Interactive light polarization simulator

Understand the polarization of light by controlling two orthogonal sinusoids

Change the amplitudes and phase difference of the x- and y-components of the electric field. Watch the polarization ellipse from the face view, and see how the same wave appears in the side and top views as it propagates along z.

1

Two orthogonal components

Light polarization is determined by the relationship between Ex and Ey at the same frequency.

2

Phase difference sets shape

δ = 0 or π gives linear polarization, while δ = ±π/2 with equal amplitudes gives circular polarization.

3

Amplitude ratio sets axes

Changing Ax and Ay transforms a circle into an ellipse and rotates the resulting polarization state.

4

Front, side, and top views

The same electromagnetic wave can be understood through its xy trajectory and its xz and yz propagation views.

State—
Orientation ψ—
Ellipticity χ—
Stokes (s1, s2, s3)—
Handedness—

Face view (xy): polarization trajectory

Looking into the propagation axis z.

Side view (xz)

Snapshot of the wave propagating along +z.

Top view (yz)

The orthogonal component across the same propagation axis.

Component waveforms: Ex(t) and Ey(t)

The phase shift between these sinusoids determines the polarization state.

Mathematical model

The electric field is decomposed into two orthogonal harmonic components with the same optical frequency:

Ex(t,z) = Ax cos(kz − ωt),
Ey(t,z) = Ay cos(kz − ωt + δ)

For polarization, the key free parameters are the amplitude ratio Ay/Ax and the phase difference δ.

The normalized Stokes parameters for these ideal components are:

s1 = (Ax2 − Ay2) / S0
s2 = 2AxAy cosδ / S0
s3 = 2AxAy sinδ / S0

How to interpret the views

  • Face view (xy): directly shows the polarization ellipse traced by the electric-field tip.
  • Side view (xz): shows the x-component of the field as the wave propagates along z.
  • Top view (yz): shows the y-component of the field along the same propagation axis.
  • Waveform plot: compares Ex(t) and Ey(t) in time.
Pure polarization states require the two components to oscillate at the same frequency. The simulator therefore keeps a common frequency and lets you vary amplitudes and relative phase.

Suggested experiments

  • Set δ = 0° and compare Ax ≠ Ay versus Ax = Ay.
  • Set Ax = Ay and vary δ from 0° to 90° to see linear → elliptical → circular polarization.
  • Flip δ from +90° to −90° to reverse the handedness.
  • Use the preset buttons and compare the Stokes parameters.
  • Try Ax = 1 and Ay = 0.4 at δ = 60° to create a generic elliptical state.

Classification rules used here

  • Linear: |sinδ| ≈ 0 or one amplitude vanishes.
  • Circular: Ax ≈ Ay and |δ| ≈ 90°.
  • Elliptical: all other non-degenerate cases.

The orientation angle ψ and ellipticity angle χ are computed from the Stokes parameters.