Elliptically Polarized Wave Power Calculator

Enter Wave Parameters

Electric field amplitude Ex (V/m): Electric field amplitude Ey (V/m):

Average Power per unit area ⟨S⟩ = -- W/m²

Workflow & Math Behind

For an elliptically polarized wave traveling in the +z direction, the electric field is:

𝐄(z, t) = x̂ Ex cos(kz - ωt) + ŷ Ey cos(kz - ωt + δ)

Step-by-Step Workflow:

• Step 1: Identify the amplitudes along x and y axes: Ex and Ey.
• Step 2: Compute the magnetic field using: H = (1/η) (ẑ × E)
• Step 3: Compute the instantaneous Poynting vector: S = E × H
• Step 4: Time-average over one cycle to get average power per unit area.

Math Formula:

The time-averaged power is:

⟨S⟩ = (Ex² + Ey²) / (2 η)

Where:

• Ex, Ey = peak amplitudes along x and y axes
• η = intrinsic impedance of medium (≈ 377 Ω for free space)
• Note: Phase difference δ does not affect total average power

Example Calculation:

• Ex = 10 V/m, Ey = 5 V/m, η = 377 Ω
• ⟨S⟩ = (10² + 5²) / (2 × 377) = 125 / 754 ≈ 0.1657 W/m²