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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.
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f1: Coordinate system and geometrical magnitudes.

Mentions: where A is a constant related to the focal length and the wavelength, k = 2π/λ is the wave number, θM is the semi-aperture angle, r = (r, ϕ, z) denotes the polar coordinates at the focal area, θ and φ are the coordinates at the Gaussian sphere and is the wave-front vector. The numerical aperture (NA) and θM are related by means of NA = sin θM (see Fig. 1 for details). E0 is the so-called vectorial angular spectrum, namely


Polarisers in the focal domain: Theoretical model and experimental validation
Coordinate system and geometrical magnitudes.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f1: Coordinate system and geometrical magnitudes.
Mentions: where A is a constant related to the focal length and the wavelength, k = 2π/λ is the wave number, θM is the semi-aperture angle, r = (r, ϕ, z) denotes the polar coordinates at the focal area, θ and φ are the coordinates at the Gaussian sphere and is the wave-front vector. The numerical aperture (NA) and θM are related by means of NA = sin θM (see Fig. 1 for details). E0 is the so-called vectorial angular spectrum, namely

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.