## 4 2-D Multicolored Sidebands Arrays  
[PERSON] and his coworkers first observed 2-D multicolored arrays in 2006 in a quadratic nonlinear medium (BBO crystal) with two closely-overlapped femtosecond laser beams from Ti:sapphire amplifier and its SHG signal [71]. The cause of the 2-D pattern was thought to be the cascaded quadratic nonlinear process, together with spatial breakup of the quadratic spatial solitons induced by ellipticity of the input beams. The 2-D structure could also be suppressed by another weak SHG beam. [PERSON] also generated 2-D multicolored arrays in diamond plate with three pump beams [61], attributed to the interaction of two different sets of cascaded stimulated Raman scattering processes. We observed a similar structure in a cubic nonlinear medium, sapphire plate, with only two pump beams in 2008 [55,56]. 2-D multicolored arrays were generated when pump energy was increased. Figure 15 shows the 2-D multicolored arrays generated under various conditions. The 2-D multicolored arrays could be controlled by changing the intensity, delay, or polarization of one input beam. We performed another experiment to study the characteristics of the 2-D multicolored arrays in detail. The schematic of this experiment is shown in Figure 16a. The two pump beams had a cross-angle of 1.8\({}^{\circ}\), and a beam size of 300 \(\upmu\)m in sapphire plate. Stable 2-D multicolored arrays were generated when Beam 1 and Beam 2 overlapped in time and space in the sapphire plate, as shown in Figure 16b. Spatially well-separated multicolored sidebands with \(>\)10 columns and rows were observed. The columns were approximately normal to the center row while the rows adjacent to the center row were not parallel to each other. The 2-D multicolored array sidebands are defined as B\({}_{\text{m,n}}\) for convenience, as shown in Figure 16c. B\({}_{0,0}\) and B\({}_{-1,0}\) stand for the two pump beams, Beam 1 and Beam 2, respectively. \begin{table}
\begin{tabular}{c c c c c c} \hline
**Sidebands** & **AS1** & **AS2** & **AS3** & **AS4** & **AS5** & **S1** \\ \hline Power (\(\upmu\)W) & 34.0 & 6.1 & 2.5 & 1.3 & 0.8 & 31.4 \\ \hline \end{tabular}
\end{table} 
Table 2: Output power of AS1-AS5 and S1 with average power of 0.855 mW and 0.856 mW for Beam 1 and Beam 2, respectively [62]. Figure 15: Photographs of the multicolored arrays generated with (**a**) pulse energy of beam 2 of 220 \(\upmu\)J, (**b**) pulse energy of beam 2 of 250 \(\upmu\)J; (**c**) time delay of two pump beams of 7 fs and pulse energy of beam 2 of 250 \(\upmu\)J; and (**d**) a short-pass filter cut-off wavelength at 820 nm inserted in the Beam 1 path [55]. The spectra of the sidebands on the center row B\({}_{\text{m},0}\) and the second column B\({}_{\text{2,n}}\) were measured, as shown in Figure 17. The sidebands on the central row were generated through a CFWM process, which is almost the same as discussed in previous sections. The center wavelengths between neighboring spots on the same column were approximately the same, as shown in Figure 17b. A more accurate experiment using pump beams with narrower spectra will help to confirm these characteristics. The powers of Beam 1 and Beam 2 were set to 0.1 and 25 mW, respectively. The measured powers of some sidebands at this pump rate are shown in Figure 18a. The powers of sidebands on the rows of B\({}_{\text{m},0}\), B\({}_{\text{m},1}\), B\({}_{\text{m},-1}\), B\({}_{\text{m},2}\), B\({}_{\text{m},-2}\) are shown as the star, red circle, black square, green triangle and blue triangle, respectively. We found that the power of the sidebands on B\({}_{\text{m},1}\) and B\({}_{\text{m},-1}\) were approximately the same as the value of m. The sidebands in B\({}_{\text{m},2}\) and B\({}_{\text{m},-2}\) also had this property, showing that the power distribution had mirror symmetry with the central line of B\({}_{\text{m},0}\). The power dependence of three sidebands, B\({}_{\text{1},0}\), B\({}_{\text{2},0}\), and B\({}_{\text{2},1}\), on the input power of Beam 2 are shown in the inset of Figure 18a.