Abstract

The ability to generate optical frequency combs in nonlinear resonators has attracted significant attention over the last decade [1]. While the majority of studies have considered resonators dominated by the third-order Kerr nonlinearity, more recent investigations have shown that comb generation is also possible through second order 𝜒⁽²⁾ nonlinear effects [2, 3]. Experimental works have in particular demonstrated that combs can arise in driven ⁽²⁾ resonators via second-harmonic generation (SHG), both in the presence [2] and absence [3] of a phase-mismatch. Theoretical works have so far focussed almost exclusively on the case of perfect phase-matching [4, 5]. This is somewhat surprising, for it is well-known that phase-mismatched SHG can give rise to a strong effective Kerr nonlinearity coefficient whose sign can be controlled with the phase-mismatch [6].

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