  We investigate second harmonic (SH) generation in a doubly resonant
metamaterial. We show that SH generation can be enhanced when the resonant
condition is satisfied for the SH frequency as well as for the fundamental
frequency. A unit cell of the doubly resonant metamaterial consists of two
coupled resonators, one of which resonates at the fundamental frequency,
whereas the other resonates around the SH frequency. We observe that the SH
generation in the doubly resonant metamaterial is 4.6 times as large as that in
a singly resonant metamaterial.
