Analysis of phase-matching conditions in flexural-wave modulated fiber Bragg grating

Effective refractive indexes of the core mode and various cladding modes of a tapered single-mode step-index fiber were calculated for identifying the cladding modes of phase matching for coupling with the core mode, caused by a prewritten Bragg grating together with an applied flexural wave (microbending) in the tapered region. With these coupling mechanisms, the previously reported reflection wavelength switching could be well interpreted. Between the core mode and a cladding mode, the Bragg grating caused contradirectional coupling and the flexural wave resulted in codirectional coupling of either first- or second-order diffraction. Meanwhile, the period of the acoustic-induced flexural wave was calibrated to be a few hundreds of micrometers. Based on the phase-matching calculations, the relationship between cladding radius and flexural wave period with a chosen wavelength for reflection switching was provided. Such design considerations should be helpful in implementing wavelength switches, based on flexural wave modulation of fiber Bragg grating (FBG), for the applications of wavelength division multiplexing (WDM) fiber communications.