LIWEI LI, LEI SHI, DOUG BRYANT, TONY VAN HEUGTEN, DWIGHT DUSTON, and PHILIP J. BOS
Liquid-crystal “electronic” lenses have long been considered a potential candidate for replacing or simplifying bulky conventional optics. Given their advantages—which include tunable power, small size, low cost, low power consumption, and high-speed switching—such lenses are likely to have a tremendous impact upon future optical system designs.
Conventional lenses are made by the radial shaping of materials like glass and plastics that exhibit a constant refractive index. Diffraction-limited performance can be achieved using precise shaping and polishing, but is often not achievable within the economic design constraints placed on the optical systems of many consumer products. Typically, such systems have undesirable optical distortions or aberrations that are corrected using more than one lens group, commonly having spherical elements. The system can be simplified by replacing several spherical lenses with a high-quality aspheric lens with a parabolic profile, but that generally adds cost to the system. In addition, a conventional lens has one fixed focal length. To vary the focal length of an imaging system, an array of lenses is typically used and the focal length is changed by mechanically moving components that adjust the distance between lenses. This approach inevitably makes the system bulky and inefficient, and unsuited to some applications.
Many optical systems designers have, therefore, been driven to seek alternative solutions that can vary the focus without moving parts, be small in size and weight, low in cost, and be robust enough to survive harsh shocks. In a classic lens design, the optical path difference across the lens aperture has a profile, such as sphere or parabola, that's determined only by the polished shape of the material surface, and the refractive index is homogeneously constant. Optically equivalent to a thickness variation, the index of refraction can be controlled to give the same phase profile across the aperture. Liquid-crystal (LC) materials have, therefore, become a very promising option since their refractive index can be tuned by application of a voltage.
Unlike LC displays, which are based on a change in the polarization state of transmitted light resulting from the refractive index modulation, LC lenses use the resultant phase of linearly polarized light exiting the surface. Generating the desired refractive index profile with an external field becomes the key to the performance, and various electrode structures and addressing approaches have been introduced, such as a set of the discrete ring-patterned electrodes addressed individually with different voltages, the spatial distribution of electric field on a hole-patterned electrode plate to control the index profile, or a spherical shape of the electrode, which can be addressed to tune the power continuously.1-3 To more precisely control the phase profile, we designed and fabricated a liquid crystal lens based on the ring-patterned approach, and the voltage profile applied to the electrodes can be calculated to optimize the index profile for a desired power.
Liquid-crystal materials and LC lenses
Liquid crystals are mesophases between crystalline solids and isotropic liquids, typically consisting of elongated, rod-like organic molecules with a size of a few nanometers. These molecules contain both the rigid and flexible parts of the crystal. One of the simplest LC molecules is 5CB, with a biphenyl rigid core, favoring both the orientational and positional order, and a hydrocarbon chain as a flexible tail, favoring flow like liquids (see Fig. 1a). With both parts balanced, the molecules can exhibit optical, birefringence-like crystalline solids, and flow like regular liquids, depending on the external conditions such as temperature and external field.
Generally, at high temperature, LC materials are in the isotropic liquid state without any orientational or positional order. At lower temperature, the phase changes to nematic, which is the most common LC phase. The molecules then have orientational order but no positional order; they can flow around with a certain viscosity, while the directors (long molecular axis of all molecules averaged) preferentially orient along a common direction. As the molecules are elongated and have different molecular polarizabilities along the long and short axis, the refractive index for each axis direction is different—that is, the effective refractive index depends on the angle of long axis of the molecules and the linear polarization of the incident light (see Fig. 1b). When light is polarized along the long axis, the index of refraction is ne (see Fig. 1c); when the polarization direction is along the short axis, it is no (see Fig. 1e); in case of an arbitrary angle, the index can be calculated as a function of this angle (see Fig. 1d).
When an electric field is applied to liquid crystals, dipole moments are induced in the crystals. For most materials, with larger induced dipole moment along the director axis, the director will tend to reorient along the electric field direction. The equilibrium orientation of the director depends on the magnitude of the applied electric field and the competing effect of the alignment layers applied to the surfaces of the cell.
A typical LC cell consists of two glass substrates with thin transparent ITO (indium tin oxide) layers on opposing surfaces to apply an electric field. The polyimide alignment layer is coated on each plate and rubbed along one direction to cause a preferred orientation of molecules, so that the director field through the cell will be always in the plane containing the cell normal and the rub directions. As the voltage is varied to a local area of the cell, the director orientation changes from being parallel to the surface to being closer to perpendicular to the surface, which causes the effective refractive index to change within the maximum range (see Fig. 1e).
In LC cells, if the index of refraction is spatially varied by having electrodes with different voltages applied, the light passing through different electrode areas will have different propagating speeds. As a result, with the proper voltage profile, the wavefront of the constant phase will start to tilt, which makes the light bend after passing through the LC cell (see Fig. 1f). Moreover, light can refract more as the curvature of the index profile increases (see Fig. 1g). An LC lens, therefore, becomes possible with a proper design of ring electrodes and a precise voltage profile, so that the optical path difference across the aperture can be parabolic in shape, and light can be focused in a certain plane after exiting the cell (see Fig. 1h).
LC lens design and fabrication
As an example, consider a 1 diopter lens with an approximate diameter of 4.7 mm. The electrode pattern on one plate consists of about 80 discrete ring electrodes with equal inter-ring resistors. Given the diameter and focal length, the ideal OPD (optical path difference) across the aperture can be obtained.4 Outward from the center, the width of each electrode is determined by its phase step within each electrode region equal to about 1/8 λ (for green light, λ = 543.5 nm), which tends to minimize quantization phase aberration in the refractive index profile caused by the discrete nature of electrode patterns.5 To minimize the index aberration within the interstitial space between electrodes, the gap between electrodes should be small, compared to thickness of the cell.6 In this design, the gap between pair electrodes is 3 μm, and the cell has a thickness of 10 μm. To avoid the complexity of electrical connections to all the electrodes, we address about every 10th ring with external bus lines, such as 1st, 11th, 21st, and so on. Hence, a total of nine electrodes are addressed individually, and the lens has eight regions of linear voltage drop because of the constant inter-ring resistors between any two adjacent electrodes (see Fig. 2a).
Three major photolithographic patterning steps are required to fabricate the electrode plate. First, the ring mask is designed and used to create the ring ITO structure with the desired dimensions (see Fig. 2b, c). Next, a silica (SiO2) layer is deposited on the ITO layer for insulating electric connections between layers (see Fig. 2d). On approximately every 10th electrode, a small via is generated through the SiO2 layer (see Fig. 2e). Nickel material is deposited and patterned as nine bus lines connecting the electrodes to the addressing voltage profile through the vias (see Fig. 2f). In Fig. 2h, the real top-view of the patterned ITO plate under microscope is shown.
After the patterning process, a polyimide alignment layer is coated and rubbed along one direction to fix the directors everywhere in the cell to be coplanar (see Fig. 2g). The cell is assembled by facing the interior surfaces of both plates to each other (see Fig. 2i), and glue sealing with 10 μm sphere spacers uniformly distributed in the active area. Most importantly, the thickness variation across the cell needs to be controlled to a small fraction of the wavelength of light for a good optical performance. Finally, the cell is filled with a liquid crystal material with a large birefringence such as Δn = 0.27. A flex connector, bonded on the nickel lines with one side, supplies the externally generated voltage profile to the cell.
Modeling of the desired voltage profile
Our model takes as input the electrode pattern and applied voltages, the cell thickness, and the material properties of the liquid crystal, and numerically calculates the director profile throughout the cell. Then the phase profile of device can be calculated by integrating the effective refractive index across the cell thickness for each point on the surface of the cell.
The voltage profile can be optimized by calculating the phase profile on each electrode, and comparing it with the desired OPD profile. In case of any deviation from the desired profile, the voltage for each electrode will be adjusted, and the new voltage profile will be generated. The program will keep optimizing until the phase tolerance condition is met.
Optical performance
With the optimized voltage profile applied on the lens, the actual OPD phase profile across the lens can be measured by a Mach-Zehnder interferometer setup (see Fig. 3a–c). The actual OPD is very close to parabolic shape, due to our strictly controlled fabrication process as well as the precisely calculated voltage profile (see Fig. 3d). The image of an eye chart through the LC lens shows good resolution and contrast (see Fig. 3e).
With the advantages of variable power, small size and weight, low cost and power consumption, liquid-crystal lenses will be very useful in portable devices, requiring variable focus or zoom within a limited space. Stacking of several layers of these cells is possible to achieve high optical power and for polarization independence. Overall, liquid-crystal lenses are much more than just a concept or idea; their intrinsic advantages and current development status point to use in mainstream optical systems in the near future.
REFERENCES
1. G. Li et al., Proc. Natl. Acad. Sci., 103, 16, 6100–6104 (2006).
2. Y. Mao and S. Susumu, Opt. Comm., 4–6, 225, 277–280 (2003).
3. R. Hongwen et al., Opt. Exp., 15, 18 (2007).
4. M. Born and E. Wolf. Principles of Optics, Sixth Edition, Cambridge University Press, Cambridge, UK (1980).
5. M.B. Stern, “Binary optics fabrication” in Micro-optics: Elements, Systems and Applications, H.P. Herzig, Taylor & Francis, London (1997).
6. P.F. Brinkley et al., Appl. Opt., 27, 4578–4586 (1988).
Liwei Li is a graduate student, Lei Shi was a graduate student, Doug Bryant is manager of display engineering, and Philip J. Bos is associate director and professor at the Liquid Crystal Institute, Kent State University, Kent, OH 44240; e-mail [email protected]. Tony Van Heughten is chief technology officer and Dwight Duston is executive VP for research & development at eVision Inc., Roanoke, VA 24019.