Objective In recent years, photon orbital angular momentum, as a new degree of freedom, has attracted wide attention.The Laguerre -Gaussian (LG) beam is a commonly used orbitalangularmomentum (OAM) beam and is widely studied.Among a large amount of research, the mode conversion of LG beam attracts much attention from researchers. It is found that an LG beam can be converted into a Hermite -Gaussian (HG) beam with the help of cylindrical lenses. In addition, the nonlinear beam shaping technique can change the condition of phase matching in the nonlinear process to realize wavefront modulation, and harmonic waves with shaped wavefronts can be achieved by this technique during nonlinear optical processes. By combining these hot topics, we propose a novel mode conversion method for special beams in nonlinear 1419001 -8 研究论文 第 43 卷 第 14 期/2023 年 7 月/光学学报 processes, and the local quasiphasematching (LQPM) theory is employed to design the required optical superlattice (OSL). The function of mode converters is concentrated on the superlattice structure, and the phasematching condition is satisfied in the nonlinear mode conversion.Methods LQPM is used to design the OSL structure required by the nonlinear mode conversion process. Different from the conventional quasiphasematching (QPM) method in the reciprocal space, the LQPM is a nonlinear beam manipulation theory in real space. According to the principle of LQPM, the OSL structure function for the nonlinear mode conversion ofLG beams can be obtained. The domain structure shows a curved boundary, and the function of cylindrical lenses is integrated into the OSL. Matlab software is used to carry out numerical simulations for the nonlinear mode conversion process. The finitedifference method is employed in the numerical simulation process to calculate the field distribution in the twodimensional OSL. The field distribution and intensity curves of the secondharmonic wave after nonlinear mode conversion are obtained. It can be found that the designed OSL structure shows positive results on both mode conversion and frequency doubling.
Result and DiscussionsIn this paper, we propose an OSL structure that can realize the nonlinear mode conversion of theLG beam, and the curved domain structure is designed based on the LQPM theory. After analyzing the forms of the isophase planes of the structure, two different modes which we called positive mode and negative mode can be obtained (Fig. 1). It is found that both modes can be used to achieve nonlinear mode conversion under the phasematching condition, but the positive mode has better effect and can achieve perfect mode conversion. The LG beam with p=0 is taken as the fundamental wave to perform functional simulation on the designed OSL, and the converted HG beam image is observed as expected (Fig. 5). The relationship between the LG beam and the HG beam mode index is verified by observing the light and dark fringes. According to the above theoretical calculation and simulation results, it can be seen that the designed OSL integrates...
