## 3 Results and Discussion
### Design and Properties of HD Multilayer Media  
To suppress this heat diffusion effect and control the shapes of the fringes, a stacking structure composed of Bi:RIG and transparent HDLs is effective for diffusing the excess heat from the garnet layers into the HDLs. The fundamental concept of HDLs is shown in Figure 7a. Most of the excess heat at the heated spots caused by the absorption of light energy diffuses to the HDLs, so the amount of heat laterally diffused in the Bi:RIG decreases. Therefore, the temperature increase next to the heated spots in the Bi:RIG decreases, and the increase in the width of the fringes decreases. As a result, the shape of the fringes may be maintained. For the actual design of HD multilayer media, the thicknesses of the HDLs and garnet layers are important for controlling the heat flow and temperature in the Bi:RIG. A simple model to evaluate their thicknesses shown in Figure 7b is assumed; a Bi:RIG layer with thickness \(d_{\mathrm{RIG}}\) is sandwiched by HD layers, and the temperature of the heated spot with width \(W_{\mathrm{H}}\) is set to \(T_{\mathrm{H}}\). The heat of this heated spot diffuses to adjacent regions, shown in light orange, and this diffused heat increases the temperature in the adjacent regions within distances \(x\) and \(y\) in the garnet and HDL. In this process, the temperature of the original heated spot and its adjacent regions shown in orange and light orange in Figure 7b, respectively, is assumed to be a uniform temperature \(T\). In addition, the ratio of the heated length in the garnet and HD layers, \(x/y\), is assumed to be the ratio of the characteristic diffusion length:  
\[\frac{x}{y}=\sqrt{\frac{k_{\mathrm{RIG}}/C_{\mathrm{RIG}}}{k_{\mathrm{HD}}/C_{ \mathrm{HD}}}}, \tag{3}\]  
where \(k_{\mathrm{RIG}}\) and \(k_{\mathrm{HD}}\) are thermal conductivities of the Bi:RIG and HD layers, and \(C_{\mathrm{RIG}}\) and \(C_{\mathrm{HD}}\) are volume heat capacities of the Bi:RIG and HD layers, respectively. In this case, considering the heat balance before and after heat diffusion, we can calculate the size of the region heated up to the Curie temperature, \(T=T_{\mathrm{C}}\), as a function of \(T_{\mathrm{H}}\) and \(d_{\mathrm{RIG}}\) as follows:  
Figure 6: **(a)** Calculated diffraction efficiency at 1500 line-pairs/mm. The usual diffraction efficiency (black circles) is saturated at energy densities higher than 60 mJ/cm\({}^{2}\), while continuously increasing, when the virtual fringes immediately after laser irradiation are used (red squares). **(b)** Shapes of magnetic fringes recorded at various energy densities. **(c)** Variation in temperature distribution after laser irradiation recorded at 81 mJ/cm\({}^{2}\). The shape of the regions with a temperature higher than the Curie temperature (150 \({}^{\circ}\)C) is surrounded by green lines. \[\frac{2x}{W_{\rm H}}=\frac{T_{\rm H}-T_{\rm L}}{2(T_{\rm C}-T_{\rm L})\bigg{(}1+ \frac{W_{\rm H}}{d_{\rm RIC}}\sqrt{\frac{k_{\rm ER}C_{\rm RIS}}{k_{\rm RIC}-R_{ \rm RIC}}}\bigg{)}}, \tag{4}\]  
where \(T_{\rm L}\) is the temperature of the nonheated region. Based on Equations (3) and (4), we can determine the appropriate thicknesses of the Bi:RIG and HD layers by determining the acceptable widening of the magnetic fringes \(2x/W_{\rm H}\) for a given \(T_{\rm H}\). In the HDL recording media, because the temperature distribution in the Bi:RIG film differs depending on the thickness to be recorded, it is necessary to design an HD multilayer medium according to the recording thickness. Figure 8a shows the calculated diffraction efficiency of the HD multilayer media using Al\({}_{2}\)O\({}_{3}\) as the HD material and single-layer medium. The diffraction efficiency of the HD multilayer media increases with the recording energy density up to approximately 150 mJ/cm\({}^{2}\), and all HD multilayer media show diffraction efficiencies higher than those in the single-layer medium with the same Bi:RIG thickness.