There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Photonic crystal fibers guide light by corralling it within a periodic array of microscopic air holes that run along the entire fiber length Largely through their ability to overcome the limitations of conventional fiber optics—for example, by permitting low-loss guidance of light in a hollow core—these fibers are proving to have a multitude of important technological and scientific applications spanning many disciplines The result has been a renaissance of interest in optical fibers and their uses

https://science.sciencemag.org/content/sci/299/5605/358.full.pdf

Photonic crystal fibers

A topical review of numerical and experimental studies of supercontinuum generation in photonic crystal fiber is presented over the full range of experimentally reported parameters, from the femtosecond to the continuous-wave regime. Results from numerical simulations are used to discuss the temporal and spectral characteristics of the supercontinuum, and to interpret the physics of the underlying spectral broadening processes. Particular attention is given to the case of supercontinuum generation seeded by femtosecond pulses in the anomalous group velocity dispersion regime of photonic crystal fiber, where the processes of soliton fission, stimulated Raman scattering, and dispersive wave generation are reviewed in detail. The corresponding intensity and phase stability properties of the supercontinuum spectra generated under different conditions are also discussed.

Supercontinuum generation in photonic crystal fiber

We demonstrate experimentally for what is to our knowledge the first time that air–silica microstructure optical fibers can exhibit anomalous dispersion at visible wavelengths. We exploit this feature to generate an optical continuum 550 THz in width, extending from the violet to the infrared, by propagating pulses of 100-fs duration and kilowatt peak powers through a microstructure fiber near the zero-dispersion wavelength.

Visible continuum generation in air–silica microstructure optical fibers with anomalous dispersion at 800 nm

The electronic ground state of a periodic system is usually described in terms of extended Bloch orbitals, but an alternative representation in terms of localized "Wannier functions" was introduced by Gregory Wannier in 1937. The connection between the Bloch and Wannier representations is realized by families of transformations in a continuous space of unitary matrices, carrying a large degree of arbitrariness. Since 1997, methods have been developed that allow one to iteratively transform the extended Bloch orbitals of a first-principles calculation into a unique set of maximally localized Wannier functions, accomplishing the solid-state equivalent of constructing localized molecular orbitals, or "Boys orbitals" as previously known from the chemistry literature. These developments are reviewed here, and a survey of the applications of these methods is presented. This latter includes a description of their use in analyzing the nature of chemical bonding, or as a local probe of phenomena related to electric polarization and orbital magnetization. Wannier interpolation schemes are also reviewed, by which quantities computed on a coarse reciprocal-space mesh can be used to interpolate onto much finer meshes at low cost, and applications in which Wannier functions are used as efficient basis functions are discussed. Finally the construction and use of Wannier functions outside the context of electronic-structure theory is presented, for cases that include phonon excitations, photonic crystals, and cold-atom optical lattices.

Maximally-localized Wannier Functions: Theory and Applications

The dispersion properties of photonic crystal fibers are calculated by expression of the modal field as a sum of localized orthogonal functions. Even simple designs of these fibers can yield zero dispersion at wavelengths shorter than 1.27 µm when the fibers are single mode, or a large normal dispersion that is suitable for dispersion compensation at 1.55 µm.

Group-velocity dispersion in photonic crystal fibers.

The properties of photonic crystal fibers with large air holes can be modeled by a silica rod in air. Such approximate calculations show that the dispersion of photonic crystal fibers could exceed -2000 ps/mm/km, or they could compensate (to within /spl plusmn/0.2%) the dispersion of 35 times their length of standard fiber over a 100-nm range.

Dispersion compensation using single-material fibers

The authors report measurements of group velocity dispersion in photonic crystal fibre using low coherence techniques. The results confirm theoretical predictions that photonic crystal fibre, unlike conventional step-index fibre, can exhibit anomalous waveguide dispersion while remaining singlemode. This allows the design of singlemode fibres with zero dispersion points at wavelengths much shorter than is possible in standard fibre.

Experimental measurement of group velocity dispersion in photonic crystal fibre

We present a novel, general, and numerically efficient treatment of electromagnetic modes localized at defects in two-dimensional (2-D) photonic crystals. The method represents the fields in terms of orthogonal functions localized at the defect and is a fully vector treatment.

Localized function method for modeling defect modes in 2-D photonic crystals

We report on an intrinsic relationship between the maximum-likelihood quantum-state estimation and the representation of the signal. A quantum analogy of the transfer function determines the space where the reconstruction should be done without the need for any ad hoc truncations of the Hilbert space. An illustration of this method is provided by a simple yet practically important tomography of an optical signal registered by realistic binary detectors.

http://arxiv.org/pdf/quant-ph/0606042.pdf

Dmitri Mogilevtsev

Papers

Group-velocity dispersion in photonic crystal fibers.

Dispersion compensation using single-material fibers

Experimental measurement of group velocity dispersion in photonic crystal fibre

Localized function method for modeling defect modes in 2-D photonic crystals

Biased tomography schemes: an objective approach.