Theory of free space coupling to high-Q whispering gallery modes

A theoretical study of free space coupling to high-Q whispering gallery modes both in circular and deformed microcavities are presented. In the case of a circular cavity, both analytical solutions and asymptotic formulas are derived. The coupling efficiencies at different coupling regimes for cylinder incoming wave are discussed, and the maximum efficiency is estimated for the practical Gaussian beam excitation. In the case of a deformed cavity, the coupling efficiency can be higher if the excitation beam can match the intrinsic emission well and the radiation loss can be tuned by adjusting the degree of deformation. Employing an abstract model of slightly deformed cavity, we found that the asymmetric and peak like line shapes instead of the Lorentz-shape dip are universal in transmission spectra due to multi-mode interference, and the coupling efficiency can not be estimated from the absolute depth of the dip. Our results provide guidelines for free space coupling in experiments, suggesting that the high-Q ARCs can be efficiently excited through free space which will stimulate further experiments and applications of WGMs based on free space coupling.Comment: 8 pages, 4 figure

The SpoIIQ-SpoIIIAH complex of C

Engulfment of the forespore by the mother cell is a universal feature of endosporulation. In Bacillus subtilis, the forespore protein SpoIIQ and the mother cell protein SpoIIIAH form a channel, essential for endosporulation, through which the developing spore is nurtured. The two proteins also form a backup system for engulfment. Unlike in B. subtilis, SpoIIQ of Clostridium difficile has intact LytM zinc‐binding motifs. We show that spoIIQ or spoIIIAH deletion mutants of C. difficile result in anomalous engulfment, and that disruption of the SpoIIQ LytM domain via a single amino acid substitution (H120S) impairs engulfment differently. SpoIIQ and SpoIIQ(H120S) interact with SpoIIIAH throughout engulfment. SpoIIQ, but not SpoIIQ(H120S), binds Zn(2+), and metal absence alters the SpoIIQ‐SpoIIIAH complex in vitro. Possibly, SpoIIQ(H120S) supports normal engulfment in some cells but not a second function of the complex, required following engulfment completion. We show that cells of the spoIIQ or spoIIIAH mutants that complete engulfment are impaired in post‐engulfment, forespore and mother cell‐specific gene expression, suggesting a channel‐like function. Both engulfment and a channel‐like function may be ancestral functions of SpoIIQ‐SpoIIIAH while the requirement for engulfment was alleviated through the emergence of redundant mechanisms in B. subtilis and related organisms