We model the optical properties of L3 photonic crystal nano-cavities as a function of the photonic crystal membrane refractive index n using a guided mode expansion method. Band structure calculations revealed that a TE-like full band-gap exists for materials of refractive index as low as 1.6. The Q-factor of such cavities showed a super-linear increase with refractive index. By adjusting the relative position of the cavity side holes, the Q-factor was optimised as a function of the photonic crystal membrane refractive index n over the range 1.6 to 3.4. Q-factors in the range 3000-8000 were predicted from absorption free materials in the visible range with refractive index between 2.45 and 2.8.
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