| Electric-field components | For light traveling along the z-axis, the transverse electric field can be represented by components Ex and Ey. | Their relative amplitudes and phase determine the polarization state. |
| Jones vector | A fully polarized field is represented by a two-component complex vector, such as (Ex, Ey)T. | It describes the amplitudes and relative phase of the two orthogonal field components. |
| Horizontal linear polarization | Normalized Jones vector: (1, 0)T Normalized Stokes vector: (1, 1, 0, 0) | The electric field oscillates along the x-axis. |
| Vertical linear polarization | Normalized Jones vector: (0, 1)T Normalized Stokes vector: (1, −1, 0, 0) | The electric field oscillates along the y-axis. |
| Linear polarization at +45° | Normalized Jones vector: (1, 1)T/√2 Normalized Stokes vector: (1, 0, 1, 0) | The x and y components have equal amplitudes and are in phase. |
| Linear polarization at −45° | Normalized Jones vector: (1, −1)T/√2 Normalized Stokes vector: (1, 0, −1, 0) | The x and y components have equal amplitudes and opposite signs. |
| Circular polarization | Example Jones vector: (1, i)T/√2 Normalized Stokes vector under the convention below: (1, 0, 0, 1) | The orthogonal components have equal amplitudes and a phase difference of 90°. The handedness name depends on the convention used. |
| Stokes parameters | S0 is total intensity; S1 compares horizontal and vertical components; S2 describes the ±45° balance; S3 describes circular polarization. | The Stokes vector (S0, S1, S2, S3) can describe fully or partially polarized light. |
| Polarization modulator | An optical device that changes a light beam’s polarization, often by controlling the phase difference between orthogonal field components. | Changing the relative phase can convert, for example, linear polarization into elliptical or circular polarization. |
| Electro-optic modulation | An applied electric field can change a material’s refractive indices through the electro-optic effect, altering the phase delay between polarization components. | The polarization can be varied electrically, with the result depending on the material, device geometry, and applied voltage. |
| Retardance | The phase delay between two orthogonal components. A quarter-wave retardance is π/2 radians; a half-wave retardance is π radians. | With a suitable input polarization and device orientation, these phase delays can produce circular or rotated linear polarization, respectively. |
| Convention note | The normalized Stokes values use S1 = |Ex|² − |Ey|², S2 = 2 Re(Ex*Ey), and S3 = 2 Im(Ex*Ey). Circular-polarization handedness labels and the sign assigned to S3 can differ between conventions. |