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A transfer matrix of an arbitrary period in a long-period fiber grating (LPFG) is derived. Cascade of such matrixes can easily be used to calculate the overall performance of LPFG, with fast variation in parameters (which is common practice in LPFGs) such as period length, strength, etc. Results show that the difference in transmittivity between our work and traditional coupled-mode theory becomes obvious, when abrupt change such as /spl pi/ phase-shift occurs. This method can be used in the mask design aiming at overall performance optimization through period-by-period pattern adjustment.