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Localization of electrons in 1D disordered systems is usually described inthe random phase approximation, when distributions of phases \varphi and\theta, entering the transfer matrix, are considered as uniform. In the generalcase, the random phase approximation is violated, and the evolution equationsare written in terms of the Landauer resistance \rho and the combined phases\psi=\theta-\varphi and \chi=\theta+\varphi. The distribution of the phase \psiis found to exhibit an unusual phase transition at the point E_0 when changingthe electron energy E, which manifests itself in the appearance of theimaginary part of \psi. The distribution of resistance P(\rho) has nosingularity at the point E_0, and the transition seems unobservable in theframework of condensed matter physics. However, the theory of 1D localizationis immediately applicable to the scattering of waves propagating in asingle-mode optical waveguide. Modern optical methods open a way to measurephases \psi and \chi. As a result, the indicated phase transition becomesobservable.

Unusual phase transition in 1D localization and its observability in optics