Note: Electrical modeling and characterization of voltage gradient in liquid crystal microlenses

Abstract

In this work, a novel equivalent electric circuit for modeling liquid crystal microlenses is proposed. This model is focused on explaining a lens behavior at the micrometric scale, using its manufacturing parameters. It suggests an approach to predict the solution of the voltage gradient distribution across a microlens. An interesting feature of the model is that it provides an analytical solution for microlenses with modal and hole-patterned electrode schemes, by a simple software tool. The model flexibility allows lens designers to apply complex waveform signals with different harmonics. The voltage distribution has been tested. The simulated and measured voltage profiles are fairly in agreement. The design of new liquid crystal (LC) microlenses is involving currently important research resources. Prototypes based on this technology take advantage of the tunable electrooptical properties of these materials mainly for the focal length tunability. This distinctive feature together with a reduced weight and volume of the devices, compared to other technologies, makes them good candidates for a wide range of applications. Cell phone cameras, auto-focusing, 2D/3D switchable displays, tunable photonic devices, or devices in optical communication systems are potential applications for providing final added value. In order to simplify the structures and to decrease the device control voltage, many topologies have been researched. Furthermore, the capacity of manufacturing LC microlenses is limited at the micrometric scale with the constraint of lithographic resolution. Some approaches, such as Fresnel zone method, with arrangements of multiple electrodes, complicate the final design. Other strategies consist of creating a lens effect by shaping the electric field generated with a hole-patterned electrode structure. In holepatterned electrode structures, the phase gradient is generated by the fringe field as the diameter/thickness ratio is less than 2-3. 1 Fig. 1(a) shows the design of a cylindrical microlens following this approach; a top view of its hole-patterned electrode is depicted in the upper part. The spreading of the electric field lines, yielded from the teeth of the comb electrode to the center, creates a gradient of the LC director profile that simulates a lens response. Nevertheless, this approach does not work properly as the lens aperture increases in size, because of the electric field vanishes gradually without reaching the entire area of the hole. An option to mitigate this problem is to exploit the modal control technique. This method consists in adding a layer of high sheet resistance in areas which are free of the comb electrode. Fig. 1(b) illustrates a modal cylindrical microlens; in this arrangement, an electric field gradient is generated across the high resistivity layer. a) Author to whom correspondence should be addressed. Electronic mail:vurruchi@ing.uc3m.es. This inclusion can be a possible solution to avoid the use of several electrodes in lenses with wider apertures. On the contrary, mod...

Multifrequency Driven Nematics

“…This dependence gives raise to the possibility of designing liquid crystal mixtures with very low relaxation frequencies of electric permittivity parallel ε∥, which is useful for many applications [16]. Apart from traditional SLM, the unique properties of this LC mixture can be used in all kind of optical phase modulators recently reported, e.g., adaptive lenses [17], beam steering [18], correction of aberrations [19], 3D vision applications [19][20][21][22], novel aberrations correctors for rectangular apertures [23], microaxicon arrays [24], multioptical elements [25], hole-patterned microlenses [26], multifocal microlenses [27], high fill-factor microlenses [28], frequency controlled [29] microlenses, optical vortices [30], lensacons, and logarithmic axicons [31]. The LC mixtures used in this work have been designed by mixing three different families of LC compounds to meet the requirements of the LC to be controlled by low frequencies of the electrical applied voltage.…”

Liquid Crystal Microlenses for Autostereoscopic Displays

“…It is demonstrated how some classical aberrations as spherical or coma are controlled with voltage more than –1 and 2 waves, respectively. Finally, other research works have been focused on modeling the electric field distribution in order to have optimal designs [32,71]. These studies reveal a critical interrelation between the structural parameters of the microlens in order to distribute the voltage with a parabolic profile.…”

Liquid Crystal Temperature Sensor Based on Three Electrodes and a High-Resistivity Layer

“…The governing equations of the proposed structure can be derived from the transmission line theory [22]. For this, the LC is modelled as a capacitor parallel to a resistance (Fig.…”

“…The Frank-Oseen equations have to be solved in order to estimate this distribution which in turn will affect the voltage gradient. An iterative algorithm can solve this problem [22]. In this case, as a homeotropic alignment has been considered, the positive anisotropy of the permittivity gives the molecules a perpendicular position regardless to the applied voltage.…”