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The renormalized energy Ẽ i of the i-th level is calculated by including the mean-field shift due to the polariton population in all the modes. To satisfy the phase-matching condition, the signal and idler fields can oscillate with frequencies a little off-resonant with respect to the renormalized polariton eigenfrequencies. However, if the mismatch becomes too large, the parametric oscillation switches off.
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