RESUMO
We investigate numerically the effect of the competition of disorder, nonlinearity, and boundaries on the Anderson localization of light waves in finite-size, one-dimensional waveguide arrays. Using the discrete Anderson-nonlinear Schrödinger equation, the propagation of the mode amplitudes up to some finite distance is monitored. The analysis is based on the calculated localization length and the participation number, two standard measures for the statistical description of Anderson localization. For relatively weak disorder and nonlinearity, a higher disorder strength is required to achieve the same degree of localization at the edge than in the interior of the array, in agreement with recent experimental observations in the linear regime. However, for relatively strong disorder and/or nonlinearity, this behavior is reversed and it is now easier to localize an excitation at the edge than in the interior.
RESUMO
We investigate theoretically the existence of bulk and surface discrete breathers in a one-dimensional magnetic metamaterial comprised of a periodic binary array of split-ring resonators; the two types of resonators used have different resonant frequencies caused by unequal slit sizes. We use the rotating-wave approximation and construct several types of breather excitations both for the energy-conserving as well as dissipative-driven case; we corroborate these approximate results trough numerically exact computations. We demonstrate that discrete breathers can appear spontaneously in the dissipative-driven system as a result of a fundamental instability.