Radiation from the dipole
The program calculates the radiation of electromagnetic waves from a dipole. In the calculation, not only the far field but also the near field in the immediate vicinity of the dipole is treated correctly. In order to achieve sufficient calculation speed, the entire problem is calculated in two dimensions. As a result, the amplitude of the wave decreases outwards somewhat more slowly than in the real three-dimensional case, but otherwise all the interesting effects are at least qualitatively the same as in reality.
A Gaussian current density distribution is specified, which periodically reverses its current direction. Maxwell's equations are solved in the entire (2-dim.) space shown and the temporal development of the electric field (E-field) and the magnetic field (B-field) is calculated. The Poisson equation is used to calculate the resulting charge distribution from the E-field. The edges are treated as ideally reflecting mirrors, so that after some time a standing wave is produced in a cavity resonator. To prevent this, absorption can be added between the dipole and the edge.
Downloads
Dipol.exe
Dipol-neu.exe
(with field lines)
Representation
The E-field is displayed in blue and the B-field in yellow. If the E-field and B-field are in phase (far field), the blue and yellow colors add up to white. In the near field, they are out of phase with each other and can therefore be recognized individually. Later in the standing waves, the E-field and B-field are again out of phase in time and place and can therefore be easily distinguished by color. The colouring is always proportional to the magnitude of the field strength, the polarization is not visible. It can also be switched to display current density (green) and charge density (red=positive, blue=negative). The oscillation of the dipole is thus easily recognizable.
Operation
The width and height of the area to be calculated is defined with n and m (number of square grid cells). The x-direction is horizontal on the screen, the y-direction vertical. The orientation of the dipole allows you to select whether it should oscillate along the y-axis or along the z-axis, i.e. in the plane or perpendicular to the screen. The frequency and size of the dipole can be adjusted using sliders. In addition, an absorption can be set which increases with increasing distance to the dipole like r2. This prevents reflections on the walls that would hinder observation of the radiation from the dipole.
The calculation can be paused with "Stop" and continued again with "Continue". If the calculation has been stopped, field lines can be drawn into the image by clicking on the left mouse button. In the case of "Dipole moment in y-direction", these are the field lines of the E-field. In this case, the B field points in the z direction and is therefore perpendicular to the screen. For the case "Dipole moment in z-direction", the field lines of the B field are shown. In this case, the E field is perpendicular to the screen. (Due to numerical inaccuracies, spiral field lines are drawn in a few unfavorable cases, which are unphysical and must therefore be discarded).
The brightness of the display can be adjusted so that areas of low field strength can also be easily recognized. After pressing the start button, the amplitude of the current density is slowly increased to its full value in order to prevent interference from switch-on effects. The speed of the display is determined by the calculation speed.
Numerical realization
A second-order finite difference method is used to solve Maxwell's equations. Universal units are used for the calculation where the speed of light is c=1. As a result, the E-field and B-field have the same magnitude in a plane electromagnetic wave. The results can be scaled appropriately by adapting the length and time scale to the actual speed of light and scaling the strength of the E and B fields accordingly.
Notes
Small dipoles radiate high frequencies better, large dipoles radiate low frequencies better. If the electromagnetic waves hit the reflective walls, a time-dependent charge and current density can also be found there, as occurs with every reflection on metal surfaces (not shown in the program). If the frequency is applied to an oscillation mode of the cavity resonator, the amplitude of the standing wave increases continuously. If you are between two modes, the amplitude may rise and fall, similar to Rabi oscillations in quantum mechanics.