1. INTRODUCTION

Polarization gratings (PGs) are diffractive elements composed of an in-plate, linearly varying optical anisotropy, which act as polarizing beam splitters [1,2]. Unlike conventional gratings, they affect the local polarization state of light passing through them, called a geometric-phase effect [3–5], which can be caused by optical anisotropy [6,7] or nanostructures within a metasurface [8–10]. There are several methods to create a PG with a first grating period, including holography [11–14], proximity [15–18] or projection [9] lithography of a single mask, and nanoimprinting [19]. However, each of these methods must be reconfigured in order to create a second grating period, which can involve a significant time delay or the substitution of potentially expensive optical elements or both. As such, several other methods have been developed that can easily change the grating period, including direct-write laser scanning [20,21], spatial-light-modulator imaging [22], and microrubbing [23,24]. Unfortunately, these methods require substantial up-front equipment cost. What is missing is a simple method that can create a wide range of PG grating periods with little or no change in the setup.

In this paper, to the best of our knowledge, we suggest a new technique to fabricate PGs, enabling both easy tuning of the grating period and arbitrarily large periods. Moreover, the setup is very compact and solid, so that it is more robust to the vibration compared to other approaches. This technique can also be easily scaled for large-area recording while maintaining the size of the setup.

2. BACKGROUND

The most popular approach to record PGs has been to use a photo-alignment layer (PAL) [25] exposed via polarization holography, creating a linearly varying optic axis orientation angle in a subsequently applied liquid crystal layer. In this method, the PG pattern can be recorded in the PAL by interfering two orthogonal, circularly polarized beams, as shown in Fig. 1(a). While the intensity of the interference is constant, the electric field pattern is not, composed of linear polarization everywhere with an orientation that varies linearly along one dimension. The PAL therefore captures this linearly polarized standing wave, which has a repeat unit $\mathrm{\Lambda }$, called the grating period, following

 

Fig. 1. Holographic approach. (a) PG profile created by an interference of two beams orthogonally circularly polarized: right-handed circularly polarized (RCP); left-handed circularly polarized (LCP). (b) A layout of conventional holography setup to create the PG profile, which includes mirrors (M), beam splitter (BS), and quarter-wave plates (QWP).

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One significant drawback of the conventional approach is the practical upper limit of realizable $\mathrm{\Lambda }$, e.g., periods $\mathrm{\Lambda }\gg 20\mathrm{\mu m}$. Periods larger than this are often desired for PGs in nonmechanical beam steering devices [26,27]. As shown in Eq. (1), the period created by the holographic interference is a function of the half-angle $\theta$. To set the angle, the two recording beams have to be recombined at the sample at a distance away from the beam splitter. But very long distance is required to set a small angle, which results in a large period of the PG, since the distance scales according to the angle. For example, the setup requires more than 10 m distance to record a 100 μm period within a 25 mm active area, which is not usually feasible. Moreover, due to the large number of elements involved, the complexity, volume, and cost of this recording setup increases exponentially with the recording area (i.e., sample size). Additionally, a significant realignment of the setup is required to adjust $\theta$ while at the same time ensuring a high-quality polarization state of the beams, which is essential to achieve the desired period with good quality of the recording pattern.

3. OPERATION PRINCIPLE

The recording process described here brings together two prior concepts. The first aspect of the approach is the use of a PG as a template to create a subsequent replica. This has been demonstrated with a single grating [15–18] used as a polarizing beam splitter to generate orthogonally circularly polarized beams. The output beams interfere and create a spatially varying linear polarization pattern as being similar to the conventional holography approach. The second concept is the use of two rotating gratings stacked over each other to control the output beam angle [28,29]. The two gratings optimized for a predetermined design wavelength can make any output angle within a field of view as their grating axes are rotating.

The essence of the new setup is using these two concepts to achieve two orthogonally circular outputs and to tune an angle of the outputs. This can be done as simply rotating two gratings (i.e., mask PGs), as shown in Fig. 2(a). The mask PG is designed to have half-wave retardation at the recording wavelength ${\lambda }_0$ to split nearly 100% of the linearly polarized light into two first orders with equal power. Therefore, the linearly polarized laser light can be split into two orthogonally circularly polarized beams by the first mask PG, as shown in Fig. 2(b). Then, the two circular output beams pass through the second mask PG, which redirects each beam with almost 100% efficiency with a splitting angle $\mathrm{\Theta }$, as shown in Fig. 2(c).

 

Fig. 2. Dual rotating mask approach described here. (a) A schematic of the setup with two rotating masks: ${\mathrm{\Psi }}_1$ and ${\mathrm{\Psi }}_2$ are azimuthal rotating angles of the masks. (b) Two orthogonal circular outputs from a single mask PG: ${\theta }_d={\sin }^{-1}({\lambda }_0/\mathrm{\Lambda })$. (c) Output from the two mask PGs generating splitting angle $\mathrm{\Theta }$.

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Here we select the grating period ($\mathrm{\Lambda }$) of the mask PGs to be the same (i.e., the same diffraction angle, ${\theta }_d$). When these two mask PGs are aligned close to parallel (e.g., ${\mathrm{\Psi }}_1-{\mathrm{\Psi }}_2\approx 180°$), the angle between the output beams can be very small (e.g., $\mathrm{\Theta }\approx 0$), which leads to a very large grating period. At the other extreme, when the mask PGs are aligned antiparallel [26] to each other (e.g., ${\mathrm{\Psi }}_1={\mathrm{\Psi }}_2$), the output beams have the maximum angle (e.g., $\mathrm{\Theta }\approx 2{\theta }_d$), where ${\theta }_d$ is diffraction angle of the mask PG. This determines the smallest grating period achievable in this configuration. In this manner, the setup can easily create various grating periods between these two extremes by controlling the relative grating orientation of the two mask PGs.

The diffraction behavior of a single grating at normal incidence can be easily described by the grating equation. However, diffraction from multiple gratings for oblique incidence is more complex because the angle relationship is nonlinear. Therefore, it is often convenient to introduce the direction cosine space where diffraction can be represented as a simple, linear vector [30]. Figure 3 shows the operation principle of the setup with the vector representation. The projections of the propagation vectors in the $x-y$ plane for both the diffracted orders from the first mask PG with its grating vector at an angle ${\mathrm{\Psi }}_1=\varphi$ with respect to the $x$ axis, are represented by ${\mathbf{G}}_1^R$ and ${\mathbf{G}}_1^L$ in Fig. 3(a). Now consider the second mask PG alone whose grating vector is at ${\mathrm{\Psi }}_2=180°-\varphi$ with respect to the $x$ axis. The diffracted orders from this PG can be represented similarly by vectors ${\mathbf{G}}_2^R$ and ${\mathbf{G}}_2^L$, respectively, as shown in Fig. 3(b). When these two PGs are arranged after each other, the exiting diffracted orders can be simply represented by ${\mathbf{G}}^R={\mathbf{G}}_1^R+{\mathbf{G}}_2^R$ and ${\mathbf{G}}^L={\mathbf{G}}_1^L+{\mathbf{G}}_2^L$, as shown in Fig. 3(c). Note that in this situation, ${\mathbf{G}}^R$ and ${\mathbf{G}}^L$ are identical in magnitude but are pointed in the opposite direction. The direction cosines of these beams are given by

 

Fig. 3. Operation principle of the setup with the vector representation in direction cosine space: (a) input beam separation (${\mathbf{G}}_1^R$, ${\mathbf{G}}_1^L$) by the first mask; (b) redirection (${\mathbf{G}}_2^R$, ${\mathbf{G}}_2^L$) of the beams by the second mask; (c) output beams (${\mathbf{G}}^R$, ${\mathbf{G}}^L$) described as vector sum.

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Figure 4 shows the splitting angle and the recorded grating period ${\mathrm{\Lambda }}_{\text{replica}}$ for different grating orientations $\varphi$ of the mask PG. We assume the diffraction angle ${\theta }_d$ of the mask is 2.5° at the recording wavelength ${\lambda }_0$, 325 nm. Note that the maximum splitting angle $\mathrm{\Theta }$ is nearly double of the diffraction angle when the two mask PGs are aligned antiparallel to each other. The net angle decreases as $\varphi$ increases, and closes to zero when the PGs are aligned parallel to each other. Moreover, a grating period of the replicated PG increases with $\varphi$, as shown in the same plot.

 

Fig. 4. Splitting angle ($\mathrm{\Theta }$) and corresponding grating period (${\mathrm{\Lambda }}_{\text{replica}}$) of the replicated PG for different grating orientations ($\varphi$) of the mask when ${\theta }_d=2.5°$ and ${\lambda }_0=325\mathrm{nm}$.

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4. EXPERIMENTAL RESULTS

We first fabricated mask PGs using conventional holography setup and commercial materials. The period of the mask was 7.5 μm, which corresponds to a 2.5° diffraction angle at 325 nm. We used the material LIA-C001 (DIC Corporation, Japan Ltd.) as a PAL and reactive LC prepolymer mixture RMS-E ($\mathrm{\Delta }n=0.25$ at 589 nm, Merck Chemicals, Ltd.) to form the grating structure. The masks were formed on 1 mm thick, 50 mm diameter round glass substrates, using spin coating. The thickness of the LC layer was adjusted by the spin coating to achieve half-wave retardation at the recording wavelength. To minimize reflection loss, the mask PGs were fabricated on antireflection coating substrates (PG&O), and they were laminated with the same substrate with optical glue (NOA-63, Norland).

Then, we built the new exposure setup using the mask PGs. The mask PGs were placed next to each other as mounted on two rotation mounts, as shown in Fig. 5. The input beam laser (He–Cd, 325 nm) was expanded and collimated to 25 mm diameter as passing through several optics (not shown in the figure). For large-area exposure, additional optics can be placed before the setup to make the output diverging. We have studied the impact of the diverging input on a variation of the grating period [31]. The sample was prepared with PAL coating (LIA-CO01) and placed close to the setup.

 

Fig. 5. Recording setup with the two mask PGs mounted on rotation mount. Inset, output beam overlap at the sample plane when (a) $\varphi =89°$, $\mathrm{\Theta }=0.1°$; (b) $\varphi =60°$, $\mathrm{\Theta }=2.5°$; (c) $\varphi =0°$, $\mathrm{\Theta }=5.0°$.

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We used various setup parameters to form the PG structure and created different grating periods. The inset pictures of Fig. 5 show overlapped output beams at the sample plane, which were captured by a UV fluorescence card. They show three representative cases where the masks are aligned (a) parallel, (c) anti-parallel, and (b) in-between. When the masks are aligned almost parallel (${\mathrm{\Psi }}_1-{\mathrm{\Psi }}_2\approx 180°$) to each other, for example, the output beams create a small splitting angle ($\mathrm{\Theta }\approx 0°$), which brings a small offset of the beams, as shown in Fig. 5(a). Then, the beams can record a large grating period as we expected in Fig. 4. The opposite case is shown in Fig. 5(c), where the output beams create the largest splitting angle, which accordingly records the smallest grating period of the replicated PG.

Using the new exposure setup, we created the PG pattern on the sample. The sample was prepared with the same PAL as the mask PG. By controlling the rotation angle $\varphi$ of the setup, we could easily tune the splitting angle $\mathrm{\Theta }$ of the output beams, which corresponds to the grating period. Especially, the setup was able to achieve a large period ($\ge 20\mathrm{\mu m}$) without any significant effort, while conventional holography required a complex setup with careful alignment of polarizing optics. The detailed setup parameter and corresponding grating period ${\mathrm{\Lambda }}_{\text{replica}}$ are listed in Table 1. After exposing the samples, we used the same LC prepolymer (RMS-E) as the mask PG to form the grating structure. The thickness of the LC prepolymer was adjusted by spin coating to achieve half-wave retardation at 633 nm, which results a maxima in the first order at the wavelength.

Table 1. Characterization Data of the PGs Fabricated at 633 nm

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Figure 6 shows the first-order ${\eta }_{+1}$ and zero-order ${\eta }_0$ efficiency spectra of the PG fabricated. The PG is highly efficient, showing most of incident light redirected into the $+1$ order at the target wavelength when the input is circularly polarized. We can also enhance the spectrum using a multilayer LC structure from our previous works [32,33] to get high efficiency for a wide range of the spectrum (e.g., whole visible, 400–700 nm or near infrared, 800–1400 nm). The PG itself presents no observable scattering, due to the good LC layer alignment and lack of defects, as shown in the inset of Fig. 6. The inset pictures are microscope images of the PGs between crossed polarizers, from which we can qualitatively see good alignment, low defect density, and no discernible variation in pitch. We also experimentally quantify the efficiency at the target wavelength (He–Ne laser, 633 nm) as ${\eta }_m=P_m/(P_{-1}+P_0+P_{+1})$, where $P_m$ is the measured power of the $m$th diffraction order, when the input is circularly polarized. The PGs exhibit nearly ideal diffraction properties showing nearly 99% first-order efficiency without observable zero and other orders (${\eta }_0\le 0.6\%$, ${\eta }_{-1}\le 0.1\%$), as shown in Table 1.

 

Fig. 6. First- and zero-order diffraction efficiency spectra of the PG fabricated. Inset, measured polarizing optical micrograph under crossed polarizers. They were fabricated for different periods: (a) ${\mathrm{\Lambda }}_{\text{replica}}=20\mathrm{\mu m}$; (b) ${\mathrm{\Lambda }}_{\text{replica}}=89\mathrm{\mu m}$; (c) ${\mathrm{\Lambda }}_{\text{replica}}=178\mathrm{\mu m}$ (scale bars, 100 μm; 200 μm; 200 μm).

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5. CONCLUSION

In summary, we proposed a new technique, to the best of our knowledge, for PG exposure that can easily tune the grating period of the sample, while conventional approaches include several optics that are needed to be aligned carefully, which causes difficulty on tuning a grating period and scaling size of the sample due to the complexity of the setup. However, the new approach can tune th grating period as easily as rotating the two masks that are packaged into a small volume. The suggested setup does not require any other optics, and it can pattern a very large grating period, which is generally hard to achieve via conventional approaches. Using the setup, we demonstrated PG fabrication with large grating periods ($\ge 20\mathrm{\mu m}$). The PGs fabricated showed fairly high diffraction efficiency at the target wavelength without observable other orders.