超穎透鏡，以其輕量化和小型化的特點，將在未來的光學模組產品中展現出更強大的潛力。與傳統透鏡相比，超穎透鏡的體積與重量得到了顯著的縮小，使得其在應用於各種精密與高科技設備時，顯得更具彈性與便利。超穎結構在設計上，一般是利用對希望的操作頻率上做計算，設計出能夠達成相位匹配的結構，如 PB 相位法，然而，如面對多頻或寬頻的入射光的情況下，超穎透鏡的相位匹配設計可能因為頻率過大的變化導致聚焦錯誤，進而產生像差。
為了解決此問題，我們嘗試採用拓樸優化密度模型來最佳化氮化鎵（GaN）多頻超穎透鏡的結構。此方法的目的在於優化出能在面對多頻入射光時，達到最小像差和最大效率的結構，以此提升透鏡品質。
拓樸優化密度模型在反向設計上，以其極佳的優化效能與優化效率著名，然而，也有個無法避免的缺點，那即是最終優化結構有可能超出現有的實作技術。為了在優化效能與實作難易度上做出平衡，也為了驗證拓樸優化密度模型的設計潛力，我們設計了三個實驗，從原始設計目標的中心聚焦超穎透鏡，到想更進一步探索的偏離軸心聚焦的超穎透鏡與具有挑戰力的紅綠藍三色分開聚焦的超穎透鏡。三種設計的目標是為了達到對不同頻率的入射光進行精確偏折，進而增強超穎透鏡在處理多頻入射光情況下的性能。

Metalenses, with their lightweight and miniature characteristics, will demonstrate more powerful potential in future optical module products. Compared to traditional lenses, metalenses have significantly reduced volume and weight, making them more flexible and convenient when applied to various precision and high-tech devices. The design of a metasurface structure generally involves calculations at the desired operating frequency,
and designing structures that can achieve phase matching, such as the Pancharatnam–Berry (PB) phase method. However, when facing multi-frequency or broadband incident light, the phase matching design of the metalens may be incorrect due to too large frequency variations, resulting in aberrations.
To solve this problem, we attempt to use the topology optimization density model to optimize the structure of gallium nitride (GaN) multi-frequency metalenses. The goal of this method is to optimize a structure that can achieve minimal aberration and maximum efficiency when facing multi-frequency incident light, thereby improving lens quality.
The topology optimization density model is renowned for its excellent optimization performance and efficiency in inverse design. However, it also has an inevitable drawback, which is that the final optimized structure may exceed existing implementation techniques.
To strike a balance between optimization performance and implementation difficulty, and to verify the design potential of the topology optimization density model, we designed three experiments. Starting from the center-focus metalens that we initially wanted to improve, to the off-axis focused metalens we wanted to further explore, and the challenging red, green, and blue separate-focus metalens. The goal of the three designs is to achieve precise deflection for incident light of different frequencies, thereby enhancing the performance of metalenses when dealing with multi-frequency incident light.

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