Reflection and transmission spectra of dynamic optical fiber gratings

Due to elasto-optical effect, dielectric index of silica is a function of stress. Therefore, two beams of counter-propagating sonic wave inside optical fibers may induce periodical refractive index change along fiber axis. This sonic wave-stimulated periodical index change acts like time dependent fiber gratings. In this article, we deduced the relationship between dielectric index and strain, as well as the time and space distribution of dynamic fiber gratings. Reflection and transmission models of dynamic fiber gratings were built based on coupled mode theory, with or without the consideration of attenuation of sonic wave. Furthermore, we discussed the characters of reflection and transmission spectra in detail. Resonant wavelength shift was found mathematically for the first time, to our best knowledge. The influence of fiber length between two sonic sources were also discussed. From the results, it is possible to use DFBG as a generator of laser pulse series, or a periodical optical shutter.