This paper presents, for the first time, the general solution of noncircular uniform waveguides in an arbitrary coordinate system. It can be expressed as exp {i(\bar β +Δ βV)z} E0(x,y), where V is a matrix dependent uniquely on the angle θ between the polarization principal axis (PPA) and the coordinate axis, and we present the method for finding \bar β, Δ β, and V(θ ) . This method is very easy to use for analyzing the Loyt depolarizer and twist fiber, compared with the Jones matrix.


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