## 2 Micrograting of a Micro Holographic Storage System
### Numerical Results for Micrograting  
Figure 4 shows the spatial refractive index modulation of a micrograting induced by the interference of two focused counter-propagating beams using vector diffraction theory.  
In this paper, the micrograting was modulated by 532 nm wavelength, objective lens (OL) of 0.65 NA, and photopolymer. The micrograting pattern of the two beams was created by the corresponding spatial modulation of the complex refractive index in the photopolymer. The modulation range of the micrograting, created by focused Gaussian beams, was approximately  
Figure 3: Scheme of focal shift associated with (**a**) wavelengths and (**b**) refractive indices.  
confined to the double Rayleigh range, \(2z_{R}\). The modulation range of the refractive index rapidly decreased with increasing distance \(z\) from the center of the micrograting. The micrograting in the recording region consisted of both transversal and longitudinal components. To investigate the effects of vector diffraction theory, we carried out a comparison of the resulting micrograting size for the various NAs and wavelengths, as summarized in Table 1.  
For comparison, we calculated the FWHM by the \(\lambda/(2\text{NA})\) to compare scalar and vector diffraction theories. The calculated micrograting size in the focal region is shown in Table 2.  
\begin{table}
\begin{tabular}{c c|c} \hline
**Effective NA** & **0.6/0.7/0.8** \\ \hline Polarization & Circular \\ Media & Recording & Photopolymer \(n=1.53\), Thickness \(=400\) μm \\ Substrate & Glass \(n=1.53\), Top \(=600\) μm, Bottom \(=600\) μm \\ Wavelength & & 405/532/633 nm \\ \hline \end{tabular}
\end{table}
Table 1: Optical parameters for numerical simulation model.  
Figure 4: Calculated refractive index modulation of a grating induced by two counter-propagating beams. The intensity pattern created using vector diffraction theory: (**a**) transverse and (**b**) longitudinal components. The gray scale indicates an increment of refractive index modulation, and the axis scale is calculated in terms of wavelength unit.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{\(\lambda\)**(nm)**} & **NA** & \multirow{2}{*}{\(\lambda\)**(2 NA) (nm)**} & \multirow{2}{*}{**Scalar (nm)**} & \multicolumn{2}{c}{**Vector (nm)**} \\ \cline{5-6}  & & & & **Transverse** & **Total** \\ \hline \multirow{4}{*}{532} & 0.6 & 443 & 457 & 444 & 458 \\  & 0.7 & 380 & 390 & 405 & 422 \\  & 0.8 & 332 & 342 & 325 & 349 \\  & 0.6 & 337 & 348 & 338 & 349 \\
405 & 0.7 & 289 & 297 & 308 & 321 \\  & 0.8 & 253 & 260 & 248 & 266 \\ \hline \end{tabular}
\end{table}
Table 2: Comparison of micrograting size using scalar diffraction theory and vector diffraction theory analyses.  
In the case of scalar diffraction theory, the recorded micrograting size was equal to \(0.514\,\lambda_{0}\)/NA, and could be expressed as the FWHM of Airy ring pattern \(\tau_{Airy}=0.610\,\lambda_{0}\)/NA. As the NA increased, the FWHM given by vector diffraction theory was larger size. The micrograting, as calculated with scalar theory was almost equal to the transversal component. The difference in the calculated size is attributed to the side-lobe of the longitudinal component, as shown in Figure 5. In Figure 5b, the transversal component has circular shape (_i.e._, TEM\({}_{00}\)-mode) and strong intensity strength; in contrast, the longitudinal component has a doughnut shape and weak intensity strength.