Electromagnetic waves confined within waveguides are fundamental to microwave engineering, telecommunications, and particle accelerators, yet visualizing the invisible fields and understanding how different modes combine within the guide can be challenging. To bridge this gap, we introduce the Waveguide Pattern Visualizer, an interactive web application designed specifically to simulate and display the power distribution across a rectangular waveguide’s cross-section.
Seeing the invisible patterns formed by energy propagation presents a significant hurdle. Energy travels through a waveguide in specific configurations known as modes, such as TEmn and TMmn. At a given frequency, it’s common for multiple modes to exist simultaneously, each carrying a fraction of the total power and possessing a unique phase relationship to the others. The intricate interaction and superposition of these modes establish a distinct power intensity pattern across the waveguide’s area. Grasping this pattern is vital for educational purposes, helping students comprehend concepts like waveguide modes, cutoff frequencies, and field superposition. It also aids in design by providing intuition about energy concentration and potential hotspots, and it can be useful in troubleshooting by offering clues about possible mode contamination issues. A traditional laboratory method for visualization involves placing thermally sensitive paper across the waveguide aperture; the paper darkens where heat, and thus power, is concentrated. Our web tool aims to replicate this very phenomenon digitally.
The Waveguide Pattern Visualizer provides a user-friendly interface that allows users to define the geometry of a rectangular waveguide by specifying its width ‘a’ and height ‘b’. Users can also set the operating frequency ‘f’ and input a detailed list of the modes present within the waveguide, specifying not just the mode name but also its relative power level and phase. Furthermore, the resolution of the simulation can be adjusted by setting the number of horizontal and vertical grid points (Nx and Ny). With these parameters set, the application generates a clear heatmap visualization representing the calculated power density pattern across the waveguide’s cross-section.
Underpinning the visualizer are the fundamental principles of waveguide theory. The process begins with mode identification; the application calculates the cutoff frequency for each mode provided by the user, considering the waveguide dimensions. Only those modes whose cutoff frequency is below the operating frequency are capable of propagating and contributing to the final pattern. Modes that are below cutoff, or inherently invalid combinations like TM modes with zero indices, are correctly ignored. For each mode identified as propagating, the tool calculates the spatial distribution of its transverse electric field components, Ex and Ey, throughout the cross-section using established analytical formulas. These field components are treated as complex phasors to account for both magnitude and phase. Subsequently, these base field components are adjusted based on the user’s input: they are scaled by the square root of the specified power for that mode and mathematically rotated according to the specified phase angle. The next critical step is superposition, where the scaled and phase-adjusted complex field components from all contributing propagating modes are summed vectorially at every point on the defined simulation grid. Finally, the power intensity at each grid point is determined by summing the squared magnitudes of the total resulting transverse electric field components, following the relationship Intensity = |Total Ex|² + |Total Ey|². This array of intensity values is then rendered as a two-dimensional heatmap using the Plotly.js library. To effectively simulate the appearance of thermal paper, the colorscale is configured to range from white, representing low intensity, to black, representing high intensity.
Using the application is a straightforward process. First, the user enters the waveguide width ‘a’ and height ‘b’, typically in millimeters. Then, the operating frequency ‘f’ is input, usually in Gigahertz. The user also specifies the desired computational resolution by setting the number of horizontal grid points, Nx, and vertical grid points, Ny. Following this, the mode data is entered into the provided text area. Each line should detail one mode, following the format ModeName, Power, Phase_deg, for example, TE10, 100, 0 or TM11, 20, 50. Once all parameters are entered, clicking the “Generate Pattern” button initiates the calculation. The application then presents the results, first showing an informational summary indicating which of the input modes are propagating at the selected frequency and which are below cutoff or invalid. The main output is the heatmap plot itself, graphically displaying the computed power distribution across the waveguide cross-section, mapping the width from x=0 to ‘a’ and the height from y=0 to ‘b’.
In summary, the Waveguide Pattern Visualizer offers interactive input for waveguide dimensions, frequency, and grid resolution, coupled with flexible mode definition that allows multiple TE and TM modes with individual power and phase settings. It performs automatic cutoff frequency calculations and identifies propagating modes, accurately superimposes complex field phasors, and presents the results in a clear heatmap visualization using a white-to-black “thermal paper” colorscale. Built with standard web technologies like HTML, Javascript, and Plotly.js, it ensures broad accessibility.
Ultimately, the Waveguide Pattern Visualizer serves as a valuable resource for anyone engaged in learning about or working with rectangular waveguides. It effectively demystifies the complex interplay of electromagnetic modes by offering a direct visual representation of the power flow, mirroring the outcome one might expect from a physical thermal paper measurement. Whether utilized for educational exploration or for gaining preliminary design insights, this interactive application provides a convenient and powerful way to “see” inside the waveguide, encouraging exploration into the fascinating world of mode superposition.