Abstract:
A phase modulator for polarized light, comprising a first substrate with a first surface and a second substrate with a second surface, a liquid crystal layer between the two substrates and an electrode arrangement. The phase modulator is usable as a variable deflection grating, and liquid crystal materials which are currently conventional are usable for its production. A phase modulator has an out-of-plane angle of the liquid crystal molecules next to the two surfaces whose magnitude is greater than 0 but less than or equal to 45 degrees, and an electrode arrangement controllable such that an in-plane component of the liquid crystal molecule orientation is adjustable in an angle range of up to 180 degrees, and the rotation sense of the liquid crystal molecules next to the first surface is opposite to the rotation sense of the liquid crystal molecules next to the second surface.

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This application claims the priority of PCT/EP2014/053667, filed on Feb. 26, 2014, which claims priority to German Application No. DE 10 2013 101 964.1, filed on Feb. 27, 2013, the entire contents of each of which are incorporated fully herein by reference. 
     FIELD OF THE INVENTION 
     The present invention relates to a phase modulator for polarized light, comprising a first substrate with a first surface and a second substrate with a second surface, a liquid crystal layer (also referred to as an LC layer) between the two substrates and an electrode arrangement, based on an LC alignment (LC=liquid crystal) with a large pretilt angle, as well as to a method for producing such a phase modulator. 
     BACKGROUND OF THE INVENTION 
     WO 2011/067265 A1 describes a phase modulator for modulating light interacting with the phase modulator. The phase modulator described in WO 2011/067265 A1 for modulating the phase of circularly polarized light contains inter alia a first and a second substrate and a liquid crystal layer between the two substrates, the surfaces of the substrates being configured in order to orientate the liquid crystal molecules next to the first surface in a direction which is substantially parallel to the first surface, and to orientate the liquid crystal molecules next to the second surface in a direction which is substantially perpendicular to the second surface. Such an orientation is also referred to as hybrid alignment of a nematic (HAN) liquid crystal. 
     As disclosed by WO 2011/067265 A1, such a HAN configuration is used in order selectively to achieve a rotation of the in-plane component of the liquid crystal molecule orientation, for example from 0 to +90 degrees or from 0 to −90 degrees, as a function of the sign of the electric field applied to the electrodes, and therefore to achieve overall a phase modulation of from 0 to 2π by such control of the applied field. The thickness of the LC layer is in this case preferably selected in such a way that its optical function corresponds to a λ/2 plate. 
     The sign-dependent rotation in the electric field is in this case based on flexoelectric polarization. This polarization is based on a mechanical deformation of the LC, or the LC molecules, by the hybrid alignment. 
     WO 2011/067265 A1 also describes such a phase modulator, which is configured in such a way that the light interacting with the phase modulator can be variably deviated as a result of diffraction in a predeterminable direction, and that the function of a variably adjustable deflection grating can thereby be achieved. 
     A variable deflection grating based on phase modulation, used in a manner comparable to that described in DE 10 2009 028 626 A1, may be produced by individual driving of individual in-plane electrodes. 
     Because of the hybrid alignment, the LC molecules are partially oriented out-of-plane, specifically as an average value over the layer thickness approximately at 45 degrees, with a linear variation between approximately 0 and 90 degrees from one surface of the liquid crystal layer to the other. 
     The effective birefringence for light which passes through an LC layer, the LC molecules being tilted at an angle β with respect to the direction in which the light passes through, is 
               Δ   ⁢           ⁢     n   eff       =       n   2     -         n   1     ·     n   2                 n   1   2     ·     sin   2       ⁢   β     +         n   2   2     ·     cos   2       ⁢   β                   
where n 1  and n 2  are the ordinary and extraordinary refractive indices of the liquid crystal with the birefringence Δn=n 2 −n 1 .
 
     For a hybrid alignment, the angle β varies over the layer thickness between 0 and 90 degrees, and Δn eff  consequently also varies over the thickness of the LC layer. The effective optical path difference (opd), which in the case of uniform LC orientation is usually described as opd=dΔn with the layer thickness d and the birefringence Δn, is in this case
 
opd=∫ 0   d   Δn   eff ( z ) dz  
 
     For hybrid orientation, an average effective birefringence over the layer thickness is approximately  Δn eff   ≈0.5Δn 
     and the optical path difference is opd HAN ≈0.5dΔn. 
     The effective optical path difference for light passing perpendicularly through the liquid crystal layer is less than the case would be with a liquid crystal layer in which the liquid crystal molecules are oriented in-plane. In order to achieve the optical function of a λ/2 plate, the product of the layer thickness of the LC layer and the birefringence of the LC material must therefore be relatively large. In the case of a layer thickness of 3 micrometers, approximately a Δn of 0.18 is required in order to adjust a λ/2 plate for green light. Specifically, with these numerical values opd HAN ≈0.5·0.18·3 μm=0.27 μm, which corresponds approximately to half the value of the wavelength of green light. 
     Usually, it is difficult to achieve this birefringence of 0.18 or a similar value as a material property in combination with, at the same time, a low viscosity. The use of an LC material with increased viscosity, however, compromises the maximum adjustable adjustment speed of the variably adjustable phase modulator. 
     The sign-dependent rotation of the liquid crystal molecules in the electrical in-plane field is based on flexoelectric polarization. The interaction of the polarization with the field is linear. Besides flexoelectric polarization, a quadratic interaction of the dielectric anisotropy Δ∈ with the field also takes place. 
     In particular, the dielectric interaction may have the effect that, with higher fields, besides the desired rotation of the in-plane component of the LC molecule orientation an undesired rotation, coupled therewith, of the out-of-plane component of the LC molecule orientation also takes place in the field. This rotation of the out-of-plane component of the LC molecule orientation has the effect that the LC layer no longer fulfills the optical function of a λ/2 plate. In the worst case, the optical path through the LC layer may be doubled. This is because if all the LC molecules are oriented in-plane, i.e. parallel to the substrates, the optical path would be
 
opd parallel   =dΔn =2·opd HAN .
 
     A change in the optical path with the in-plane rotation angle leads, particularly when using the phase modulator as a variable deflection grating, to a reduced diffraction efficiency of the deflection grating. Less light thus enters the desired diffraction order, and under certain circumstances undesired perturbing light enters other diffraction orders. 
     Correct functioning of the HAN phase modulator as a variable deflection grating therefore requires a liquid crystal material with a high flexoelectric coefficient and, at the same time, a low dielectric anisotropy Δ∈. Preferably, Δ∈ lies in the range of less than 2, ideally less than 0.2. As described above, this is required in combination with a high birefringence Δn of the liquid crystal material, preferably in the range of from 0.15 to 0.2. 
     It would be desirable to have a phase modulator which can also be used as a variable deflection grating, which avoids the described disadvantages and which in particular makes it possible to use liquid crystal materials whose material parameters lie closer to standard values of currently used materials. 
     For example, the birefringence Δn of liquid crystal materials used at present in displays typically lies in the range of from 0.8 to 0.10 and the dielectric anisotropy Δ∈ typically lies in the range of from 5 to 10. 
     U.S. Pat. No. 7,564,510 B2 describes a liquid crystal display device which contains pixels, each pixel being subdivided into a number of regions, and the direction of an electric field—substantially parallel to the substrates—in one of the regions being opposite to the field direction in another region, and in the case of which there is furthermore a polarization in the liquid crystal layer when no field is applied. U.S. Pat. No. 7,564,510 B2 therefore describes a pixel structure which generates a uniform brightness impression for large observer angle in that different regions of a pixel compensate for one another in the overall brightness of the pixel for different viewing directions. For example, when observed from one particular direction, a first region of the pixel appears brighter and a second region appears darker. Observed from another direction, the situation is reversed. Yet since the eye cannot resolve the regions of the pixel individually, there is a uniform brightness impression. 
     To this end, in U.S. Pat. No. 7,564,510 B2, a rotation of the liquid crystal molecule orientation as a function of the sign of the electric field is used so that the liquid crystal molecules in different regions of a pixel thus rotate oppositely. It is described that this sign-dependent rotation may likewise be based on flexoelectric polarization. 
     FIG. 3 of U.S. Pat. No. 7,564,510 B2 describes a configuration with parallel rubbing on the two surfaces of the substrates. This leads to a mirror-symmetrically equal alignment of the LC molecules on the two substrates (with a mirror plane parallel to the substrates in the middle of the LC layer) and a splay deformation in the LC layer between the two substrates. This splay deformation generates flexoelectric polarization. 
     The arrangement described in U.S. Pat. No. 7,564,510 B2 would not, however, be usable as a phase modulator since the different regions of a pixel would respectively generate different phase values, so that a full pixel would not have uniform phase modulation. 
     SUMMARY OF THE INVENTION 
     It is therefore an object of the present invention to describe a phase modulator which avoids the aforementioned disadvantages, which can furthermore be used as a variable deflection grating, and for the production of which it is possible in particular to use liquid crystal materials which are currently conventional. 
     The object is achieved by a phase modulator as claimed in claim  1 . 
     A phase modulator, which is used in particular for modulating the phase of polarized light interacting with the phase modulator, which is generally circularly polarized light, comprises a first substrate, which has a first surface, and a second substrate, which has a second surface, the two substrates being arranged facing one another, a liquid crystal layer, which is arranged between the two substrates and contains liquid crystal molecules, an electrode arrangement on at least one of the substrates, the two surfaces of the substrates being configured in order to orientate the liquid crystal molecules next to the respective surface in a direction which respectively forms an out-of-plane angle with the respective surface of the respective substrate. 
     In the phase modulator according to the invention, the magnitude of this is more than 0 degrees but less than or equal to 45 degrees. The out-of-plane angle, or polar angle, that is to say the angle which the optical long axis of the liquid crystal molecules makes with the surface of the respective substrate, is also known as the pretilt angle in so far as this describes the initial state of the orientation of these liquid crystal molecules in relation to the respective substrate—i.e. without reorientation by application of an electric field by means of the electrode arrangement. Here, orientation is always intended to mean the alignment of the optical long axis of the liquid crystal molecule or of another alignable birefringent material. 
     In the phase modulator according to the invention, furthermore, the electrode arrangement can be driven in such a way that an in-plane component φ, also known as azimuthal component, of the liquid crystal molecule orientation can be adjusted in an angle range of up to 180 degrees, and that the rotation sense of the liquid crystal molecules which are next to the first surface is opposite to the rotation sense of the liquid crystal molecules which are next to the second surface. 
     In other words, a phase modulator in which the aforementioned problems are avoided, or at least reduced, is configured as follows: 
     It comprises a first and a second substrate, an electrode arrangement and a liquid crystal layer comprising liquid crystal molecules. The first substrate is arranged facing the second substrate. The liquid crystal layer is arranged between the two substrates. The first substrate has a first surface, and the second substrate has a second surface. The first surface is configured in order to orientate the liquid crystal molecules next to the first surface in a direction which forms a first out-of-plane angle α(0), or a first polar angle, with respect to the first surface of the first substrate. The magnitude of α(0) is in this case greater than 0 degrees but less than or equal to 45 degrees. The second surface is configured in order to orientate the liquid crystal molecules next to the second surface in a direction which forms a second out-of-plane angle α(d), or a polar angle, with respect to the second surface of the second substrate. The magnitude of α(d) is likewise greater than 0 degrees but less than or equal to 45 degrees. According to the invention, the rotation sense of the out-of-plane angles α(0) and α(d), and therefore of the liquid crystal molecules next to the surfaces, is opposite relative to the surface. In other words, the signs of the angles α(0) and α(d) are different. The angle α moreover corresponds to the angle β described above for the special case in which light passes through the phase modulator perpendicularly. In the preferred case of the use of the phase modulator according to the invention, the light enters the phase modulator perpendicularly, although any other entry angles may be envisioned. 
     In this case, the electrode arrangement can be driven in such a way that an in-plane component, or azimuthal component, of the liquid crystal molecule orientation can be adjusted in an angle range of up to 180 degrees. 
     This ensures that the liquid crystal molecules with their in-plane component can assume any possible position, since liquid crystal molecules are optically symmetrical molecules which thus form an ellipsoid in relation to their optical properties. 
     In the phase modulation of the polarized light, carried out by the phase modulator, deflection of the light may also take place. The light modulator described here may thus also be used as a phase deflector. 
     In a special embodiment of the phase modulator according to the invention, the “liquid crystal layer”, which is arranged between the two substrates, in this case contains a different alignable birefringent material instead of the liquid crystal molecules or in addition to the liquid crystal molecules. Often, phase modulators are configured with a liquid crystal material, which is the best-characterized material group, including a multiplicity of specific liquid crystal materials, for such optical purposes. In principle, however, other alignable birefringent materials may also be used here, for example nonspherical nanoparticles of different materials, i.e. different dielectric materials or metals, and in particular carbon nanotubes. These may then be used in a similar way to the liquid crystal molecules described here. They are likewise symmetrical in relation to their optical properties. 
     In one embodiment of the phase modulator according to the invention, the in-plane component can be adjusted between −φ 1  and −φ 2  degrees, with φ 1 , φ 2  90 degrees, in relation to a predeterminable average orientation which corresponds to the orientation when no voltage is applied. Values of φ 1 , φ 2  with 70 degrees φ 1 , φ 2  90 degrees are preferred in this case. 
     In a particularly preferred phase modulator according to the invention, the in-plane component can be adjusted between −90 and +90 degrees, in relation to a predeterminable average orientation. 
     According to a preferred embodiment, the angles α(0) and α(d) are equal in magnitude but differ in sign, so that there is a mirror-image orientation of the LC molecules with respect to one another at the two surfaces. 
     If this mutual mirror-image orientation of the liquid molecules on the two surfaces continues over planes parallel to the surfaces respectively with equal distances from the two surfaces, and if a mirror plane or symmetry plane in relation to the mirror-image orientation can be imagined in the middle of the liquid crystal layer between the two surfaces of the two substrates, then the phase modulator in a preferred embodiment according to the invention has a splay deformation across the liquid crystal layer. 
     The magnitude of the out-of-plane angles α(0) and α(d) in a particularly preferred embodiment of the phase modulator according to the invention respectively lies in a range of between 20 and 40 degrees. In particular, the magnitudes of the angles α(0), α(d) may be essentially equal. 
     More particularly preferably, the phase modulator is configured in such a way that the light interacting with the phase modulator can be variably deflected in a predeterminable direction because of diffraction. The phase modulator according to the invention, in particular when it is configured and driven in such a way that it operates as a phase deflector, may be used in a manner comparable to that of the phase deflector described in WO 2011/039286 A1. The disclosure content of WO 2011/039286 A1 is therefore fully incorporated here. The diffractive elements, for example phase modulators or phase deflectors, which can be used in holographic displays for observer tracking, are described for example in DE 10 2009 028 626 A1 or in WO 2010/149587 A2, where they are referred to as a diffraction device. Since the phase modulator or phase deflector according to the invention can be used inter alia in a manner comparable to that of the diffraction device described in DE 10 2009 028 626 A1 or in WO 2010/149587 A2, the disclosure content of DE 10 2009 028 626 A1 and that of WO 2010/149587 A2 are fully incorporated here. 
     A preferred configuration, in which a phase modulator, in which α(0) and α(d) are equal in magnitude but differ in sign, so that there is a mirror-image orientation of the LC molecules with respect to one another at the two surfaces, and in which the magnitude of α(0) and α(d) lies in the range between 20 degrees and 40 degrees, has the following advantages: 
     The average value over the LC layer thickness of the magnitude of the out-of-plane angle of the LC orientation corresponds to half the magnitude of α(0). In the case in which α(0)=30°, for example, the LC molecules are oriented on average 15 degrees out-of-plane. 
     With an angle of 15 degrees, for example, Δn eff ≈0.95Δn 
     The optical path difference, which is in turn given as an integral over the thickness of the LC layer, opd=∫ 0   d Δn eff (z)dz, is significantly greater than in the case of a hybrid orientation. 
     The product of the layer thickness and the birefringence, which is required in order to adjust a λ/2 plate, thus does not differ substantially from a fully in-plane oriented LC. 
     For example, with a full in-plane orientation of the liquid crystal molecules, a layer thickness of 3 micrometers and a Δn of 0.09 would be required in order to produce a λ/2 plate for green light. In the described arrangement with α(0) of 30 degrees (and with α(d) of −30 degrees) a Δn of about 0.095 would instead be required in order to produce a λ/2 plate for green light. This Δn lies in a range which is typical for LC mixtures in displays. 
     The orientation of the liquid crystal molecules with a different sign of the angle at the two surfaces generates a splay deformation. A flexoelectric polarization is generated by the deformation. This allows sign-dependent switching, or alignment, of the LC molecules. 
     The flexoelectric polarization is defined as
 
 P   f   =e   s   n (∇ n )+ e   b   n×∇×n  
 
     Here, n is the director, that is to say a vector in the direction of the longitudinal axis of the LC molecules, ∇ is the del (nabla) operator, ∇·n is the divergence of the director n, × denotes the cross product, ∇·n is the rotation of the director n, e s  is the splay flexoelectric coefficient, and e b  is the bend flexoelectric coefficient. 
     The flexoelectric coefficients e s  and e b  represent material constants, the value of which depends on the geometrical shape of the LC molecules and on the electric dipole and quadrupole moments of these LC molecules. 
     In theoretical models of flexoelectric polarization, it is described for example that an electric quadrupole moment contributes to the two coefficients e s  and e b  even in the case of an ideally rice-grain shaped LC molecule. 
     Electric dipole moments contribute when there is a deviation of the shape of the LC molecules from the model of a rice grain. A more pear-shaped molecule shape in combination with a longitudinal electric dipole moment (i.e. placed in the direction of the long molecule axis) favors a high splay flexoelectric coefficient e s . A more banana-shaped molecule shape in combination with a transverse electric dipole moment (placed transversely to the long molecule axis) favors a higher bend flexoelectric coefficient e b . 
     A contribution of the splay flexoelectric coefficient e s  to the flexoelectric polarization occurs, according to the equation above, in particular when the divergence ∇·n of the director is nonzero. 
     In the case of an LC orientation with an out-of-plane angle α(0) on one substrate and an angle α(d) different to α(0) (in sign and/or magnitude) on the other substrate, there is such a nonzero divergence of the director n. 
     The rotation ∇·n of the director n in the case of such an orientation of the LC molecules is, however, small, so that the bend flexoelectric coefficient e b  in this case contributes only little to the flexoelectric polarization. 
     Advantageously, such LC molecules as have a high splay flexoelectric coefficient e s  are thus used in this arrangement. 
     A rotation of the in-plane component of the liquid crystal molecule orientation of, for example, from 0 to +90 degrees, or from 0 to −90 degrees, takes place selectively as a function of the sign of the electric field. 
     For a fixed LC material, however, the splay deformation and therefore also the flexoelectric polarization advantageously increase with the magnitude of the angles α(0) and α(d). Small angles, for example 5 degrees, would typically lead only to a small polarization. In the case of large angles, for example of 45 degrees, although there is a large flexoelectric polarization, in the case of large angles, the Δn eff  disadvantageously becomes smaller. The preferred range of from 20 to 40 degrees for α(0) and α(d) represents a compromise between the two factors. 
     In this case as well, the interaction with an electric field takes place both via the flexoelectric polarization and via the dielectric anisotropy. The dielectric anisotropy Δ∈ can have the effect that, in the case of a strong in-plane field, the out-of-plane orientation of the liquid crystals changes. 
     Since, however, as shown above, the difference in the optical path between a full liquid crystal in-plane orientation and an orientation with for example +/−30 degrees on the surfaces is small, the negative effect of the dielectric interaction on the optical function as a phase modulator, and in particular also as a variable deflection grating, is small. That is to say, the diffraction efficiency of a variable deflection grating is only insubstantially reduced by the Δ∈. 
     On the other hand, a somewhat higher dielectric anisotropy Δ∈ advantageously makes it possible to use lower voltages for driving the phase modulator. 
     In a preferred embodiment, therefore, a liquid crystal layer which contains a liquid crystal material with a dielectric anisotropy of Δ∈≧5 is used. In the preferred configuration, therefore, both the birefringence Δn (as described above) and the dielectric anisotropy Δ∈ lie in a range which is typical for liquid crystal materials such as are used in displays. In addition, however, increased flexoelectric coefficients are furthermore preferred, in particular an increased splay-flexo coefficient e s , for example of e s≧ 5 pC/m (picocoulomb/meter) or even of e s ≧10.pC/m. 
     In one embodiment, the electrodes are arranged only on a first substrate. The electrodes on the first substrate are preferably individually controllable. 
     In another embodiment, in-plane electrodes are used on the two substrates, the electrodes on one substrate being oriented at an angle of approximately 90 degrees relative to the electrodes on the other substrate. In this case, “in-plane” electrodes or “in-plane” electrode arrangement means that an electrode arrangement parallel to the substrate surface is involved. 
     Here again, an increased dielectric anisotropy Δ∈ is preferably used. The electrodes on the first substrate are then used for the sign-dependent switching on of the electric field by a combination of flexoelectric and dielectric interaction. With an increased rotation angle, with increased Δ∈ the flexoelectric polarization in this case also decreases since the LC molecules are oriented more strongly in-plane by the dielectric interaction. The electrodes on the second substrate are used for actively switching off the electric field. The rotation of the LC molecules is carried out while being dominated by the dielectric interaction. In this way, rapid switching can be carried out in both directions. 
     In particular, such a phase modulator, which contains both an electrode arrangement on the first substrate and an electrode arrangement on the second substrate, may advantageously have an electrode arrangement on the second substrate in the form of two inter-engaged combs or comb-like structures, between which a global voltage value can be adjusted. Individual controlling of the electrodes on the second substrate is therefore unnecessary. This embodiment according to the invention allows a rapid switching behavior: both switching processes, both switching on and switching off, can therefore respectively be controlled actively by an electric field. 
     In another embodiment, which is less preferred, it is also possible to use an LC material with a very high splay flexoelectric coefficient e s ≧20 pC/m and a very low dielectric anisotropy Δ∈≦0.2. In this case, the interaction of the flexoelectric polarization with the electric field would also dominate for large in-plane rotation angles of the LC molecule and active switching off can be carried out by an electric field with the opposite sign. A phase modulator with rapid switching times can likewise be produced in this way. The embodiment advantageously only requires electrodes on one substrate. It is less preferred merely because an LC material with the described properties is more difficult to produce. 
     The phase modulator according to the invention may now be used in a spatial light modulator. A multiplicity of pixels are arranged regularly next to one another therein, a uniform adjustable phase value respectively being generated over the entire surface of a pixel by using the above-described structure of the phase modulator according to the invention. 
     Advantageously, each pixel is in this case divided into two regions, which respectively have a mirror-symmetrically opposite orientation of the liquid crystal molecules near the surfaces of the substrates. 
     In order to produce the phase modulator according to the invention, a method is used wherein, on a first substrate and a second substrate, a surface is formed in such a way that an alignment layer is created, by which the liquid crystal molecules which enter onto or into the vicinity of this surface adjust an intended orientation with a desired out-of-plane angle. The two substrates are subsequently assembled facing one another by using spacers, and the intermediate space is filled with liquid crystal material. In this case, according to the invention, the out-of-plane angle, which in this initial orientation is also referred to as the pretilt angle, as well as the anchoring energy on the two substrates, are adjusted by a combination of chemical properties of the alignment layers, process parameters of the production of the alignment layers, and the chemical properties of the liquid crystal material, the respective out-of-plane angle, or pretilt angle, on the two substrates lying in the range of between 0 and 45 degrees, preferably between 20 and 40 degrees. 
     The best-known method, which is conventional in the industrial production of LC displays, for adjusting a particular orientation (alignment) and surface anchoring of LC molecules on a substrate is mechanical rubbing (or buffing) of an orientation layer (alignment layer). Polyimides are typically used as an orientation layer. 
     By a combination of chemical properties of the alignment layer and parameters of the rubbing process (for example the application pressure), the anchoring energy as well as the pretilt angle are adjusted. The pretilt angle furthermore also depends on the chemical properties of the LC material. 
     In the arrangement described according to the invention, the pretilt angle on a first substrate would thus correspond to the out-of-plane angle α(0), and the pretilt angle on a second substrate would correspond to the out-of-plane angle α(d). These angles are set up when the substrates previously treated by rubbing are assembled by using spacers and the intermediate space is filled with LC. 
     With the conventionally used polyimide alignment materials and rubbing, pretilt angles in the range of about 1 degree to 8 degrees are achievable. 
     A configuration of the invention in which angles α(0) and α(d) are adjusted by conventional mechanical rubbing of polyimide would preferably use a polyimide which adjusts an angle at the upper end of the range achievable by rubbing, i.e. pretilt angles of 7-8 degrees. It is also known that chemical properties of the LC material have an effect on the pretilt angle. Preferably, LC mixtures whose chemical composition favors a somewhat higher pretilt angle are used. 
     For the switching speed of a phase modulator according to the invention, it is however advantageous if an angle can be adjusted which is higher than the range achievable by conventional mechanical rubbing. 
     In another configuration of the invention, therefore, the out-of-plane angles α(0) and α(d) are adjusted not by means of rubbing but by means of photoalignment. 
     Instead of the conventional polyimide alignment layers for rubbing, a photo-orientable alignment layer is used instead. This alignment is exposed by means of UV light. The out-of-plane or pretilt angle can in this case be adjusted by adapting the exposure dose of the UV light. 
     Two substrates exposed with a correspondingly adapted exposure dose are then assembled to form a cell, so that the angles α(0) and α(d) are set up on the two substrates. 
     Further methods with which high pretilt angles can be adjusted, and which may therefore be used for other configurations of the invention, are
         The use of alignment layers consisting of obliquely vapor-deposited SiO2 or SiNx layers,   The use of a mixture respectively of one polyimide for vertical alignment and one for horizontal alignment. By means of a suitable mixing ratio an increased pretilt can also be adjusted by conventional rubbing in this case.   The use of a doped polyimide layer, in which the surface energy of the polyimide is modified by means of a dopant, and the pretilt is adjusted by means of this influencing of the surface energy.       

     The invention is not restricted to the configurations described. 
     There are now various possibilities for advantageously configuring and refining the teaching of the present invention. In this regard, reference is to be made on the one hand to the claims dependent on patent claims  1  and  15 , and on the other to the following explanation of the preferred exemplary embodiments of the invention with the aid of the figures. The first configurations and refinements of the teaching will also be explained in general in connection with the explanation of the preferred exemplary embodiments of the invention with the aid of the figures. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The figures respectively show in a schematic representation: 
         FIG. 1 a    a sectional view of a phase modulator according to the prior art, 
         FIG. 1 b    a sectional view, rotated 90 degrees, of the phase modulator of  FIG. 1   a,    
         FIG. 2 a    a sectional view of a first exemplary embodiment of a phase modulator according to the invention, 
         FIG. 2 b    a sectional view, rotated 90 degrees, of the phase modulator of  FIG. 2 a    with the electric field switched off, 
         FIG. 3 a    sectional view of an exemplary embodiment of a phase modulator according to the invention with the electric field switched on, 
         FIG. 4 a    a sectional view of a second exemplary embodiment of a phase modulator according to the invention, 
         FIG. 4 b    a sectional view, rotated 90 degrees, of the phase modulator of  FIG. 4 a    with the electric field switched off, 
         FIG. 4 c    a sectional view of the phase modulator of  FIGS. 4 a  and 4 b    with the electric field switched on, and 
         FIGS. 5 a  to 5 d    various sectional views of a third exemplary embodiment of a phase modulator according to the invention. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     In the figures, components or elements which are the same are denoted by the same references. 
       FIG. 1 a    schematically shows a section through a phase modulator  1  according to the prior art. This phase modulator  1  comprises two glass substrates  2 ,  3 . In principle, at least one of the glass substrates  2 ,  3  may also be replaced with another substrate material. One of the substrates could, for example, also be configured to be optically reflective. At least one of the substrates, however, is generally configured to be optically transparent for the light interacting with it. Electrodes  4  are arranged on the first glass substrate  2 . An electrode  4  is schematically represented in the plane of the drawing. Between this electrode  4  and further electrodes (not represented), which are arranged in front of or behind the plane of the drawing, it is possible to apply an electric field which is essentially perpendicular to the plane of the drawing.  FIG. 1 a    shows the LC molecules  10  respectively in “rice-grain shape”, the LC orientation with the electric field switched off being represented. The glass substrates  2 ,  3  respectively have a surface  5 ,  6 . In this example, the surfaces of the glass substrates  2 ,  3  are respectively coated with polyimide  7 ,  8  (PI), so that the surface  5 ,  6  of the respective polyimide layer  7 ,  8  acts as a boundary layer for the LC molecules  10 , or for the LC layer  9 . Close to the lower polyimide layer  7 , the LC molecules  10  of the LC layer  9  are oriented because of the surface structure of the polyimide layer  7  in such a way that they are approximately parallel to the surface  5 . The expression approximately parallel may also include a small angle α(0) in the range of about 1 to 3 degrees. The surface structure of the polyimide layer  7  is generated here by “rubbing”, i.e. mechanical brushing of the polyimide layer  7 . Close to the surface  6  of the upper polyimide layer  8 , the LC molecules  10  are oriented approximately perpendicularly to the surface  6  because of the surface property of the polyimide layer  8 . 
       FIG. 1 b    shows for better understanding a detail of a view, rotated through 90 degrees in comparison with  FIG. 1 a   , of the same phase modulator  1  according to the prior art. Here, three electrodes  4  lying next to one another are shown on the lower substrate  2 . The actual number of electrodes  4 , particularly in a variable deflection grating, may however be much greater. In this view, the electric field which can be applied between the electrodes  4  would lie in the plane of the drawing. By individual controlling of the individual electrodes  4 , a variable deflection grating may for example be provided. 
       FIG. 2 a    shows, in a manner comparable to  FIG. 1 a   , a configuration of a phase modulator  1  according to the invention. The configuration likewise comprises two glass substrates  2 ,  3  and electrodes  4  on the lower glass substrate  2 . The electrodes  4  and the profile of the electric field correspond substantially to those of the phase modulator  1  of  FIG. 1   a.    
     The configuration likewise comprises two polyimide layers  7 ,  8  and a liquid crystal layer  9 . The orientation of the LC molecules (=liquid crystal molecules)  10  close to the two surfaces  5 ,  6  differs, however, according to the invention from that of the prior art shown in  FIG. 1 . The LC molecules  10  close to the lower surface  5  are oriented at an angle α(0), and the LC molecules  10  close to the upper surface  6  are oriented at an angle α(d). The rotation sense (i.e. the sign) of the angle α(0), α(d) at the lower and upper surface  6 ,  5  is opposite. 
     In the exemplary embodiment, the magnitude of the angle α(0), α(d) at the two surfaces  5 ,  6  is the same. This corresponds to a mirror-image orientation of the LC molecules  10  at the upper surface  6  in comparison with the lower surface  5 , an imaginary mirror plane  11  extending though the middle of the liquid crystal layer  9  and parallel to the substrates  2 ,  3 , or their surfaces  5 , 6 . For illustration, this mirror plane  11  is also indicated as a dashed line. 
     In other configurations (which are less preferred), the angles α(0) and α(d) may also have different magnitudes. For example, |α(0)|=20° and |α(d)|=40° would be possible. 
       FIG. 2 b    shows, in a manner comparable to  FIG. 1 b   , a detail of the view, rotated through 90 degrees, of the exemplary embodiment of the phase modulator  1  according to the invention. Here as well, only three electrodes  4  are indicated schematically, standing for a larger number of electrodes. 
     In WO 2011/067265 A1,  FIG. 1  thereof describes a phase modulation of circularly polarized light and an arrangement which acts as a λ/2 plate.  FIG. 4  therein shows this arrangement with individually controllable electrodes for a variable deflection grating.  FIG. 5  therein shows a polarization grating with a fixed grating period according to the prior art.  FIGS. 9 and 10  therein show examples of voltages which are applied to the electrodes in order to produce deflection gratings with a particular grating period. These figures may analogously also be used to to explain the present invention. To this extent, reference is made in respect of further comments to WO 2011/067265 A1, the disclosure content of WO 2011/067265 A1 being fully incorporated here. 
       FIG. 3  shows very schematically sign-dependent rotation, induced by the flexoelectric polarization, of the LC molecules  10  in the electric field. In this example, the central electrode  4  is at 0 volts, and the left and right electrodes  4  are respectively at the same voltage V 1 . The sign of the electric field therefore differs in the left and right halves. Correspondingly, the rotation sense of the LC molecules  10  also differs in these halves of the detail of the phase modulator  1  as shown in  FIG. 3 . In a manner similar to FIG. 9 of WO 2011/067265 A1, a voltage sequence may be applied over a large number of electrodes  4  in order to produce a variable deflection grating. 
       FIGS. 4 a  and 4 b    show in two different views an arrangement similar to  FIGS. 2 a  and 2 b   . In addition, here the upper substrate  3  contains further electrodes  12 , which are arranged at an angle of approximately 90 degrees to the electrodes  4  on the lower substrate  2 . A field between the electrodes  12  on the upper substrate  3  would thus in  FIG. 4 a    lie approximately in the plane of the drawing and in  FIG. 4 b    approximately perpendicularly to the plane of the drawing.  FIG. 4 b    shows the orientation of the liquid crystals  10  when an electric field is applied neither to the lower electrodes  4  nor to the upper electrodes  12 . 
       FIG. 4 c    schematically shows, in the same view as  FIG. 4 b   , the orientation of the liquid crystals  10  when an electric field is applied between the electrodes  4  on the lower substrate  2 . In this exemplary embodiment, the material parameters of the liquid crystal are adjusted in such a way that it has a dielectric anisotropy of Δ∈≧5. The flexoelectric coefficient e s  is, for example, approximately 10 pC/m. When an electric field is applied, an in-plane rotation of the LC molecules  10  takes place. Because of the flexoelectric polarization, the rotation direction of the LC molecules  10  is dependent on the sign of the electric field. This also applies for a combination of dielectric and flexoelectric interaction with the electric field. This is because the torque on the LC molecules  10  due to flexoelectric interaction behaves proportionally to the cosine of the angle between the polarization vector of the flexoelectric polarization of the LC molecules  10  and the E-field vector, i.e. it is greater when this angle is 90 degrees. The torque caused by the dielectric interaction, however, is proportional to the product of the cosine times the sine of the angle between the electric field of the orientation of the LC molecules  10 . With an angle of exactly 90 degrees, this torque has a value of zero. 
     The ratio of the two torques, however, varies with the sine of the angle. Furthermore, with an increasing electric field, the dominance of the dielectric interaction increases. It thus dominates the dielectric interaction beyond a particular rotation angle, depending on the ratio Δ∈/e s . 
     In addition, in the case of a relatively strong electric field, the dielectric interaction advantageously also causes a change in the out-of-plane orientation of the LC molecules  10 . Because of this change in the out-of-plane orientation with an increasing in-plane rotation angle, the splay deformation also becomes less and therefore the flexoelectric polarization also becomes less. With a sufficiently large Δ∈or a sufficiently large ratio Δ∈/e s , for rotation angles close to 90 degrees the LC molecules are then almost entirely oriented in-plane and the flexoelectric polarization is very small. 
     Rapid active rotation of the LC molecules  10  back to their original orientation then takes place with an electric field which is applied to the electrodes  12  on the upper substrate  3 . When the parameters Δ∈ and e s  of the LC material are adjusted in such a way that the polarization becomes less with an increasing rotation angle, the dielectric interaction advantageously dominates for the rotation back (despite a modified angle of close to 90 degrees between the electric field and the LC orientation due to the modified direction of the electric field). In combination with the elastic forces in the liquid crystal and the surface anchoring, the LC molecules  10  are then rotated back into their original orientation independently of the sign of the electric field. Advantageously, the electrodes  12  on the upper structure  3  may have the structure of the inter-engaged combs. Individual controlling of the electrodes  12  on the substrate  3  is thus not necessary, rather it is merely necessary to apply a global voltage value between the combs. Advantageously, such a configuration also has a very rapid switching behavior, since the two switching processes, switching on and off, can respectively be controlled actively by an electric field. 
     On the other hand, the change in the optical path of light through the LC layer, which is caused by a modified out-of-plane orientation, is sufficiently small for the LC layer  9  to behave approximately as a λ/2 plate independently of the in-plane rotation angle. The diffraction efficiency of a variable deflection grating, or of the phase modulator  1 , is thus only insubstantially reduced by the described configuration. 
       FIGS. 5 a  to 5 d    show an exemplary embodiment of a phase modulator  1 , which may be used in the function of a spatial light modulator. In this exemplary embodiment, the phase modulator  1  is thus used not as a deflection grating but as a spatial light modulator (SLM) having a plurality of regularly arranged pixels  13  and having a phase value which can be adjusted as uniformly as over the surface of a pixel  13 .  FIGS. 5 a  and 5 b    respectively show a section along the lines  5   a - 5   a  and  5   b - 5   b  according to  FIG. 5 d    of a phase-modulating pixel  13  of the phase modulator  1 .  FIG. 5 d    shows a sectional view of the pixel  13  along the line  5   d - 5   d  according to  FIG. 5 c   , an electric field which also generates the alignment of LC molecules  10  shown in  FIG. 5 c    in regions  14 ,  15  being applied to the electrodes  4  in  FIG. 5 d   . The phase-modulating pixel  13  is divided into two regions  14 ,  15 , which respectively have a mirror-symmetrically opposite orientation of the LC molecules  10  close to the surface  5  or  6 , respectively. The approximate separation of the regions  14 ,  15  is indicated by the vertically dashed line in  FIGS. 5 c  and 5 d   . In region  14 , the LC molecules  10  are arranged, or aligned, on the lower side at an angle α(0) on the surface  5  and on the upper side on the surface  6  with an angle α(d). In region  15 , the LC molecules  10  are arranged, or aligned, on the lower side at an angle −α(0) on the surface  5  and on the upper side on the surface  6  with an angle −α(d). 
       FIG. 5 c    shows a view, rotated through 90 degrees, of a pixel  13  (along the line  5   c - 5   c  in  FIG. 5 d   ) when an electric field is applied. The region  14  of the sectional view of  FIG. 5 a    can be seen in the left-hand part of  FIG. 5 c   . A region  15  of one of the two sections of  FIG. 5 b    can be seen in the right-hand part of  FIG. 5   c.    
     Despite a modified direction of the electric field, uniform rotation of the LC molecules  10  takes place in both regions of the pixel  13 , see the arrows indicated centrally between the surfaces  5 ,  6 . A uniform phase value is thus generated in the entire pixel  13 . A conventional electrode structure can then advantageously be used for the pixel  13 . 
     In conclusion, it may more particularly be pointed out that the configurations explained above merely serve to describe the claimed teaching, but do not restrict it to the configuration. In particular, configurations described above could—insofar as is possible—be combined with one another.