Evolutionary Optimization of Dielectric Lens Design through Biased Initialization

Öz

In high-dimensional dielectric lens designs, randomly generated initial populations often increase the number of full-wave electromagnetic simulations and computational costs due to the presence of low-performance solutions. In this study, a hybrid optimization approach is proposed that combines a statistically guided initial population with a genetic algorithm and simultaneous perturbation stochastic approximation to reduce this problem without restricting the design space. The performance of the proposed approach is evaluated on a fully dielectric planar lens using full-wave electromagnetic simulations based on the two-dimensional finite-difference time-domain solution of Maxwell’s equations. By employing the biased initialization strategy, the average fitness value is improved from below 0.4 to above 0.77. Furthermore, a similarity exceeding 88% and focusing performance close to the diffraction limit are achieved for an ideal point source, while an input–output correlation above 98% is obtained for a more realistic input distribution. These results demonstrate that the proposed approach provides an effective and generalizable optimization strategy for high-dimensional electromagnetic inverse design problems by enabling faster convergence with fewer simulations.

Anahtar Kelimeler

• Dielectric lens
• Electromagnetic inverse design
• Biased initialization

Destekleyen Kurum

The Scientific and Technological Research Council of Türkiye (TUBITAK)

Proje Numarası

225E079

Teşekkür

The author gratefully acknowledges the financial support of the Scientific and Technological Research Council of Türkiye (TÜBİTAK) under Project No. 225E079 entitled “Machine Learning-Assisted, Equivalence Theorem-Based Reconfigurable Photonic Device Prototype.” The author would also like to thank Bilgehan Barış Öner for his valuable contributions to the successful realization of the project.

Yanlı Başlatma Yaklaşımı ile Dielektrik Mercek Tasarımının Evrimsel Optimizasyonu

Öz

Yüksek boyutlu dielektrik mercek tasarımlarında rastgele başlangıç popülasyonları, düşük performanslı çözümler nedeniyle tam dalga elektromanyetik benzetim sayısını ve hesaplama maliyetini artırmaktadır. Bu çalışmada, çözüm uzayını sınırlandırmadan bu sorunu azaltmak amacıyla istatistiksel olarak yönlendirilmiş başlangıç popülasyonunu genetik algoritma ve eşzamanlı pertürbasyon stokastik yaklaşım algoritması ile birleştiren hibrit bir optimizasyon yaklaşımı önerilmektedir. Yaklaşımın başarımı, Maxwell denklemlerinin iki boyutlu zaman alanında sonlu farklar yöntemiyle çözülmesine dayanan tam dalga elektromanyetik benzetimler kullanılarak tamamen dielektrik düzlemsel bir mercek üzerinde değerlendirilmiştir. Yanlı başlatma yaklaşımının uygulanması sayesinde ortalama uygunluk değeri 0,4’ün altından 0,77’nin üzerine çıkarılmış; ideal noktasal kaynak için %88’in üzerinde benzerlik ve kırınım limitine yakın odaklama, daha gerçekçi giriş dağılımı için ise %98’in üzerinde giriş–çıkış korelasyonu elde edilmiştir. Bu sonuçlar, önerilen yaklaşımın daha az benzetimle daha hızlı yakınsama sağlayarak yüksek boyutlu elektromanyetik tersine tasarım problemleri için etkili ve genellenebilir bir optimizasyon stratejisi sunduğunu göstermektedir.

Anahtar Kelimeler

• Dielektrik mercek
• Elektromanyetik tersine tasarım
• Yanlı başlatma yaklaşımı

Destekleyen Kurum

Türkiye Bilimsel ve Teknolojik Araştırma Kurumu (TÜBİTAK)

Proje Numarası

225E079

Teşekkür

Yazar, “Makine Öğrenme Destekli, Eşdeğerlik Teoremleri Tabanlı Yapılandırılabilir Fotonik Cihaz Prototipi” başlıklı 225E079 numaralı proje kapsamında Türkiye Bilim ve Teknolojik Araştırma Konseyi (TÜBİTAK) tarafından sağlanan mali desteğe minnettar olduğunu belirtir. Yazar ayrıca, projenin başarılı bir şekilde gerçekleştirilmesine yaptığı değerli katkılarından dolayı Bilgehan Barış Öner'e teşekkür eder.

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