Doubly resonant second harmonic generation (SHG) in a monolithic cavity is theoretically analysed. Using a non birefringent material as non linear medium, it is shown that both the double resonance condition and the phase matching condition between the two counter propagating second harmonic intracavity waves can be satisfied with a cavity length equal to the coherence length of the non linear process, and with well designed mirror phases. It is also shown theoretically how the double resonance can be maintained with only one tuning parameter. A SHG cavity enhancement of a few tens of thousands may be achieved at double resonance.
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