1. Introduction

Polarization holography is the coherent interference of the beams that can have the different polarized states [1]. Besides amplitude and phase, polarization is additionally recorded in such materials that have the polarization-sensitive molecular orientations [2–11]. Due to its ability to record polarization, polarization holography has invoked much interest and experienced continuously developments both in theory and experiments since its discovery.

The early-stage theory of polarization holography is based on Jones matrix [12,13], where the paraxial approximation is assumed. As a result, the theory is only valid for the geometry of interfering beams with a small crossing angle. In recent years, a new tensor theory of polarization holography, i. e., the response of a polarization hologram can be expressed as the tensor product of the total electric field [14], was proposed to eliminate the limit of paraxial approximation. Thanks to this theory, the research of polarization holography has been greatly accelerated [15–17]: Not only the recording angle expands from small (< 5°) to arbitrary ones, but also the polarization states of the interfering beams evolve from linear to complex polarizations. Very recently, an extraordinary null reconstruction (ENR) of polarization hologram [18], recorded by two orthogonal circular polarizations at large crossing angle, was observed in our experiment.

In this paper, we will perform a thorough investigation of the ENR phenomenon in polarization hologram, exploring its physical conditions. Aiming at the physical mechanisms that rule the ENR, an interferometry was built to analyze the interfering effects within the reconstructed waves. The experiments secure a phase difference of π (destructive interference) between the same polarization components in the reconstruction, which is consistent with our theoretical expectations.

2. Polarization-sensitive materials

Phenanthrenequinone-doped poly(methyl methacrylate(PQ/PMMA) photopolymer is the material used in our experiment due to its sensitivity to polarization [19–21]. For PQ/PMMA, methyl methacrylate (MMA) solution, azo-bis-isobutyronitrile(AIBN), and phenanthrenequinone(PQ) were used as the monomer, the thermo-initiator, and the sensitizer, respectively. We made the material under the temperature of 333K and the saturation concentration of AIBN and PQ dissolved in MMA solution we chose were 0.4% and 0.8%, respectively. After uniformly mixing the raw materials, we put the materials into a ultrasonic cleaner(JR-120D) at the temperature of 333K for 1.5 hours to make the solution mixed thoroughly. Then, we placed the solution in a dying oven(DGX-9003) to make it viscous and the temperature was set at 333K. Subsequently, we poured viscous solution into a container and put it in the drying oven of 333K again for about 20 hours to complete the polymerization process. Finally, the container was put into a freezer for an hour to stop the polymerization reaction. The sample was took out from the container and covered with tinfoil to block the light. The size of the sample is 50 × 40 × 1(W × L × H) mm³.

To confirm the polarization-sensitivity of the home-made material, we measured its photo-anisotropy spectrum within the wavelength range of 600-820 nm by using an ellipsometer (J.A. Woollam Company VASE). Before exposure, the molecules were randomly distributed in all directions in the material. As shown in Fig. 1(a), the material was isotropic, since there was no retardance between the polarizations. After the material being exposed by s-linearly polarized beam at the wavelength of 473nm for about 10 minutes, the orientations of molecules were modulated by the polarization and an obvious spectral curve of phase-retardance between s and p polarizations, shown in Fig. 1(b), solidly guarantees the material being changed from isotropic to anisotropic.

 

Fig. 1 The photo-anisotropy of the material (a) before and (b) after exposure. Insets: the status of molecules before and after exposure.

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3. Ensure the condition of null reconstruction (α + β = 0)

In our experiment, the two orthogonal circular polarizations, i. e., $O=\frac{1}{\sqrt{2}}(s_O+i{p}_O)$, $R=\frac{1}{\sqrt{2}}(s_R-i{p}_R)$, were used to record the hologram. Using the original (R) and orthogonal ($\overline{R}$) reference polarizations to read the hologram, the reconstructed beams $S$ and $\overline{S}$ could be written as,

A laser at the wavelength of 473 nm was used to record and reconstruct the hologram (see Fig. 2). The beam reflected from PBS1 served as signal beam, and it was regulated to left-handed circular polarized beam by P1 and QWP1. Likewise, the beam transmitted through PBS1 was regulated to right-handed circular polarization by using P2 and QWP2. The signal and reference beams were plane waves and the intensity ratio of them was 1:1. They were incident in the common plane with the crossing angle of θ≈42°(non-paraxial approximation). The diameter of the beam exposed on the material was about 6-mm, and the power density was 13.35mW/cm². The left- and right-handed circularly polarized components of the reconstructed beam could be regulated to p- and s-linearly polarized beams by using QWP3 and PBS2. The intensity of each component could then be respectively measured.

 

Fig. 2 Experimental setup of polarization holography based on the orthogonal circularly polarized wave: BE, beam expander; HWP, half-wave plate; QWP, quarter-wave plate; BS, beam splitter; PBS, polarization beam splitter; M, mirror; P, polarizer. Inset: schematic of the recording and reading process.

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In Eq. (1), the coefficient of component s_O-ip_O is 1/4(α + β)(1-cos²θ). Thus, the large crossing angle θ≈42° in our experiment setup guarantees that α + β = 0 can be secured when the intensity of component s_O-ip_O in the reconstruction goes to zero. Figure 3 shows the intensity of left- and right-handed circularly polarized components of the reconstructed beam that was reconstructed by the original reference beam. After about 100s’ exposure, the right-handed circularly polarized component (s_O-ip_O) of the reconstructed wave decreased to the minimum, indicating that the condition of α + β = 0 for ENR was satisfied.

 

Fig. 3 The intensity of the component s_O-ip_O in the reconstructed beam. The intensity drops down to the minimum at the exposure time of 100 s, indicating the status of α + β = 0 being secured in the material.

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4. Explore the ENR through an interferometry

From Eq. (2), we get to know that ENR takes place in the hologram at α + β = 0, when $\overline{R}=s_R+i{p}_R$is used to read the hologram. The most straightforward way is to decompose the $\overline{R}$ into two linearly polarized beams s_R- and ip_R- and then analyze the correlations between the two reconstructions. In the case of α + β = 0 when ENR occurs, using s_R- and ip_R- to read the hologram, the two reconstructions are written as,

The opposite sign of the coefficients shows a phase difference of π between the same polarizations in the two reconstructions, indicating a destructive interference that leads to ENR. However, in the practical interferometry, it is difficult to guarantee an exact π/2 phase delay between s_R and p_R, that is to say, instead of s_R and ip_R, the two linearly polarized reading waves should be s_R and e^iφp_R, where φ is the actual delay between s_R and p_R. Using e^iφp_R to read the hologram, the reconstruction of hologram at α + β = 0 is expressed as,

Comparing Eq. (3) and Eq. (5), the phase difference between the same polarizations are φ + π/2. Since φ is not precisely controlled, our strategy is to measure both φ + π/2 and φ through two isolated interference patterns. If the values of φ obtained from two interferences agree with each other, the phase difference of φ + π/2 between the same polarizations can thus be verified.

As shown in Fig. 4, two linearly polarized waves, e^iφp_R and s_R, respectively transmitted through upper-open aperture 2 and lower-open aperture 3. A linear polarization s was generated by P4 to interfere with the reconstructed waves ${\underset{¯}{S}}_{{\sout{e}}^{\underset{¯}{i\phi }}\overline{PR}}$ and ${\underset{¯}{S}}_{\sout{S}\sout{R}}$. Demonstrated in Fig. 5a, the displacement of upper and lower fringes captured by CMOS 1 records the phase difference φ + π/2≈π/2 between s components in ${\underset{¯}{S}}_{{\sout{e}}^{\underset{¯}{i\phi }}\overline{PR}}$ and ${\underset{¯}{S}}_{\sout{S}\sout{R}}$. Similarly, a 45° -orientation linearly polarized wave was generated by P3 to interfere with the directly transmitted s_R and e^iφp_R. As expected, almost no displacement, shown in Fig. 5b, is found between the upper and lower fringes captured by CMOS 2, again verifying φ≈0.

 

Fig. 4 Experimental setup of simultaneous reconstructions by s and e^iφp linearly polarized beams: BE, beam expander; HWP, half-wave plate; QWP, quarter-wave plate; BS, beam splitter; PBS, polarization beam splitter; M, mirror; P, polarizer.

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Fig. 5 Interference patterns on (a) CMOS1 and (b) on CMOS2

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The values of φ measured by two interferences being nicely in agreement with each other, solidly guarantee the phase difference of φ + π/2 between the same polarizations in Eq. (3) and Eq. (5). Therefore, at φ = π/2, i. e., using circular polarization to read the hologram, a π- phase destructive interference is proved to bring the ENR phenomenon.

5. Conclusion

We have systematically investigated the extraordinary null reconstruction in polarization volume hologram. By decomposing the reading wave into s and e^iφp linear polarizations, the phase difference of φ + π/2 between the same polarizations in the reconstructed wave was experimentally verified. At this stage, it is safe to conclude that, at the status of α + β = 0, ENR only occurs in such polarization hologram when using circular polarization as the reading wave. Because only the circular polarization with φ = π/2 provides the π-phase destructive interference effect that is able to generate the ENR. In the following work, the recording and reading waves will be extended to more complex polarization states and some other interesting phenomenon may be discovered at the status of α + β = 0.