Orthogonality-breaking sensing model based on the instantaneous Stokes vector and the Mueller calculus: erratum

Noé Ortega-Quijano; Julien Fade; Muriel Roche; François Parnet; Mehdi Alouini

doi:10.1364/JOSAA.34.001383

Abstract

For J. Opt. Soc. Am. A 33, 434 (2016) [CrossRef] , a corrected version of Eq. (9) is provided owing to typographical errors in the original article. The original full article text and calculations are unchanged. Another typo is corrected in Eq. (A5) of Appendix A.

In [1], the notation convention used in Eq. (9) should be as follows:

\vec{E} (t) = \frac{E_{0}}{\sqrt{2}} e^{- i 2 π ν t} ([\begin{matrix} a_{1} \\ b_{1} \end{matrix}] + \sqrt{γ} e^{i 2 π Δ ν t} [\begin{matrix} a_{2} \\ b_{2} \end{matrix}]),

to be consistent with subsequent mathematical derivations.

Moreover, due to a typo that went unnoticed after manuscript production, Equation (A5) of Appendix A must read

M_{ED} = ρ [\begin{matrix} 1 & d C_{2 ϕ} C_{2 ε} & d S_{2 ϕ} C_{2 ε} & d S_{2 ε} \\ d C_{2 ϕ} C_{2 ε} & \frac{1 + 3 T}{4} + \frac{1 - T}{4} [C_{4 ε} + 2 C_{4 ϕ} C_{2 ε}^{2}] & \frac{1 - T}{2} S_{4 ϕ} C_{2 ε}^{2} & \frac{1 - T}{2} C_{2 ϕ} S_{4 ε} \\ d S_{2 ϕ} C_{2 ε} & \frac{1 - T}{2} S_{4 ϕ} C_{2 ε}^{2} & \frac{1 + 3 T}{4} + \frac{1 - T}{4} [C_{4 ε} - 2 C_{4 ϕ} C_{2 ε}^{2}] & \frac{1 - T}{2} S_{2 ϕ} S_{4 ε} \\ d S_{2 ε} & \frac{1 - T}{2} C_{2 ϕ} S_{4 ε} & \frac{1 - T}{2} S_{2 ϕ} S_{4 ε} & \frac{1 + T}{2} - \frac{1 - T}{2} C_{4 ε} \end{matrix}] .

REFERENCES

1. N. Ortega-Quijano, J. Fade, M. Roche, F. Parnet, and M. Alouini, “Orthogonality-breaking sensing model based on the instantaneous Stokes vector and the Mueller calculus,” J. Opt. Soc. Am. A 33, 434–446 (2016). [CrossRef]

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\vec{E} (t) = \frac{E_{0}}{\sqrt{2}} e^{- i 2 π ν t} ([\begin{matrix} a_{1} \\ b_{1} \end{matrix}] + \sqrt{γ} e^{i 2 π Δ ν t} [\begin{matrix} a_{2} \\ b_{2} \end{matrix}]),

M_{ED} = ρ [\begin{matrix} 1 & d C_{2 ϕ} C_{2 ε} & d S_{2 ϕ} C_{2 ε} & d S_{2 ε} \\ d C_{2 ϕ} C_{2 ε} & \frac{1 + 3 T}{4} + \frac{1 - T}{4} [C_{4 ε} + 2 C_{4 ϕ} C_{2 ε}^{2}] & \frac{1 - T}{2} S_{4 ϕ} C_{2 ε}^{2} & \frac{1 - T}{2} C_{2 ϕ} S_{4 ε} \\ d S_{2 ϕ} C_{2 ε} & \frac{1 - T}{2} S_{4 ϕ} C_{2 ε}^{2} & \frac{1 + 3 T}{4} + \frac{1 - T}{4} [C_{4 ε} - 2 C_{4 ϕ} C_{2 ε}^{2}] & \frac{1 - T}{2} S_{2 ϕ} S_{4 ε} \\ d S_{2 ε} & \frac{1 - T}{2} C_{2 ϕ} S_{4 ε} & \frac{1 - T}{2} S_{2 ϕ} S_{4 ε} & \frac{1 + T}{2} - \frac{1 - T}{2} C_{4 ε} \end{matrix}] .

Abstract

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Journal of the Optical Society of America A