Viernes 14

10ª Reunión Española de Optoelectrónica, OPTOEL17

- 158 - F.J. MARTÍNEZ et al.

Modeling parallel aligned liquid crystal devices

Francisco J. MARTÍNEZ (1,2), Andrés MÁRQUEZ (1,2), Sergi GALLEGO(1,2), Jorge FRANCÉS(1,2), Victor NAVARRO-FUSTER(2), Inmaculada PASCUAL(2,3), Augusto

BELÉNDEZ(1,2)

1. Departamento de Física, Ingeniería de Sistemas y Teoría de la señal, Universidad de Alicante, Crta. San Vicent del Raspeig s/n

2. Instituto Universitario de Física Aplicada a las Ciencias y las Tecnologías, Universidad de Alicante, Crta. San Vicent del Raspeig s/n

3. Departamento de Óptica, Farmacología y Anatomía, Universidad de Alicante, Crta. San Vicent del Raspeig s/n

Contact name: Martínez, F. J. (fj.martinez@ua.es).

ABSTRACT:

The Parallel Aligned Liquid Crystal microdisplays (PA-LC) has become a widely used device for optics and photonics applications. In this work we propose a PA-LC model that allows us to predict the device performance in a wide range of incidence angles and for any wavelength in the visible.

From a reduced amount of measurements we apply a reverse engineering process that re-veals some important parameters related with the manufacturing of the device. This knowledge eases the design of our photonic application or experiment, and it serves us to analyze the physics and dynamics of PA-LC cells since we can infer the LC molecules tilt angle as a function of applied voltage.

Key words: Liquid-Crystal devices, Parallel-Aligned, Photonics, Modeling, Birefringence, Spatial Light Modulators, Displays.

1.- Introduction

Liquid crystal (LC) devices are widely used in optics and photonics[1,2]. One of the common uses is in Spatial Light Modulation (SLM) applications, where the parallel-aligned geometry enables phase-only opera-tion scheme without amplitude modulationcoupling [3,4].

We developed a characterization method based on time-average Stokes polarimetry [5], with this method we can obtain the retardance value introduced by a variable retarder even if it presents some flicker in the introduced retardance. This method can be applied to electro-optic devices such as liquid crystal on silicon (LCoS) displays, and it provides robust and precise measurements.

If we know the different parameters that characterize the LC, (such as ordinary and

extraordinary refractive indices, cell gap, pre-tilt angle, refraction index of the glass used, viscosity, etc.) we can make accurate calculations of the performance of our LC-cell [2,6]. But, in most of the cases users do not have access to these parameters. We can use a simplified model or reverse-engineering approach to enable some analyt-ical expressions [7].

In the present work we propose and demons-trate a novel physical model using a reverse-engineering approach. This model is able tocalculate the linear retardance as a function of applied voltage, and it works for different incidence angles and wavelenghts. The mo-del is based on three physical parameters whose values are obtained without ambigui-ties by fitting a limited amount of calibration measurements obtained with the time-

10ª Reunión Española de Optoelectrónica, OPTOEL17

- 159 - F.J. MARTÍNEZ et al.

average Stokes polarimetry method presented in a previous work [5].

2.- Modeling PA-LCoS

A PA-LC cell can be considered as a portion of LC sandwiched between a mirrored back-plane and a glass front window.

Fig. 1: Diagram for the PA-LC cell used in the model proposed.

In figure 1 we show the scheme of the PA-LC considered in our model. We consider a reflective cell with a cell gap d. Incidence plane and LC director are along the XZ plane. LC molecules present an angle be-tween their director axis and the light beam direction of propagation. The refraction angle in the LC medium is LC. The only voltage dependent magnitude is the angle , that it is the tilt of the director axis with respect the entrance face. Since the PA-LCoS are reflec-tive devices, at the backplane the light beam will be reflected and it will travel along the cell again. This effect will be added and it is equivalent to a forward propagation at an angle - inc.

As users, in order to use this model, we do not know most of this parameters, such as the ordinary (no) and extraordinary (ne) refractionindexes of the LC used, and the cell gap d. To avoid this lack of knowledge we define two off-state parameters that are a combina-tion of these parameters. They are OPL=dno

and , which correspond respective-ly to the magnitudes of the optical path length for the ordinary component and the optical path difference between extraordinary and ordinary components.

=( )

( )1 (1)

The retardance ( ) introduced is calculated using equation (1), where angle is given by,

( , ) = + ( ) ( ) (2)

, the minus (plus) sign applies for the for-ward (backward) propagation. A proper deri-vation of this expressions can be found in [8].

2.1.- Results

In this work we consider a commercially available PA-LCoS microdisplay, model PLUTO distributed by the company HOLOEYE. It is filled with a nematic liquid crystal, with 1920x1080 pixels and 0.7" di-agonal. The retardance measurements are obtained applying the time-average Stokes polarimetric technique described in [5]. With this technique, we obtain the retardance measurements at 3º, 23º, 35º and 45º incident angles, and the retardance with the microdisplay plugged off (off-state). We will use the measurements taken at 3º and 35º for obtaining the OPD and OPL parameters, and the measurements at 23º and 45º will be used to analyze the predictive capability of the proposed model [8]

We minimize the quadratic difference bettween the proposed model, defined by equations (1) and (2) for the off-state, and with no pre-tilt angle, ; and the exper-imental data obtained with average Stokes polarimetric technique.

Once, OPD and OPL are obtained from the off-state data, then we can obtain the relation from the on-state data. To do that we minimize the quadratic retardance differenceas before, but this time for every gray level and considering OPD and OPL as constants.

10ª Reunión Española de Optoelectrónica, OPTOEL17

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Fig. 2: Experiment (dots) and theoretical fit-ting with the proposed (dashed line) and the reference(continuous lines) models for the wavelengths 473, 532 and 633 nm. (a) inci-dence angle of 3º and (b) incidence angle of 35º.

In figure 2 we see the results obtained and their comparison with the experimental data. We show the results from the proposed mo-del, the one where we calculate OPD and OPL, and the reference model that it is the one obtained without coupling the unknown variables, that means calculating d, no and ne

separately, that we further introduce in [8].The reference model, as we can see in the figure, adjusts fine. However, it leads us to different solutions depending on the starting values assigned to the parameters [8], thus it does not give us physical information on the LC-cell. Proposed model is more consistent and provides unique non-ambiguous valuesabout OPD and OPL parameters, that are related with physical information, regardless the starting point used to perform the mini-mization process.

The results are in good agreement for the three wavelengths used. From this on-state adjustment we can extract the relation be-tween gray level and the tilt angle of the LC-molecule. Figure 3 shows this relation for the proposed and reference model. As in figure 2

the difference between the two model are minimal. The reference model does not have a better performance when compared with the proposed model, probably due to the various effects not taken into account, like multiple internal reflection, pretilt angle, Fresnel coefficients at the interfaces, or in-homogeneous LC director orientation when a voltage is applied (on-state).

Figure 3 shows a non linear relation between gray level and tilt angle. This is designed to produce a linear retardance response versus gray level as shown in figure 2, and it is pro-grammed in the device driver.

Fig. 3: Tilt angle as a function of gray level obtained when applying the reference and the proposed model.

With all these information obtained: OPD, OPL and the relation between Gray level and Tilt angle, we can predict the performance of the display for others incident angles.

10ª Reunión Española de Optoelectrónica, OPTOEL17

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Fig. 4: Experiment (dots) and prediction for the retardance vs tilt angle for incidences at 23º(a) and 45º(b).

In figure 4 we show the results obtained for the retardance as a function of tilt angle for the incidences angles of 23º (figure 4a) and45º (figure 4b). The predicted results are compared with the experimental results for the three wavelengths used.

In addition, we can predict the retardance range for different incidence angles and for a wide range of wavelengths. We used the extended Cauchy [9] relation to fit the OPD parameter and a linear interpolation to fit OPL.

Fig. 5: Theoretical simulations of the retardance dynamic range vs wavelength for three different incidence angle.

In figure 5 we can see how the dynamic range is affected by changing the incidence angle and the wavelength used in our exper-iments. This will allow us to predict the per-formance of our PA-LCoS microdisplay or even design our future experiments.

3.- Conclusions

We have presented and validated a proposed semi-physical model for PA-LC cells that can be used to predict the performance of our displays in an specific experiment.

It is remarkable that all the information ex-tracted is originated from a very easy to im-plement characterization method as the aver-age stokes polarimetry presented in a previ-ous work [5]

Acknowledgements: This work has been sup-ported by Ministerio de Economía y Competitividad of Spain (projects FIS2014-596100-C02-1-P and FIS2015-66570-P), and Generalitat Valenciana of Spain (projectPROMETEOII/2015/015).

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