Theory of the positive column of a gas discharge

An attempt is made to provide a theoretical explanation of the effect of the positive column on the voltage-current characteristic of a glow or an arc discharge. Such theories have been developed before, and all are based on balancing the production and loss of charged particles and accounting for the energy supplied to the plasma by the applied electric field. Differences among the theories arise from the approximations and omissions made in selecting processes that affect the particle and energy balances. This work is primarily concerned with the deviation from the ambipolar description of the positive column caused by space charge, electron-ion volume recombination, and temperature inhomogeneities.

The presentation is divided into three parts, the first of which involved the derivation of the final macroscopic equations from kinetic theory. The final equations are obtained by taking the first three moments of the Boltzmann equation for each of the three species in the plasma. Although the method used and the equations obtained are not novel, the derivation is carried out in detail in order to appraise the validity of numerous approximations and to justify the use of data from other sources. The equations are applied to a molecular hydrogen discharge contained between parallel walls. The applied electric field is parallel to the walls, and the dependent variables—electron and ion flux to the walls, electron and ion densities, transverse electric field, and gas temperature—vary only in the direction perpendicular to the walls. The mathematical description is given by a sixth-order nonlinear two-point boundary value problem which contains the applied field as a parameter. The amount of neutral gas and its temperature at the walls are held fixed, and the relation between the applied field and the electron density at the center of the discharge is obtained in the process of solving the problem. This relation corresponds to that between current and voltage and is used to interpret the effect of space charge, recombination, and temperature inhomogeneities on the voltage-current characteristic of the discharge.

The complete solution of the equations is impractical both numerically and analytically, and in Part II the gas temperature is assumed uniform so as to focus on the combined effects of space charge and recombination. The terms representing these effects are treated as perturbations to equations that would otherwise describe the ambipolar situation. However, the term representing space charge is not negligible in a thin boundary layer or sheath near the walls, and consequently the perturbation problem is singular. Separate solutions must be obtained in the sheath and in the main region of the discharge, and the relation between the electron density and the applied field is not determined until these solutions are matched.

In Part III the electron and ion densities are assumed equal, and the complicated space-charge calculation is thereby replaced by the ambipolar description. Recombination and temperature inhomogeneities are both important at high values of the electron density. However, the formulation of the problem permits a comparison of the relative effects, and temperature inhomogeneities are shown to be important at lower values of the electron density than recombination. The equations are solved by a direct numerical integration and by treating the term representing temperature inhomogeneities as a perturbation.

The conclusions reached in the study are primarily concerned with the association of the relation between electron density and axial field with the voltage-current characteristic. It is known that the effect of space charge can account for the subnormal glow discharge and that the normal glow corresponds to a close approach to an ambipolar situation. The effect of temperature inhomogeneities helps explain the decreasing characteristic of the arc, and the effect of recombination is not expected to appear except at very high electron densities.

Optimizations for the uniformity of the non-volatile volume grating in doubly doped LiNbO3 crystals

The formation of the non-uniformity of the non-volatile volume grating in doubly doped LiNbO3 crystals is studied in detail. We find that the non-uniformity of the grating is mainly caused by strong ultraviolet light absorption, and the average saturation space-charge field is small and the diffraction efficiency is low as a result of the non-uniformity of the grating. In order to optimize the uniformity of the grating, we propose the recording scheme by using two sensitizing beams simultaneously from the two opposite sides of the crystals. Theoretical simulations and experimental verifications are performed. Results show that the well uniformed grating with high diffraction efficiency can be obtained by using this optimization scheme. (c) 2004 Elsevier B.V. All rights reserved.

Pulse shaping properties of volume holographic gratings in anisotropic media

Based on a modified coupled wave theory, the pulse shaping properties of volume holographic gratings (VHGs) in anisotropic media VHGs are studied systematically. Taking photorefractive LiNbO3 crystals as an example, the combined effect that the grating parameters, the dispersion and optical anisotropy of the crystal, the pulse width, and the polarization state of the input ultrashort pulsed beam (UPB) have on the pulse shaping properties are considered when the input UPB with arbitrary polarization state propagates through the VHG. Under the combined effect, the diffraction bandwidth, pulse profiles of the diffracted and transmitted pulsed beams, and the total diffraction efficiency are shown. The studies indicate that the properties of the shaping of the o and e components of the input UPB in the crystal are greatly different; this difference can be used for pulse shaping applications. (c) 2006 Optical Society of America.

Wavefront conversion by local volume holograms between cylindrical and plane waves with reconstruction at a different readout wavelength

Based on the two-dimensional coupled-wave theory, the wavefront conversion between cylindrical and plane waves by local volume holograms recorded at 632.8 nm and reconstructed at 800 nm is investigated. The proposed model can realize the 90 degrees holographic readout at a different readout wavelength. The analytical integral solutions for the amplitudes of the space harmonics of the field inside the transmission geometry are presented. The values of the off-Bragg parameter at the reconstructed process and the diffracted beam's amplitude distribution are analysed. In addition, the dependences of diffraction efficiency on the focal length of the recording cylindrical wave and on the geometrical dimensions of the grating are discussed. Furthermore, the focusing properties of this photorefractive holographic cylindrical lens are analysed.

Herpetofaunal Inventories of the National Parks of South Florida and the Caribbean: Volume II. Virgin Islands National Park

Amphibian declines and extinctions have been documented around the world, often in protected natural areas. Concern for this alarming trend has focused attention on the need to document all species of amphibians that occur within U.S. National Parks and to search for any signs that amphibians may be declining. This study, an inventory of amphibian species in Virgin Islands National Park, was conducted from 2001 to 2003. The goals of the project were to create a georeferenced inventory of amphibian species, use new analytical techniques to estimate proportion of sites occupied by each species, look for any signs of amphibian decline (missing species, disease, die-offs, etc.), and to establish a protocol that could be used for future monitoring efforts. Several sampling methods were used to accomplish these goals. Visual encounter surveys and anuran vocalization surveys were conducted in all habitats throughout the park to estimate the proportion of sites or proportion of area occupied (PAO) by amphibian species in each habitat. Line transect methods were used to estimate density of some amphibian species and double observer analysis was used to refine counts based on detection probabilities. Opportunistic collections were used to augment the visual encounter methods for rare species. Data were collected during four sampling periods and every major trail system throughout the park was surveyed. All of the amphibian species believed to occur on St. John were detected during these surveys. One species not previously reported, the Cuban treefrog (Osteopilus septentrionalis), was also added to the species list. That species and two others (Eleutherodactylus coqui and Eleutherodactylus lentus) bring the total number of introduced amphibians on St. John to three. We detected most of the reptile species thought to occur on St. John, but our methods were less suitable for reptiles compared to amphibians. No amphibian species appear to be in decline at this time. We found no evidence of disease or of malformations. Our surveys provide a snapshot picture of the status of the amphibian species, so continued monitoring would be necessary to determine long-term trends, but several potential threats to amphibians were identified. Invasive species, especially the Cuban treefrog, have the potential to decrease populations of native amphibians. Introduced mammalian predators are also a potential threat, especially to the reptiles of St. John, and mammalian grazers might have indirect effects on amphibians and reptiles through habitat modification. Finally, loss of habitat to development outside the park boundary could harm some important populations of amphibians and reptiles on the island.

Herpetofaunal Inventories of the National Parks of South Florida and the Caribbean: Volume III. Big Cypress National Preserve

Amphibian declines and extinctions have been documented around the world, often in protected natural areas. Concern for this trend has prompted the U.S. Geological Survey and the National Park Service to document all species of amphibians that occur within U.S. National Parks and to search for any signs that amphibians may be declining. This study, an inventory of amphibian species in Big Cypress National Preserve, was conducted from 2002 to 2003. The goals of the project were to create a georeferenced inventory of amphibian species, use new analytical techniques to estimate proportion of sites occupied by each species, look for any signs of amphibian decline (missing species, disease, die-offs, and so forth.), and to establish a protocol that could be used for future monitoring efforts. Several sampling methods were used to accomplish these goals. Visual encounter surveys and anuran vocalization surveys were conducted in all habitats throughout the park to estimate the proportion of sites or proportion of area occupied (PAO) by each amphibian species in each habitat. Opportunistic collections, as well as limited drift fence data, were used to augment the visual encounter methods for highly aquatic or cryptic species. A total of 545 visits to 104 sites were conducted for standard sampling alone, and 2,358 individual amphibians and 374 reptiles were encountered. Data analysis was conducted in program PRESENCE to provide PAO estimates for each of the anuran species. All of the amphibian species historically found in Big Cypress National Preserve were detected during this project. At least one individual of each of the four salamander species was captured during sampling. Each of the anuran species in the preserve was adequately sampled using standard herpetological sampling methods, and PAO estimates were produced for each species of anuran by habitat. This information serves as an indicator of habitat associations of the species and relative abundance of sites occupied, but it will also be useful as a comparative baseline for future monitoring efforts. In addition to sampling for amphibians, all encounters with reptiles were documented. The sampling methods used for detecting amphibians are also appropriate for many reptile species. These reptile locations are included in this report, but the number of reptile observations was not sufficient to estimate PAO for reptile species. We encountered 35 of the 46 species of reptiles believed to be present in Big Cypress National Preserve during this study, and evidence exists of the presence of four other reptile species in the Preserve. This study found no evidence of amphibian decline in Big Cypress National Preserve. Although no evidence of decline was observed, several threats to amphibians were identified. Introduced species, especially the Cuban treefrog (Osteopilus septentrionalis), are predators and competitors with several native frog species. The recreational use of off-road vehicles has the potential to affect some amphibian populations, and a study on those potential impacts is currently underway. Also, interference by humans with the natural hydrologic cycle of south Florida has the potential to alter the amphibian community. Continued monitoring of the amphibian species in Big Cypress National Preserve is recommended. The methods used in this study were adequate to produce reliable estimates of the proportion of sites occupied by most anuran species, and are a cost-effective means of determining the status of their populations.

Anisotropic diffraction of stratified volume holographic grating in photorefractive media

We have studied the anisotropic diffraction properties of the stratified volume holographic gratings recorded in photorefractive media using the anisotropic coupled wave theory. It is shown that the diffraction efficiency of such system exhibit the uniform periodic Bragg selectivity properties. In addition the dependence of the stratified volume holographic optical elements (SVHOEs) diffraction properties on the buffer-layer thickness, grating-layer thickness, number of modulation layers, and total thickness of system are discussed in detail. (c) 2005 Elsevier GrnbH. All rights reserved.

Diffraction properties of volume holographic gratings for an ultrashort pulsed beam with different polarization states readout

The diffraction properties of volume holographic gratings are studied when the gratings are illuminated by an ultrashort pulsed beam with different polarization states. The developed coupled wave theory of Kogelnik is used. Considering the dispersion effect of the grating media, solutions for the diffracted and transmitted intensities, diffraction efficiencies and the bandwidths of the gratings are given in transmission volume holographic gratings and reflection volume holographic gratings. The bandwidths of the gratings are reduced by the dispersion effect of the grating media. They also have different influences on the diffraction of an ultrashort pulsed beam with different polarization states. For different values of the ratio of the spectral bandwidth of the input pulse to that of the grating, the changes of the spectral and temporal distributions of the diffracted intensities, as well as the diffraction efficiencies of the gratings are shown.

Diffraction of an ultrashort pulsed beam with arbitrary polarization state from a volume holographic grating in LiNbO3 crystals

Based on a modified coupled wave theory of Kogelnik, we have studied the diffraction of an ultrashort pulsed beam with an arbitrary polarization state from a volume holographic grating in photorefractive LiNbO3 crystals. The results indicate that the diffracted intensity distributions in the spectral and temporal domains and the diffraction efficiency of the grating are both changed by the polarization state and spectral bandwidth of the input pulsed beam. A method is given of choosing the grating parameters and input conditions to obtain a large variation range of the spectral bandwidth of the diffracted pulsed beam with an appropriate diffraction efficiency. Our study presents a possibility of using a volume holographic grating recorded in anisotropic materials to shape a broadband ultrashort pulsed beam by modulating its polarization state.

Analysis of an ultrashort pulsed finite beam diffracted by volume gratings

We obtain analytical solutions of the coupled wave equations that describe the Bragg diffraction of ultrashort pulsed finite beams by a thick planar grating, using two-dimensional coupled wave theory. The diffraction properties for the case of an ultrashort pulsed finite beam with Gaussian profiles in both the time and spatial domains are investigated. The spectral bandwidth of the diffracted beam, the Bragg selectivity bandwidth and the diffraction efficiency of the volume grating are influenced by the geometry parameter and the input bandwidth. Therefore extra attention should be paid to designing optical elements based on volume gratings for use with ultrashort pulsed waves in applications of pulse shaping and processing.

Diffraction properties of ultrashort pulsed beams with arbitrary temporal profiles studied with a volume holographic grating

Using modified two- dimensional coupled- wave theory, the diffraction properties of ultrashort pulsed beams with arbitrary temporal profiles are studied with a volume holographic grating. Analytical expressions for the profiles of the transmitted and diffracted beams are obtained. It is shown that the Bragg selectivity bandwidth of the volume grating can be influenced by the geometry parameter. Numerical results are illustrated for three different temporal profiles. For different temporal profiles, the ratios of the diffraction bandwidths to input bandwidths are discussed.

Three-dimensional coupled wave study for finite-sized anisotropic volume holographic gratings under ultrashort pulsed beam readout

The three-dimensional coupled wave theory is extended to systematically investigate the diffraction properties of finite-sized anisotropic volume holographic gratings (VHGs) under ultrashort pulsed beam (UPB) readout. The effects of the grating geometrical size and the polarizations of the recording and readout beams on the diffraction properties are presented, in particular under the influence of grating material dispersion. The wavelength selectivity of the finite-sized VHG is analyzed. The wavelength selectivity determines the intensity distributions of the transmitted and diffracted pulsed beams along the output face of the VHG. The distortion and widening of the diffracted pulsed beams are different for different points on the output face, as is numerically shown for a VHG recorded in a LiNbO3 crystal. The beam quality is analyzed, and the variations of the total diffraction efficiency are shown in relation to the geometrical size of the grating and the temporal width of the readout UPB. In addition, the diffraction properties of the finite-sized and one-dimensional VHG for pulsed and continuous-wave readout are compared. The study shows the potential application of VHGs in controlling spatial and temporal features of UPBs simultaneously. (C) 2007 Optical Society of America

Effect of recording conditions on the anisotropic diffraction of volume holographic gratings

The anisotropic Bragg diffraction of the volume holographic gratings in photorefractive crystals are investigated based on the model of anisotropic coupled-wave theory. The effect of the initial intensity ratio and the recording angles of the two recording waves on the anisotropic Bragg diffraction properties is discussed. It is shown that both the ratio of the initial intensity and the incident angles of the recording waves are selective action for the anisotropic Bragg diffraction efficiency of the volume holographic gratings, while these two recording conditions are not selective action for the isotropic Bragg diffraction. Furthermore, the Bragg phase matching condition of anisotropic diffraction is analyzed when the recording angles change. (C) 2006 Elsevier GmbH. All rights reserved.

Anisotropic Bragg diffraction of finite-sized volume holographic grating in photorefractive crystals

Anisotropic diffraction of uniform plane wave by finite-sized volume holographic grating in photorefractive crystals is considered. It is found that the anisotropic diffraction can take place when some special conditions are satisfied. The diffracted image is obtained in experiment for the anisotropic Bragg diffraction in Fe:LiNbO3 crystals. A coupled wave analysis is presented to study the properties of anisotropic diffraction. An analytical integral solution for the amplitudes of the diffracted beams is submitted. A trade off between high diffraction efficiency and the deterioration of reconstruction fidelity is analyzed. Numerical evaluations also show that the finite-sized anisotropic volume grating exhibits strong angular and wavelength selectivity. All the results are useful for the optimizing design of VHOE based on finite-sized volume grating structures. (c) 2006 Elsevier GmbH. All rights reserved.