Method of producing a phase device based on a twisted liquid crystal having optimized structure operating under unpolarized light

Abstract

The invention relates to a method of producing a phase device operating at at least one wavelength () comprising a cell containing a liquid crystal possessing a helical structure, inserted between two alignment layers possessing rubbing axes and means for applying a voltage to said cell, said helical structure exhibits a number of helical turns k, said liquid crystal exhibiting a defined angle of twist between the rubbing axes of the two alignment layers, characterized in that it comprises the following steps: the determination of a compensation angle satisfying the following equation: (formula) with: N the integer closest to (formula) the angle of twist =2Kn: the birefringence of the liquid crystal; d: the thickness of the liquid crystal cell; : the wavelength of the light beam which passes through the liquid crystal cell; the rubbing of one of the faces in a direction of alignment of said liquid crystal molecules, defining the angle of twist: =2K. $\mathrm{.Math.}=2k-N\sqrt{1-\frac{d^2{n}^2}{N^2{}^2}})$$2k\sqrt{\left(1+\frac{d^2{n}^2}{4k^2{}^2}\right)}$

Claims

1. A method of producing a phase device operating at least at one wavelength (), the phase device including a cell containing a liquid crystal which has a helical structure and is inserted between two alignment layers each having rubbing axes, and means for applying a voltage to said cell, said helical structure having a number of helix turns k, and said liquid crystal having a twist angle defined between the rubbing axes of the two alignment layers, the method comprising the following steps: determining a compensation angle satisfying the following equation: $\mathrm{.Math.}=2k-N\sqrt{\left(1-\frac{d^2{n}^2}{N^2{}^2}\right)}$ with: N the integer closest to $2k\sqrt{\left(1+\frac{d^2{n}^2}{4k^2{}^2}\right)},$ said compensation angle being an angle for minimizing a residual ellipticity of the liquid crystal and making a rotation amplitude of the light beam which passes through the liquid crystal to be equal to an integer multiple of 2; determining the twist angle =2k based upon the compensation angle ; where n: the birefringence of the liquid crystal; d: the thickness of the liquid-crystal cell; : the wavelength of the light beam which passes through the liquid-crystal cell; and rubbing one of the faces along an alignment direction of said liquid-crystal molecules based upon the twist angle: =2k.

2. The method of producing a phase device as claimed in claim 1, wherein the phase device is a lens.

3. The method of producing a phase device as claimed in claim 2, wherein the lens is a lens with a kinoform profile.

4. The method of producing a phase device as claimed in claim 1, operating at least in the wavelength band from 400 nm to 700 nm, the calculation of the compensation angle being carried out at a wavelength close to 475 nm.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) The invention will be better understood, and other advantages will become apparent, on reading the following description which is given without implying any limitation, and by virtue of the appended figures in which:

(2) FIG. 1a-1c schematizes the orientation of liquid-crystal molecules under the action of an electric field;

(3) FIGS. 2a, 2b and 2c illustrate the cumulative and separate phenomena of the action of polarized light on a twisted liquid crystal;

(4) FIG. 3 illustrates the cholesteric molecules along a helix in a liquid-crystal device and the polarization of the light along the thickness of said cell;

(5) FIG. 4 illustrates the change in the Z coordinate as a function of the number of turns for a liquid-crystal cell having a thickness d equal to 5.1 m and an index variation n=0.2139, and for light with a wavelength of =0.55 m;

(6) FIG. 5 illustrates the change in the ellipticity as a function of the entry azimuth angle for cells whose thickness is constant and whose helix pitch is variable;

(7) FIG. 6 illustrates the change in the ellipticity as a function of the entry azimuth angle for cells whose helix pitch is constant and whose thickness is variable;

(8) FIG. 7 in turn illustrates, in the scope of a liquid-crystal cell having 7 helix turns, the residual ellipticity with an antiparallel treatment as a function of the entry azimuth angle and the residual ellipticity obtained with the method of the invention;

(9) FIG. 8 illustrates the residual ellipticities at different wavelengths.

DETAILED DESCRIPTION

(10) The Applicant has assumed that the action of an oblong liquid-crystal molecule, twisted by an angle , on polarized light can be represented on the Poincar sphere as that: of an elliptical birefringent with coordinates X and Z defined below:

(11) $X=\frac{\frac{2n}{}}{\sqrt{{\left(\frac{2n}{}\right)}^2+\frac{4{}^2}{d^2}}}$$Z=\frac{\frac{2}{d}}{\sqrt{{\left(\frac{2n}{}\right)}^2+\frac{4{}^2}{d^2}}},$

(12) the rotation amplitude of the elliptical birefringent being defined as follows:

(13) $\mathrm{Amp}=d\sqrt{{\left(\frac{2n}{}\right)}^2+\frac{4{}^2}{d^2}}$ with: n: index of the crystal : twist angle d: thickness of the liquid-crystal cell : the wavelength of the light beam which passes through the liquid-crystal cell; followed by a rotation dependent on the total twist.

(14) FIGS. 2a, 2b and 2c illustrate the two phenomena cumulatively and separately.

(15) FIG. 2b demonstrates notably the entry polarization Pol.sub.e of the beam at , as well as the entry birefringent, showing the entry director CL. The phenomenon can thus be broken down into a first action (that of the birefringent Bi) which takes a point on the equator Eq and puts it somewhere on the Poincar sphere in order to make it into elliptical light, the second action being the rotation associated with the total twist, said actions being schematized by the references Ac.sub.I and AC.sub.II, ACI.sub.If indicating the end of the rotation action.

(16) It can thus be seen that, with =2k and k being the number of cholesteric turns, the greater k is, the more the axis of the elliptical birefringent is positioned vertically (as shown by the change in FIG. 2b in the axis of the birefringent as a function of the number k). In parallel, FIG. 3 illustrates the number of helix turns within a liquid-crystal cell inserted between two electrodes E.sub.1 and E.sub.2, the faces of which are treated in order to impart a twist angle, in the example in which k is equal to 5.

(17) By way of indication, FIG. 4 shows the change in the Z coordinate as a function of the number of turns for a liquid-crystal cell having a thickness d equal to 5.1 m and an index variation n=0.2139, and for light with a wavelength =0.55 m. When the number of turns is large enough, the coordinate tends to Z=1, an indication of a vertical birefringent axis and a zero induced ellipticity.

(18) By greatly increasing the number of turns of the cholesteric, it is therefore possible to tend to suppress the ellipticity by tending to obtain a linear polarization, although in this case it becomes necessary to apply a higher and higher control voltage.

(19) In this context, the Applicant has ascertained that, when the Poincar sphere and the action of the elliptical birefringent on the light are observed, it is seen that if the rotation amplitude is a multiple of 2, i.e. Amp=2N, any linear polarization returns to the equator after action of the birefringent.

(20) This is expressed mathematically by the following equation:

(21) $=\sqrt{N^2-\frac{d^2{n}^2}{{}^2}}=2k-\mathrm{.Math.},$

(22) which means both that the amplitude of the birefringent is equal to 2N but also that the angle must approach 2k as closely as possible while remaining less than 2k,

(23) $i.e.\text{:}\frac{\mathrm{.Math.}}{}=2k-\sqrt{N^2-\frac{d^2{n}^2}{{}^2}},$

(24) with N being an integer and being the compensation angle: a decreasing function of the number N.

(25) is a minimum when the integer N is close to

(26) $2k\sqrt{\left(1+\frac{d^2{n}^2}{4k^2{}^2}\right)}.$

(27) It is thus possible to determine the angle such that:

(28) $\mathrm{.Math.}=2k-N\sqrt{1-\frac{d^2{n}^2}{N^2{}^2}}),$

(29) with N the closest integer to

(30) 0$2k\sqrt{\left(1+\frac{d^2{n}^2}{4k^2{}^2}\right)},$

(31) corresponding to the compensation angle which must be provided so that the twist is equal to 2k- and the residual ellipticity is thus eliminated.

(32) Specifically, the light passing through the cholesteric experiences a residual rotational effect: thus, if the intention is to start with polarized light at the entry and obtain polarized light at the exit, it is found that the rotation of the birefringent is more than 2, and it is therefore expedient to impart a slightly lower twist angle so that this amplitude exactly constitutes an integer times 2.

(33) This means that the angle should be equal to 2k in order to obtain the condition: Amp=2N, and that the smallest value of is obtained for N=2k.

(34) In general, the ellipticity generated on a light beam depends on the thickness of the liquid-crystal cell and on the helix pitch of the liquid crystal as a function of the twist angle.

(35) Furthermore, as already mentioned, depending on the illumination wavelength and the pitch of the helix, such structures may behave partially as a mirror if the following condition is satisfied: p=/n with being the wavelength of the wave and n being the index of the liquid-crystal medium.

(36) In the case of a device designed to operate in transmission, this means that the pitch of the helix should not correspond to a wavelength such that a Bragg mirror is formed. Thus, cell thickness conditions and a number of helix turns k intended to lie outside these conditions are selected. Typically, for a device which is to operate in the visible range, conditions such that the reflection takes place in the infrared range rather than in the ultraviolet range are preferably selected.

(37) By way of example, FIGS. 5 and 6 illustrate the change in the ellipticity as a function of the entry azimuth angle for cells respectively: whose thickness is constant and whose number of helix turns is variable (curve C.sub.5a for 2, curve C.sub.5b for 4, curve C.sub.5c for 6, curve C.sub.5d for 8, curve C.sub.5e for 10, curve C.sub.5f for 12 and curve C.sub.5g for 14); whose helix pitch is constant and whose thickness is variable (curve C.sub.6a for 1 m, curve C.sub.6b for 2 m, curve C.sub.6c for 4 m, curve C.sub.6d for 6 m, curve C.sub.6e for 8 m, curve C.sub.6f for 10 m).

(38) The response time also increases as a function of the square of the thickness of the cell. An example of a satisfactory compromise can be achieved with a liquid crystal having an index variation n of the order of 0.2 and a cell thickness of the order of 5 m and a pitch of 0.71 m. A pitch of 0.83 m may also be selected, which contributes to a reduction of the control voltage by increasing the induced ellipticity.

(39) Example of a Lens with a Kinoform Profile According to the Invention:

(40) According to this example, the lens operating in the visible range comprises a layer of liquid crystal referenced MCL2062 from the company Merck, inserted between two control electrodes on which surface treatments for alignment have been carried out. The thickness of the liquid-crystal layer is selected so that the optical path variation experienced by the light in the kinoform lens is 2 at the wavelength in question. Typically, this thickness is therefore equal to 0.55/(0.5 n) for a wavelength of 0.55 m.

(41) It can be seen from the equations above, corresponding to a liquid-crystal cell having 3 helix turns, that a compensation angle =61 can be found which makes it possible to cancel the residual ellipticity, this compensation angle being applied during the antiparallel rubbing treatment.

(42) Likewise, for a liquid-crystal cell having a number of helix turns equal to 5, a compensation angle =36 can be determined.

(43) According to the method of the present invention, the surface treatments conventionally carried out by antiparallel rubbing between the two surfaces are corrected by the angle determined beforehand in this way.

(44) In the context of a liquid-crystal cell having 7 turns, FIG. 7 illustrates the residual ellipticity with an antiparallel treatment as a function of the entry azimuth angle (curve 7a) and the residual ellipticity obtained with the method of the invention (curve 7b) thus reduced to zero.

(45) The device of the present invention may also be operational in a wavelength range and not just at a single wavelength.

(46) To this end, the Applicant has studied the way in which the residual birefringence varies at wavelengths other than the one for which the optimization to cancel the residual ellipticity is carried out.

(47) In the case of a diffractive lens with a kinoform profile, for which zero action is desired in the OFF mode and zero birefringence is desired in the OFF mode (with the same liquid-crystal parameters as mentioned above) and 7 full turns for the cholesteric, a residual action as represented in the graph illustrated in FIG. 8 is obtained. Curve C.sub.8a relates to a conventional surface treatment, curve C.sub.8b relates to an optimization carried out at a wavelength of 550 nm, curve C.sub.8c relates to an optimization carried out at a wavelength of 450 nm, and curve C.sub.6d relates to an optimization carried out at a wavelength of 400 nm.

(48) It can be seen that, in the case of optimization calculated for 450 nm, a considerable improvement is obtained throughout the entire spectrum compared with a nonoptimized device. Typically, this represents a 38 correction on the rubbing direction of the alignment layer (still with the aforementioned liquid-crystal parameters).