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README.md
README.md
 
 
em_wave_analysis.py
em_wave_analysis.py
 
 
requirements.txt
requirements.txt
 
 

README.md

Electromagnetic Wave Visualization Code

Python implementation for visualizing electromagnetic wave structure from the CM-Maxwell unified equation.

Requirements

  • Python 3.8+
  • numpy >= 1.24.0
  • plotly >= 5.14.0

Installation

pip install -r requirements.txt

Usage

Basic Execution

python em_wave_analysis.py

This generates em_wave_analysis.html in the current directory. Open it in any modern web browser for interactive 3D visualization.

Output Description

The visualization shows:

  • Red arrows: Electric field E at discrete z positions
  • Blue arrows: Magnetic field B at discrete z positions
  • Green arrows: Poynting vector S = (1/μ₀)E×B
  • Red helix: Continuous trajectory of E field
  • Blue helix: Continuous trajectory of B field

All three vectors (E, B, S) originate from the same point on the z-axis, demonstrating their orthogonal relationship and phase synchronization.

Customization

Key Parameters

Edit em_wave_analysis.py to adjust:

# Line 6-7: Wave parameters
wavelength = 1.0          # Wavelength in meters
num_positions = 12        # Number of sample points along z

# Line 12-15: Arrow display
arrow_length = 0.5        # Base arrow length
head_length = 0.1         # Arrow head length
head_width = 0.05         # Arrow head radius
shaft_width = 6           # Arrow shaft line width

Camera View

Modify line 121 to change viewing angle:

camera=dict(eye=dict(x=-1.8, y=-1.8, z=1.5))
  • Positive x/y: View from positive quadrant
  • Negative x/y: View from negative quadrant (current: ensures +z points away from viewer)
  • z: Elevation angle

Field Strength Ratio

Line 98-99 controls E/B visual length relative to S:

u_E = arrow_length * 0.55 * np.cos(phase[idx])  # 0.55 = scaling factor

Adjust 0.55 to balance visual appearance (physical lengths are equal in the equations).

Physical Interpretation

The code implements the plane wave solution in vacuum:

E(z,t) = E₀ cos(kz - ωt) x̂
B(z,t) = B₀ cos(kz - ωt) ŷ  
S(z,t) = (1/μ₀) E × B = const ẑ

Where:

  • k = 2π/λ (wave number)
  • c = 1/√(ε₀μ₀) (speed of light)
  • E ⊥ B ⊥ S (mutual orthogonality)

Troubleshooting

Issue: Arrows appear too small/large
Solution: Adjust arrow_length parameter

Issue: Colors hard to distinguish
Solution: Modify color strings in add_arrow() calls (lines 96-107)

Issue: Browser performance issues
Solution: Reduce num_positions or helix resolution (line 110: z_fine divisions)

Technical Notes

  • Arrow construction uses manual mesh geometry (not Plotly Cone) for consistent visual sizing
  • Camera position set to ensure +z propagation direction points away from viewer
  • Annotations positioned in 3D space; may require adjustment if parameters change significantly

License

MIT License - see repository root LICENSE file.