Topics in Particle and Dispersion Science

Measures of polarization

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Several measures of polarization of light are is use (for example, Rochford K 2001; I, Q, U, and V in the following text are components of the Stokes vector):

• degree of polarization, P:

  P = √( Q 2 + U 2 + V 2 ) / I

  (1)

  It follows from Eq. 3 in Stokes vector that 0 ≤ P ≤ 1.

  
  

• degree of linear polarization, P_L:

  PL = √( Q 2 + U 2 ) / I

  (2)

  Note that P_L can be expressed as follows (for example, Hecht E 1987):

  PL =

  Imax - Imin Imax + Imin

  (2a)

  where I_max is the maximum value of irradiance of the beam measured following a linear polarizer as the latter is rotated about the beam axis, and I_min is the irradiance of the beam measured following that polarizer rotated by 90° from the direction corresponding to I_max. It follows that 0 ≤ P_L ≤ 1. Al-Qasimi A et al (2007) have shown that the above operational definition of the degree of polarization is a valid representation of that degree, as defined rigorously (for example, Born M and Wolf 1980) if I_max and I_min are eigenvalues of the following polarization (coherence) matrix

  <EmaxEmax*>  <Emax* Emin>      <EmaxEmin*>  <EminEmin*>

  (2a')

  of the beam. As usual, <x> denotes the time average of x and the asterisk denotes the complex conjugate.

  If U = 0 (linearly or elliptically polarized light with the major polarization direction parallel or perpendicular to the reference plane, see Eq. 2.81 in Bohren CF and Huffman 1983) we have:

  PL = | Q | / I

  (2b)

  Note that a ratio, P_Q (for example, Mischenko and Travis 2004)

  PQ = -Q / I

  (2c)

  indicates in this case (i.e. for U = 0) not only the degree of linear polarization but also its direction (see also Bohren CF and Huffman 1983, their Eq. 4.78). Indeed, it is positive for light partially polarized linearly in a plane perpendicular to the reference plane and negative otherwise. Unfortunately, P_Q is also frequently referred to as a degree of linear polarization, which may cause confusion, because the degree of linear polarization is nonnegative.

  
  

• degree of circular polarization, P_C:

  PC = V / I

  (3)

  P_C is positive for right-handed circular polarization and negative for left-handed circular polarization.

  
  

CITATION: Jonasz M. 2006. Measures of polarization (www.tpdsci.com/Tpc/StoVecDegPol.php). In: Top. Part. Disp. Sci. (www.tpdsci.com).

HISTORY: Published: 22-Mar-2006 Modified: 09-Jun-2007 Reviewed: 11-Mar-2008

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