The Prediction of Chiral Metamaterial Resonance using Convolutional Neural Networks and Conventional Machine Learning Algorithms

Abstract

Electromagnetic resonance is the most important distinguishing property of metamaterials to examine many unusual phenomena. The resonant response of metamaterials can depend many parameters such as geometry, incident wave polarization. The estimation and the design of the unit cells can be challenging for the required application. The research on resonant behavior can yield promising applications. We investigate the resonance frequency of the chiral resonator as a unit of chiral metamaterial employing both traditional machine learning algorithms and convolutional deep neural networks. To our knowledge, this is the very first attempt on chiral metamaterials in that comparing the impact of various machine learning algorithms and deep learning model. The effect of geometrical parameters of the chiral resonator on the resonance frequency is studied. For this purpose, convolutional neural networks, support vector machines, naive Bayes, decision trees, random forests are employed for classification of resonance frequency. Extensive experiments are performed by varying training set percentages, epoch sizes, and data sets.

Keywords

• Chiral metamaterials
• Convolutional neural network
• Deep learning
• Machine learning
• Microwave resonance

Kaynakça

1. [1] Lord Kelvin, in Baltimore Lectures on Molecular Dynamics and the Wave Theory of Light, Clay and Sons: London, 1904, p. 449.
2. [2] Barron, Laurence D. Molecular light scattering and optical activity. Cambridge University Press,2004.
3. [3] Smith, D. R., Padilla, W. J., Vier, D. C., Nemat-Nasser, S. C., Schultz, S. "Composite medium with simultaneously negative permeability and permittivity." Physical review letters 84.18 (2000), 4184.
4. [4] Zhao, R., Zhang, L., Zhou, J., Koschny, T., Soukoulis, C. M. "Conjugated gammadion chiral metamaterial with uniaxial optical activity and negative refractive index." Physical Review B, 83.3 (2011): 035105.
5. [5] Wang, B., Zhou, J., Koschny, T., Soukoulis, C. M. "Nonplanar chiral metamaterials with negative index." Applied Physics Letters 94.15 (2009): 151112.
6. [6] Zhou, J., Dong, J., Wang, B., Koschny, T., Kafesaki, M., Soukoulis, C. M. "Negative refractive index due to chirality." Physical Review B 79.12 (2009): 121104.
7. [7] Kenanakis, G., Zhao, R., Stavrinidis, A., Konstantinidis, G., Katsarakis, N., Kafesaki, M., Economou, E. N. "Flexible chiral metamaterials in the terahertz regime: a comparative study of various designs." Optical Materials Express 2.12 (2012): 1702-1712.
8. [8] Zhang, S., Park, Y. S., Li, J., Lu, X., Zhang, W., Zhang, X. "Negative refractive index in chiral metamaterials." Physical review letters 102.2 (2009): 023901.

9. [9] Kuwata-Gonokami, M., Saito, N., Ino, Y., Kauranen, M., Je_movs, K., Vallius, T., Svirko, Y. "Giant optical activity in quasi-two- dimensional planar nanostructures." Physical review letters 95.22 (2005): 227401.
10. [10] Dong, J., Zhou, J., Koschny, T., Soukoulis, C. "Bi-layer cross chiral structure with strong optical activity and negative refractive index." Optics Express 17.16 (2009): 14172-14179.
11. [11] Marqus, R., Medina, F., Ra_i-El-Idrissi, R. "Role of bianisotropy in negative permeability and left-handed metamaterials." Physical Review B 65.14 (2002): 144440.
12. [12] Marqus, R., Mesa, F., Martel, J., Medina, F. "Comparative analysis of edge-and broadside-coupled split ring resonators for metamaterial design-theory and experiments." IEEE Transactions on antennas and propagation 51.10 (2003): 2572-2581.
13. [13] Huangfu, J., Ran, L., Chen, H., Zhang, X. M., Chen, K., Grzegorczyk, T. M., Kong, J. A. "Experimental con_rmation of negative refractive index of a metamaterial composed of –like metallic patterns." Applied Physics Letters 84.9 (2004): 1537-1539.
14. [14] Ran, L., Huangfu, J. T., Chen, H. S., Li, Y., Zhang, X., Chen, K., Kong, J. A. "Microwave solid- state left-handed material with a broad bandwidth and an ultralow loss." Physical Review B , 70.7 (2004): 073102.
15. [15] Aydin, K., Li, Z., Hudlika, M., Tretyakov, S. A., Ozbay, E. "Transmission characteristics of bianisotropic metamaterials based on omega shaped metallic inclusions." New Journal of Physics, 9.9 (2007): 326.
16. [16] Jaggard, D. L., Mickelson, A. R., Papas, C. H. "On electromagnetic waves in chiral media." Applied physics 18.2 (1979): 211-216.
17. [17] Tretyakov, S. A., Mariotte, F., Simovski, C. R., Kharina, T. G., Heliot, J. P. "Analytical antenna model for chiral scatterers: Comparison with numerical and experimental data." IEEE Transactions on Antennas and Propagation 44.7 (1996): 1006-1014.
18. [18] Saenz, E., Semchenko, I., Khakhomov, S., Guven, K., Gonzalo, R., Ozbay, E., Tretyakov, S. "Modeling of spirals with equal dielectric, magnetic, and chiral susceptibilities." Electromagnetics 28.7 (2008): 476-493.
19. [19] Guven, K., Saenz, E., Gonzalo, R., Ozbay, E., Tretyakov, S. "Electromagnetic cloaking with canonical spiral inclusions." New Journal of Physics 10.11 (2008): 115037.
20. [20] I. Malkiel, M. Mrejen, A. Nagler, U. Arieli, L. Wolf and H. Suchowski, "Deep learning for the design of nano-photonic structures," 2018 IEEE International Conference on Computational Photography (ICCP), Pittsburgh, PA, 2018, pp. 1-14, doi: 10.1109/ICCPHOT.2018.8368462.
21. [21] Kiarashinejad, Yashar, et al. "Deep learning reveals underlying physics of lightmatter interactions in nanophotonic devices." Advanced Theory and Simulations 2.9 (2019): 1900088.
22. [22] Ma, Wei, Feng Cheng, and Yongmin Liu. "Deep-learning-enabled on-demand design of chiral metamaterials." ACS nano 12.6 (2018): 6326-6334.
23. [23] Yao, Kan, Rohit Unni, and Yuebing Zheng. "Intelligent nanophotonics: merging photonics and artifcial intelligence at the nanoscale." Nanophotonics 8.3 (2019): 339-366.
24. [24] Peurifoy, John, et al. "Nanophotonic particle simulation and inverse design using arti_cial neural networks." Science advances 4.6 (2018).
25. [25] Malkiel, Itzik, et al. "Plasmonic nanostructure design and characterization via deep learning." Light: Science Applications 7.1 (2018): 1-8.
26. [26] Ma, W., Cheng, F., Xu, Y., Wen, Q., Liu, Y. (2019). Probabilistic Representation and Inverse Design of Metamaterials Based on a Deep Generative Model with SemiSupervised Learning Strategy. Advanced Materials, 31(35), 1901111.
27. [27] Ahmed, Waqas W., et al. "Deterministic and probabilistic deep learning models for inverse design of broadband acoustic cloak." Physical Review Research 3.1 (2021): 013142.
28. [28] Huang, Wei, et al. "Inverse engineering of electromagnetically induced transparency in terahertz metamaterial via deep learning." Journal of Physics D: Applied Physics 54.13 (2021): 135102.
29. [29] Tao, Zilong, et al. "Optical circular dichroism engineering in chiral metamaterials utilizing a deep learning network." Optics Letters 45.6 (2020): 1403-1406.
30. [30] Lininger, Andrew, Michael Hinczewski, and Giuseppe Strangi. "General Inverse Design of Thin-Film Metamaterials with Convolutional Neural Networks." arXiv preprint arXiv:2104.01952 (2021).
31. [31] McCallum, A., Nigam, K." A comparison of event models for naive bayes text classification." In AAAI-98 workshop on learning for text categorization (Vol. 752, No. 1, pp. 41-48),1998.
32. [32] Manning, C., Schutze, H. "Foundations of statistical natural language processing." MIT press,1999.
33. [33] Kilimci, Z. H., Gven, A., Uysal, M., Akyokus, S." Mood detection from physical and neurophysical data using deep learning models." Complexity, 2019.
34. [34] Kilimci, Z. H., Omurca, S. I." Extended feature spaces based classifier ensembles for sentiment analysis of short texts." Information Technology and Control, 47(3), 457-470, 2018.
35. [35] Kilimci, Z. H., Akyokus, S." Deep learning-and word embedding-based heterogeneous classifier ensembles for text classification." Complexity, 2018.
36. [36] Kilimci, Z. H., Ganiz, M. C. "Evaluation of classification models for language processing." In 2015 International Symposium on Innovations in Intelligent SysTems and Applications (INISTA) (pp. 1-8). IEEE, 2015.
37. [37] Joachims T. "Text Categorization with Support Vector Machines: Learning with Many Relevant Features." In: 10th European Conference on Machine Learning; 1998; Chemnitz, Germany: pp.137-142.
38. [38] Burges CJC." A Tutorial on Support Vector Machines for Pattern Recognition." In: 3rd International Conference on Knowledge Discovery and Data Mining; 1998; New York, USA: pp. 121-167.
39. [39] Yang Y, Liu X. "A Re-examination of Text Categorization Methods." In: 22nd Annual nternational ACM SIGIR Conference on Research and Development in Information Retrieval; 1999; Berkeley, CA, USA: pp. 42-49.
40. [40] Kilimci, Z. H., Akyuz, A. O., Uysal, M., Akyokus, S., Uysal, M. O., Atak Bulbul, B., Ekmis, M. A." An improved demand forecasting model using deep learning approach and proposed decision integration strategy for supply chain." Complexity, 2019.
41. [41] Quinlan, J. R. (1986)."Induction of decision trees. Machine learning." 1(1), 81-106.
42. [42] Kilimci, Z. H., Akyokus, S. (2019, July). "The analysis of text categorization represented with word embeddings using homogeneous classifiers." In 2019 IEEE International Symposium on Innovations in Intelligent SysTems and Applications (INISTA) (pp. 1-6). IEEE.
43. [43] Kilimci, Z. H., Omurca, S. I. (2017, August). "A Comparison of Extended Space Forests for Classifier Ensembles on Short Turkish Texts." In International Academic Conference on Engineering, IT and Artificial Intelligence (pp. 96-104).
44. [44] L. Breiman, "Random forests." Machine Learning, vol. 45, no. 1, pp. 532, 2001.
45. [45] Kilimci, Z. H., Akyokus, S., Omurca, S. I. (2016, August). "The effectiveness of homogenous ensemble classifiers for Turkish and English texts." In 2016 International Symposium on Innovations in Intelligent SysTems and Applications (INISTA) (pp. 1-7). IEEE.
46. [46] Kilimci, Z. H., Akyokus, S., Omurca, S. . (2017, July). "The evaluation of heterogeneous classifier ensembles for Turkish texts." In 2017 IEEE International Conference on Innovations in Intelligent SysTems and Applications (INISTA) (pp. 307-311). IEEE.
47. [47] Y. Lecun, L. Bottou, Y. Bengio, and P. Ha_ner, "Gradientbased learning applied to document recognition." Proceedings of the IEEE, vol. 86, no. 11, pp. 22782324, 1998.
48. [48] J. Schmidhuber, "Deep learning in neural networks: an overview." Neural Networks, vol. 61, pp. 85117, 2015.
49. [49] Y. LeCun, Y. Bengio, and G. Hinton, "Deep learning." Nature, vol. 521, no. 7553, pp. 436444, 2015.
50. [50] Tanberk, S., Kilimci, Z. H., Tkel, D. B., Uysal, M., Akyoku, S. "A Hybrid Deep Model Using Deep Learning and Dense Optical Flow Approaches for Human Activity Recognition." IEEE Access, 8, 19799-19809, 2020.
51. [51] Kilimci, Z. H., Akyokus, S." The evaluation of word embedding models and deep learning algorithms for Turkish text classification." In 2019 4th International Conference on Computer Science and Engineering (UBMK) (pp. 548-553). IEEE.
52. [52] Kilimci, Z. H. "Sentiment Analysis Based Direction Prediction in Bitcoin using Deep Learning Algorithms and Word Embedding Models." International Journal of Intelligent Systems and Applications in Engineering, 8(2), 60-65, 2020.
53. [53] Kilimci, Z. H. "Borsa tahmini için Derin Topluluk Modelleri (DTM) ile finansal duygu analizi." Journal of the Faculty of Engineering Architecture of Gazi University, 35(2), 635-650, 2020.
54. [54] Cevik, F., Kilimci, Z. H."The evaluation of Parkinson's disease with sentiment analysis using deep learning methods and word embedding models." Pamukkale University Journal of Engineering Sciences, 27(2), 151-161, 2021.
55. [55] Othan, D., Kilimci, Z. H., Uysal, M." Financial Sentiment Analysis for Predicting Direction of Stocks using Bidirectional Encoder Representations from Transformers (BERT) and Deep Learning Models." In Proc. Int. Conf. Innov. Intell. Technol., vol. 2019, pp. 30-35, 2019.