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Polarisers in the focal domain: Theoretical model and experimental validation

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ABSTRACT

Polarisers are one of the most widely used devices in optical set-ups. They are commonly used with paraxial beams that propagate in the normal direction of the polariser plane. Nevertheless, the conventional projection character of these devices may change when the beam impinges a polariser with a certain angle of incidence. This effect is more noticeable if polarisers are used in optical systems with a high numerical aperture, because multiple angles of incidence have to be taken into account. Moreover, the non-transverse character of highly focused beams makes the problem more complex and strictly speaking, the Malus’ law does not apply. In this paper we develop a theoretical framework to explain how ideal polarisers affect the behavior of highly focused fields. In this model, the polarisers are considered as birefringent plates, and the vector behaviour of focused fields is described using the plane-wave angular spectrum approach. Experiments involving focused fields were conducted to verify the theoretical model and a satisfactory agreement between theoretical and experimental results was found.

No MeSH data available.


Coordinate system and geometrical magnitudes.(a) General view. (b) View of e1, ,  and . (c) Profile view of the z- and c- plane.
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f6: Coordinate system and geometrical magnitudes.(a) General view. (b) View of e1, , and . (c) Profile view of the z- and c- plane.

Mentions: Polarisers and retarder plates have been described as a uniaxial anisotropic plane-parallel media of thickness L with the optical axis (c-axis) parallel to the plate surfaces2122. This description provides an appropriate mathematical framework for explaining the behaviour of light when interacts with these devices. The coordinate system is selected in such a way that the z-axis is orthogonal to the plate surface, being β the angle between the c- and the x-axes. Accordingly, the direction of the c-axis is described by vector . Figure 6 describes the geometrical magnitudes involved in the problem. In particular, angle Ψ [see Eq. (6)] is defined by and e1, where and are the ordinary and extraordinary unit vectors.


Polarisers in the focal domain: Theoretical model and experimental validation
Coordinate system and geometrical magnitudes.(a) General view. (b) View of e1, ,  and . (c) Profile view of the z- and c- plane.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC5304165&req=5

f6: Coordinate system and geometrical magnitudes.(a) General view. (b) View of e1, , and . (c) Profile view of the z- and c- plane.
Mentions: Polarisers and retarder plates have been described as a uniaxial anisotropic plane-parallel media of thickness L with the optical axis (c-axis) parallel to the plate surfaces2122. This description provides an appropriate mathematical framework for explaining the behaviour of light when interacts with these devices. The coordinate system is selected in such a way that the z-axis is orthogonal to the plate surface, being β the angle between the c- and the x-axes. Accordingly, the direction of the c-axis is described by vector . Figure 6 describes the geometrical magnitudes involved in the problem. In particular, angle Ψ [see Eq. (6)] is defined by and e1, where and are the ordinary and extraordinary unit vectors.

View Article: PubMed Central - PubMed

ABSTRACT

Polarisers are one of the most widely used devices in optical set-ups. They are commonly used with paraxial beams that propagate in the normal direction of the polariser plane. Nevertheless, the conventional projection character of these devices may change when the beam impinges a polariser with a certain angle of incidence. This effect is more noticeable if polarisers are used in optical systems with a high numerical aperture, because multiple angles of incidence have to be taken into account. Moreover, the non-transverse character of highly focused beams makes the problem more complex and strictly speaking, the Malus’ law does not apply. In this paper we develop a theoretical framework to explain how ideal polarisers affect the behavior of highly focused fields. In this model, the polarisers are considered as birefringent plates, and the vector behaviour of focused fields is described using the plane-wave angular spectrum approach. Experiments involving focused fields were conducted to verify the theoretical model and a satisfactory agreement between theoretical and experimental results was found.

No MeSH data available.