Symmetrical invariant transformation of localization length in one-dimensional randomly-perturbed periodic structure

Based on the spectral symmetry of the one-dimensional periodic structure, a new invariant transformation, named symmetrical invariant transformation, of localization length is presented for the one-dimensional randomly-perturbed periodic structure. The validity of the transformation is confirmed by numerical stimulations performed by means of transfer-matrix method. Since the symmetrical invariant transformation explores ark equivalent relation of localization length at different frequencies between different structures, it is expected to provide a new tool for further investigation of the light localization in disordered structures.