Liquid Crystal Phase Gratings (Chuck Titus)
OUTLINE:
Introduction
One advantage of using liquid crystals to construct a diffraction grating is that a pure phase grating can be designed. Hence, it is possible to make use of all incident light. Of course, this is not possible with amplitude gratings, which modulate the intensity of incident light in order to produce diffraction.
In addition, the phase profile of liquid crystal gratings is easily sculpted by means of patterned surface alignment, and from such a starting point can be controlled using the well-known electro-optical behavior of liquid crystals.
This discussion centers around two liquid crystal phase gratings. The "Optically Active Device" is a transmissive "phase" grating in which light is rotated rather than retarded, as is normally done in a phase-type diffraction grating. The "Orthogonal-Twist" reflective grating employs the same principle.
Each of the proposed liquid crystal phase gratings consists of alternating stripes of nematic liquid crystal. Different surface orientation and/or different twist sense differentiate the alternating stripes. This type of device can produce a diffraction efficiency approaching 100%, with complete removal of diffraction at low applied voltage. Experimental work has confirmed the operation principles.
The following discussion covers operational principles, device modeling and design, and fabrication and testing of the most promising devices.
Contributions to the work discussed here come from the following:
The new ("Orthogonal Twist") design for a reflective liquid-crystal phase grating may be of use in large-screen projection display systems. Its efficient use of pixel aperture and polarization independence can improve image intensity, while the fully dark state provides for good contrast.
This device, and the new ("Optically Active Device") transmissive liquid crystal grating, may be of use in other beam steering and light valve applications requiring efficient performance and simple construction
The earliest liquid-crystal projection displays involved transmissive light valves (LV’s). Incident light was projected directly through an AMLCD-type liquid-crystal display. These light valves required the use of polarizers, eliminating at least 50% of incident light. The required patterning of switching devices in those devices further reduced useable intensity because of aperture reduction.
At least three methods of improving intensity and contrast of LV’s have been investigated. First, lenticular lenses can reduce the aperture problem by steering incident light around unused switching areas. Second, useable aperture can be increased by operating in reflection mode, hiding each switching mechanism hidden behind a reflective pixel. Third, practical polarization conversion is being researched.
Both polarization and aperture issues are addressed by reflective LV’s based on scattering principles, such as PDLC light valves. PDLC devices have two drawbacks: High switching voltage and dark-state leakage, which reduces contrast. One disadvantage of this type of device is the high switching voltage. Another drawback is the tradeoff between image resolution and contrast ratio. A thin PDLC film does not scatter all incident light in its dark state, and this leakage limits the contrast ratio. Thicker PDLC films improve the contrast ratio, but at the expense of image resolution.
Another type of scattering LCLV employs switching between ordered and defect-filled smectic A LC. Here, again, the problem of dark-state leakage is an issue.
Liquid crystal diffraction gratings are an attractive alternative to LCLV devices because of the potential for polarization-independent operation. Among the early LC phase gratings were those based on the formation of Williams’ domains in an untwisted nematic LC film. These devices required high voltage for operation and exhibited relatively poor polarization-dependent diffraction performance. Hence, such devices are probably unsuitable for use in projection systems.
Hori proposed a transmissive LC grating design based on field-induced tunable birefringence. However, the untwisted device exhibited polarization dependent performance and required high voltage to achieve a high contrast ratio. It also required closely spaced interdigitated electrodes within each pixel, resulting in increased possibility of shorts across electrodes and greater impact of fringing fields on diffraction performance.
Fritsch investigated polarization-independent LC gratings. The result was a reflective device based on field-controlled birefringence difference between alternating stripes inside each pixel. This device also required high resolution patterning of electrodes.
Another type of reflective LC phase grating is the FQM. The FQM makes use of a twisted LC layer and a quarter wave plate to obtain polarization independence. Again, this device requires small stripe electrodes in order to produce the desired grating within each pixel.
To solve the problems brought on by the use of interdigitated electrodes, Gibbons suggested the use of patterned alignment instead. Because the differently patterned domains require no separation, diffraction efficiency is increased and the risk of shorting is reduced. The use of patterned alignment with an optically active device has been demonstrated, producing high contrast and low voltage operation. However, this was a transmissive device, which has the expected aperture limitation.
Transmissive Diffractive Liquid Crystal Light Valves
4.A. Optically Active Liquid Crystal Light Valve
The Optically Active Device (OAD) is a transmissive liquid crystal grating. Each pixel consists of alternating striped domains of opposite twist sense. The thickness and liquid crystal filler are chosen to produce perfect optical rotation in each of the two types of domains when no voltage is applied. In this state, light transmitted through the two types of stripes appears to be 180 degrees out of phase. The diffractive zero order is extinguished, and (ideally) only odd diffraction orders will appear.
When a voltage of modest strength (approx. 10,000 V/cm) is applied, the twist is "removed" from the domains, which become optically identical. The odd diffraction orders are extinguished, and only the zero order appears.
Opposite twist sense in the adjacent stripe domains was obtained by alternating the pretilt directions. No chiral additive was required.
One substrate was prepared with uniform surface alignment direction. The other was photo-patterned so that adjacent stripe domains possessed pretilts of opposite direction.
The photo-patterning method is similar to work done by Takatori and Gibbons.
The device was placed in the experimental setup shown below. The louvered element has regularly-spaced openings and is placed propitiously to block the zero order and allow odd diffraction orders to pass through, whereupon that light is collected by a lens and focused onto the detector surface.
In this arrangement, the largest signal will be detected when no voltage is applied to the OAD, because in that state the OAD diffracts "all" of the incident light into odd orders. As the voltage is increased, the OAD becomes less diffractive, the increasingly intense zero order is blocked, and the detector signal decreases. The signal vanishes when the adjacent stripes become optically identical.
Transmissive liquid crystal devices such as the OAD, when fabricated in an active matrix array, possess one important drawback. Opaque features of the active matrix limit the maximum transmission of this type of device. This built-in loss of intensity means transmissive liquid crystal devices may be less than desirable in applications such as projection displays, for which efficient use of the illumination lamp’s intensity is of paramount importance. Hence the need for a reflective liquid crystal grating, which allows the active matrix circuitry to be hidden behind the reflective area.
What is needed is a reflective device (in order too overcome aperture limitations), which uses patterned alignment (in order to reduce fringing fields and the risk of shorting), is polarization independent (so all of the source can be utilized), and can operate at low voltage. In addition, gray-scale performance is desirable for use in projection displays.
Three devices are investigated here. In each the individual pixels are liquid crystal diffraction gratings. Within each pixel the grating is formed by alternating stripes of two different LC orientations. The two orientations are chosen such that with no applied field, normally incident light is diffracted out of the zero order and into odd orders (assuming a perfect "square wave" grating). Application of a high field "undoes" the difference in orientation between alternating domains, resulting in non-redirected reflection of incident light. Gray scaling can be induced by application of intermediate field strengths, resulting in partial steering a controllable fraction of incident light out of the zero order.
In a practical display device, the dark state should be as dark as possible in order to maximize contrast ratio. This is usually the non-diffracting state (100% into zero order) of the device. The zero order light is blocked by a propitiously placed louver. Any intensity remaining in the zero order here results in an imperfect dark state, reducing contrast. For another value of applied voltage, the grating must diffract as much of the incident light into higher (all odd) orders as possible. Those orders are passed through the louver and recondensed onto the viewing screen.
The "fully diffractive" state could be employed as a dark state by shifting the louvers if all light is diffracted into odd orders. In that case, the voltage which minimizes diffraction provides the light state. However, this choice requires a perfect square wave grating in order that all the diffracted light will be found in odd orders. In practical switchable LC devices, such a grating is difficult to obtain.
The first device is similar to that proposed by Gibbons. It is composed of alternating Freedericksz domains and will be labeled the "No Twist" grating. Each domain has parallel rub directions on its two substrate surfaces. Rub directions of neighboring domains are perpendicular. This grating owes its variably diffractive performance to the field-tunable birefringence of the two domains. This design is included in the study in order to provide a comparative base for the two following designs.
The second grating, called "Reverse Twist", consists of twisted nematic (TN) domains with opposite twist sense. Reverse twisting can be induced as described for the
OAD. With no field applied, light reflected from one domain is phase shifted with respect to the other. Thickness can be optimized to reduce or eliminate diffraction into the zero order. Application of moderate voltage tilts the director at the center of each domain perpendicular to the substrate, eliminating diffraction out of the zero order.The third grating is called "Orthogonal Twist". The two alternating TN domain stripes within each pixel have identical twist sense. The rub direction of one domain is perpendicular to the other at both surfaces. It operates in a manner similar to the reverse-twist configuration
5.A. No-Twist Device
The "No-Twist" grating pixel consists of alternating stripes whose liquid crystal is oriented as shown below. This is a true phase grating. Phase difference between neighboring stripes occurs because light passing through one type of stripe experiences the liquid crystal’s ordinary refractive index, while light passing through the other type of stripe experiences the extraordinary index. In order to provide the desired half-wave phase difference between adjacent stripes, thickness and liquid crystal filler (i.e. magnitude of birefringence) must be carefully chosen.
Removing the diffractive behavior of such a pixel requires fairly high voltage, typical of tunable birefringence devices.
5.B. Reverse-Twist Device
Employed in a transmissive device (e.g. the OAD), the "Reverse-Twist" grating owes its diffractive nature to rotation of polarization. When optimized as a perfect optical rotator, such a grating can produce, in theory, 100% diffraction efficiency because the output fields of adjacent domains are one-half wavelength out of phase. However, this grating will not perform as well in a reflective device. Under conditions producing pure optical rotation, all incident polarizations are rotated back to their incident state, outputs from adjacent domains are identical, and no diffraction occurs. In order for any diffraction to take place,
D nd/l must not equal the condition for perfect optical rotation. Light emerging from adjacent domains will be elliptically polarized, producing less than perfect constructive interference.
Diffraction is removed from this grating when sufficient potential difference is applied across the substrates. Liquid crystal molecules having positive dielectric anisotropy will be tilted toward the substrate normal. This occurs initially midway between the substrates. All twist moves to this region. As a result, the domains appear optically identical.
The "Orthogonal-Twist" configuration makes use of both optical rotation, because of the twisted nematic domains, and retardation, because the surface orientations of adjacent domains are perpendicular to each other. There are values of
D nd/l (given by the Gooch and Tarry minima conditions) for which the polarization state of incident light is preserved on reflection, resulting in no diffraction. However, at D nd/l values approximately one-fourth above those minima, retardation effects work with the twist-induced ellipticicity to produce perfect diffraction conditions. Light reflected from any domain is elliptically polarized, but now both components are one-half wave out of phase with respect to corresponding components reflected from adjacent domains.As with the Reverse Twist grating, diffraction is removed from this grating when sufficient potential difference is applied across the substrates. Liquid crystal molecules having positive dielectric anisotropy will be tilted toward the substrate normal. This occurs initially midway between the substrates. All twist moves to this region. As a result, the domains appear optically identical.
5.D. Design and Modeling
The director configuration for each of the three (No-Twist, Reverse-Twist, Orthogonal Twist) grating’s two domains was computed using a relaxation technique applied to Euler-Lagrange minimization of the Frank free energy. Material parameters for the E7 LC blend were employed. Each "cell" was 10
mm thick.Optical propagation was computed using Jones calculus. All optical calculations were performed for 550-nm light. In order to check for polarization independence, diffractive performance was calculated for all three gratings with two different (perpendicular) incident polarization fields. That data is not shown here, but all three gratings proved polarization independent.
Optical propagation through the domains was modeled by dividing each domain into thin layers and treating each as a separate retarder. A constant director orientation was assumed for each layer. Jones calculus was applied separately to the sequence of layers in each domain. Light normally incident on the domain was propagated through the layers, reflected off a mirror, and propagated back to the entry surface. The reflected fields of the domain pairs were superimposed to determine the fraction of incident intensity diffracted out of the zero order. This simplistic analysis treats adjacent domains within each type of grating as point sources. One pair of domains is used in the diffraction calculations.
Optimization: The dark state should be as dark as possible in order to maximize contrast. In a practical device, it is easier to block a single zero order than many odd orders. Thus, dark state is obtained when some value of voltage is applied which destroys the diffractive nature of these gratings. The lower this dark-state voltage, the better. We (somewhat arbitrarily) chose five volts.
For the light, the grating must diffract as much of the incident light into the odd orders as possible. Those orders are passed through the louver (if properly constructed and aligned) and recondensed onto the viewing screen. The optimal light state is some value of applied voltage which produces strong diffraction. If these three types of gratings are properly engineered, that will usually be zero volts.
Optimization of each grating’s performance was performed by varying the thickness-birefringence product for the design wavelength. The optimum value is that which produces as little diffraction as possible at five volts and as much as possible at zero volts.
Results: The No-Twist grating is the only one of the three which did not exhibit a fully dark state for the same thickness-birefringence product as a bright (highly diffractive) light state. As a result, thickness and birefringence had to be chosen which provided a bright light state but a less than perfect dark state. This is a result of its lack of LC director rotation. Very high voltages are required to make the two domains in this grating appear optically similar, which is a necessary condition for maximum intensity into the blocked zero order.
The optimized Reverse-Twist grating provides less intensity but higher contrast than the No-Twist grating. At the optimal first interference thickness- birefringence value, this grating diffracts 70% of normally incident light out of the zero order at 0 Volts, 0% at 5 Volts, with a fairly linear transition for gray-scaling.
The optimized Orthogonal-Twist grating provides a brighter light state than the Reverse-Twist grating and a more completely dark state than the No-Twist grating. The operating principle is the same as for the Reverse-twist case. Diffraction efficiency as a function of applied voltage results in >90% efficiency at 0 Volts, 0% at 5 Volts, and a fairly linear transition for gray scaling. The second interference minimum condition for the Orthogonal-Twist grating produced even greater on-off contrast, but the electro-optic curve in that case is not monotonic (as is desired for gray-scale operation).
Each type of grating can be designed to provide gray-scale capability. For the No-Twist grating, this choice is at the cost of contrast. The other gratings are optimized with a non-diffracting dark state, which provides better contrast. Of those two, the Orthogonal-Twist device exhibits the greater contrast ratio.
5.E. Experimental
We then fabricated an Orthogonal-Twist grating to check our predictions. 125-micron wide domains were produced using the photo-patterned double-rubbing technique applied to substrates coated with Nissan 7311 polyimide. The transparent substrate was ITO coated glass. The reflective substrate was aluminum-coated glass.
We assembled the test device in a wedge configuration in order to provide both the first and second optimal conditions in a single device. The wedge incline was parallel to the domain (stripe) axis. The cell was filled with ZLI-4792 liquid crystal blend (
D n=0.09). After filling the cell, the substrates were aligned manually while viewing the device in a polarizing microscope.The electro-optical performance of the Orthogonal-Twist wedge cell was determined experimentally. The grating was illuminated with an He-Ne laser. The reflected diffraction pattern was passed through a set of louvers, placed so that only the first five odd orders were collected onto a detector. This selection of odd orders is similar the operation of a Schlieren optical projection system.
The laser was first directed at a location which produced the first optimal state. Measurements were taken with the laser polarized parallel and then perpendicular to the domain stripes. The measured response was normalized to the signal detected with the louver removed and 20 Vrms applied to the cell. A second set of data was taken with the laser directed at a location which produced the second optimal state.
Both sets of data indicate polarization independent performance. The switching voltages are slightly higher than predicted because ZLI-4792 was substituted for E7 in the experimental device, and because domain boundary walls were not included in the calculation.
The measured intensities are lower than predicted for several reasons. First, we collected only the first 5 odd orders, whereas the predicted electro-optic data is a collection of all non-zero orders. Second, disclinations at the domain boundaries reduce the diffraction efficiency. Third, the domain boundaries were not perfectly straight, parallel and of equal width due to use of a low quality photolithography mask. Fourth, inspection of the grating under a polarizing microscope indicated some surface flaws.
The latter two imperfections are easily addressed by improved fabrication parts and processes. Higher quality masks, more precise photolithography, and automated spin-coating, rubbing, and alignment should enhance diffractive performance.
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