Fundamental limits on radiative χ(2) second harmonic generation

Jewel Mohajan, Pengning Chao, Weiliang Jin, Sean Molesky, Alejandro W. Rodriguez

Research output: Contribution to journalArticlepeer-review


Recent advances in fundamental performance limits for power quantities based on Lagrange duality are proving to be a powerful theoretical tool for understanding electromagnetic wave phenomena. To date, however, in any approach seeking to enforce a high degree of physical reality, the linearity of the wave equation plays a critical role. In this manuscript, we generalize the current quadratically constrained quadratic program framework for evaluating linear photonics limits to incorporate nonlinear processes under the undepleted pump approximation. Via the exemplary objective of enhancing second harmonic generation in a (free-form) wavelength-scale structure, we illustrate a model constraint scheme that can be used in conjunction with standard convex relaxations to bound performance in the presence of nonlinear dynamics. Representative bounds are found to anticipate features observed in optimized structures discovered via computational inverse design. The formulation can be straightforwardly modified to treat other frequency-conversion processes, including Raman scattering and four-wave mixing.

Original languageEnglish (US)
Pages (from-to)44212-44223
Number of pages12
JournalOptics Express
Issue number26
StatePublished - Dec 18 2023
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Atomic and Molecular Physics, and Optics


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