Model retardance, thickness, and birefringence for wave plates. Compare orders, tilt, and wavelength response quickly. Build accurate polarization control with dependable optical engineering calculations.
Use design mode to size a plate. Use analysis mode to evaluate a known thickness.
| Material | Wavelength (nm) | n_o | n_e | Angle (deg) | Order | Approx. Thickness (um) |
|---|---|---|---|---|---|---|
| Quartz | 632.8 | 1.5442 | 1.5533 | 0 | 0 | 17.385 |
| Quartz | 532.0 | 1.5470 | 1.5562 | 0 | 1 | 43.370 |
| MgF2 | 550.0 | 1.3780 | 1.3900 | 0 | 0 | 11.458 |
For a quarter-wave plate, the optical retardance target is 90 degrees, plus any full half-wave multiples added by order selection.
Selected-order thickness: t = ((2m + 1) lambda) / (4 delta_n)
Retardance: delta = (2 pi delta_n t) / lambda
Extraordinary effective index: n_e,eff = (n_e n_o) / sqrt(n_e^2 cos^2(theta) + n_o^2 sin^2(theta))
Effective birefringence: delta_n = |n_e,eff - n_o|
These equations support quick sizing, sensitivity checks, and comparison between zero-order and multiple-order plates in optical engineering work.
Zero-order plates are thinner and usually less sensitive to wavelength drift and temperature changes. Multiple-order plates are thicker and easier to manufacture, but they often produce larger retardance errors away from the design point.
Using the effective extraordinary index helps estimate off-axis behavior. This is useful when the beam is not perfectly aligned to the optic axis or when the plate is slightly tilted inside an optical system.
It introduces a 90 degree phase shift between orthogonal polarization components. That phase shift can convert linear polarization into circular polarization when the input is set at 45 degrees to the principal axes.
At 45 degrees, the input field splits equally along the fast and slow axes. Equal amplitudes are needed for ideal circular polarization after a quarter-wave phase delay.
Zero-order plates use the thinnest quarter-wave thickness. Multiple-order plates add whole half-wave cycles, making them thicker and generally more sensitive to wavelength and temperature variation.
Retardance depends directly on birefringence, which is the index difference seen by the two polarization components. Small changes in indices can noticeably change the required thickness.
Yes. It estimates an effective extraordinary index from the propagation angle to the optic axis. That gives a practical engineering approximation for off-axis optical paths.
Enter wavelength in nanometers and thickness in micrometers. The calculator also reports thickness in millimeters for easier manufacturing and drawing references.
The thickness, indices, wavelength, or angle may not match the selected order. Even small deviations can move the retardance away from the intended quarter-wave target.
It is very useful for design screening and engineering estimates. Final fabrication should still include supplier data, measured dispersion curves, tolerances, and metrology results.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.