Introduction to Spectropolarimetry (2003)(en)(244s) by Jose Carlos del Toro Iniesta

By Jose Carlos del Toro Iniesta

Whole assessment of spectropolarimetry for graduates and researchers.

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3 The polarization tensor and the Stokes parameters 23 However, the determinant of the polarization tensor is not necessarily zero. 13) or, in other terms, det(C) = C11 C22 − C12 C21 ≥ 0. 14) The non-diagonal terms of the coherency matrix are generally complex, but they are conjugates of each other (the polarization tensor is a Hermitian matrix). , monochromatic) radiation. 20). Note that all four Stokes parameters are real and have dimensions of energy. They are thus measurable. The actual value of κ is irrelevant in practice since only Q/I , U/I , and V /I are sought in most cases.

Possible states for totally polarized radiation. The monochromatic wave is elliptically polarized in general (right-handed states are in the upper row and left-handed states are in the lower row). When one of the Cartesian components is zero or when both have different amplitudes but a phase difference equal to 0 or π, the ellipse becomes a straight line. When the amplitudes of the Cartesian components are equal and δ = π/2 or 3π/2, the ellipse becomes a circle. possible states of polarization of a monochromatic wave are sketched in Fig.

Where the dielectric permittivity is now a tensor (a 3 × 3 matrix). 2) simplifies in a given reference frame. 3) where ε1 , ε2 , and ε3 are the eigenvalues of the dielectric tensor. If we change the {ˆx, yˆ , zˆ} reference frame by this transformation, we obtain the new frame {ˆe1 , eˆ 2 , eˆ 3 | eˆ i · eˆ j = δi, j , i, j = 1, 2, 3}. This frame is called the principal reference frame and the unit vectors are oriented in the so-called principal directions of the medium. 2) becomes      D1 E1 ε1 0 0  D2  =  0 ε2 0   E 2  .

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