Fundamental limits on radiative χ⁽²⁾ second harmonic generation.

Area of Science:

• Photonics and Optics
• Nonlinear Optics
• Computational Electromagnetics

Background:

• Lagrange duality provides powerful theoretical limits for electromagnetic wave phenomena.
• Current methods for evaluating linear photonics limits rely heavily on the linearity of wave equations.
• Incorporating nonlinear optical processes into these theoretical limits has been a significant challenge.

Purpose of the Study:

• To generalize existing performance limit frameworks for linear photonics to include nonlinear optical processes.
• To develop a method for bounding the performance of nonlinear optical devices, specifically second harmonic generation.
• To demonstrate the applicability of the framework to wavelength-scale, free-form structures.

Main Methods:

• Generalization of the quadratically constrained quadratic program (QCQP) framework.
• Incorporation of nonlinear processes under the undepleted pump approximation.
• Development of a model constraint scheme combined with convex relaxations.

Main Results:

• The developed framework successfully bounds performance for nonlinear optical processes.
• Representative bounds accurately anticipate features observed in computationally designed structures.
• The framework shows promise for predicting performance in second harmonic generation.

Conclusions:

• The generalized framework effectively incorporates nonlinear dynamics into performance limit calculations for photonic devices.
• This approach provides a valuable tool for designing and optimizing nonlinear optical structures.
• The formulation is adaptable to other frequency-conversion processes like Raman scattering and four-wave mixing.