Study On Oscillatory Properities Of The Forward And Backward Waves In The Fiber Gratings

Employing the coupled mode theory, properties in the uniform fiber grating is numerically simulated and theoretically studied. The numerical simulation shows that the forward wave and backward wave as well as their interference are all vibrating in the gating. The distributions of forward and backward wave powers decay along the grating, yet their interference one is oscillatory with a period as same as the grating period in the forbidden gap. Beside the forbidden gap, the forward and backward are oscillatory. It is same to their interference ,but different in the period that their interference period is equal to the grating period, but interference envelope period is equal to the forward and backward ones which varies with incident wavelength that more is the departure between incident wavelength and Bragg one, less is the period. The theoretically study shows that, when incident wavelength is defined in the following paper, the forward and backward waves amplitudes develop sinusoidally along the grating, the number of their amplitude maximums is equate to the corresponding rank of wavelength, their maximums are dependent of the wavelength rank, independent of their position in the grating, and their maximums distribute periodically along the grating; the minimum of backward wave amplitude is zero.Employing transmission matrix method, the backward wave properties in the linearly chirped fiber grating, Gauss apodized fiber grating and half-Gauss apodized fiber grating which is first given in the paper are numerically simulated. The results are found, for the linearly chirped grating, that oscillation is harder, and reflectivity band is broaden, for the apodized fiber grating, that sibelobe is avoided, and oscillation is forbidden. Besides these, there are new properties of half-gauss fiber grating. The effect of left half-gauss apodized grating is best among three apodized fiber gratings. Considering linearly chirp, the left half-gauss apodized fiber grating is better at right half part that wavelength is more than center wavelength, and worse at left one. The right half-gaussapodized fiber grating is reverse. Gauss apodized fiber grating is between them.The coupled mode equation, reflectivity formula and transmission matrix formula are strictly educed in the appendices.