Diffraction and localization in low-dimensional photonic bandgaps

Optics Letters

Volumn 29, Issue 22, 2004, Pages 2653-2655

  Longhi, Stefano ^a   Janner, Davide ^a  

^a POLITECNICO DI MILANO   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

LOCALIZATION; PERIODIC LAYERED STRUCTURES; PHOTONIC BANDGAPS;

BANDWIDTH; CRYSTAL STRUCTURE; CRYSTALS; MATHEMATICAL MODELS; NATURAL FREQUENCIES; SET THEORY; WAVE PROPAGATION;

PHOTONS;

EID: 9144273275     PISSN: 01469592     EISSN: None     Source Type: Journal    
DOI: 10.1364/OL.29.002653     Document Type: Article

References (16)

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13. Neglecting the second-order derivative in Eq. (5) corresponds, for an isotropic medium, to the well-known paraxial approximation, which is valid provided that the transverse beam size of, e.g., a Gaussian beam is much larger than its Rayleigh range. As θ diverges, the paraxial approximation breaks down, and higher-order derivative terms should be included, marking a continuous transition from the parabolic to the hyperbolic (or elliptic) diffractive regimes.
14. This is due to the fact that in the monochromatic regime the wave equation in isotropic media is always of the elliptic type, and only the inclusion of temporal degree of freedom may lead to a hyperbolic equation supporting X waves.
15. P. Yeh, Optical Waves in Layered Media (Wiley, New York, 1988).
16. Most usual X waves, such as those considered in Refs. 9 and 10, actually correspond to a spectral amplitude F(k∥) x exp(-αk∥); we consider here a different spectral shape for better comparing the transition from parabolic to hyperbolic localization for a transverse Gaussian field distribution.