1. Introduction

Holography is a key technology for three-dimensional displays, shape measurement, and high-capacity data storage [1–6]. Hologram memory is a promising candidate for next-generation data-storage technology with high recording densities of greater than 1 TB/disk and high transfer rate [6–9]. Photosensitive media such as photopolymers are widely used as write-once holographic recording media [10,11] because they show high diffraction efficiency, which is an index of brightness of a reconstructed image written in a medium. On the other hand, several types of rewritable holographic media have been proposed in the past few decades [12–14]. Among them, we had selected the transparent magnetic garnet as a rewritable medium, in which magnetic holograms can be written as a distribution of magnetization directions using thermomagnetic recording and reconstructed using the magneto-optical (MO) effect [15,16]. In addition to rewritability, magnetic holograms afford environmental stability because the transparent garnets are stable oxides. Long-term stability of magnetically-written information has been achieved through several magnetic recording media with high coercivity, and it implies that magnetic holograms formed by thermomagnetic recording have potentially high magnetic stability. High tolerance of light exposure for magnetic holograms is also an advantage over photosensitive materials. We demonstrated that a volumetric hologram can be written in garnet films [17,18] with bismuth substituted yttrium iron garnet system [19], in particular Bi_1.3Dy_0.85Y_0.85Fe_3.8Al_1.2O₁₂ (BiDyAlYIG) film, which has high transparency and shows large MO effect. However, its diffraction efficiency was shown to be insufficient to achieve a bright and clear image [18].

The diffraction efficiency for magnetic holograms η_opt is theoretically expressed as

 

Fig. 1 Schematic illustration of collinear volumetric magnetic holography with a magnetophotonic microcavity. Incident light is focused near a magnetophotonic microcavity, where the light is confined in the magnetic layer through Fabry–Pérot resonance between two Bragg mirrors (BMs). A magnetic hologram recorded in the optical cavity system will be reconstructed with high efficiency because optical resonance results in the enhancement in magneto-optical effect and deep hologram writing.

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2. Numerical calculations of diffraction efficiencies for MPM media

The optical properties of MPMs significantly depend on its structural parameters such as the thickness of the garnet layer, t_G, and the number of repeated pairs in BMs, r. We first investigated the structural parameters to achieve high diffraction efficiency through a numerical approach using a model based on a two-beam interferometer [18,21]. MPM structures were formed on a substituted gadolinium gallium garnet (SGGG) substrate, SGGG / (Ta₂O₅ / SiO₂)^r / BiDyAlYIG / (SiO₂ / Ta₂O₅)^r (Fig. 2(a))

 

Fig. 2 (a) Structure of MPM media. (b) Thickness dependence of the transmittance. (c) Thickness dependence of the diffraction efficiency. The efficiency of each media showed the maximum value at a thickness determined by the balance between T, θ_F, and d_w. All the points indicate the maximum diffraction efficiency with tuned optical power density at the writing process for each structure. (d) Dependence of the T and θ_F at t_M on the number of repeated pairs in BMs, r.

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The diffraction efficiencies were evaluated using the finite-element method (COMSOL Multiphysics 4.3a). Two Gaussian beams with the wavelength of 532 nm—the signal and reference beams—were irradiated on the medium at 23° tilt from the normal of the medium surface to form an interference pattern with a spatial frequency of 1500 line pair/mm, which corresponds to the maximum spatial frequency generated using the collinear interferometer with the objective lens NA ~0.55 [21]. In all the calculations throughout this paper, the intensity of the incident beam used for writing was varied to obtain the maximum diffraction efficiency of each structure because the diffraction efficiency depends on the incident power. For reconstruction, the intensity of the incident reference beam was kept constant, and we evaluated the intensity of diffracted light as the diffraction efficiency. The diffraction efficiency η_opt is determined as the ratio of the intensity of the reconstructed beam I₁ to that of the incident reference beam I_in by the equation η_opt = I₁ / I_in × 100 (%). In the calculation, the number of repeated pairs in the BMs, r, was varied from 0 (monolayer) to 4.

Figures 2(b) and 2(c) show the effect of the YIG layer thickness, t_YIG, on transmittance and diffraction efficiency, respectively; here, the values of t_YIG were set as the resonant thicknesses. The transmittance decreased with increasing garnet thickness and number of r-pairs in the MPM medium because of the elongated light path through the garnet, as shown in Fig. 2(b). Because of this reduction in transmittance, the diffraction efficiency showed the maximum value at a certain thickness t_M for each structure, and the value of t_M decreased with increasing r, which is determined by the balance between T, θ_F, and d_w. Figure 2(d) shows the r dependence of T and θ_F at t_M for each medium. The value of θ_F increased with increasing r in the MPM structures. On the other hand, the transmittance decreased with increasing r; even t_M decreased at large r. This complementary relationship between T and θ_F results in the differences in t_M for each structure, and MPM structures having BMs with a large number of r-pairs, which have an extended light path, decrease the thickness t_M.

The calculated shapes of the magnetic fringes are shown in Figs. 3(a)-3(d). The fringe in the monolayer film was arch-shaped overall, and only the center reached the bottom of the film. In contrast to such continuous fringes, the depth of fringes near the edges increased, and discrete fringes were formed in the MPM media. These fringes originate from the behavior of optical cavities; multiple reflections between BMs produce a standing wave in the garnet layer under the resonant condition, and the peak intensities of the standing wave are sufficiently high to increase the temperature of the medium beyond the Curie temperature. Consequently, the maximal diffraction efficiency at t_M was increased with the MPM structures, and the efficiency of 0.02% was twice that of the monolayer film. However, because of the low transmittance, the diffraction efficiency of the four-pair MPM was lower than that of the monolayer film, irrespective of how high θ_F is.

 

Fig. 3 Magnetic fringes (a) in the monolayer film at t_YIG = 1.9 μm, (b) in the one-pair MPM at t_YIG = 1.6 μm, (c) in the two-pair MPM at t_YIG = 1.3 μm, and (d) in the four-pair MPM at t_YIG = 0.8 μm. Uniform hologram writing was achieved in the MPMs by modulating the optical interference through the cavity resonance.

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In this analysis, there is no notable difference between the diffraction efficiencies of the one-pair and two-pair MPMs. The light transmitted through the magnetic medium without diffraction alters noise by grain-boundary scattering. From this viewpoint, a medium with lower transmittance shows lower noise under the same diffraction efficiency. Therefore, we employed the two-pair MPM for the experimental evaluation to prove the effectiveness of the MPM structure in collinear holography.

3. Experimental demonstration of magnetic holograms in MPM media

Based on the simulation results, we fabricated the two-pair MPM structure, (Ta₂O₅ / SiO₂)² / BiDyAlYIG / (SiO₂ / Ta₂O₅)², on an SGGG substrate with a garnet-layer thickness of 1.05 μm. The thickness of each layer in BMs was λ/4n, where λ = 532 nm is the designed wavelength of the photonic band gap and n is the refractive index. The bottom BMs were deposited using electron-beam evaporation on an SGGG substrate. Then, a BiDyAlYIG film was deposited through ion-beam sputtering. The sample was annealed at 750°C for 15 min to obtain a polycrystalline BiDyAlYIG film because the as-deposited film was not crystallized. Finally, the top BMs were deposited by ion-beam sputtering to complete the MPM structure. For comparison, a 1.2-μm-thick BiDyAlYIG monolayer film was prepared on an SGGG substrate. According to the observed θ_F spectrum, a resonant peak due to the enhancement in the Faraday effect was observed at 534 nm, which is very close to the designed wavelength of 532 nm. The rotation angle at the resonant peak was 3.21°, which was 43% higher than that of the monolayer film with nearly the same thickness.

The collinear interferometer system schematically shown in Fig. 4(a) was used to write and reconstruct magnetic holograms. The incident beam (λ = 532 nm) was divided into a signal part and reference part using a digital mirror device (DMD), and it was focused near the medium. The laser was irradiated for 50 ps to record a magnetic hologram, and the reconstructed-signal image was observed by irradiating only the reference part onto the medium. Figure 4(b) shows the original signal pattern used for writing, and Figs. 4(c) and 4(d) show the images reconstructed from magnetic hologram with the monolayer film and MPM medium, respectively. As shown in these figures, the image reconstructed from the MPM medium was brighter than that from the monolayer film, as expected, even though the power of the reference beam in the reconstructing process was identical in these experiments. As discussed above, both the enhancement in θ_F and increase in d_w in the MPM medium contribute to this high brightness.

 

Fig. 4 Experimental setup and reconstructed two-dimensional data pattern. (a) Schematic illustration of the experimental setup for writing and reconstructing magnetic holograms. The image modulated with a DMD is divided into two parts: the signal part and the reference part. (b) Original signal pattern shown with a DMD at the writing process. Reconstructed signal pattern from (c) the monolayer film and (d) the two-pair MPM structure. The MPM medium provided a clear, bright reconstructed image because the diffraction efficiency of the MPM medium was double that of the monolayer film.

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We evaluated the average gray levels (from 0 to 100) over the white pixels L₁ and black pixels L₀ in the signal part of the original image. The values of L₁ were 17 and 40 for the monolayer film and MPM medium, respectively, and the brightness of the image obtained from MPM is more than twice that of the image obtained from the monolayer film. This increase is in good agreement with the aforementioned calculation result. On the other hand, the values of L₀ were 10 and 13 for the monolayer and MPM media, respectively, indicating that the background intensity was nearly identical. The signal contrast ratio, C = L₁ / L₀, of the MPM medium was C_MPM = 3.1, which was approximately twice that of the monolayer film of C_mono = 1.7. This implies that the increased signal intensity played a dominant role in the aforementioned high brightness.

4. Summary

We experimentally demonstrated a bright reconstructed image using the MPM medium in collinear volumetric magnetic holography. Based on a numerical analysis with a two-beam interferometer, we found that the use of the MPM medium resulted in high diffraction efficiency because of high θ_F and large d_w, which were accomplished through the effects of Fabry–Pérot resonance in the cavity. The experimental value of the brightness of the image reconstructed from the MPM medium was twice that of the image reconstructed from the monolayer film, which is in good agreement with the simulation result. The approach of introducing a simple layered structure such as the MPM structure can improve holographic efficiency without modifying materials and is quite effective. Employing this method with the investigation of optimal materials may result in further improvement in efficiency to produce high-quality images in magnetic holography. In addition, detailed holographic characteristics such as multiplexing will be evaluated in advance for applying the MPC media to holographic data storage.