Jones Matrix Calculator Form
Use the responsive calculator grid below. Large screens show three columns, smaller screens show two, and mobile shows one.
Formula Used
Jout = M × JinThe output Jones vector equals the selected element matrix multiplied by the incident Jones vector.
Jin = [Ax e^(iφx), Ay e^(iφy)]ᵀAmplitudes set component magnitudes. Phases define the relative polarization state.
M(θ) = R(-θ) × Mlocal × R(θ)This rotates a local polarizer, retarder, or attenuator into the laboratory frame.
Ix = |Ex|², Iy = |Ey|², Itotal = Ix + IyΔφ = phase(Ey) - phase(Ex)
S0 = |Ex|² + |Ey|²S1 = |Ex|² - |Ey|²S2 = 2 Re(Ex Ey*)S3 = -2 Im(Ex Ey*)
How to Use This Calculator
- Enter the incident field amplitudes and phases for the x and y components.
- Choose the optical element you want to model.
- Set the orientation angle, retardance, attenuation, or custom matrix entries as needed.
- Press Calculate Jones Matrix to generate the transformed state.
- Review the active matrix, output vector, intensities, phases, Stokes values, and polarization angles.
- Use the CSV or PDF buttons to export the current result summary.
- Study the Plotly graph to compare input and output component intensities quickly.
Example Data Table
| Case | Input state | Element | Key setting | Typical output interpretation |
|---|---|---|---|---|
| 1 | Ex = 1∠0°, Ey = 0∠0° | Linear polarizer | Axis = 0° | Horizontal linear polarization remains unchanged. |
| 2 | Ex = 1∠0°, Ey = 1∠0° | Quarter-wave plate | Axis = 45° | Linear 45° input becomes nearly circularly polarized. |
| 3 | Ex = 1∠0°, Ey = 0∠0° | Optical rotator | Rotation = 30° | Polarization direction rotates without ideal loss. |
| 4 | Ex = 1∠0°, Ey = 1∠-90° | Half-wave plate | Axis = 0° | Handedness reverses for circular polarization. |
Frequently Asked Questions
1) What does a Jones matrix represent?
A Jones matrix represents how an optical element transforms the complex electric-field components of fully polarized light. It tracks amplitude and phase changes in the x and y directions.
2) When should I use a Jones matrix instead of a Mueller matrix?
Use a Jones matrix for fully polarized coherent light when phase matters. Use a Mueller matrix when you need to model partially polarized or unpolarized light and intensity-based measurements.
3) Why are the field components complex numbers?
Complex numbers store both amplitude and phase in one form. That makes interference, retardance, and phase shifts easier to calculate and display accurately.
4) What does the orientation angle control?
The angle rotates the local optical axis or transmission axis relative to the laboratory frame. It strongly affects how polarization is filtered, retarded, or rotated.
5) Can this calculator model unpolarized light?
No. Jones calculus assumes fully polarized light. For unpolarized or partially polarized beams, a Mueller-matrix approach is more appropriate.
6) Why can output intensity drop after the transformation?
A polarizer or attenuator can remove or reduce components of the incident field. That lowers total transmitted intensity even if the polarization state becomes better defined.
7) What is retardance in this calculator?
Retardance is the phase delay introduced between orthogonal field components. Quarter-wave and half-wave plates are common fixed-retardance cases.
8) Can I enter my own custom optical element?
Yes. Select the custom matrix option and enter the real and imaginary parts of all four Jones matrix elements to model your own system.