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Convert linear component representation of field to circular component representation



cfv = pol2circpol(fv) converts the linear polarization components of the field or fields contained in fv to their equivalent circular polarization components in cfv. The expression of a field in terms of a two-row vector of linear polarization components is called the Jones vector formalism.


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Express a 45° linear polarized field in terms of right-circular and left-circular components.

fv = [2;2]
fv = 2×1


cfv = pol2circpol(fv)
cfv = 2×1 complex

   1.4142 - 1.4142i
   1.4142 + 1.4142i

Specify two input fields [1+1i;-1+1i] and [1;1] in the same matrix. The first field is a linear representation of a left-circularly polarized field and the second is a linearly polarized field.

fv=[1+1i 1;-1+1i 1]
fv = 2×2 complex

   1.0000 + 1.0000i   1.0000 + 0.0000i
  -1.0000 + 1.0000i   1.0000 + 0.0000i

cfv = pol2circpol(fv)
cfv = 2×2 complex

   1.4142 + 1.4142i   0.7071 - 0.7071i
   0.0000 + 0.0000i   0.7071 + 0.7071i

Input Arguments

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Field vector in its linear component representation specified as a 1-by-N complex row vector or a 2-by-N complex matrix. If fv is a matrix, each column in fv represents a field in the form of [Eh;Ev], where Eh and Ev are the field’s horizontal and vertical polarization components. If fv is a vector, each entry in fv is assumed to contain the polarization ratio, Ev/Eh. For a row vector, the value Inf designates the case when the ratio is computed for a field with Eh = 0.

Example: [1;-i]

Example: 2 + pi/3*i

Data Types: double
Complex Number Support: Yes

Output Arguments

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Field vector in circular component representation returned as a 1-by-N complex-valued row vector or 2-by-Ncomplex-valued matrix. cfv has the same dimensions as fv. If fv is a matrix, each column of cfv contains the circular polarization components, [El;Er], of the field where El and Er are the left-circular and right-circular polarization components. If fv is a row vector, then cfv is also a row vector and each entry in cfv contains the circular polarization ratio, defined as Er/El.


[1] Mott, H., Antennas for Radar and Communications, John Wiley & Sons, 1992.

[2] Jackson, J.D. , Classical Electrodynamics, 3rd Edition, John Wiley & Sons, 1998, pp. 299–302

[3] Born, M. and E. Wolf, Principles of Optics, 7th Edition, Cambridge: Cambridge University Press, 1999, pp 25–32.

Extended Capabilities

Version History

Introduced in R2013a