Symmetry and degeneracy in microstructured optical fibers

Steel, M. J.; White, Thomas P.; Sterke, C. Martijn de; McPhedran, R. C.; Botten, L. C.

doi:10.1364/ol.26.000488

Cited by 235 publications

(125 citation statements)

References 11 publications

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“…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] . Any dramatic change to the building blocks will generate a completely new range of optical devices.…”

Section: Introductionmentioning

confidence: 99%

“…A high-index core surrounded by a cladding with a lower refractive index has been the most basic requirement 7 . Recently, 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.…”

Section: Introductionmentioning

confidence: 99%

“…17 is uniform in the longitudinal direction. The most common waveguides based on triangular lattices are photonic crystal fibers [8][9][10] . In the study of the fiber problem, the mode is confined in the transverse plane while carrying electromagnetic energy in the longitudinal direction; thus, the propagating effect along the fiber axis is essential for these devices to operate.…”

Section: Introductionmentioning

confidence: 99%

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Fiber guiding at the Dirac frequency beyond photonic bandgaps

et al. 2015

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Light 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.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Fiber guiding at the Dirac frequency beyond photonic bandgaps

et al. 2015

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“…[9][10][11][12] Polarization-maintaining or single-polarization fibers are required in the fields of telecommunication, measurement, and sensing, such as polarization multiplexing/polarization multiplexed bi-directional transmissions, optical interferometric systems (e.g., interferometric fiberoptic sensors), and connections to polarization strongly dependent photonic integrated circuits. Compared to axisymmetric circular fibers and photonic crystal fibers with sixfold rotational symmetry 13 consisting of air holes arranged in a triangular lattice, in which the fundamental mode is doubly degenerate, waveguides with a rectangular cross-section are excellent in polarizationpreserving capability.…”

Section: Introductionmentioning

confidence: 99%

Single-polarization hollow-core square photonic bandgap waveguide

Eguchi

Tsuji

2016

AIP Advances

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Materials with a periodic structure have photonic bandgaps (PBGs), in which light can not be guided within certain wavelength ranges; thus light can be confined within a low-index region by the bandgap effect. In this paper, rectangular-shaped hollow waveguides having waveguide-walls (claddings) using the PBG have been discussed. The design principle for HE modes of hollow-core rectangular PBG waveguides with a Bragg cladding consisting of alternating high- and low-index layers, based on a 1D periodic multilayer approximation for the Bragg cladding, is established and then a novel single-polarization hollow-core square PBG waveguide using the bandgap difference between two polarized waves is proposed. Our results demonstrated that a single-polarization guiding can be achieved by using the square Bragg cladding structure with different layer thickness ratios in the mutually orthogonal directions and the transmission loss of the guided mode in a designed hollow-core square PBG waveguide is numerically estimated to be 0.04 dB/cm.

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“…A distinctive structural feature of many photonic-bandgap fibers, including some of the most widely used geometries, is their symmetry, i.e., six-fold rotational and reflection symmetry (at least in the idealized case). This symmetry results in an exact double degeneracy of the fundamental modes [2], [3]. Small perturbations that break this symmetry, for example a slight ellipticity of the core region, lift this degeneracy and introduce birefringence.…”

mentioning

confidence: 99%

Birefringence Analysis of Photonic-Bandgap Fibers Using the Hexagonal Yee's Cell

Aghaie

Fan

Digonnet

2010

IEEE J. Quantum Electron.

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Abstract-A full-vectorial finite-difference scheme utilizing the hexagonal Yee's cell is used in this paper to analyze the modes of photonic-bandgap fibers with C 6 symmetry. Because it respects the fiber's native symmetry, this method is free from any numerical birefringence. We also incorporate in it techniques for reducing the memory requirement (up to 3 to 4 times) and computational time, in particular by exploiting some of the symmetry properties of these fibers. Using sub-pixel averaging, we demonstrate quadratic convergence for the fundamental mode's effective index dependence on spatial resolution. We show that this method can be used to calculate the beat length of PBFs in which a birefringence is introduced by applying a small unidirectional stretch to the fiber cross section along one of its axes. Abrupt variations of the modeled fiber geometries with spatial resolution lead to oscillatory beat length convergence behavior. We can obtain a better estimate for beat length by averaging these oscillations. We apply a strong perturbation analysis to the fiber's unperturbed mode, calculated by our finite-difference method, to perform this averaging in a rigorous way. By fitting a polynomial to the predicted beat lengths as a function of grid spacing, we obtain an accurate estimate of the beat length at zero grid spacing. Reasonable convergence for the beat length is observed using a single processor with 8 GB of memory.

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Symmetry and degeneracy in microstructured optical fibers

Cited by 235 publications

References 11 publications

Fiber guiding at the Dirac frequency beyond photonic bandgaps

Fiber guiding at the Dirac frequency beyond photonic bandgaps

Single-polarization hollow-core square photonic bandgap waveguide

Birefringence Analysis of Photonic-Bandgap Fibers Using the Hexagonal Yee's Cell

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