EM Waves Parametric Toolkit

Richard Ikeda, Aug 4, 2025

This interactive GeoGebra Book showcases 3D parametric visualizations of electromagnetic waves, designed to help to understand core concepts in wave optics, field interactions, and polarization. Each chapter introduces a new layer of complexity — from basic field oscillations to orbital angular momentum. Perfect for self-study, or as an interactive complement to theoretical lessons. Built entirely with native GeoGebra tools.

Table of Contents

  1. Linear Polarization
    1. E Field Oscillation – Linear
    2. B Field Oscillation – Linear
    3. Orthogonal E and B Fields
  2. Circular and Elliptical Polarization
    1. Circular Polarization – Right-Handed
    2. Circular Polarization – Left-Handed
    3. Elliptical Polarization – Phase Shifted
  3. Frequency and Modulation
    1. High-Frequency Circular Polarization
    2. Amplitude-Modulated Helix (Envelope Effect)
  4. Energy Flow and Propagation
    1. Combined E and B Fields

1.

Linear Polarization

Explore the foundational concept of linearly polarized electromagnetic waves, where electric and magnetic fields oscillate in fixed perpendicular directions.

  • 1. E Field Oscillation – Linear
  • 2. B Field Oscillation – Linear
  • 3. Orthogonal E and B Fields

1.1.

E Field Oscillation – Linear

Linear Polarization – E Field Oscillation
Represents a linearly polarized electromagnetic wave, with the electric field oscillating in the X-direction and propagating along Z. Classic E-field representation with no twist.[br][br]
– Richard Ikeda

1.2.

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1.3.

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2.

Circular and Elliptical Polarization

Visualize helical field behavior representing circular and elliptical polarizations — essential for understanding how light twists through space.

  • 1. Circular Polarization – Right-Handed
  • 2. Circular Polarization – Left-Handed
  • 3. Elliptical Polarization – Phase Shifted

2.1.

Circular Polarization – Right-Handed

The electric field vector rotates clockwise (right-handed) in the XY plane as the wave advances along the Z-axis — a classic model of right-handed circular polarization.
– Richard Ikeda

2.2.

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2.3.

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3.

Frequency and Modulation

Analyze how changes in amplitude and frequency affect wave geometry, creating complex structures like modulated and dense helices.

  • 1. High-Frequency Circular Polarization
  • 2. Amplitude-Modulated Helix (Envelope Effect)

3.1.

High-Frequency Circular Polarization

A more tightly wound helix simulating a wave with shorter wavelength and higher frequency. Useful to visualize spectral differences.[br][br]
– Richard Ikeda

3.2.

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4.

Energy Flow and Propagation

Link field orientation with wave energy flow using the Poynting vector, and understand the geometric relationship of E × B → k.

  • 1. Combined E and B Fields

4.1.

Combined E and B Fields

A full representation of E and B field vectors with correct phase and orthogonality. Includes the energy propagation direction (Z-axis), representing the Poynting vector E × B → k.
– Richard Ikeda

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