Investigations On Optical Property Of Linearly Chirped Bragg Grating

Linearly chirped fiber Bragg grating (FBG) is a grating of special structure. Therefractive index distribution of linearly chirped FBG is a periodic distribution whichis the characteristic of uniform grating. But the periodic distribution changes linearlyalong the axiallity of the grating, which is the own property of linearly chirped FBG.So it can re?ect incident light with a series of different wavelengths (frequencies).This feature makes it apply widely in the field of optical fiber communication. Forexample, it is used as a wavelength band-pass filter in a dispersion compensator, andas an end re?ector in a fiber laser. In this thesis, we systemically analyze the opti-cal properties of linearly chirped FBG with coupled mode theory and transfer matrixmethod.Coupled mode theory is a method that describes the interaction of two modes.The incident light-wave is perturbed by the non-uniform structure of linearly chirpedFBG, which produce the forward and backward spread waves. The interaction ofthis two-wave can be described by coupled mode theory. In this paper, we start fromMaxwell equations and detailed discuss the derivation of nonlinear coupled modeequations. At the same time we also derive the analytic solution of nonlinear coupledmode equations in linearly chirped FBG.By transfer matrix, the transfer matrix method describes the relation of a ?oormodel and its proximate ?oor model. In this method, linearly chirped FBGs are di-vided into many segments. The length of each segment is far larger than its period,and its refractive index distribution is seen as uniform. So each grating is describedby transfer matrix as a uniform grating, and the whole structure is described by theglobal matrix obtained by multiply the matrixes of each layer. This method is veryconvenient for writing program and simulating numerically the optical properties oflinearly chirped FBG, such as re?ection spectrum, time-delay cures, dispersion curesand so on. In this paper, we focus on analysis of the re?ection spectrum changes regu-larly with the modulation depth of refractive index, chirp parameter and the length oflinearly chirped FBG. We obtain several conclusions with regularity: the bandwidthof re?ectance spectrum widens with the increasing of three parameters. Meanwhile the oscillation in the band decreases with the increasing of refractive index modula-tion and the grating length, but the oscillation increases with the increasing of chirpparameter. And the re?ectivity in the band increases with the increasing of refractiveindex and the grating length, but the re?ectivity decreases with the increasing of chirpparameter. These conclusions have certain significance for its applications in the fieldof optical fiber communication. For instance, we can obtain sufficiently broad stop-band by replacing uniform FBG with linearly chirped FBG in the fiber grating Braggfilter.