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

The relative efficiency of any particular image-coding scheme should be defined only in relation to the class of images that the code is likely to encounter. To understand the representation of images by the mammalian visual system, it might therefore be useful to consider the statistics of images from the natural environment (i.e., images with trees, rocks, bushes, etc). In this study, various coding schemes are compared in relation to how they represent the information in such natural images. The coefficients of such codes are represented by arrays of mechanisms that respond to local regions of space, spatial frequency, and orientation (Gabor-like transforms). For many classes of image, such codes will not be an efficient means of representing information. However, the results obtained with six natural images suggest that the orientation and the spatial-frequency tuning of mammalian simple cells are well suited for coding the information in such images if the goal of the code is to convert higher-order redundancy (e.g., correlation between the intensities of neighboring pixels) into first-order redundancy (i.e., the response distribution of the coefficients). Such coding produces a relatively high signal-to-noise ratio and permits information to be transmitted with only a subset of the total number of cells. These results support Barlow's theory that the goal of natural vision is to represent the information in the natural environment with minimal redundancy.

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Relations between the statistics of natural images and the response properties of cortical cells.

We report the fabrication of a new type of optical waveguide: the photonic crystal fiber. It consists of a pure silica core surrounded by a silica-air photonic crystal material with a hexagonal symmetry. The fiber supports a single robust low-loss guided mode over a very broad spectral range of at least 458-1550 nm. Also see errata - http://eprints.soton.ac.uk/78010/

All-silica single-mode optical fiber with photonic crystal cladding

The Insects has been the standard textbook in the field since the first edition published over forty years ago. Building on the strengths of Chapman's original text, this long-awaited 5th edition has been revised and expanded by a team of eminent insect physiologists, bringing it fully up-to-date for the molecular era. The chapters retain the successful structure of the earlier editions, focusing on particular functional systems rather than taxonomic groups and making it easy for students to delve into topics without extensive knowledge of taxonomy. The focus is on form and function, bringing together basic anatomy and physiology and examining how these relate to behaviour. This, combined with nearly 600 clear illustrations, provides a comprehensive understanding of how insects work. Now also featuring a richly illustrated prologue by George McGavin, this is an essential text for students, researchers and applied entomologists alike.

The insects: structure and function.

We have measured the spatial density of cones and rods in eight whole-mounted human retinas, obtained from seven individuals between 27 and 44 years of age, and constructed maps of photoreceptor density and between-individual variability. The average human retina contains 4.6 million cones (4.08-5.29 million). Peak foveal cone density averages 199,000 cones/mm2 and is highly variable between individuals (100,000-324,000 cones/mm2). The point of highest density may be found in an area as large as 0.032 deg2. Cone density falls steeply with increasing eccentricity and is an order of magnitude lower 1 mm away from the foveal center. Superimposed on this gradient is a streak of high cone density along the horizontal meridian. At equivalent eccentricities, cone density is 40-45% higher in nasal compared to temporal retina and slightly higher in midperipheral inferior compared to superior retina. Cone density also increases slightly in far nasal retina. The average human retina contains 92 million rods (77.9-107.3 million). In the fovea, the average horizontal diameter of the rod-free zone is 0.350 mm (1.25 degrees). Foveal rod density increases most rapidly superiorly and least rapidly nasally. The highest rod densities are located along an elliptical ring at the eccentricity of the optic disk and extending into nasal retina with the point of highest density typically in superior retina (5/6 eyes). Rod densities decrease by 15-25% where the ring crosses the horizontal meridian. Rod density declines slowly from the rod ring to the far periphery and is highest in nasal and superior retina. Individual variability in photoreceptor density differs with retinal region and is similar for both cones and rods. Variability is highest near the fovea, reaches a minimum in the midperiphery, and then increases with eccentricity to the ora serrata. The total number of foveal cones is similar for eyes with widely varying peak cone density, consistent with the idea that the variability reflects differences in the lateral migration of photoreceptors during development. Two fellow eyes had cone and rod numbers within 8% and similar but not identical photoreceptor topography.

Human photoreceptor topography

Optical waveguide theory

A set of coupled-mode equations is derived to describe mode propagation in uniform and slightly nonuniform cylindrical optical-fiber systems. The coupling between fibers of an array made up of n identical fibers each at the vertex of a polygon and one at the center, which is not necessarily the same as its n neighbors, is determined. Examples of this array are two fibers, three fibers in a row, and a hexagonal array with a fiber in the center. Very simple expressions for the coupling coefficients are presented. Mode coupling on a lossy fiber is investigated and a simple expression for the loss of a HE11 mode is given.

Coupled-Mode Theory for Optical Fibers

An asymptotic technique is presented, resulting in an analytically simple self-consistent description of the modes of a circular dielectric structure. When the dielectric difference between the rod and surrounding medium is small, the asymptotic expressions are valid for all frequencies. Even when the inside dielectric constant is twice the outside, less than a 10 percent error is usually involved. A simple functional expression for the eigenvalues of both the circular rod and the dielectric slab results from the analysis, thus eliminating the need for numerical or graphical methods.

Asymptotic Expressions for Eigenfunctions and Eigenvalues of a Dielectric or Optical Waveguide

A simple method is presented for finding the modes on those optical waveguides with a cladding refractive index that differs only slightly from the refractive index of the core. The method applies to waveguides of arbitrary refractive index profile, arbitrary number of propagating modes, and arbitrary cross section. The resulting modal fields and their progagation constants display the polarization properties of the waveguide contained within the ∇ ∊ term of the vector wave equation. Examples include modes on waveguides with circular symmetry and waveguides with two preferred axes of symmetry, e.g., an elliptical core. Only a minute amount of eccentricity is necessary for the well-known LP modes to be stable on an elliptical core, while the circle modes couple power among themselves.

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Modes of optical waveguides

The two fundamental limitations to resolving power of compound eyes are the wave (diffraction) and particle (photon noise) nature of light. By appreciating their interrelationship we gain insight into the design and limitation of eyes. In particular, we determine the dependence of eye design on the environmental light intensity.

1.

The limitations to resolving power include: the intensity of light, angular motion, receptor grain, lens-pupil blur, finite diameter of rhabdom, and neural convergence.




2.

Only those animals that are active in bright sunlight and normally have low angular velocity, profit by having some region of their eyes near the diffraction limit, i.e.DΔφ ≅ 0.58λ, whereD is the facet diameter,Δφ the interommatidial angle and λ the wavelength in vacuum. If these conditions are not fulfilled, it is better to have a largerDΔφ.




3.

The effect of an animal undergoing angular velocityu is equivalent to a reduction in light intensity by the amount exp−1.78(φtΔφ)2, where φt is the amount the animal turns in one integration time. Taking this into account, we present a possible explanation forMusca havingDΔφ about 4.5 times greater than the diffraction limit.




4.

Various strategies for dark-adaptation are considered with the conclusion that neural pooling combined with a widening of the acceptance angle is most effective for coping with reduced intensities.

Allan W. Snyder

Papers

Optical waveguide theory

Coupled-Mode Theory for Optical Fibers

Asymptotic Expressions for Eigenfunctions and Eigenvalues of a Dielectric or Optical Waveguide

Modes of optical waveguides

Acuity of compound eyes: Physical limitations and design