Polarization gratings for oblique incidence angles

1. A polarization grating for deflecting light of a predeterminable polarization, optimized for a fixed or variable oblique angle of incidence of light, comprising

at least one liquid-crystal layer on a substrate, the liquid-crystal layer containing liquid-crystal molecules having a first periodic variation, in one or two mutually orthogonal directions within the plane of the liquid-crystal layer, of their orientation;

the liquid crystal molecules having at least a second orientation variation, said second orientation variation being adjusted according to the fixed oblique angle of incidence of light or adjustable according to the variable oblique angle of incidence of light by an electrode structure in such a way that incident light experiences a predeterminable phase retardation when passing through the liquid-crystal layer;

said at least second orientation variation of the liquid crystal molecules being formed as a twist, where a rotation angle of the twist is adjusted or adjustable to a value τ=180°·d·tan(α′)/Λ, where d is the thickness of the liquid-crystal layer, α′ is the angle at which the light ray with the angle of incidence α propagates in the liquid-crystal layer and Λ is the grating period, and

the diffraction efficiency in the +1 st or −1 st diffraction order being maximized for an angle of incidence of light provided in a range between 20° and 50°.

2. The polarization grating as claimed in claim 1 , wherein the light experiences a maximum diffraction efficiency in the +1st or −1st diffraction order when passing through the liquid-crystal layer.

3. The polarization grating as claimed in claim 1 , wherein it is formed as a grating whose grating period can be controlled, with a controllable periodic variation, within the plane of the liquid-crystal layer, of the orientation, and at least one further controllably adjustable orientation variation.

4. The polarization grating as claimed in claim 1 , wherein it is formed as a passive grating with a fixed periodic variation of the orientation within the plane of the liquid-crystal layer, and at least one further fixed orientation variation.

5. The polarization grating as claimed in claim 1 , wherein it is formed as a switchable grating with a fixed periodic variation of the orientation within the plane of the liquid-crystal layer, and at least one further switchably or controllably adjustable orientation variation.

6. The polarization grating as claimed in claim 1 , wherein the part of the orientation of the liquid-crystal molecules in the plane of the at least one liquid-crystal layer and the part of the orientation of the liquid-crystal molecules outside the plane of the liquid-crystal layer determine the profile of the birefringence of the liquid-crystal layer as a function of position.

7. The polarization grating as claimed in claim 1 , wherein the liquid-crystal molecules in the plane of the liquid-crystal layer are periodically rotated relative to one another at least in one direction, and additionally have a twist perpendicularly to the liquid-crystal layer, the rotation angles of the twist being displaced along the liquid-crystal layer in such a way that light rays with a predeterminable angle of incidence strike positions of equal rotation angle when passing through the liquid-crystal layer.

8. The polarization grating as claimed in claim 7 , wherein the twist is predetermined by means of the concentration and type of a chiral dopant, which is admixed with the liquid-crystal layer.

9. The polarization grating as claimed in claim 7 , further comprising at least a second substrate, the liquid-crystal layer being located between the substrates and the rotation angle of the twist of the liquid-crystal molecules is predetermined by the mutual lateral displacement of one alignment layer respectively on each substrate.

10. The polarization grating as claimed in claim 7 , wherein the thickness of the liquid-crystal layer is adapted to a preferred angle of incidence and a preferred wavelength in such a way that the phase change of the light between ordinary and extraordinary rays when passing through the liquid-crystal layer substantially corresponds to one half wavelength at this angle of incidence and this wavelength.

11. The polarization grating as claimed in claim 7 , wherein the displacement of equal rotation angles of the twist between the upper and lower sides of the liquid-crystal layer corresponds substantially to one half grating period.

12. The polarization grating as claimed in claim 1 , wherein at least one optically rewritable alignment layer is contained.

13. The polarization grating as claimed in claim 1 , wherein it contains a suitable electrode structure, with which the orientation of the liquid-crystal molecules in the liquid-crystal layer can be modified by applying a suitable voltage profile.

14. The polarization grating as claimed in claim 13 , wherein it contains an alignment layer with fixed structuring on one substrate and a second substrate with a comb-like electrode structure for twisting the liquid molecules relative to this alignment layer.

15. The polarization grating as claimed in claim 1 , wherein the polarization grating contains a plurality of liquid-crystal layers lying behind one another, equal rotation angles of the twist being displaced along the liquid-crystal layers in such a way that light rays with a predeterminable angle of incidence strike positions of equal rotation angle when passing through the liquid-crystal layers.

16. The polarization grating as claimed in claim 1 , wherein it contains at least one further liquid-crystal layer, of which the sign of the birefringence of the liquid-crystal molecules differs from the first liquid-crystal layer, and both liquid-crystal layers have the same grating period.

17. The polarization grating as claimed in claim 1 , wherein at least one substrate comprises a fine-structured electrode structure of individually drivable electrodes, in order to control the rotation angle of the twist of the liquid-crystal molecules by applying a variable voltage profile to the electrode structure in one or two directions in the plane of the liquid-crystal layer, in such a way that light rays with a variable angle of incidence strike positions of equal rotation angle when passing through the one or the plurality of liquid-crystal layers.

18. The polarization grating as claimed in claim 17 , wherein the exit angle of the light rays after passing through the at least one liquid-crystal layer can be controlled by varying the period of the voltage profile.

19. The polarization grating as claimed in claim 1 , wherein the period of the variation of the orientation of the liquid-crystal molecules is locally variable in one or two directions in the plane of the liquid-crystal layer.

20. An arrangement for one- or two-dimensional fixed or variable light deflection, wherein at least one polarization grating as claimed in claim 1 is contained in the arrangement.

21. An arrangement for the reconstruction of holographically encoded three-dimensional scenes, wherein at least one polarization grating as claimed in claim 1 is contained in it.

22. An arrangement for directing sunlight onto a photosensitive surface, wherein at least one polarization grating as claimed in claim 1 is contained in it.

23. A method for one- or two-dimensional fixed or variable light deflection, wherein the light deflection is carried out partially or fully with at least one polarization grating as claimed in claim 1 .

24. The polarization grating as claimed in claim 1 , wherein the angle of incidence of light is about 35°-40°; the rotation angle of the twist is about τ=60°.