For type-0 ppKTP SPDC, the optimal pump and collection focal parameters that maximize pair-collection rate depend strongly on the LG mode indices, so one pump focus cannot simultaneously optimize multiple modes.
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Optimizing brightness of SPDC source in Laguerre-Gaussian modes using type-0 periodically-poled nonlinear crystal
For type-0 ppKTP SPDC, the optimal pump and collection focal parameters that maximize pair-collection rate depend strongly on the LG mode indices, so one pump focus cannot simultaneously optimize multiple modes.