2010
DOI: 10.1364/oe.18.001151
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Generalized phase matching condition for lossy periodic photonic structures

Abstract: The phase matching condition relating the real transverse wave vectors across a periodic boundary has been generalized to the case of complex transverse wave vectors. Based on this generalization, we describe diffraction of a complex Bloch wave propagating within a composite prism, and show that the resulting light in free space is an inhomogeneous plane wave in the presence of losses within the prism.

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Cited by 6 publications
(3 citation statements)
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“…Although a unified view of the effective refractive index of metamaterials made of ordered arrays of such particles, as well as of photonic crystals (PC) producing negative refraction [14] was established [15], the characterization of these composites as effective homogeneous media to the propagating wave has generally employed the method of the scattering (S) parameter by inversion of the complex transmittances and reflectances [1]. Then, it remained the question of whether the effective constitutive parameters ǫ ef f and µ ef f derived from effective medium homogenization procedures commonly employed [8,9,11,13], were the same as those obtained by those methods that took into account the wave interaction with the microstructure of the composite unit cell.…”
Section: Introductionmentioning
confidence: 99%
“…Although a unified view of the effective refractive index of metamaterials made of ordered arrays of such particles, as well as of photonic crystals (PC) producing negative refraction [14] was established [15], the characterization of these composites as effective homogeneous media to the propagating wave has generally employed the method of the scattering (S) parameter by inversion of the complex transmittances and reflectances [1]. Then, it remained the question of whether the effective constitutive parameters ǫ ef f and µ ef f derived from effective medium homogenization procedures commonly employed [8,9,11,13], were the same as those obtained by those methods that took into account the wave interaction with the microstructure of the composite unit cell.…”
Section: Introductionmentioning
confidence: 99%
“…Indeed, Re(ε y ) and Re(µ z ) are both negative in this wavelength region. We caution, however, that although the negative effective index is capable of predicting the phase advance and the refraction angle in a prism experiment [11], these local homogeneous material parameters are approximate, and predictions based on their values may still deviate from the macroscopic electromagnetic behavior of the composite, as we have shown previously [22].…”
mentioning
confidence: 75%
“…Another is local surface plasmon [3,4], which is generated by the interaction of the external field and the free conduction electrons on the plasmonic nanostructure surface. In addition, when the oscillation frequency of the external field and the natural frequency of the surface plasmon satisfy the phase matching condition [5], resonance can be induced and the surface electric and magnetic field intensity are enhanced, which is called surface plasmon resonance [6,7].…”
Section: Introductionmentioning
confidence: 99%