# Electromagnetic Wave Simulator - 3D Plane Wave, Jones Calculus, Poincaré Sphere, EM Spectrum

> Animated 3D EM plane wave with E and B, intensity and radiation pressure calculator, Jones-matrix polarization, Poincaré sphere and an EM spectrum explorer.

- URL: https://qilingtools.com/en/physics/em-wave
- Category: Physics Tools (https://qilingtools.com/en/physics)
- Tags: [Physics](https://qilingtools.com/en/tags/physics)
- Last updated: 2026-10-29
- Price: Free, no sign-up
- Privacy: Runs locally in the browser; files are never uploaded

This tool brings three core parts of electromagnetic waves together. A rotatable 3D plane-wave animation shows E, B and the propagation direction mutually perpendicular and in phase, and converts between field amplitude, magnetic amplitude, intensity and radiation pressure. The polarization page sends a Jones vector through polarizers, quarter-wave and half-wave plates, drawing the E-vector tip, the Stokes parameters and the path on the Poincaré sphere. The spectrum page lets you drag from gamma rays to long-wave radio and read the wavelength, frequency, photon energy and how much reaches the ground.

## How to use

1. On the 3D plane wave page, pick a polarization, drag the canvas to rotate the view and play or pause the animation
2. Choose a scenario (sunlight, laser pointer, Wi-Fi…) or enter the frequency, refractive index and any one known quantity to get E₀, B₀, intensity and radiation pressure
3. On the polarization page, set the input Jones vector, add polarizers and wave plates, and watch the polarization ellipse after each element and the path on the Poincaré sphere
4. On the spectrum page, drag the marker or type a wavelength, frequency or photon energy to see the band, typical sources, uses and detectors

## Features

- Rotatable 3D plane-wave animation with E, B and the Poynting vector; linear, circular and elliptical polarization
- E₀ ↔ B₀ ↔ intensity ↔ radiation pressure conversion with refractive index and photon flux
- Jones-matrix chain of polarizers, quarter-wave, half-wave, arbitrary retarders and rotators (up to 6 elements)
- Stokes parameters, orientation and ellipticity angles, and handedness in both the optics and IEEE conventions
- Rotatable Poincaré sphere showing each wave plate as a rotation about an equatorial axis
- Log-scale spectrum from gamma rays to radio with schematic atmospheric transmission and notes for every band

## FAQ

### Why are E and B always perpendicular and in phase?

Maxwell's equations require a plane wave in vacuum or a uniform medium to satisfy B = (1/v) k̂ × E. B points along the propagation direction crossed with E, so E, B and k are mutually perpendicular, and since the relation holds at every point and instant, B peaks exactly when E does. In magnitude B₀ = E₀/v, or E₀/c in vacuum, which is why the roughly 1000 V/m electric field of sunlight comes with a magnetic field of only about 3.4 μT.

### How do intensity, field amplitude and radiation pressure relate?

Intensity is the time-averaged Poynting vector, I = ½ n c ε₀ E₀², which in vacuum is E₀²/(2Z₀) with Z₀ ≈ 376.73 Ω. The solar constant of 1361 W/m² corresponds to E₀ ≈ 1013 V/m. Light carries momentum: an absorbing surface feels a pressure p = I/c, and a perfect mirror at normal incidence twice that, 2I/c. Sunlight pushes with only about 4.5 μPa, yet that is what accelerates a solar sail.

### Why does a quarter-wave plate at 45° turn linear light circular?

A quarter-wave plate delays the component along its slow axis by 90° relative to the fast axis. With the fast axis at 45°, horizontal light splits into two equal components along the two axes, which leave 90° out of phase, so the tip of the total field traces a circle. At any other angle the components are unequal and the result is elliptical. Run it backwards and a quarter-wave plate turns circular light back into linear.

### Why are left- and right-circular polarization so confusing?

Two opposite conventions are in use. Optics texts (Born & Wolf, Hecht) look towards the source and call a clockwise rotation right-handed; the IEEE convention looks along the direction of travel and calls clockwise right-handed, which is the opposite. This tool always says whether the field turns clockwise or counter-clockwise as seen facing the oncoming beam and gives the name in both conventions. Jones vectors use the e^{i(kz−ωt)} convention, where S₃ > 0 means counter-clockwise facing the beam.

### What does a point on the Poincaré sphere mean?

Treat the normalized Stokes parameters (S₁, S₂, S₃)/S₀ as 3D coordinates and every fully polarized state lands on the unit sphere. The equator holds linear polarizations at every angle, the poles are the two circular states and everything else is elliptical. Longitude is twice the ellipse orientation and latitude twice the ellipticity angle. A wave plate rotates the point about an axis in the equatorial plane by its retardance, while a polarizer projects it onto a point on the equator and throws away intensity.

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