  We demonstrate that the resonance frequencies of high-Q microcavities in
two-dimensional photonic crystal membranes can be tuned over a wide range by
introducing a subwavelength dielectric tip into the cavity mode.
Three-dimensional finite-difference time-domain (FDTD) simulations show that by
varying the lateral and vertical positions of the tip, it is possible to tune
the resonator frequency without lowering the quality factor. Excellent
agreement with a perturbative theory is obtained, showing that the tuning range
is limited by the ratio of the cavity mode volume to the effective
polarizability of the nano-perturber.
