of cavity optomechanics [@ref:aspelmeyer2014co; @ref:favero2014fom; @ref:metcalfe2014aco], for instance to observe quantum correlations at room temperature [@purdy2017quantum], cooling of a nanomechanical oscillator into its quantum ground state [@Chan2011], ultra-sensitive torque magnetometry [@Wu:17], and to realize laser [@Zhang:10] and electro-optic modulator technologies [@Shakoor:14]. Many methodologies for designing defects within nanobeam waveguides typically patterned with holes to define PCCs have been discussed. One of the most successful approaches relies on tailoring the envelope of the electric field in the central region of the nanobeam by gradually varying the hole shape or spacing [@Chan:09]. By following a deterministic design procedure based on gradually varying the bandgap of each unit cell of the nanobeam [@Quan10; @Quan11], optical modes with ultra-high quality factors ($Q_o$) can be created with fields concentrated in the high-index dielectric or lower-index air/vacuum regions, referred to as dielectric- and air-modes, respectively.

Cavities supporting air-modes are advantageous for applications such as sensing and optomechanics due to their high concentration of optical energy in the lower index regions surrounding the mechanically moving boundaries of the device [@Johnson02]. Air-mode PCC’s have been demonstrated with $Q_o$ &gt; $10^5$ at optical [@Liang2015] frequencies, and have applications such as temperature and refractive index sensing [@Yang:15] and detecting single 