Information about Jones Calculus
In optics one can describe polarization using the Jones calculus, invented by R. C. Jones in 1941. Polarized light is represented by a Jones vector, and linear optical elements are represented by Jones matrices. When light crosses an optical element the resulting polarization of the emerging light is found by taking the product of the Jones matrix of the optical element and the Jones vector of the incident light.
The Jones vector for polarized light is defined by
, where 
and 
are the x and y components of the electric field of the light wave. It is common to normalize Jones vectors such that the sum of the squares of their components is 1. This discards the amplitude information needed for absorption calculations, but simplifies analysis in other cases. It is also common to constrain the first component of the Jones vectors to be a real number. This discards the phase information needed for calculation of interference with other beams.
The following table gives examples of normalized Jones vectors. (
is the imaginary unit, 
.)
The following table gives examples of Jones matrices.
If an optical element is rotated about the optical axis by angle θ, the Jones matrix for the rotated element, M(θ), is constructed from the matrix for the unrotated element, M, by the transformation
Note that Jones calculus is only applicable to light that is already fully polarized. Light which is unpolarized, partially polarized, or incoherent must be treated using Mueller calculus.
The Jones vector for polarized light is defined by
, where and are the x and y components of the electric field of the light wave. It is common to normalize Jones vectors such that the sum of the squares of their components is 1. This discards the amplitude information needed for absorption calculations, but simplifies analysis in other cases. It is also common to constrain the first component of the Jones vectors to be a real number. This discards the phase information needed for calculation of interference with other beams.
The following table gives examples of normalized Jones vectors. (
is the imaginary unit, .)
| Polarization | Corresponding Jones vector |
| Linear polarized in the x-direction |  |
| Linear polarized in the y-direction |  |
| Linear polarized at 45° from the x-axis |  |
| Right circular polarized |  |
| Left circular polarized |  |
The following table gives examples of Jones matrices.
| Optical element | Corresponding Jones matrix |
| Linear polarizer with axis of transmission horizontal |
 |
| Linear polarizer with axis of transmission vertical |
 |
| Linear polarizer with axis of transmission at 45° |
 |
| Linear polarizer with axis of transmission at -45° |
 |
Linear polarizer with axis of transmission at angle  |
 |
| Left circular polarizer |
 |
| Right circular polarizer |
 |
| Half-wave plate with fast axis in the horizontal direction |
 |
| Quarter-wave plate with fast axis in the horizontal direction. |
 |
If an optical element is rotated about the optical axis by angle θ, the Jones matrix for the rotated element, M(θ), is constructed from the matrix for the unrotated element, M, by the transformation
,
- where
.
Note that Jones calculus is only applicable to light that is already fully polarized. Light which is unpolarized, partially polarized, or incoherent must be treated using Mueller calculus.
References
- E. Collett, Field Guide to Polarization, SPIE Field Guides vol. FG05, SPIE (2005). ISBN 0-8194-5868-6.
- E. Hecht, Optics, 2nd ed., Addison-Wesley (1987). ISBN 0-201-11609-X.
- R. C. Jones, "New calculus for the treatment of optical systems," J. Opt. Soc. Am. 31, 488–493, (1941).
- Frank L. Pedrotti, S.J. Leno S. Pedrotti, Introduction to Optics, 2nd ed., Prentice Hall (1993). ISBN 0-13-501545-6
See also
Optics (ὀπτική appearance or look in Ancient Greek) is a branch of physics that describes the behavior and properties of light and the interaction of light with matter.
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polarization (Brit., polarisation) is the property of electromagnetic waves, such as light, that describes the direction of the transverse electric field. More generally, the polarization of a transverse wave describes the direction of oscillation in the plane
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19th century - 20th century - 21st century
1910s 1920s 1930s - 1940s - 1950s 1960s 1970s
1938 1939 1940 - 1941 - 1942 1943 1944
Year 1941 (MCMXLI
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1910s 1920s 1930s - 1940s - 1950s 1960s 1970s
1938 1939 1940 - 1941 - 1942 1943 1944
Year 1941 (MCMXLI
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matrix (plural matrices) is a rectangular table of elements (or entries), which may be numbers or, more generally, any abstract quantities that can be added and multiplied.
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In physics, absorption is the process by which the energy of a photon is taken up by another entity, for example, by an atom whose valence electrons make transition between two electronic energy levels. The photon is destroyed in the process.
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In mathematics, the real numbers may be described informally as numbers that can be given by an infinite decimal representation, such as 2.4871773339…. The real numbers include both rational numbers, such as 42 and −23/129, and irrational numbers, such as π and
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Interference is the addition (superposition) of two or more waves that results in a new wave pattern.
As most commonly used, the term interference usually refers to the interaction of waves which are correlated or coherent with each other, either because they
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As most commonly used, the term interference usually refers to the interaction of waves which are correlated or coherent with each other, either because they
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In mathematics, the imaginary unit (or sometimes the Latin or the Greek iota, see below) allows the real number system to be extended to the complex number system . Its precise definition is dependent upon the particular method of extension.
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A polarizer is a device that converts an unpolarized or mixed-polarization beam of electromagnetic waves (e.g., light) into a beam with a single polarization state (usually, a single linear polarization).
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wave plate or retarder is an optical device that alters the polarization state of a light wave travelling through it.
A wave plate works by shifting the phase of the light wave between two perpendicular polarization components.
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A wave plate works by shifting the phase of the light wave between two perpendicular polarization components.
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wave plate or retarder is an optical device that alters the polarization state of a light wave travelling through it.
A wave plate works by shifting the phase of the light wave between two perpendicular polarization components.
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A wave plate works by shifting the phase of the light wave between two perpendicular polarization components.
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Mueller calculus is a matrix method for manipulating Stokes vectors, which represent the polarization of incoherent light. It was developed in 1943 by Hans Mueller, then a professor of physics at the Massachusetts Institute of Technology.
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Mueller calculus is a matrix method for manipulating Stokes vectors, which represent the polarization of incoherent light. It was developed in 1943 by Hans Mueller, then a professor of physics at the Massachusetts Institute of Technology.
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The Stokes parameters are a set of values that describe the polarization state of electromagnetic radiation (including visible light). They were introduced by George Gabriel Stokes in 1852, as a mathematically convenient alternative to the more common description of incoherent or
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polarization (Brit., polarisation) is the property of electromagnetic waves, such as light, that describes the direction of the transverse electric field. More generally, the polarization of a transverse wave describes the direction of oscillation in the plane
..... Click the link for more information.
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