Abstract

In this work we present a detailed study of the propagation length of Bloch modes along the surface between a bulk medium and a one-dimensional truncated photonic crystal and how this quantity is affected by different parameters like the number of periods composing the photonic crystal, absorption of materials, the leak of energy due to the intrinsic structure of the system, and the roughness of involved surfaces that is inherently present depending on the manufacturing method and the materials themselves. To analyze the influence of different factors affecting the propagation length, we use essentially three different methods: the characteristic matrix for systems composed of smooth surfaces, along with the numerical fitting of a Lorentz curve around the resonance; the boundary integral method based on the Green function for two-dimensional systems that include random rough surfaces; and the numerical analysis of the energy propagation along the surface when a Gaussian beam impinges on it. We have found that the propagation length can vary from a few nanometers to some millimeters depending on the different mentioned factors, along with the relative position of the modes within the bandgaps. Bloch modes located at the center of bandgaps propagate longer distances than those residing near the edges. Absorption and roughness provoke a drastic decreasing of the propagation length as they increase at small rates. Finally, the number of periods composing the structure also produces an increase of the propagation length reaching a maximum and then dropping almost suddenly to zero when it grows at a constant pace.

© 2021 Optical Society of America

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