General Geometric Optics Formalism in Plasmas

Effects of an inhomogeneous anisotropic plasma layer on the propagation of a Gaussian envelope carrier pulse are studied numerically. It is found that the magnitude of the right‐handed circularly polarized component of the transmitted wave increases with increasing magnetostatic field in the direction of propagation. However, the magnitude of the left‐handed circularly polarized component of the transmitted wave first decreases with increasing magnetostatic field, up to a critical point, then increases with the increasing magnetostatic field; the critical point is dependent on the carrier frequency.

In this paper, we explore the theory of optical deformations due to continuous variations of the refractive index of the air, and present several efficient implementations. We introduce the basic equations from geometrical optics, outlining a general method of solution. Further, we model the fluctuations of the index of refraction both as a superposition of blobs and as a stochastic function. Using a well known perturbation technique from geometrical optics, we compute linear approximations to the deformed rays. We employ this approximation and the blob representation to efficiently ray trace non linear rays through multiple environments. In addition we present a stochastic model for the ray deviations derived from an empirical model of air turbulence. We use this stochastic model to precompute deformation maps.KeywordsForce FieldComputer GraphicGeometrical OpticStochastic FunctionIEEE Computer GraphicThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

The state-space method is used to obtain an exact solution for radiation from a spherical antenna coated by a lossy and inhomogeneous layer of plasma. It is assumed that the plasma is isotropic and the density decreases sinusoidally with radial distance. Between the antenna and the coating a plasma sheath is also introduced. The results show that for appropriate dimensions of the antenna and the plasma layer, a considerable increase can be obtained in the radiation of the antenna, by lowering the antenna frequency below the maximum frequency of the plasma.

A graded dielectric inhomogeneous nosecone radome design with superior electromagnetic (EM) performance characteristics for airborne applications is presented. The radome wall is designed in such a way that the middle layer has the maximum dielectric parameters (dielectric constant and electric loss tangent). On either side of the middle layer, the dielectric parameters of the constituent layers decrease in a graded (or step‐wise) manner. This wall configuration facilitates better impedance matching as required for radome applications. The computation of the EM performance parameters of a tangent ogive nosecone radome based on the above‐mentioned wall configuration, enclosing an X‐band slotted waveguide planar array antenna, is carried out using ‘geometric optics’ based three‐dimensional ray tracing along with the ‘aperture integration’ method. EM performance analysis shows that the proposed graded inhomogeneous dielectric radome design is a better choice for streamlined airborne radomes compared with the ‘variable thickness radome’ (VTR) designs based on monolithic half‐wave and multilayered radome wall configurations. Furthermore, it excludes the constraints on fabrication that generally occur in the case of streamlined airborne VTRs.

A ray tracing method based on the geometrical optics and physical optics approximation is proposed for calculation of the scattering from rough metal surface with rough coating in terahertz regime. Geometrical optics is utilized to describe the wave propagation concerning the reflection and transmission, whereas physical optics is applied to obtain the scattering fields by equivalent currents on the surfaces. The method provides a reliable treatment of scattering from rough layers involving identical/different roughness. The scattering predictions of the rough layers are compared to the multilevel fast multipole algorithm (MLFMA) to demonstrate the efficiency and accuracy of the proposed method. Once validated, we use the method to carry out a sensitivity study of the bistatic radar scattering cross section to variations in layer parameters of interest in terahertz coating target detection, such as the roughness of the coating and metal surface, thickness of the coating layer.

This paper is concerned with proposing a numerical method to predict the wave front movement of optical rays based on the Dijkstra algorithm. Data for refractive index of the medium through which optical rays propagate are assigned to all nodes of rectangular meshes and its values apart from the mesh nodes can be approximated in terms of linear interpolation. The velocity of the wave front of an optical ray can be calculated by the refractive index assigned to each node and it varies from one node to another due to the medium in homogeneity. Since the wave front movement of any waves is governed by the Fermat principle, it can be easily estimated based on the Dijkstra algorithm. In this paper we discuss the Dijkstra algorithm relevant to optical rays propagating through the inhomogeneous media such as Luneburg lens and Maxwell's fish-eye lens. We also show some numerical examples to demonstrate the effectiveness of the proposed method for analyzing ray front movement and ray tracing.

A comparison of the accuracy of intraocular lens (IOL) power calculation formulae, including SRK/T, HofferQ, Holladay 1, Haigis, MM, Barrett Universal II (BUII), Emmetropia Verifying Optical (EVO), and AS-OCT ray tracing, was performed. One hundred eyes implanted with either the Rayone EMV RAO200E (Rayner Intraocular Lenses Limited, Worthing, UK) or the Artis Symbiose (Cristalens Industrie, Lannion, France) IOL were included. Biometry was obtained using IOLMaster 700 (Carl Zeiss Meditec AG, Jena, Germany) and MS-39 AS-OCT (CSO, Firenze, Italy). Mean (MAE) and median (MedAE) absolute errors and percentage of eyes within ±0.25D, ±0.50D, ±0.75D, and ±1.00D of the target were compared, with ±0.75D considered a key metric. The highest percentage within ±0.75D was found with MM (96%) followed by the Haigis (94%) for the enhanced monofocal IOL. SRK/T (94%) had the highest percentage within ±0.75D, followed by Holladay 1, MM, BUII, and ray tracing (all 90%) for the multifocal IOL. No statistically significant difference in MAE was found with both IOLs. EVO showed the lowest MAE for the enhanced monofocal and ray tracing for the multifocal IOL. EVO and ray tracing showed the lowest MedAE for the two respective IOLs. A similar performance with high accuracy across formulae was found. MM and ray tracing appear to have similar accuracy to the well-established formulae and displayed a high percentage of eyes within ±0.75D.

Two major model sets are used to model a radio wave propagation problem. The first is empirical, based on measurements and statistics. Empirical models are easy to implement and fast. They only consider Tx-Rx separation and thus are not accurate enough as different objects of the environment are not taken into account. The second is deterministic exploiting physical laws to simulate signal propagation. Deterministic propagation prediction models based on a combination of Geometrical Optics (GO) and the Uniform Theory of Diffraction (UTD) represent the unique solution for reliable estimations. The most famous of the second approach is the well-known ray tracing like model, based on the computation of the different paths according to the geometrical optical laws. Concerning the transmitted signal bandwidth (BW), the propagation channel appears differently to Ultra Wideband (UWB) wireless systems than it does to Narrow Band (NB) sine wave systems. The main objective of this paper is to develop a ray tracing Matlab code to estimate the power received as a function of frequency in a given environment. The results were experimentally validated according to time domain corporation specifications where the BW was selected to cover the 3.1-5.3 GHz band with center frequency of 4.3 GHz.

For laser pointers and designators, far-field analyses based on geometrical optics or Fraunhofer diffraction are often inadequate and erroneous. To obtain useful results, we must apply Fresnel's diffraction theory, but at the cost of having to abandon a traditional way of defining "focus," as well as having to invent a new depth-of-focus formula. One consequence of Fresnel analysis is that we may "ray trace" Gaussian beams. Gaussian-beam ray trace is similar to geometric ray trace, but it leads to radically different results that often confound common sense. This paper begins with examples of systems in which geometric and Fraunhofer analyses fail, demonstrates how Fresnel analysis applies, points out the need for precise definitions of focus and depth of focus, and ends with some simple rules of thumb based on wave front aberrations and the characteristic Fresnel number.

The authors study the interference that occurs between the high-frequency and low-frequency portions of a proposed dual-band antenna when the antennas transmit into free space or into an inhomogeneous plasma layer. They analyze two limiting cases, namely, (1) when the apertures of the antenna are backed by infinite waveguide sections, and (2) when the apertures are backed by cavities and the rectangular cavity contains a probe in it and the ridged waveguide section does not. Numerical examples are presented. >

The results of cylindrical F-Layer model [1] are generalized for the case of a flat-layer of an inhomogeneous, magnetized plasma, which seems to be more adequate for describing the Earth's ionospheric F-Layer. Two opposite models are considered: a plasma layer with sharp boundaries and an inhomogeneous plasma layer with smooth plasma density profile. The mechanism of whistlers absorption due to oblique Langmuir waves excitation or their emission outside the F-Layer is discussed. It is shown that this mechanism may be important only in the model of plasma layer with sharp boundaries.

Whistler mode waves are known to propagate in the Earth’s magnetosphere along complex trajectories and have a significant impact on space weather processes and radiation belt energy dynamics. Most past work on propagation trajectories of whistler mode waves has been done using ray tracing, which is appropriate for smoothly varying background plasma densities. Recent spacecraft observations suggest that the cold plasma density in the magnetosphere can often be highly inhomogeneous. In this study, we investigate the propagation of whistler mode waves in cold, inhomogeneous plasma, with a focus on the combined effects of geomagnetic curvature and density irregularities known as magnetospheric ducts. Using both a comprehensive full wave model and a ray tracing model, we simulate wave behavior under conditions representative of Van Allen Probe observations. The presence of magnetospheric ducts produces a more complex wave behavior in the full wave model, leading to a strong spatial modulation, efficient confinement and the formation of shadow region as a result of geomagnetic curvature. The ray tracing simulation provides a complementary perspective, highlighting the propagation paths of individual rays in the background cold plasma density and, demonstrates the reflection, bending and guiding of rays due to density gradients. Employing both of these models provides insight into the effects of density ducts in the whistler mode wave propagation and understanding of the wave power distribution in global magnetospheric models.

We study the high-frequency propagation of acoustic plane and spherical waves in random media. With the geometrical optics and the perturbation approach, we obtain the travel-time mean and travel-time variance at the second order. The main hypotheses are the Gaussian distribution of the acoustic speed perturbation and a factorized form for its correlation function. The second-order travel-time variance explains the nonlinear behaviour at large propagation distance observed with numerical experiments based on ray tracing. Usually, homogeneity and isotropy of the refractive index are considered. Using the geometrical anisotropy hypothesis we extend the theory to a general class of statistically anisotropic random media.

To gauge the extent to which differences in the refractive error axial length relationship predicted by geometrical optics are observed in actual refractive/biometric data. This study is a retrospective analysis of existing data. Right eye refractive error [RX] and axial length [AXL] data were collected on 343 6-to-7-year-old children [mean 7.18years (S.D. 0.35)], 294 12-to-13-year-old children [mean 13.12years (S.D. 0.32)] and 123 young adults aged 18-to-25-years [mean 20.56years (S.D. 1.91)]. Distance RX was measured with the Shin-Nippon NVision-K 5001 infrared open-field autorefractor. Child participants were cyclopleged prior to data collection (1% Cyclopentolate Hydrochloride). Myopia was defined as a mean spherical equivalent [MSE] ≤-0.50D. Axial length was measured using the Zeiss IOLMaster 500. Optical modelling was based on ray tracing and manipulation of parameters of a Gullstrand reduced model eye. There was a myopic shift in mean MSE with age (6-7years +0.87D, 12-13years -0.06D and 18-25years -1.41D), associated with an increase in mean AXL (6-7years 22.70mm, 12-13years 23.49mm and 18-25years 23.98mm). There was a significant negative correlation between MSE and AXL for all age groups (all p<0.005). RX: AXL ratios for participant data were compared with the ratio generated from Gullstrand model eyes. Both modelled and actual data showed non-linearity and non-constancy, and that as axial length is increased, the relationship between myopia and axial length differs, such that it becomes more negative. Optical theory predicts that there will be a reduction in the RX: AXL ratio with longer eyes. The participant data although adhering to this theory show a reduced effect, with eyes with longer axial lengths having a lower refractive error to axial length ratio than predicted by model eye calculations. We propose that in myopia control intervention studies when comparing efficacy, consideration should be given to the dampening effect seen with a longer eye.

Realistic computer graphics and free form surfaces