Jones Calculus
Chain Jones matrices for polarizers, waveplates, and rotators. Up to 5 elements.
Input State
E_x = 1.000
E_y = 0.000
Element Chain (0/5)
Add elements to build the optical chain. Light propagates left → right.
Propagation Results
Input Intensity
1.0000
Output Intensity
1.0000
Transmission
100.00%
Output state: Linear, ψ = 0.0°, χ = 0.0°
Convention (Goldstein): RCP = [1, i]/√2 turns clockwise as seen by the receiver; S₃ > 0 is right-handed.
| Stage | E_x | E_y | Intensity | Jones Matrix |
|---|---|---|---|---|
| Input | 1.000 | 0.000 | 1.0000 | [1.000, 0.000] [0.000, 1.000] |
Model and references
Exact. The equations are exact within the stated assumptions, or are a standard's tabulated values. The results are as good as the inputs. About the tiers
Ideal Jones matrices applied in turn, Goldstein convention: RCP = [1, i]/√2 with S₃ > 0, a retarder is diag(1, e^(−iΓ)) with its fast axis at 0°, a rotator by +θ turns counter-clockwise. Not modelled: losses.
- Jones R. C. (1941). A new calculus for the treatment of optical systems, I. Description and discussion of the calculus. J. Opt. Soc. Am. 31(7), 488–493. doi:10.1364/JOSA.31.000488
- Goldstein D. H. (2011). Polarized Light, 3rd ed., ch. The Jones Matrix Formalism, pp. 201–231. CRC Press. doi:10.1201/b10436