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The resonance wavelength, where a fiber mode converter grating written using periodic external perturbations achieves phase matching, is both a critical design parameter and a device parameter. However, a method to precisely predict the resonance wavelength for any new fiber and grating writing apparatus has been missing so far. The missing link was the lack of direct experimental methods to estimate the modified intermodal phase after writing with external perturbations. The presented method can make this estimation from a single experiment, over a broad wavelength range, based on a novel mathematical connection between two-mode interference and mode conversion. Using the novel methods, experimentally measured resonance wavelengths for different pitch and irradiation conditions have been predicted within relative errors of 4×10^−3.

AbstractCarl Friedrich Gauss is often given credit for providing the first correct proof of the fundamental theorem of algebra in his 1799 doctoral dissertation. However, Gauss's proof contained a significant gap. In this paper, we give an elementary way of filling the gap in Gauss's proof.

We report our experimental observations of variation in on-off statistics and fluorescence intensity of single Rhodamine6G molecules in presence of resonantly driven surface plasmon of silver nanoparticle. Derived lifetimes from on-off statistics of fluorophore show that interaction between the fluorophore and the subwavelength metal nanoparticle improves photostability and enhances fluorescence intensity. This enhancement follows the trend predicted by the dipole-dipole interaction model.