Polarization is an important characteristic in the optical field. Compared with the conventional holography, which only focuses on the amplitude and phase, polarization holography focuses more on the polarization state of the optical field in the hologram recording and reconstructing stages [1–4]. Polarization-sensitive material can record the polarization distribution of the interfering optical field. Some polarization-sensitive material has been developed [5–11]. The previous study on polarization holography is based on Jones’ theory [2,3], which can correctly describe the polarization state of a reconstructed wave under the condition of paraxial approximation.

In 2011, Kuroda et al. proposed a polarization holography theory described based on the tensor method [4], where the influence of the optical field on the optical properties of polarization-sensitive media is described by the dielectric tensor during exposure. The tensor polarization holography theory can correctly describe the amplitude, phase, and polarization of the reconstructed wave at an arbitrary interference angle. The dielectric tensor is expressed as

In 2012, Kuroda et al. researched the reconstruction characteristics of polarization holography and pointed out that the dielectric tensor coefficients $A$ and $B$ have opposite symbols [21]. In this Letter, based on the tensor polarization holography theory, we propose a method for measuring the exposure response coefficient $A/B$ of polarization sensitive media under various recording conditions. By this method, we studied the change of the dielectric tensor coefficient $A/B$ of the polarization-sensitive media PQ/PMMA (phenanthrenequinone-doped polymethyl methacrylate) [22] with the exposure energy.

The recording and reconstructing stages of the linear polarization wave are shown in Fig. 1. To simplify the description, the angle between the propagation directions of two recording waves inside the material is $\theta$ and the interference angle is $\theta = {\theta _ +} + {\theta _ -}.\,{{\textbf{G}}_ +},\,{{\textbf{G}}_ -},\,{{\textbf{F}}_ -}$, and ${{\textbf{G}}_F}$ represent the signal wave, the reference wave, the reading wave, and the reconstructed wave, respectively. The angle $\alpha$, $\beta$, and $\gamma$ of the linear polarization wave is the angle of the direction of the electric field from the $p$-polarization.

 

Fig. 1. Schematic diagram of polarization holography. (a) Recording stage and (b) reconstructing stage.

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As shown in Fig. 1(a), in the recording stage, two polarized waves interfere in the polarization-sensitive media and form a hologram, which records all the information of the signal wave. In the reconstructing stage, as shown in Fig. 1(b), the reading wave satisfying the Bragg condition irradiates the hologram and produces the reconstructed wave [3,4] as

As Eqs. (2) and (3) show, the reconstructed wave is still linearly polarized, and its polarization state is affected by $A$, $B$, $\theta$, $\alpha$, $\beta$, and $\gamma$. By controlling these values, we can control the polarization angle of the reconstructed wave. We define the linear polarization angle of the reconstructed wave obtained in the experiment as $\chi$. The ratio of the $s$-polarization to the $p$-polarization amplitude component in the reconstructed wave is $\tan \chi$. So Eq. (4) can be written as

As shown in Eq. (4), under general conditions, the polarization state of the reconstructed wave only depends on the $A/B$ value, not on $A$ and $B$ alone, and the values of $A$ and $B$ change with the exposure energy [4]. Therefore, the value of $A/B$ is defined as the exposure response coefficient of the polarization-sensitive media. Eq. (4) is recombined as

 

Fig. 2. Schematic diagram of experiment. SF, spatial filter; M, mirror; HWP, half-wave plate; PBS, polarization beam splitter; SH, shutter; PM, power meter.

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In the experiment, the diameter of the laser with a wavelength of 532 nm is extended to 5 mm along with the beam-extending system. Then, the beam goes through the first polarization beam splitter (PBS1) and splits into a signal path ($s$ branch) and a reference path ($p$ branch). We control the first half-wave plate (HWP1) to get the equal value (${81.5}\;{{\rm mW/cm}^2}$) in the signal wave and the reference wave. The 1.5 mm-thick PQ/PMMA sheets are prepared in our lab and used as the polarization-sensitive media in the experiment [22]. The refractive index of the PQ/PMMA material is 1.492. The interference angle of the two incident waves inside the material is 40°. By controlling the HWP2, the reference and reading waves are both $s$-polarization, while the polarization angle $\alpha$ of the signal wave is changed to 0°, 15°, 30°, 45°, 60°, 75°, and 90° in the experiment by controlling the HWP3. The experimental scheme is shown in Table 1.

Table 1. Recording and Reconstructing Stages of Linear Polarization Holography

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As shown in Table 1, when the polarization angle of the signal wave is 0° or 90°, i.e., the signal wave is $p$- or $s$-polarization, the reconstructed wave can be faithfully reconstructed for any $A/B$ value. When the signal wave is taken for other polarization angles, the polarization angle of the reconstructed wave will be affected by the $A/B$ value.

For this experimental scheme, the null reconstruction cannot occur in the reconstructing stage, so the influence of the polarized wave on the polarization-sensitive media during exposure can be fully expressed by the change of exposure response coefficient $A/B$. This experimental scheme can be applied to arbitrary interference angles and includes various recording conditions. Therefore, the exposure response coefficient $A/B$ measured in this way is convenient and reliable. For the experimental conditions shown in Table 1, Eq. (5) can be written as

In the experiment, the reading wave illuminates the hologram for a short time in order to observe the real-time response of the PQ/PMMA material with the polarized wave. The recording and reconstructing times are controlled by two shutters (SHs), SH1 and SH2. The recording time was 15 s, and the reconstructing time was 0.5 s. The reconstructed wave is split by the PBS2 and captured by the power meter (PM). The polarization angle $\chi$ of the reconstructed wave can be calculated by the light intensity values captured in the two PMs. The experimental result is shown in Fig. 3.

 

Fig. 3. Variation of polarization angle of the reconstructed wave with the exposure energy for the different linearly polarized signal wave, where polarization angles of the signal wave are 0°, 15°, 30°, 45°, 60°, 75°, and 90°.

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In Fig. 3, when the polarization angle of the signal wave is 90°, the experimental phenomena are consistent with Table 1. When the polarization angle of the signal wave is 0° and the exposure energy exceeds ${50}\;{{\rm J/cm}^2}$, the experimental phenomena are also consistent with Table 1. When the polarization angle of the signal wave is 0° and the exposure energy is between 0 and ${50}\;{{\rm J/cm}^2}$, the polarization angle of the reconstructed wave decreases rapidly from 53° to about 0.8°. The reason for these phenomena is that at the beginning, the hologram satisfying the theory of polarization holography has not been formed in the material. When the reading wave satisfying the Bragg condition is used to irradiate the partially formed hologram, the polarization angle of the reconstructed wave mainly depends on that of the reading wave. In the experiment, the polarization angle of the reading wave is 90°, which makes the signal wave with a polarization angle of 0° have a larger polarization angle of the reconstructed wave at the beginning of exposure.

Next, we studied the change of exposure response coefficient $A/B$ with the exposure energy under different recording conditions. From Fig. 3, we can know the polarization angle $\chi$ of the reconstructed wave. Then by Eq. (6), the change of the exposure response coefficient $A/B$ with the exposure energy under different recording conditions is shown in Fig. 4. It is worth noting that we cannot use Eq. (6) to determine the $A/B$ value when the polarization angle of the signal wave is 0° or 90°.

 

Fig. 4. Change of dielectric tensor coefficient $A/B$ with the exposure energy for the different linearly polarized signal wave, where polarization angles of the signal wave are 15°, 30°, 45°, 60°, and 75°.

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As shown in Fig. 4, under different recording conditions the values of $A/B$ change with the increase of exposure energy, and the range is 0.3–8.7. At the beginning of exposure, we find that the $A/B$ average values of the signal waves with different polarization angles are around 8.4, which indicates that the initial value of the exposure response coefficient of the PQ/PMMA material is about 8.4. When the exposure energy is approximately ${0} \text- {140}\;{{\rm J/cm}^2}$, the exposure response coefficient $A/B$ values show a similar downward trend under different recording conditions. This is due to the limited number of polarization-responsive molecules in the polarization-sensitive media, and they are quickly depleted. When the exposure energy exceeds ${140}\;{{\rm J/cm}^2}$, the number of polarization-responsive molecules in the polarization-sensitive media decreases gradually, and the effect of the exposure energy on the polarization characteristics of the hologram weakens gradually, so the value of the exposure response coefficient $A/B$ gradually becomes stable. The exposure response coefficient $A/B$ cannot be obtained by the aforementioned method when the polarization angle of the signal wave is 0° or 90°. Therefore, when polarization angle of the signal wave is closer to 0° or 90°, e.g., 15° or 75°, it is difficult for the value of $A/B$ to reflect the true change of the dielectric tensor with the exposure energy. So, as shown in Fig. 4, when the polarization angle of the signal wave is the middle value of 0–90°, i.e., 45°, its trend of $A/B$ is roughly the same as that of the average value.

In order to verify our measured exposure response coefficient $A/B$ values, we designed an experiment where the initial value of the exposure response coefficient $A/B$ of 8.4 is applied to realize the null reconstruction of the linear polarization wave. The experiment is to make the amplitude of the $s$- and $p$-polarization components zero in Eq. (2). For convenience, we still use the experimental setup, as shown in Fig. 2. As shown in Table 2, we give the values of $A/B$, $\theta$, and $\alpha$. Through Eq. (2), we determine the values of $\beta$ and $\gamma$.

Table 2. Theoretical Calculation of the Conditions Required for Null Reconstruction of Linear Polarization Wave, where ${A/B} = {8.4}$

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In the recording stage, the polarization angles of the signal and reference waves are 25° and 113°, respectively. The polarization angle of the reading wave is 165° in the reconstructing stage. The diffraction efficiency is the ratio of the reconstructed wave intensity to the reading wave intensity. The experimental result is shown in Fig. 5.

 

Fig. 5. Diffraction efficiency of the reconstructed wave with exposure energy.

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As shown in Fig. 5, the maximum diffraction efficiency is 0.005 at ${800}\;{{\rm J/cm}^2}$ exposure energy. Such low diffraction efficiency indicates that the linearly polarized wave achieves null reconstruction. However, the data is obtained by reading the hologram with a 165° polarization angle. Whether other polarization angles can achieve a lower diffraction efficiency needs verification. When the exposure energy is ${108.4}\;{{\rm J/cm}^2}$, we quickly restore the fast axis of the HWP2 to the horizontal direction, then rotate it 90°. The rotation direction is shown in Fig. 2. Currently, the polarization angle of the reading wave changes from 0° to 180°. The experimental result is shown in Fig. 6.

 

Fig. 6. Diffraction efficiency of the reconstructed wave with the polarization angle of the reading wave.

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As shown in Fig. 6, when the polarization angle of the reading wave is 161°, the diffraction efficiency of the reconstructed wave is the lowest, which is close to 165° of the theoretical value. The difference may be due to the following fact. Since the exposure response coefficient $A/B$ changes with the exposure energy, it is difficult to guarantee that $A/B$ is just at 8.4 in the experiment.

In this work, based on the tensor polarization holography theory, a method for measuring the dielectric tensor coefficient of polarization-sensitive media using linear polarization wave is proposed. The initial value of the exposure response coefficient $A/B$ of the PQ/PMMA is about 8.4. Based on this initial value, the null reconstruction of the linear polarization wave is achieved. This method is helpful for measuring the exposure response coefficient of polarization-sensitive media and for controlling the polarization state of the reconstructed wave. Additionally, the PQ/PMMA materials used in this Letter are prepared by the same manufacturing process. Preliminarily experiments have found that different preparation processes of the PQ/PMMA material will change the initial value of $A/B$. Next, we will study this aspect and suggest the work needed to improve holographic storage density [23,24] using polarization holography.