Abstract
AbstractLight trapping within waveguides is a key practice of modern optics, both scientifically and technologically. Photonic crystal fibers traditionally rely on total internal reflection (index-guiding fibers) or a photonic bandgap (photonic-bandgap fibers) to achieve field confinement. Here, we report the discovery of a new light trapping within fibers by the so-called Dirac point of photonic band structures. Our analysis reveals that the Dirac point can establish suppression of radiation losses and consequently a novel guided mode for propagation in photonic crystal fibers. What is known as the Dirac point is a conical singularity of a photonic band structure where wave motion obeys the famous Dirac equation. We find the unexpected phenomenon of wave localization at this point beyond photonic bandgaps. This guiding relies on the Dirac point rather than total internal reflection or photonic bandgaps, thus providing a sort of advancement in conceptual understanding over the traditional fiber guiding. The result presented here demonstrates the discovery of a new type of photonic crystal fibers, with unique characteristics that could lead to new applications in fiber sensors and lasers. The Dirac equation is a special symbol of relativistic quantum mechanics. Because of the similarity between band structures of a solid and a photonic crystal, the discovery of the Dirac-point-induced wave trapping in photonic crystals could provide novel insights into many relativistic quantum effects of the transport phenomena of photons, phonons, and electrons.
Highlights
Optical resonators and waveguides are widely used in modern optics[1], including optical couplers/filters[2,3,4], microlasers[5,6], and mainstream optical fibers[7,8,9,10]
A novel class of optical fibers that permit the guidance of light in a low-index core region has emerged[8,9,10]
Photonic crystals have been studied extensively for their bandgap[1] and special in-band dispersion effects such as negative refraction[13]. Another really interesting feature of photonic crystals is the Dirac points that appear at corners of the Brillouin zone[14,15,16,17]
Summary
Optical resonators and waveguides are widely used in modern optics[1], including optical couplers/filters[2,3,4], microlasers[5,6], and mainstream optical fibers[7,8,9,10]. A novel class of optical fibers that permit the guidance of light in a low-index core region has emerged[8,9,10]. These so-called photonic-bandgap fibers operate through bandgap effects of photonic crystals[11,12], which occur because of periodic microstructuring of the dielectric in the cladding region. A Dirac point, as illustrated, is a conical singularity surrounded by a region of linear dispersion in the band structure of triangular, hexagonal, or kagome lattices. The Maxwell equations can be replaced by the two-dimensional massless Dirac equation for relativistic particles: 2ivD(sxhx1syhy)Y5(v2vD)Y, where vD is the group velocity, vD/2p isthe Dirac frequency, sx and sy are Pauli matrices, and
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