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We introduce a class of critical states which are embedded in the continuum (CSC) of one-dimensional optical waveguide array with one non-Hermitian defect. These states are at the verge of being fractal and have real propagation constant. They emerge at a phase transition which is driven by the imaginary refractive index of the defect waveguide and it is accompanied by a mode segregation which reveals analogies with the Dicke super -radiance. Below this point the states are extended while above they evolve to exponentially localized modes. An addition of a background gain or loss can turn these localized states to bound states in the continuum.
We study the level-spacing distribution function $P(s)$ at the Anderson transition by paying attention to anomalously localized states (ALS) which contribute to statistical properties at the critical point. It is found that the distribution $P(s)$ fo
Nonlinear nanostructured surfaces provide a paradigm shift in nonlinear optics with new ways to control and manipulate frequency conversion processes at the nanoscale, also offering novel opportunities for applications in photonics, chemistry, materi
We analyze the quantum dynamics of periodically driven, disordered systems in the presence of long-range interactions. Focusing on the stability of discrete time crystalline (DTC) order in such systems, we use a perturbative procedure to evaluate its
We have estimated the critical exponent describing the divergence of the localization length at the metal-quantum spin Hall insulator transition. The critical exponent for the metal-ordinary insulator transition in quantum spin Hall systems is known
We study the localization properties of electrons moving on two-dimensional bi-partite lattices in the presence of disorder. The models investigated exhibit a chiral symmetry and belong to the chiral orthogonal (chO), chiral symplectic (chS) or chira