Holographic memory is expected to become a high-capacity data storage. Magnetic volumetric holograms are rewritable holograms that are recorded as magnetization directions through thermomagnetic recording. However, the effective depth of magnetic holograms is limited by thermal diffusion that causes merging of magnetic fringes. In this study, we propose the insertion of heat-sink layers (HSLs) for retaining well-defined magnetic fringes during volumetric writing. Magnetophotonic microcavity media were used for demonstrating the HSL effect, and the structural design principle was established in numerical calculations. The results indicate that deep and clear magnetic fringes and an improvement in the diffraction efficiency can be achieved by the insertion of HSLs.
© 2016 Optical Society of America
Holographic memory is a promising data-storage technology, characterized by fast transfer rates and recording densities exceeding 1 TB/disk [1–6]. Compared with conventional holographic memory recorded by using photopolymers, magnetic holograms formed by using thermomagnetic recording provide rewritability and long-term stability. In the recording process, volumetric holograms are recorded as a direction of magnetization in magnetic films, while reconstruction involves using the magneto-optical (MO) effect [7–9]. Thermomagnetic writing is a commonly used method for manipulating the magnetization via exposure to light. This method uses the absorbed light for forming a temperature distribution in a medium, which corresponds to the intensity distribution of the interference light. This temperature distribution yields the reversal of magnetization (induced by a reversed stray magnetic field and/or an applied magnetic field) in the regions in which the temperature exceeds the Curie temperature, with the resulting magnetization distribution corresponding to the interference pattern. Previously, we demonstrated that a hologram can be magnetically written by using this thermomagnetic writing and reconstructed from transparent magnetic films of Bi1.3Dy0.85Y0.85Fe3.8Al1.2O12 (BiDyAlYIG); however, the diffraction efficiency was insufficient for applying this to actual data storage devices [10,11].
Recently we reported that the use of magnetophotonic microcavities (MPMs) or magnetophotonic crystals as recording media provides high diffraction efficiency, because the Faraday rotation angle and the depth of the formed magnetic fringes were increased [12–14]. An MPM structure is a stacked medium in which a transparent magnetic film is sandwiched between two Bragg mirrors (BMs) and acts as an optical cavity for enhancing the Faraday rotation angle [15,16]. In addition, the localization of light in the magnetic layer results in deep holographic writing by modulating the interference of light in the microcavity . However, thermomagnetic writing with high incident optical power for forming deep magnetic fringes produces excessively high temperature near the medium surface. As a result, the excess heat in the high-temperature region diffuses laterally, and fringes become wider and merge with adjacent fringes near the surface . Owing to this undesirable merging that occurs in volumetric recording, the information on some fringes is lost, affecting the formation of deep fringes. To suppress the heat diffusion effect and to control the fringes’ shapes, a stacking structure composed of a magnetic garnet and transparent heat-sink layers (HSLs) is thought to be effective for diffusing the excess heat from garnet layers into HSLs. In this study, we propose a hybrid magnetic medium in which HSLs are inserted into MPM structures for controlling the thermal diffusion in an optical cavity and forming clear magnetic fringes, yielding high diffraction efficiency.
2. Calculation method
The media used in our calculations were optical microcavities with garnet/alumina multilayers as defects, with alumina used as a heat-sink material; the defect layers were sandwiched between two pairs of (Ta2O5/SiO2)2 BMs. The resonant thickness, tres, was:Fig. 1(a) for several angles of φ. In this study, the total thickness of the garnet layers was 3.88 μm, corresponding to a resonant thickness at the resonance order m = 30.
The shapes of the obtained magnetic fringes and diffraction efficiencies were numerically evaluated in a multiphysics analysis by using the finite element method (COMSOL Multiphysics 4.3a) [11–13]. Two Gaussian beams, namely the signal beam and the reference beam, each with a wavelength of λ = 532 nm, were irradiated on the medium at 23.5° relative to the normal to the medium surface to form an interference pattern with a spatial frequency of 1500 lps/mm. Based on the numerical calculations, the diffraction efficiency was evaluated by using the following equation :
3. Results and discussion
The insertion positions of HSLs were determined according to a design principle determined by a simple thermal analysis that was described in another report . According to this principle, we associated the initial temperature profile in the garnet layer for each writing condition with the relationship between the temperature of the heated region and the combination of HSL-garnet thicknesses for determining the appropriate structure of the elementary components (HSL/garnet). In this work, the structure was determined for suppressing the volume expansion of the fringes with HSLs. The position and thickness of the HSLs were determined from top to bottom based on the initial temperature profile, under the condition in which the total HSLs thickness was as small as possible for completing the multilayer structure (MPM + HSLs).
As an example, Fig. 1(b) shows the calculated initial temperature profile of the MPM medium for the writing power density of Ew = 92 mJ/cm2. The oscillations owing to the standing wave in the temperature profile were observed in the MPM media. These temperature oscillations make it difficult to determine the temperature criteria for designing the garnet/alumina multilayer structure in the aforementioned systematic way. To determine the temperature criteria, we fitted the original oscillating profile to an exponentially decaying function, because such a decay function is theoretically suitable for describing the light absorption. Since this smoothed profile was in a good agreement with the average of the original temperature profile, the HSL structure could be designed based on the smoothed profile as shown in Figs. 1(b) and 1(c).
In addition to the above-described fundamental design principle for thermal diffusion, we have to consider the optical properties of the microcavity with HSLs. The fundamental requirement for maintaining the MPM resonance is that the cavity with HSLs should satisfy the Fabry–Pérot resonant condition, similar to Eq. (1), as follows:Eq. (3), the cavity is in the resonance condition and the structure acts as the MPM, even after inserting the HSLs. To meet this requirement, we designed “top-HSL-tuned MPM+HSLs” structures by adjusting the thickness of the top HSL (i.e., tA(1)) to satisfy Eq. (3) for each writing energy density.
Figure 2(a) shows the dependence of diffraction efficiency on the writing energy density, Ew, for the top-HSL-tuned MPM + HSLs media. The diffraction efficiencies of these media are higher than those of the standard MPMs. At Ew = 80 mJ/cm2, no merging of the magnetic fringes was observed in the MPM + HSLs medium as shown in Fig. 2(b), indicating that the insertions of HSLs are effective for forming well-defined magnetic fringes by transferring excess heat from the garnet layers to the HSLs. In contrast, fringe merging was observed under some conditions for high writing energy, e.g., Ew = 92 mJ/cm2, as shown in Fig. 2(c).
To determine the reason for the appearance of fringe merging, the initial temperature profile in the MPM + HSLs medium at Ew = 92 mJ/cm2 was plotted and is shown in Fig. 3. The average temperatures in the 1st –3rd BiDyAlYIG layers (G1, G2, and G3) were higher than those in the original MPM medium. The distribution of electric field strength is also shown in Fig. 3, and it is obvious that the temperature increase is related to the increased field strength near the surface. This high temperature, exceeding the temperature before the insertion of the HSLs, caused the width expansion of magnetic fringes by thermal diffusion and underlies the appearance of the observed merging. This undesirable enhancement of electric field intensity was caused by undesired phase retardation and interface reflection owing to the HSLs insertion. To maintain the original field distributions, we simply restricted the HSLs thickness; the optical thickness of each HSL should be an integral multiple of a half wavelength:Eq. (4), the electric field distributions in the cavity garnet layers are expected to be identical to those before the insertion of HSLs, except for the sign, i.e., phase differences of 0 or π are allowed, because the phase of the light passing through each HSL is just an integer multiple of π. When a multilayer structure satisfies this condition, the original field distribution of an MPM medium will be maintained and the optical properties will be unchanged. Note that when Eq. (4) is satisfied, Eq. (3) is also naturally satisfied because the garnet thickness is originally in the resonant condition in the MPM medium; thus, the condition described in Eq. (4) maintains the original electric field strength distribution and cavity resonance. Under this condition, we should consider only Eq. (4) for inserting the HSLs without disturbing the original electric field distribution.
To apply this restriction, the HSLs were inserted into the MPM medium with the optical thickness rounded up to the nearest integral multiple of a half wavelength, hereafter referred to as “all-HSLs-tuned MPM+HSLs.”
The field strength and initial temperature profiles in the all-HSLs-tuned MPM + HSLs medium at Ew = 92 mJ/cm2 are shown in Fig. 4. The electric field distribution in the garnet layers was only weakly affected, and the original temperature profile was maintained after inserting the HSLs. This result indicates that the design principle described by Eq. (4) enables to insert HSLs into an optical cavity without disturbance. Figure 5(a) shows the dependence of the diffraction efficiency on the writing power density. The diffraction efficiencies of the all-HSLs-tuned MPM + HSLs were higher than those of the original MPM and smoothly increased with increasing the writing power density, unlike the top-HSL-tuned MPM + HSLs in Fig. 2. Figures 5(b) and 5(c) show the magnetic fringes for Ew = 80 mJ/cm2 and 152 mJ/cm2. Well-defined magnetic fringes in the entire garnet area were formed in all-HSLs-tuned MPM + HSLs, and this multilayered structure design was effective for volumetric thermomagnetic writing. As shown in this figure, magnetic fringes reached the bottom of the garnet film, so the diffraction efficiencies were saturated at the high writing power density owing to this garnet thickness limitation of 3.88 μm. The results suggest that the merging of the magnetic fringes by thermal diffusion is suppressed, and the optical resonance properties are preserved after inserting the HSLs. Consequently, high diffraction efficiency of 0.9% was achieved with the MPM + HSLs medium, which was approximately three-fold higher than the MPM medium efficiency of 0.36%. This improvement in diffraction efficiency may also imply that the loss of information stored in magnetic fringes is reduced by the effect of HSL insertions, which is quite an effective method for recording volumetric magnetic holograms through thermomagnetic writing while retaining initial interference fringes.
In this article, we proposed MPM media with HSLs for maintaining the shapes of magnetic fringes by controlling the heat diffusion during volumetric thermomagnetic writing. When HSLs are inserted into an optical cavity, it is important to maintain the original resonance condition and control the electric field distribution. In this work, we inserted HSLs into MPMs where the HSL optical thicknesses were equal to an integral multiple of a half wavelength of light, which prevented undesired field intensity changes owing to the phase retardation and multiple reflections due to the inserted HSLs. The results of our calculations show that thermal-diffusion-induced merging of magnetic fringes is effectively reduced even in an optical microcavity. As a consequence, the diffraction efficiency exhibited by the MPM + HSLs medium was approximately one order of magnitude higher than that of the conventional single-layer film. The insertion of HSLs enabled the formation of deep magnetic holograms without deformation of the shapes of the initial fringes that were generated by light, and it alleviated the unavoidable limitation on the hologram writing depth owing to the merging of magnetic fringes in conventional single-layered magnetic media. This approach provides a method for accurately manipulating the magnetization by volumetric thermomagnetic recording. Moreover, the ability to insert different materials into optical cavities proposed here is expected to yield additional features (e.g., a pre-designed spatially localized resonance), beyond the ability to retain original optical characteristics.
This work was supported in part by the Grants-in-Aid for Scientific Research (S) 26220902, (A) 15H02240, and Grant-in-Aid for Japan Society for the Promotion of Science (JSPS) Fellows No. 25-8942. T.G. acknowledges JSPS KAKENHI No. 26706009, and No. 26600043. We gratefully acknowledge the work of Mr. Kan Kobayashi.
References and links
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17. Y. Nakamura, Toyohashi University of Technology, 1–1 Tempaku-cho, Toyohashi, Aichi, 441–8580, Japan, is preparing a manuscript to be called “Volumetric magnetic holography in multilayered structure composed of heat-sink layers.”