Weakly Bound States in Heterogeneous Waveguides: A Calculation to Fourth Order

P. Amore Facultad de Ciencias, CUICBAS, Universidad de Colima, Bernal Díaz del Castillo 340, Colima, Colima, Mexico

Received: January 23, 2017; In final form: September 25, 2017

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We have extended a previous calculation of the energy of a weakly heterogeneous waveguide to fourth order in the density perturbation, deriving its general expression. For particular configurations where the second and third orders both vanish, we discover that the fourth order contribution lowers in general the energy of the state, below the threshold of the continuum. In these cases the waveguide possesses a localized state. We have applied our general formula to a solvable model with vanishing second and third orders reproducing the exact expression for the fourth order.

DOI: 10.12693/APhysPolA.132.1351 topics: trapped modes, bound states, deformed waveguide, perturbation theory