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Abstract
We propose a prism-hologram-prism sandwiched recording method for the fabrication of polarization-selective substrate-mode volume holograms with a large diffraction angle. In fabrication, the C-RT20 photopolymer is sandwiched between two 45°-90°-45° prisms and the interference fringes can be easily recorded in the recording material. The experimental results are in good agreement with the theoretical predictions. The proposed method features of a reflection-type recording setup for a transmission element and belongs to a technique of longer-wavelength construction for shorter-wavelength reconstruction. In addition, the method is much easier than the traditional recording method of two incident beam interference and has application potential in holographic photonics.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Substrate-mode volume holograms (SVHs) are essentially thick holographic grating attached to a dielectric substrate. SVHs have been successfully applied to replace conventional optical elements because of its several advantages such as high diffraction efficiency, planar structure, easy coupling, and low cost [1, 2]. In addition, the SVHs could be a potential strategy to be integrated on silicon photonics elements for overcoming the difficulties in silicon-based fabrications [3–8]. Based on the coupled-wave theory, polarization-selective substrate-mode volume holograms (PSVHs) had been proposed and successfully applied to wavelength division multiplexing, optical interconnectors, and optical circulators [9–11]. However, the conventional PSVHs could encounter difficulty with the commercial recording material's limited phase modulation on insufficient thickness and refractive-index modulation strength. In 2008, our research group had proposed a new design of PSVHs with a large diffraction angle to overcome the shortage on the limited phase modulation strength [12]. However, this approach is difficult to implement due to the lack of a suitable recording method.
Accordingly, in this paper, we proposed a prism-hologram-prism sandwiched recording method to implement the fabrication of PSVHs. According to the K-vector diagrams for different recording and reconstruction wavelengths, the diffraction angle of the PSVH was derived considering the shrinkage effect of a recording material. In the recording setup, the holographic recording material is sandwiched between two right-angle prisms and the terminal prism is attached with a reflection mirror. A normally incident collimated laser beam serves as reference beam and the reflected light serves as object beam. Accordingly, a transmission-type volume phase hologram with polarization-selective function can be easily fabricated with a proper exposure by using the reflection-type recording setup. To show the feasibility of the proposed method, a PSVH was successfully fabricated and discussed in detail. To achieve a large diffraction angle, relationships between recording wavelength, and reconstruction wavelength and diffraction angle were simulated and discussed. Different from the conventional recording method, the proposed method belongs to a technique of longer-wavelength construction for shorter-wavelength reconstruction which provides advantages of a simple setup and easy operation for the fabrication of PSVH. In addition, the proposed method could be applied to develop holographic photonics and the PSVHs have a high application potential to be integrated on silicon photonics.
2. Principles
2.1 Prism-hologram-prism sandwiched recording setup
As shown in Fig. 1 is the proposed prism-hologram-prism sandwiched recording setup for polarization-selective substrate-mode volume holograms with a large diffraction angle. In Fig. 1(a), a laser beam with a wavelength of λ1 passes through an electronic shutter (ES), a spatial filter (SF), a collimating lens (CL), and an iris diaphragm (ID). The expanded beam is normally incident into the prism-hologram-prism recording optical head (PROH) in which the holographic recording material (H) is sandwiched between two right-angle prisms (P1 and P2) and a reflection mirror (M) is attached at the bottom. For ease of understanding, the glass substrate and protective coversheet (polycarbonate) of the recording material are omitted. The details of geometric relations and material related parameters are shown in Fig. 1(b). The base angles for the prism are θp1 and θp2, the refractive index of the prism is np, the thickness of the recording material is d1, and the refractive index of the recording material is nf1 (at λ1). The normally incident collimated laser beam serves as reference beam R1 and the reflection light by the mirror serves as object beam O1. The incident angles of R1 and O1 are θr1 and θo1 in the medium of prism with respect to the surface normal of the recording material; the corresponding refraction angles in the emulsion of recording material are θ′r1 and θ′o1, respectively. The R1 and O1 are two parallel beams in opposite direction inside the recording material. Accordingly, a set of interference fringes can be easily recorded with a proper exposure by using the single-beam incidence reflection-type recording setup. The corresponding K-vector diagram and geometric relations are shown in Fig. 1(c) where kR1 and kO1 (with |kR1| = 2πnf1/λ1 and |kO1| = 2πnf1/λ1) are the propagation vectors for the reference and object beams, and K1 (with |K1| = 2π/Λ1) is the grating vector with a grating period of Λ1 and a grating slant angle of ψ1.
Fig. 1 (a) Prism-hologram-prism sandwiched recording setup; ES: electronic shutter, SF: spatial filter, CL: collimating lens, ID: iris diaphragm and PROH: prism-hologram-prism recording optical head, (b) details of geometric relations and material related parameters, and (c) K-vector diagram for the recording.
2.2 Shrinkage effect of emulsion
After exposure and post-processing, the thickness of emulsion changes from d1 to d2, as shown in Fig. 2 with a variation of Δd. As a result, the grating period changes from Λ1 to Λ2 and the grating slant angle changes from ψ1 to ψ2 [13–15].
Fig. 2 Changes in the orientation and spacing of the fringe plane due to shrinkage of emulsion thickness after exposure and post-processing.
2.3 Reconstruction for the polarization-selective substrate-mode volume holograms
The fabricated hologram is set on a horizontal plane and reconstructed with a normally incident un-polarized reference beam R2 with a wavelength of λ2, in Fig. 3(a). The object beam O2 is diffracted with an angle θd inside the emulsion of recording material. The non-diffracted light penetrates the element directly (channel 1). Depends on the relative refractive index of the emulsion and the substrate, the diffracted light is guided into the emulsion or glass substrate and finally transmits through the element (channel 2) after two total internal reflections and one more diffraction. The corresponding K-vector diagram is shown in Fig. 3(b) where kR2 and kO2 are the propagation vector for the reference and object beams (with |kR2| = 2πnf2/λ2 |kO2| = 2πnf2/λ2, and nf2 is the refractive index of emulsion at λ2), and K2 (with |K2| = 2π/Λ2) is the grating vector with a grating period of Λ2 and a grating slant angle of ψ2. Accordingly, the relationship between reconstruction wavelength λ2 and recording wavelength λ1 can be expressed as
where λeff2 is the effective reconstruction wavelength inside the emulsion of recording material. With the K-vector diagram of reconstruction, the diffraction angle θd can be derived asFig. 3 (a) The reconstruction of polarization-selective substrate-mode volume hologram (not to scale) and (b) K-vector diagrams for reconstruction.
According to the coupled-wave theory, the s- and p-polarization diffraction efficiencies of the normally incident reference beam R2 can be expressed as [2, 16]
andwhere N1 = n1d2/λ2 is the effective index modulation, n1 is the modulation strength of refractive index, and a equals to (cosθd)1/2. From Eqs. (3) and (4), the diffraction efficiencies ηs and ηp are two asynchronous sine-squared functions with primitive period of Ts = aπ and Tp = π/a, respectively. As the diffraction angle θd has a large value close to 90° (corresponding to a relatively small value of a) the first peak value (100%) of ηs corresponds to a small value of ηp (~0). Therefore, a polarization-selective substrate-mode volume hologram with a large diffraction angle can be obtained.3. Experimental results and discussions
In order to show the feasibility of the proposed recording method, a polarization-selective substrate-mode volume hologram was fabricated. The optical setup for the recording is shown in Fig. 4(a). A photopolymer recording material (C-RT20, Litiholo) which requires no chemical post-processing was sandwiched between two BK7 isosceles right-angle prisms (BK7, Edmund). Castor oil was introduced for refractive-index matching (n = 1.48 at 20°C). A 632.8 nm helium–neon laser was used for the recording. The exposure power was 4.35 mW/cm2, and the exposure time was about 340 seconds. After rinse and drying, in Fig. 4(b), the fabricated PSVH shows a clearly pan-red and -yellow colored appearance which confirmed the successful recording of interference fringes.
Fig. 4 (a) Optical setup used to record a polarization-selective substrate-mode volume hologram with an electronic shutter (ES), a spatial filter (SF), a collimating lens (CL), an iris diaphragm (ID) and a prism-hologram-prism recording optical head (PROH), and (b) pan-red and -yellow colored appearance of the fabricated element.
Polarization-dependent spectrum transmittances for the PSVH were also measured with a linearly polarization controlled white-light source (LAX-C100, Asahi Spectra) and a spectrometer (HR4000CG-UV-NIR, Ocean Optics). In Fig. 5, spectrum diffraction efficiencies for s- and p-polarizations were obtained with the spectrum transmittances. The diffraction efficiencies for s-and p-polarizations at a central wavelength of 443.6 nm are 88.99% and 23.37%, respectively, which confirmed the polarization-selective function of the PSVH. Furthermore, the fabricated PSVH was reconstructed with a diode laser which has an adjacent wavelength of 446 nm. In Fig. 6(a), the separation distance AC of two orthogonally polarized lights was 19.19 mm. Figure 6(b) shows the schematic representation for the light propagation details inside the C-RT20 photopolymer recording material which consists of a polycarbonate coversheet (npc = 1.608, dpc = 180 μm), a layer of photopolymer (npp = 1.501, dpp = 16 μm), and a glass substrate (ns = 1.526, ds = 1.920 mm). The estimated diffraction angle θd inside the photopolymer emulsion was 84.09° (at 446 nm); meanwhile, at 443.6 nm the estimated diffraction angle was 83.54°. Due to a higher refraction index of polycarbonate, the s-polarization diffraction light was reflected with a reflectance of 12% at the interface between photopolymer (npp = 1.501) and glass substrate (ns = 1.526) and was trapped inside the polycarbonate (npc = 1.608) experiencing total internal reflection several times, as shown in the red-dash rectangle in Fig. 6(a). In addition, in the inset of Fig. 5, the transmission spectrum of polycarbonate is around 85% at the visible spectrum due to material absorption which causes the non-diffraction efficiencies ranged from 20% to 30% and the lower s-polarization diffraction efficiency of 88.99% in Fig. 5. The actual diffraction efficiency for s-polarization should be quite close to 100%. Therefore, a glass coversheet can be used to obtain better results.
Fig. 5 Spectrum diffraction efficiencies for s- and p-polarizations and material absorption of polycarbonate (inset).
Fig. 6 (a) Fabricated PSVH reconstructed with a 446 nm diode laser, (b) light propagation details inside the C-RT20 photopolymer recording material.
Substituting relevant parameters (θp = 45°, d1 = 16 μm, d2 = 13.88 μm) and refractive-index data with Sellmeier dispersion formula into Eqs. (1) and (2), the simulation relationships between recording wavelength λ1 (from 300 nm to 850 nm), and corresponding reconstruction wavelength λ2 (from 200 nm to 600 nm) and diffraction angle θd were shown in Fig. 7, respectively. Because the influence of refractive-index dispersion is limited, the curve of λ1 versus λ2 exhibits an approximately linear relationship. At the recording wavelength of 632.8 nm, the corresponding reconstruction wavelength and diffraction angle are 443.6 nm and 83.54° which corresponds well with the practical. When the recording wavelength is visible light, the diffraction angle is greater than 80.5 degrees. In addition, when a desired reconstruction wavelength is greater than 560 nm, it can be achieved by using two prisms with a base angle θp1 less than 45 degrees. For a fixed recording wavelength, the condition of base angle θp1 less than 45 degrees creates a more horizontal interference fringes which coincide with a longer reconstruction wavelength. Meanwhile, the recording wavelength should match the sensitivity of recording material.
Fig. 7 Simulation relationships between recording wavelength, and reconstruction wavelength and diffraction angle.
According to Eq. (3), the refractive index modulation n1 can be expressed as
which is modulated with an optimal exposure energy during the recording process. Substituting the related experimental parameters (λ2 = 443.6 nm, θd = 83.54°, and d2 = 13.88 μm) into Eq. (5), the optimal refractive index modulation n1 is about 5.36 × 10−3. Substituting the diffraction angle (θd = 83.54°) into Eqs. (3) and (4), the relationship between effective refraction modulation N1 and diffraction efficiencies of s- and p-polarizations can be obtained in Fig. 8. As the effective refractive index has a value of N1 = 0.17 the theoretical diffraction efficiencies of s- and p-polarizations are ηs = 100% and ηp = 3.18%, respectively.Compared with the conventional polarization-selective substrate-mode volume holograms, the relevant parameters and characteristic are listed in Table 1. The diffraction angle of conventional polarization-selective substrate-mode volume holograms are designed with values of 48.19° (with ηs = 100%, ηp = 0) and 60° (with ηs = 0, ηp = 100%) [2, 11]. The required effective index modulations N1 are 1.22 and 0.71, respectively. Because the maximum refractive index modulation strength of commercial holographic recording materials such as dichromated gelatins, silver-halide materials, and photopolymers are not excess 0.08 and 0.03, respectively. The required satisfied thickness d2/λ2 exceeds 8.88. Especially, recording materials with a thicker emulsion encounter more serious shrinkage effect. Therefore, they are difficult to be realized under a finite phase modulation n1d2 and a limited thickness less than 20 μm. However, the proposed method with a large diffraction angle of 83.54° requires a much smaller effective index modulation N1 of 0.17. Therefore, polarization-selective substrate-mode volume holograms can be easily achieved with the proposed method using commonly available recording materials. Different from conventional recording methods, the proposed method has a relatively simple recording setup with a single incident beam. In the method, a reflection-type recording setup is used for the recording of a transmission hologram. Because of the introduction of the prism-hologram-prism recording optical head, the Bragg condition in reconstruction confines the normal incident light to a shorter wavelength. Therefore, this method belongs to a technique of longer-wavelength construction for shorter-wavelength reconstruction. In addition, the method is applicable for the fabrication of traditional holographic optical elements and waveguide holographic optical elements.
Table 1. Compression of relevant parameters and characteristic for polarization-selective substrate-mode volume holograms designed at different diffraction angle.
4. Conclusions
Based on the coupled-wave theory, a novel prism-hologram-prism sandwiched recording method was proposed for the fabrication of polarization-selective substrate-mode volume holograms with a large diffraction angle. The C-RT20 photopolymer recording material was employed with a technique of longer-wavelength (632.8 nm) construction for shorter-wavelength (443.6 nm) reconstruction. Due to material absorption of polycarbonate, the diffraction efficiencies of s- and p-polarization were 88.99% and 23.37%, respectively. The practical diffraction efficiency for s-polarization should be quite close to 100%. The proposed method can effectively simplify the complexity of traditional holographic recording methods. Additionally, the fabricated polarization-selective substrate-mode volume hologram is suitable for operating at a short wavelength with all merits of conventional substrate-mode volume holograms which breaks the limitation of finite phase modulation of commercial recording materials. The proposed method has high potentials in the development of holographic photonics.
Funding
Ministry of Science and Technology of the Republic of China (MOST) (MOST 106-2221-E-035-074 and MOST 107-2221-E-035-069-MY2).
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