The paper presents an assessment of the accuracy of the method of choosing an integration variable for the numerical solution of the Cauchy problem in terahertz range. An example of using the method to determine ray paths in inhomogeneous media in the approximation of geometric optics is given. Unlike numerical methods of integration, where one pre-selected variable is used as an integration variable, in the considered method the integration variable is selected at each step. This approach reduces the risk of shifting to adjacent phase trajectories, which is especially important in the terahertz range. In addition, we note that using this approach allows you to effectively use computer resources. The integration method with the choice of the integration variable at each step is described. A feature of the method is that the variable with the highest rate of change is selected as the integration variable. The accuracy of the method is investigated by the example of a problem with a well-known analytical solution. The dependence of the relative error of the solution on the grid pitch is investigated. Extreme values of the grid pitch at which the relative error drops sharply are calculated. The dependence of the relative error of the solution on the direction of propagation of the rays is investigated. Shows the application of the numerical modeling algorithm for the example of constructing ray paths in inhomogeneous media in the approximation of geometric optics for geometry with three spatial coordinates. The ray paths in 3D space are presented.
This paper demonstrates the development of the analytical method of suppression of radiation pattern (RP) side lobes which is based on Woodward-Lawson method with three basic functions. The considered method allows to suppress the side lobes of the RP in a wide range of angles. It also allows to suppress RP side lobes in a desired direction. This approach can be used in digital antenna systems and the multibeam active phased antenna arrays. In the first part of the paper, linear phased antenna array (LPAA) consisting of isotropic equispaced radiators and methods of suppression of side lobes and creation of the operated minimum in a LPAA radiation pattern are considered. In the second part of the paper partial diagram method is considered. It is shown how to control the RP side lobes in wide range of angles. In the third part of the paper it is shown how to suppress RP side lobes in a desired direction. The fourth part of the paper shows how to synthesize amplitude and phase distribution to control RP side lobes. The method presented in this work allows to reduce the level of the side lobes of the radiation pattern by more than 50 dB in a wide range of angles, or in a given direction. Expressions for calculating the amplitude and phase distributions forming a minimum RP in a given direction are presented. Using LPAA with a given number of emitters, the use of the technique is demonstrated.
Development of the integration variable selection method for the numerical solution of the Cauchy problem is demonstrated. This method is applicable for the simulation of electromagnetic wave propagation in inhomogeneous media by geometric optics approximation. Usually, in the methods of the numerical solution of the Cauchy problem, the integration is carried out according to one pre-selected variable. This approach does not seem to be the most cost-efficient in terms of computing resources.
The equations of rays and eikonal in finite differences are considered, taking into account the anisotropy of the refractive index. The paper presents a block diagram of the algorithm for choosing the variable of integration. The integration is carried out on the variable selected at the current step, which is assigned the specified step value. The increments of the remaining variables are calculated by expressions depending on the selected integration variable so that the increments on the remaining variables do not exceed the value of the integration variable. The integration variable is selected again and the increments are calculated. This method saves computational resources and minimizes the risk of transition to adjacent phase trajectories. The paper presents a general flowchart of the selection algorithm and expressions for calculating the increments of other variables at each step. The algorithm for calculating increments for each variable is demonstrated. The variable selection algorithm is developed for the case of a 7-dimensional phase space. It includes the projection of the pulse on the three axes of the Cartesian coordinate system, the projection of the coordinate and the phase component. The phase component describes the phase of the wave at the selected point and is analogous to the time dependence.
The 2D electromagnetic modeling distribution of electric fields for stationary and non-stationary scattering process in the time domain mode was developed. The distributing system of the optical type was expressed. Given system allows to form 5-beam directional pattern (DP) for receiving active phased antenna radar (APAR).
At reduction of the sizes of the distributing system, distance between its output reduce in once, in contrast with distance between radiators APAR. In such event corner deflections of the ray in DP APAR will corner of the deflection less in distributing system in n once also. For considered systems reduction factor of the geometric sizes n has formed the order 7. In corresponding to number once and was increased a corner of the deflection of the ray α in distributing system.
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