Complete Mueller matrix from a partial polarimetry experiment: the 12-element case

Abstract

Conventional generalized ellipsometry instrumentation is capable of measuring twelve out of the sixteen elements of the Mueller matrix of the sample. The missing column (or row) of the experimental partial Mueller matrix can be analytically determined under additional assumptions. We identify the conditions necessary for completing the partial Mueller matrix to a full one. More specifically, such a completion is always possible if the sample is nondepolarizing; the fulfilment of additional conditions, such as the Mueller matrix exhibiting symmetries or being of special two-component structure, are necessary if the sample is depolarizing. We report both algebraic and numerical procedures for completing the partial twelve-element Mueller matrix in all tractable cases and validate them on experimental examples.

Mueller matrix polarimetry of bianisotropic materials [Invited]

“…Mueller matrix polarimetry is described as complete polarimetry [11,12], as opposed to partial polarimetry where only a subset of Mueller matrix elements are measured with simpler PSG and/or PSA devices and limitations on the polarization states that are generated and analyzed. Under special conditions it is possible to convert partial polarimetry measurements based on the determination of 9 or 12 Mueller matrix elements into complete Mueller matrices [16,17]. Circular dichroism spectrometers are, for example, partial polarimeters optimized for measuring only one of the 16 elements of the Mueller matrix.…”

Polymorphic chiral squaraine crystallites in textured thin films

“…In the following, we discuss the polymorph formation and anisotropic texture within thin films controlled by the solution and vapour‐based processing conditions. Thereby, we focus on the local polymorph specific excitonic coupling on a microscopic scale and attempt to capture the anisotropic chiroptical response by imaging Mueller matrix polarimetry …”

Completing an experimental nondepolarizing Mueller matrix whose column or row is missing

“…The recovered elements obey the symmetry relations M 14 ¼ M 41 , M 24 ¼ M 42 , and M 34 ¼ ÀM 43 expected for a sample whose polarimetric response is rotationally invariant with respect to a 180°-rotation about its normal. 3,8 It should be emphasized that the recovery procedure does not assume the validity of any symmetry relations; indeed, the latter are violated by the presence of slight asymmetries in the pattern profiles, as has been shown both theoretically 19 and experimentally. [20][21][22][23] The quality of recovery of the last column of the Mueller matrix is spectrally uniform.…”

“…7 If this is not the case, one should resort to more complex covariance-matrix-based procedures. 8 Alternatively, one may evaluate the depolarization index (or the degree of polarimetric purity) 4 of the recovered M; a value equal to the unit within the experimental error is a warrant of successful recovery.…”

“…Indeed, conventional partial Mueller polarimeter designs provide experimentally either 9 (when both a column and a row are missing) or 12 (when a column or a row is missing) elements of M. 5,6 In the first case, it has been shown that the completion problem for a partial nondepolarizing Mueller matrix M nd features exactly two distinct solutions, 7 whereas in the second one, the solution is unique. 8 In both cases, the completion of the partial 9-or 12-element M nd to a full 16-element one is based on the fact that its associated covariance matrix 2 H nd must be of unit rank. This involves the conversion of the elements of M nd into those of H nd and back, and furthermore requires making a judicious choice of equations from an overdetermined set, thus making only partial use of the information contained in H nd .…”