Polarization holography is the superposition of differently polarized beams. Due to its ability to record the polarization states, some extraordinary optical phenomena were found in the polarization holography. For example, the recently reported null-reconstruction phenomenon in polarization volume hologram is odd for the conventional holography which only records the amplitude and phase. In this paper, we perform a thorough investigation of the null reconstruction of polarization hologram recorded by orthogonal circularly polarized waves. To explore the mechanism behind this phenomenon, an interferometry was built to measure the phase difference between the same polarized components within the reconstructed wave. The phase difference of π was secured in our experiment, indicating a destructive interfering effect, which nicely explains the extraordinary null reconstruction observed in the polarization hologram.
© 2016 Optical Society of America
Polarization holography is the coherent interference of the beams that can have the different polarized states . 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 , 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 , 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.
3. Ensure the condition of null reconstruction (α + β = 0)
In our experiment, the two orthogonal circular polarizations, i. e., , , were used to record the hologram. Using the original (R) and orthogonal () reference polarizations to read the hologram, the reconstructed beams and could be written as,Eq. (2) we could find that, in the case of non-paraxial approximation, the ENR () only takes place in the condition of α + β = 0. Therefore, the first step is to lock the polarization hologram at the status of α + β = 0.
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.
In Eq. (1), the coefficient of component sO-ipO 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 sO-ipO 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 (sO-ipO) of the reconstructed wave decreased to the minimum, indicating that the condition of α + β = 0 for ENR was satisfied.
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 is used to read the hologram. The most straightforward way is to decompose the into two linearly polarized beams sR- and ipR- and then analyze the correlations between the two reconstructions. In the case of α + β = 0 when ENR occurs, using sR- and ipR- 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 sR and pR, that is to say, instead of sR and ipR, the two linearly polarized reading waves should be sR and eiφpR, where φ is the actual delay between sR and pR. Using eiφpR 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, eiφpR and sR, 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 and . 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 and . Similarly, a 45° -orientation linearly polarized wave was generated by P3 to interfere with the directly transmitted sR and eiφpR. 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.
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.
We have systematically investigated the extraordinary null reconstruction in polarization volume hologram. By decomposing the reading wave into s and eiφp 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.
This work is supported by a grant from the National Natural Science Foundation of China (Grant No. 61475019 and 61205053).
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