Perfect imaging analysis of the spherical geodesic waveguide

Negative Refractive Lens (NRL) has shown that an optical system can produce images with details below the classic Abbe diffraction limit. This optical system transmits the electromagnetic fields, emitted by an object plane, towards an image plane producing the same field distribution in both planes. In particular, a Dirac delta electric field in the object plane is focused without diffraction limit to the Dirac delta electric field in the image plane. Two devices with positive refraction, the Maxwell Fish Eye lens (MFE) and the Spherical Geodesic Waveguide (SGW) have been claimed to break the diffraction limit using positive refraction with a different meaning. In these cases, it has been considered the power transmission from a point source to a point receptor, which falls drastically when the receptor is displaced from the focus by a distance much smaller than the wavelength. Although these systems can detect displacements up to ?/3000, they cannot be compared to the NRL, since the concept of image is different. The SGW deals only with point source and drain, while in the case of the NRL, there is an object and an image surface. Here, it is presented an analysis of the SGW with defined object and image surfaces (both are conical surfaces), similarly as in the case of the NRL. The results show that a Dirac delta electric field on the object surface produces an image below the diffraction limit on the image surface.

Super-resolution properties of the Spherical Geodesic Waveguides using the perfect drain

Perfect drain for the Maxwell Fish Eye (MFE) is a nonmagnetic dissipative region placed in the focal point to absorb all the incident radiation without reflection or scattering. The perfect drain was recently designed as a material with complex permittivity ? that depends on frequency. However, this material is only a theoretical material, so it can not be used in practical devices. Recently, the perfect drain has been claimed as necessary to achieve super-resolution [Leonhard 2009, New J. Phys. 11 093040], which has increased the interest for practical perfect drains suitable for manufacturing. Here, we analyze the superresolution properties of a device equivalent to the MFE, known as Spherical Geodesic Waveguide (SGW), loaded with the perfect drain. In the SGW the source and drain are implemented with coaxial probes. The perfect drain is realized using a circuit (made of a resistance and a capacitor) connected to the drain coaxial probes. Superresolution analysis for this device is done in Comsol Multiphysics. The results of simulations predict the superresolution up to ? /3000 and optimum power transmission from the source to the drain.

Design of spherical symmetric gradient index lenses

Spherical symmetric refractive index distributions also known as Gradient Index lenses such as the Maxwell-Fish-Eye (MFE), the Luneburg or the Eaton lenses have always played an important role in Optics. The recent development of the technique called Transformation Optics has renewed the interest in these gradient index lenses. For instance, Perfect Imaging within the Wave Optics framework has recently been proved using the MFE distribution. We review here the design problem of these lenses, classify them in two groups (Luneburg moveable-limits and fixed-limits type), and establish a new design techniques for each type of problem.

Perfect imaging of point sources with positive refraction

The capability of a device called the Spherical Geodesic Waveguide (SGW) to produce images with details below the classic Abbe diffraction limit (super-resolution) is analyzed here. The SGW is an optical system equivalent (by means of Transformation Optics) to the Maxwell Fish Eye (MFE) refractive index distribution. Recently, it has been claimed that the necessary condition to get super-resolution in the MFE and the SGW is the use of a Perfect Point Drain (PPD). The PPD is a punctual receptor placed in the focal point that absorbs the incident wave, without reflection or scattering. A microwave circuit comprising three elements, the SGW, the source and the drain (two coaxial lines loaded with specific impedances) is designed and simulated in COMSOL. The super-resolution properties have been analyzed for different position of the source and drain and for two different load impedances: the PPD and the characteristic line impedance. The results show that in both cases super-resolution occurs only for discrete number of frequencies. Out of these frequencies, the SGW does not show SR in the analysis carried out.

Extreme super-resolution using the spherical geodesic waveguide

Leonhardt demonstrated (2009) that the 2D Maxwell Fish Eye lens (MFE) can focus perfectly 2D Helmholtz waves of arbitrary frequency, i.e., it can transport perfectly an outward (monopole) 2D Helmholtz wave field, generated by a point source, towards a "perfect point drain" located at the corresponding image point. Moreover, a prototype with λ/5 superresolution (SR) property for one microwave frequency has been manufactured and tested (Ma et al, 2010). Although this prototype has been loaded with an impedance different from the "perfect point drain", it has shown super-resolution property. However, neither software simulations nor experimental measurements for a broad band of frequencies have yet been reported. Here we present steady state simulations for two cases, using perfect drain as suggested by Leonhardt and without perfect drain as in the prototype. All the simulations have been done using a device equivalent to the MFE, called the Spherical Geodesic Waveguide (SGW). The results show the super-resolution up to λ/3000, for the system loaded with the perfect drain, and up to λ/500 for a not perfect load. In both cases super-resolution only happens for discrete number of frequencies. Out of these frequencies, the SGW does not show super-resolution in the analysis carried out.

On the design of spherical gradient index lenses

Classical spherical gradient index (GRIN) lenses (such as Maxwell Fish Eye lens, Eaton lens, Luneburg lens, etc.) design procedure using the Abel integral equation is reviewed and reorganized. Each lens is fully defined by a function called the angle of flight which describes the ray deflection through the lens. The radial refractive index distribution is obtained by applying a linear integral transformation to the angle of flight. The interest of this formulation is in the linearity of the integral transformation which allows us to derive new solutions from linear combinations of known lenses. Beside the review of the classical GRIN designs, we present a numerical method for GRIN lenses defined by the Abel integral equation with fixed limits, which is an ill-posed problem.

Experimental evidence of super-resolution better than lambda/105 with positive refraction

Super-resolution (SR) systems surpassing the Abbe diffraction limit have been theoretically and experimentally demonstrated using a number of different approaches and technologies: using materials with a negative refractive index, utilizing optical super-oscillation, using a resonant metalens, etc. However, recently it has been proved theoretically that in the Maxwell fish-eye lens (MFE), a device made of positive refractive index materials, the same phenomenon takes place. Moreover, using a simpler device equivalent to the MFE called the spherical geodesic waveguide (SGW), an SR of up to λ/3000 was simulated in COMSOL. Until now, only one piece of experimental evidence of SR with positive refraction has been reported (up to λ/5) for an MFE prototype working at microwave frequencies. Here, experimental results are presented for an SGW prototype showing an SR of up to λ/105. The SGW prototype consists of two concentric metallic spheres with an air space in between and two coaxial ports acting as an emitter and a receiver. The prototype has been analyzed in the range 1 GHz to 1.3 GHz.

Event no. 266-b

IMB (Irvine, Michigan, Brookline), a collaboration between the University of Michigan, the University of California at Irvine, and the U.S. Department of Energy, was an experiment designed to determine the ultimate stability of matter. Computer display of PMT [photomultiplier tubes] hits from a muon produced by a neutrino interaction in IMB detector. Fish-eye view

Species accumulation curves and their applications in parasite ecology

Species accumulation curves (SACs) chart the increase in recovery of new species as a function of some measure of sampling effort. Studies of parasite diversity can benefit from the application of SACs, both as empirical tools to guide sampling efforts and predict richness, and because their properties are informative about community patterns and the structure of parasite diversity. SACs can be used to infer interactivity in parasite infra-communities, to partition species richness into contributions from different spatial scales and different levels of the host hierarchy (individuals, populations and communities) or to identify modes of community assembly (niche versus dispersal). A historical tendency to treat individual hosts as statistically equivalent replicates (quadrats) seemingly satisfies the sample-based subgroup of SACs but care is required in this because of the inequality of hosts as sampling units. Knowledge of the true distribution of parasite richness over multiple host-derived and spatial scales is far from complete but SACs can improve the understanding of diversity patterns in parasite assemblages.

Canopy dynamics and light climates in a tropical moist deciduous forest in India

ABSTRACT. The canopy dynamics and light climates within a 20 by 60 m quadrat were studied in a disturbed moist deciduous forest near Bombay, India. A map was drawn of individual trees within the quadrat, the taxa were identified, and their phenology was followed from November 1984 to July 1985. The quadrat contained 14 species, the most common being Tectona grandis, Terminalia tomentosa, Butea monosperma, Mitragyne parviflora and Albizia procera. Some individuals were in leaf at all times, more so at the moister east end of the quadrat. In Novem- ber at the end of the rainy season, light measurements documented percentages of total daily photosynthetic photon fluence (PPF) at 10.0% of full sunlight; 44% of this flux was due to sun- flecks whose duration was approximately 17% of the daytime hours. Values for six sites were similar to mid-day measurements along a 40 m transect, and consistent with the 94% canopy cover of the sites, photographed with a fish-eye lens. The March dry season measurements re- vealed a more intense radiation environment (54% of solar PPF), and 59% of the photosyn- thetic photon flux density at mid-day along the transect. Canopy openings were increased to a mean of 59.4%. Light in the understorey in November was spectrally altered, with typical R:FR ratios of 0.30, compared to March values identical to those of sunlight, at 1.10.

Eye color as an indicator of social rank in the fish Nile tilapia

We investigated the association of eye color with the dominant-subordinate relationship in the fish Nile tilapia, Oreochromis niloticus. Eye color pattern was also examined in relation to the intensity of attacks. We paired 20 size-matched fish (intruder: 73.69 ± 11.49 g; resident: 75.42 ± 8.83 g) and evaluated eye color and fights. These fish were isolated in individual aquaria for 10 days and then their eye color was measured 5 min before pairing (basal values). Twenty minutes after pairing, eye color and fights were quantified for 10 min. Clear establishment of social hierarchy was observed in 7 of 10 pairs of fish. Number of attacks ranged from 1 to 168 among pairs. The quartile was calculated for these data and the pairs were then divided into two classes: low-attack (1 to 111 attacks - 2 lower quartiles) or high-attack (112 to 168 attacks - 2 higher quartiles). Dominance decreased the eye-darkening patterns of the fish after pairing, while subordinance increased darkening compared to dominance. Subordinate fish in low-attack confrontations presented a darker eye compared to dominant fish and to the basal condition. We also observed a paler eye pattern in dominants that shared low-attack interactions after pairing compared to the subordinates and within the group. However, we found no differences in the darkening pattern between dominants and subordinates from the high-attack groups. We conclude that eye color is associated with social rank in this species. Moreover, the association between eye color and social rank in the low-attack pairs may function to reduce aggression.

Eye color as an indicator of social rank in the fish Nile tilapia

We investigated the association of eye color with the dominant-subordinate relationship in the fish Nile tilapia, Oreochromis niloticus. Eye color pattern was also examined in relation to the intensity of attacks. We paired 20 size-matched fish (intruder: 73.69 ± 11.49 g; resident: 75.42 ± 8.83 g) and evaluated eye color and fights. These fish were isolated in individual aquaria for 10 days and then their eye color was measured 5 min before pairing (basal values). Twenty minutes after pairing, eye color and fights were quantified for 10 min. Clear establishment of social hierarchy was observed in 7 of 10 pairs of fish. Number of attacks ranged from 1 to 168 among pairs. The quartile was calculated for these data and the pairs were then divided into two classes: low-attack (1 to 111 attacks - 2 lower quartiles) or high-attack (112 to 168 attacks - 2 higher quartiles). Dominance decreased the eye-darkening patterns of the fish after pairing, while subordinance increased darkening compared to dominance. Subordinate fish in low-attack confrontations presented a darker eye compared to dominant fish and to the basal condition. We also observed a paler eye pattern in dominants that shared low-attack interactions after pairing compared to the subordinates and within the group. However, we found no differences in the darkening pattern between dominants and subordinates from the high-attack groups. We conclude that eye color is associated with social rank in this species. Moreover, the association between eye color and social rank in the low-attack pairs may function to reduce aggression.

Patterns of species diversity in the gastrointestinal helminths of a coral reef fish, Epinephelus merra (Serranidae), from French Polynesia and the south Pacific Ocean

Large-scale patterns of species diversity in the gastrointestinal helminth faunas of the coral reef fish Epinephelus merra (Serranidae) were investigated in French Polynesia and the South Pacific Ocean. The richer barrier reef community in French Polynesia supported richer parasite communities in E. merra than that on the fringing reef. While parasite communities among fish from the same archipelago were similar, differences in potential host species and the distance between archipelagos may have contributed to a qualitative difference in parasite communities between archipelagos. Digenean community diversity in coral reef fishes was greater in the western South Pacific, following similar patterns in free-living species. However, overall species diversity of camallanid nematodes of coral reef fishes does not appear to have been similarly affected.

The eyes of deep-sea fish II. Functional morphology of the retina

Three different aspects of the morphological organisation of deep-sea fish retinae are reviewed: First, questions of general cell biological relevance are addressed with respect to the development and proliferation patterns of photoreceptors, and problems associated with the growth of multibank retinae, and with outer segment renewal are discussed in situations where there is no direct contact between the retinal pigment epithelium and the tips of rod outer segments. The second part deals with the neural portion of the deep-sea fish retina. Cell densities are greatly reduced, yet neurohistochemistry demonstrates that all major neurotransmitters and neuropeptides found in other vertebrate retinae are also present in deep-sea fish. Quantitatively, convergence rates in unspecialised parts of the retina are similar to those in nocturnal mammals. The differentiation of horizontal cells makes it unlikely that species with more than a single visual pigment are capable of colour vision. In the third part. the diversity of deep-sea fish retinae is highlighted. Based on the topography of ganglion cells, species are identified with areae or foveae located in various parts of the retina, giving them a greatly improved spatial resolving power in specific parts of their visual fields. The highest degree of specialisation is found in tubular eyes. This is demonstrated in a case study of the scopelarchid retina, where as many as seven regions with different degrees of differentiation can be distinguished, ranging from an area giganto cellularis, regions with grouped rods to retinal diverticulum. (C) 1998 Elsevier Science Ltd. All rights reserved.