IPhO 2003, Експеримент — Задача 3. Part C Optical Properties of Nematic Liquid Crystal : Electro-optical switching characteristic of parallel aligned LC cell

The 34th International Physics Olympiad — Taipei, Taiwan — Experimental Competition — Wednesday, August 6, 2003 · 6 август 2003 г. · 7,5 т.

Условие

I. Introduction

Homogeneous Parallel-aligned LC Cell

For a parallel-aligned LC cell, the directors in the front and back substrates are parallel with each other, as shown in Fig. 10. When a linearly polarized light impinges on a parallel-aligned cell with its polarization parallel to the LC director (rubbing direction), a pure phase modulation is achieved because the light behaves only as an extraordinary ray.

On the other hand, if a linearly polarized light is normally incident onto a parallel aligned cell but with its polarization making $\theta = 45^{o}$ relative to the direction of the aligned LC directors (Fig. 11), then phase retardation occurs due to the different propagating speed of the extraordinary and ordinary rays in the LC medium. In this $\theta = 45^{o}$ configuration, when the two polarizers are parallel, the normalized transmission of a parallel aligned LC cell is given by

The phase retardation $\delta$ is expressed as

where $d$ is the LC layer thickness, $\lambda$ is the wavelength of light in air, $V$ is the root mean square of applied AC voltage, and $\Delta n$, a function of $\lambda$ and $V$, is the LC birefringence. It should be also noted that, at $V = 0$, $\Delta n\ (= n_e - n_o)$ has its maximum value, so does $\delta$. Also $\Delta n$ decreases as $V$ increases.

In the general case, we have

where // and $\perp$ represent that the transmission axis of analyzer is parallel and perpendicular to that of the polarizer, respectively.

II. Experiments and procedures

1. Replace NB $90^{\circ}$ TN LC cell with parallel-aligned LC cell.

2. Set up $\theta = 45^{\circ}$ configuration at $V = 0$ as shown in Fig. 11. Let the analyzer’s transmission axis perpendicular to that of the polarizer, then rotate the parallel-aligned LC cell until the intensity of the transmitted light reaches the maximum value ($T_{\perp}$). This procedure establishes the $\theta = 45^{\circ}$ configuration. Take down $T_{\perp}$ value, then, measure the intensity of the transmitted light ($T_{//}$) of the same LC cell at the analyzer’s transmission axis parallel to that of the polarizer (also at $V = 0$).

C-(1) Assume that the wavelength of laser light 650 nm, LC layer thickness 7.7 μm, and approximate value of $\Delta n \approx 0.25$ are known. From the experimental data $T_{\perp}$ and $T_{\parallel}$ obtained above, calculate the accurate value of the phase retardation $\delta$ and accurate value of birefringence $\Delta n$ of this LC cell at V=0. [2,5 т.]

3. Similar to the above experiment (1), in the $\theta = 45^{\circ}$ configuration, apply 100 Hz square wave voltage using a function generator onto the ITO portions of two glass substrates, vary the applied voltage ($V_{rms}$) from 0 to 7 Volts and measure the electro-optical switching curve ($T_{\parallel}$) at the analyzer’s transmission axis parallel to the polarizer’s transmission axis. (Hint: Measuring the $T_{\perp}$ switching curve is helpful to increase the data accuracy of the above $T_{\parallel}$ measurement; the data of $T_{\perp}$ are not needed in the following questions. )

* In the crucial turning points, take more data if necessary (especially in the range of 0.5-4.0 Volts).

C-(2) Measure, tabulate, and plot the electro-optical switching curve for $T_{\parallel}$ of this parallel aligned LC cell in the $\theta = 45^{\circ}$ configuration. [3 т.]

C-(3) From the electro-optical switching data, find the value of the external applied voltage $V_{\pi}$.

Hint: * $V_{\pi}$ is the applied voltage which enables the phase retardation of this anisotropic LC cell become $\pi$ (or $180^{\circ}$).

* Remember that $\Delta n$ is a function of applied voltage, and $\Delta n$ decreases as V increases.

* Interpolation is probably needed when you determine the accurate value of this $V_{\pi}$. [2 т.]

Отговори

Решение

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