Deterministic design of wavelength scale, ultra-high Q photonic crystal nanobeam cavities

Optics Express – Photonic crystal nanobeam cavities are versatile platforms of interest for optical communications, optomechanics, optofluidics, cavity QED, etc. In a previous work [Appl. Phys. Lett. 96, 203102 (2010)], we proposed a deterministic method to achieve ultrahigh Q cavities. This follow-up work provides systematic analysis and verifications of the deterministic design recipe and further extends the discussion to air-mode cavities. We demonstrate designs of dielectric-mode and air-mode cavities with Q over 1 billion, as well as dielectric-mode nanobeam cavities with both ultrahigh-Q (over ten million) and ultrahigh on-resonance transmissions (T over 95%).

Arxiv – Deterministic design of wavelength scale, ultra-high Q photonic crystal nanobeam cavities (14 pages)

High quality factor (Q), small mode volume (V) optical cavities provide powerful means for modifying the interactions between light and matter, and have many exciting applications including quantum information processing, nonlinear optics, optomechanics, optical trapping and optofluidics. Photonic crystal cavities (PhC) have demonstrated numerous advantages over other cavity geometries due to their wavelength-scale mode volumes and over-million Q-factors. Although small mode volumes of PhC cavities can be easily achieved by design, ultrahigh Q factors are typically obtained using extensive parameter search and optimization. In a previous work, we proposed a deterministic method to design an ultrahigh Q PhC nanobeam cavity and verified our designs experimentally. The proposed method does not rely on any trial-and-error based parameter search and does not require any hole shifting, re-sizing and overall cavity re-scaling. The key design rules we proposed that result in ultrahigh Q cavities are (i) zero cavity length (L = 0), (ii) constant length of each mirror (’period’=a) and (iii) a Gaussian-type of field attenuation profile, provided by linear increase in the mirror strength.

In this follow-up work, we provided numerical proof of the proposed principles, and systematically optimized the design recipe to realize a radiation limited cavity and waveguide coupled cavity respectively. Furthermore, we extended the recipe to the design of air-mode cavities, whose optical energies are concentrated in the low-index region of the structure.

Nanobeam cavities have recently emerged as a powerful alternative to the slab-based 2-D PhC cavities. Nanobeams can achieve Qs on par with those found in slab-based geometries, but in much smaller footprints, and are the most natural geometries for integration with waveguides. Our deterministically designed cavities have similar structures to the mode-gap cavity proposed by Notomi et al., and later demonstrated experimentally by Kuramochi et al., as well as our own work.We note that the same design principle discussed here could be directly applied to realize ultra-high Q cavities based on dielectric stacks that are of interest for realization of vertical-cavity surface emitting lasers (VCSELs) and sharp filters. Finally, it is important to emphasize that while our method is based on the frameworkof Fourier space analysis, alternative approach, based on phase-matching between different mirror segments, could also be used to guide our design, as well as to explain the origin of deterministic ultra-high Q-factors in our device

These Q-factors are comparable with those found in whispering gallery mode (WGM) cavities and have ultra-small mode volumes, typically two or three orders of magnitude smaller than WGM ones. Furthermore, energy maximum can be localized in either the dielectric region or air region with this method. Although we demonstrated designs for TE-like, transversely symmetric cavity modes, the design method is universal, and can be applied to realize nanobeam cavities that support TM-polarized modes, as well as line-defect 2D photonic crystal cavities. We believe that the proposed method will greatly ease the processes of high Q nanobeam cavity design, and thus enable both fundamental studies in strong light and matter interactions, and practical applications in novel light sources, functional optical components (filters, delay lines, sensors) and densely integrated photonic circuits

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