Spectral-crystal efficiency mapping: An analytical tool for visualizing the parametric conversion potential of broadband sources

Quasi-phase-matching in <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:msup> <a:mi>χ</a:mi> <a:mrow> <a:mo stretchy="false">(</a:mo> <a:mn>2</a:mn> <a:mo stretchy="false">)</a:mo> </a:mrow> </a:msup> </a:math> media underpins many nonlinear conversion techniques, yet conventional sinc-squared gain models assume monochromatic pumps and wavelength-independent efficiency, limiting their accuracy for broadband sources. We introduce spectral-crystal efficiency mapping (SCEM), an analytical framework that combines input spectra with the nonlinear properties of a crystal to evaluate conversion potential. SCEM incorporates pump spectral profiles, higher-order interactions, and cascaded processes, providing an upper bound on efficiency that complements more computationally demanding numerical models. The resulting maps agree with experiment and simulation, while offering experimentalists an intuitive tool for assessing nonlinear gain media and guiding optimization of broadband frequency-conversion systems.