= N. Boeuf
{c}
<N. Boeuf> and collaborators developed calculations of non-collinear <phase matching> in uniaxial and biaxial nonlinear crystals. The NIST-hosted 1999 draft extended calculations beyond cases where interacting waves all propagate along one line.<Calculating Characteristics of Non-collinear Phase-matching in Uniaxial and Biaxial Crystals by N. Boeuf and others>[Abstract and sectionII.1: energy and wavevector matching]{ref}
For <spontaneous parametric down-conversion>, the pump, signal and idler satisfy $\omega_p=\omega_s+\omega_i$ and $\mathbf k_p=\mathbf k_s+\mathbf k_i$. The second condition is a vector relation, so crystal anisotropy and propagation angles jointly constrain possible outputs. Solving only the frequency equation does not establish an efficient optical interaction.
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