  Photonic crystal cavities enable the realization of high Q-factor and low
mode-volume resonators, with typical architectures consisting of a thin
suspended periodically-patterned layer to maximize confinement of light by
strong index guiding. We investigate a heterostructure-based approach
comprising a high refractive index core and lower refractive index cladding
layers. Whilst confinement typically decreases with decreasing index contrast
between the core and cladding layers, we show that, counter-intuitively, due to
the confinement provided by the photonic band structure in the cladding layers,
it becomes possible to achieve Q-factors $>10^4$ with only a small refractive
index contrast. This opens up new opportunities for implementing high Q-factor
cavities in conventional semiconductor heterostructures, with direct
applications to the design of electrically-pumped nano-cavity lasers using
conventional fabrication approaches.
