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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.

The conditions to observe and excite electromagnetic surface modes at the interface between a two-dimensional (2D) photonic crystal (PC) and bulk metal are studied. It is shown that these modes can exist in the region where bandgaps of the PC overlap with the region below the plasma frequency of a metal in the dispersion diagram in both polarizations. The dispersion relation of these electromagnetic surface modes is determined numerically by considering a system of a thin metallic layer in contact with a finite PC of some periods. The reflectance is computed by using the finite-difference time-domain (FDTD) method. With this method, it is shown that these modes can be excited and observed even under normal incidence from a vacuum. For the studied system, the cell in contact with the metallic layer must be truncated in order to observe the interface mode. It is shown that we can select the frequency of the mode inside the bandgaps by properly choosing the truncation parameter.

For the first time, to the best of our knowledge, the existence of a surface wave at the one-dimensional photonic crystal (PC)-metal interface is verified experimentally. That surface mode is excited for both transverse electric and transverse magnetic polarizations in the frequency region where one of the bandgaps of the PC overlaps with the region below the plasma frequency of the metal in the frequency wave-vector space and is observed even under normal incidence from vacuum. For a fixed frequency its angular position is very sensitive to the thickness of the one-dimensional photonic-crystal layer adjacent to the metal.

We propose a method for the determination of the band structure, reflectance, and transmittance of one- and two-dimensional photonic crystals that is based on the solution of integral equations. The results of this method are compared with those obtained by other well-known algorithms, and good agreement between them is found. The method is also tested by considering systems that possess a complex structure in their unit cell such as fractal geometries.

The band structure of periodic multilayers that include left- and right-handed materials is studied under the formalism of equivalent layers. Although the band structure of these systems looks quite complicated, it is shown that bandgaps and bulk bands follow a simple behavior that can be explained in terms of the phase thickness of one period and the Brewster condition that can be satisfied in both polarizations. The optical tunneling is explained in terms of optical holes that are points where the gaps narrow and close owing to the zero optical thickness of the period under given conditions. It is shown that optical tunneling can be present also under nonnormal incidence.

Some general properties of one-dimensional photonic crystals are analyzed by using symmetric periodic multilayers. In this way a one-dimensional photonic crystal can be considered a single thin film with an equivalent optical admittance and an equivalent phase thickness. These functions provide important information about the optical properties of the photonic crystal, such as the band structure and the characteristic points, where the bandgaps narrow and close, including Brewster points, which are all determined by analytic expressions. With this formalism it is also possible to study in a simple way different kinds of surface modes that can be present at the interface between photonic crystal and bulk material.

We demonstrate the existence of electromagnetic surface modes and surface plasma waves in the interface of a one-dimensional photonic crystal and a metal. These modes can exist in the region in which bandgaps of the photonic crystal overlap and in the region below the plasma frequency of a metal in the frequency wave-vector space. An analytic dispersion relation to determine the existence of these electromagnetic surface modes is obtained, and it is shown that these modes can be excited and observed without prism or grating configurations even under normal incidence from vacuum.