generation, nonlinear four-wave mixing, electro-optic materials, and much more. Development of improved nonlinear optical materials is crucial for many important emerging technologies, but these materials are challenging to engineer, engineer, and manufacture.

Fundamentals of Nonlinear Optics

At core, nonlinear optical materials are materials in which the electric field of incident light produces a non-linear polarization response. What does this mean in practice?

In linear optical materials, applying an electric field $\mathbf{E}$ leads to a linear induced dipole $\mathbf{p}$, and the magnitude of the induced dipole depends linearly on the polarizability tensor $\alpha$: $\mathbf{p} = \alpha \mathbf{E}$. In nonlinear optical materials, this relationship does not hold, and the induced dipole is instead written as a Taylor-series expansion: $\mathbf{p} = \alpha \mathbf{E} + \alpha^{(2)} \mathbf{E} \mathbf{E} + \alpha^{(3)} \mathbf{E} \mathbf{E} \mathbf{E} + \cdots$

The additional tensors are the hyperpolarizabilities of the molecule: $\alpha^{(2)}$ (sometimes written $\beta$) is the first hyperpolarizibility of the molecule, $\alpha^{(3)}$ (sometimes written $\gamma$) is the second hyperpolarizibility of the molecule, and so on. These tensors are fundamental in nonlinear optics, and can be used to predict the efficacy of other processes, like two-photon absorption. (For a detailed discussion, see Piela's overview).

Computational Nonlinear Optics

Unfortunately, measuring the hyperpolarizibility for a given molecule is quite challenging. Techniques like hyper-Rayleigh scattering, the dc Kerr effect, or electric-field-induced second-harmonic generation can be used to measure hyperpolarizibility, but these methods require specialized equipment and considerable human labor.

Computation can help by making it possible to compute the hyperpolarizibility of a given molecule without even needing to acquire the molecule. Advances in computational chemistry have made it possible to reliably compute hyperpolarizibility with reasonable quantitative accuracy, although range-separated hybrid functionals and specialized nonlinear-optics basis sets are needed. These calculations make it possible to design and simulate nonlinear optical materials entirely in the computer, helping companies speed up their R&D processes and find better materials faster.

Nonlinear Optics In Rowan

Rowan is looking for an industry partner to collaborate on developing tools for nonlinear optical simulation. If you or your company is working on developing new nonlinear optic materials, reach out! We'd love to discuss how computation could save you time & money and help make your technology better.