Effect of invariant transformation in one-dimensional randomly-perturbed photonic crystal

An effect of invariant transformation in one-dimensional randomly perturbed photonic crystals is presented analytically and numerically. According to this effect, localization length can be investigated in different identical intervals, and the relations among these zones are governed by a simple expression. A concept of effective randomness is introduced as a result, which denotes the disorder of phase shifts actually. The divergent behaviour of localization length in the limit of low frequency can be interpreted directly through this effect. Since the effect is obtained without any approximation, it is expected to be useful in understanding the general intrinsic nature of one-dimensional randomly perturbed photonic crystals.