Electromagnetics Visualization Project

Explore the
World of
Waveguides.

Discover how electromagnetic waves travel through guided structures. Explore electric and magnetic field patterns, propagation modes, and signal attenuation in lossy dielectric materials through an interactive visual learning experience.

02 Waveguide Geometries
04 Mode Families
EM Wave Propagation
E-FIELD / ELECTRIC
DIRECTION OF PROPAGATION
H-FIELD / MAGNETIC
01 / Fundamental Theory

Waveguides: The Basic Theory.

Learn the fundamental concepts, field components, and propagation modes before exploring the visual simulations.

What is an Electromagnetic Waveguide?

An electromagnetic waveguide is a structure designed to guide electromagnetic energy from one point to another. It confines and directs waves by using conducting boundaries or dielectric material boundaries.

Waveguides are widely used in microwave communication, radar systems, satellite communication, antennas, and optical fiber communication. Their dimensions, material properties, and boundary conditions determine how electromagnetic waves propagate through them.

The two important metallic waveguide geometries studied in this project are the rectangular waveguide and the circular waveguide. Wave propagation in lossy dielectric materials is also investigated.

Basic Concept 01

Electromagnetic Wave Propagation

Electromagnetic waves consist of electric and magnetic fields that vary with time and space. In a waveguide, the fields form specific patterns called modes. Energy propagates along the guide's longitudinal direction, conventionally denoted by the z-axis.

The electric field is represented by E, while the magnetic field is represented by H.

E = Ex + Ey + Ez
H = Hx + Hy + Hz
Basic Concept 02

Cutoff Frequency

The cutoff frequency is the threshold frequency for propagation of a particular mode in an ideal uniform waveguide. In a hollow metallic waveguide, a mode propagates when its operating frequency exceeds its cutoff frequency. Below cutoff, its field is evanescent rather than propagating down the guide.

f > fc : Propagating mode
f < fc : Evanescent field
Basic Concept 03

TE Mode — Transverse Electric

Definition: A TE mode is an electromagnetic waveguide mode in which the electric field has no component in the direction of propagation. If propagation is along the z-axis, the longitudinal electric field is zero.

The transverse electric-field components may be nonzero, while the longitudinal magnetic-field component can be nonzero.

Ez = 0
Hz ≠ 0 (generally)
Basic Concept 04

TM Mode — Transverse Magnetic

Definition: A TM mode is an electromagnetic waveguide mode in which the magnetic field has no component in the direction of propagation. For propagation along the z-axis, the longitudinal magnetic field is zero.

The transverse magnetic-field components may be nonzero, while the longitudinal electric-field component can be nonzero.

Hz = 0
Ez ≠ 0 (generally)
Basic Concept 05

TEM Mode — Transverse Electromagnetic

Definition: A TEM mode is a wave propagation mode in which both the electric and magnetic fields have no components along the direction of propagation.

Both fields are entirely transverse. TEM propagation is supported by suitable transmission lines, such as coaxial cables, but not by an ordinary hollow, single-conductor metallic waveguide.

Ez = 0
Hz = 0
Basic Concept 06

Hybrid Modes — HE and EH

Definition: Hybrid modes have both longitudinal electric and longitudinal magnetic field components. Therefore, neither Ez nor Hz is generally zero.

HE and EH modes are especially important in dielectric waveguides and optical fibers. Their detailed field distributions depend on the structure and material properties.

Ez ≠ 0
Hz ≠ 0 (generally)
Important note: The terms transverse and longitudinal are defined relative to the direction of propagation. For a wave travelling along the z-axis, Ez and Hz are longitudinal components. TE, TM, and TEM describe the field components of a mode, not simply the shape of the waveguide.
02 / Waveguide Structures

Two Geometries. One Principle.

Waveguide geometry and boundary conditions determine the allowed field patterns and propagation characteristics.

Rectangular Waveguide

METALLIC GUIDE
a b z →

A hollow metallic structure with a rectangular cross-section. It is widely used in microwave and radar systems and supports TE and TM modes above their cutoff frequencies.

fc,mn = (v / 2) √[(m/a)² + (n/b)²]

Circular Waveguide

CYLINDRICAL GUIDE
Radius a z →

A cylindrical conducting structure that supports multiple field configurations. Circular waveguides are used in microwave links, rotating joints, and high-power systems.

Cutoff depends on Bessel-function roots
03 / Electromagnetic Modes

Understand the Wave Modes.

Compare the four mode families and their longitudinal electric and magnetic field components.

MODE / 01

TE Mode

Transverse Electric. Ez = 0; Hz is generally nonzero. Common in hollow metallic waveguides.

MODE / 02

TM Mode

Transverse Magnetic. Hz = 0; Ez is generally nonzero. Common in hollow metallic waveguides.

MODE / 03

TEM Mode

Transverse Electromagnetic. Both Ez and Hz are zero. Supported by suitable two-conductor structures.

MODE / 04

Hybrid Mode

Both longitudinal field components are generally nonzero. HE and EH modes occur in dielectric guides and optical fibers.

04 / Real-World Propagation

Wave Propagation in Lossy Dielectrics.

In a lossy dielectric, electromagnetic energy is dissipated as the wave travels through the material. The field amplitude decreases with distance because of dielectric losses and, where applicable, conductor losses.

For a uniform medium, the propagation constant is complex: γ = α + jβ. Here, α is the attenuation constant and β is the phase constant.

  • Observe decreasing field amplitude.
  • Understand attenuation and phase propagation.
  • Explore different attenuation levels.
  • Connect material properties to signal transmission.
E(z,t) = E₀ e−αz cos(ωt − βz)

Attenuation Visualizer

Adjust the attenuation coefficient to see how the wave amplitude changes with distance.

E z → 0 Distance
Moderate attenuation: the field amplitude decreases as the wave propagates.