volume | PIER Journals

Abstract

First of all we inform the audiences that this article is a Review Paper (RP) for the PIERS17 Proceedings Paper (Zheng et al. [17]). The reason why we publish this RP is that: although the paper [17] reported important ideas and simulation facts, details of the contents were insufficient, and the audiences of the report were not satisfied. This was because the page number was limited, and we saved the number of pages. However, because the contents of~[17] are important, we decided to publish an RP, which would provide additional explanations or give considerations supporting main issues. Now, we start the abstract from Section~1. Here, we mention historical topics and RP-related things. In Section~2, we explain the problem of diffraction by a conically-mounted metal grating. To save the page number, we skip the method of solution. In Section~3, we explain our method in noise free case. We show the high precision of the quadratic (or parabola) approximation. We define the workspace (WS: relation between index range of a sample and a proper azimuth angle) and one-to-one correspondence between sample index and resonance angle. In Section~4, we try our method in a noisy environments. A curve-fitting procedure and three types of noise filters work to find satisfactory solutions. That is, in both 3. and 4., the resolution of the index is 7-digit usually, which is our target from the beginning. We think that the introduction of AI or statistical processing would increase the stability of the result. In Section~5, we mention some of future works. In APPENDIX A, we explain the method: How to find the azimuth angle, which we need in solving the diffraction problems by conically-mounted grating.

1. Raeter, H., "Surface plasmon and roughness," Surface Polaritons, Chapter 9, 331-403, V. M. Argranovich and D. L. Mills (eds.), North-Holland, New York, Amsterdam, 1982.

2. Neviere, M., "The homogeneous problem," Electromagnetic Theory of Gratings, Chapter 5, 123-157, R. Petit (ed.), Springer-Verlag, Berlin, Heidelberg, New York, 1980.

3. Okuno, Y., T. Suyama, R. Hu, S. He, and T. Matsuda, "Excitation of surface plasmons on a metal grating and its application to an index sensor," IEICE Trans. Electron., Vol. 90, No. 7, 1507-1514, 2007.
doi:10.1093/ietele/e90-c.7.1507

4. Luo, Z., T. Suyama, X. Xu, and Y. Okuno, "A grating-based plasmon biosensor with high resolution," Progress In Electromagnetics Research, Vol. 118, 527-539, 2011.
doi:10.2528/PIER11060103

5. Matsuda, T., D. Zhou, and Y. Okuno, "Numerical analysis of plasmon resonance absorption in bisinusoidal metal gratings," J. Opt. Soc. Amer. A, Vol. 19, 695-701, 2002.
doi:10.1364/JOSAA.19.000695

6. Wood, R. W., "On a remarkable case of uneven distribution of light in a diffraction grating spectrum," Lond. Edinb. Dublin Philos. Mag. J. Sci., Vol. 4, 396-402, 1902.

7. Rayleigh, L., "On the dynamical theory of gratings," Proc. R. Soc. Lond. A., Vol. 79, 399-416, 1907.

8. Fano, U., "The theory of anomalous diffraction gratings and of quasi-stationary waves on metallic surfaces (Sommerfeld's Waves)," J. Opt. Soc. Am., Vol. 31, 213-222, 1941.
doi:10.1364/JOSA.31.000213

9. Maystre, D., "Theory of Wood's anomalies," Plasmonics: From Basics to Advanced Topics, 1st Edition, 39-83, Enoch S. and Bonod N. (eds), Springer, Berlin/Heidelberg, Germany, 2012.

10. Taniguchi, N., "On the basic concept of ‘Nano-Technology’," Proc. Intl. Conf. Prod. London, Part II British Society of Precision Engineering, 1974.

11. Homola, J., S. Yee, and G. Gauglitz, "Surface plasmon resonance sensors: Review," Sensors Actuators B, Vol. 54, 3-15, 1999.
doi:10.1016/S0925-4005(98)00321-9

12. Homola, J., I. Koudela, and S. Yee, "Surface plasmon resonance sensors based on diffraction gratings and prism couplers: sensitivity comparison," Sensors Actuators B, Vol. 54, 16-24, 1999.
doi:10.1016/S0925-4005(98)00322-0

13. Matsushima, A., T. Matsuda, and Y. Okuno, "Introduction to Yasuura's method of modal expansion with application to grating problems," The Generalized Multipole Technique for Light Scattering, T. Wriedt and Y. Eremin (eds.), Chapter 8, 51 pages, Springer, 2018.

14. Suyama, T., Z. Qian, F. Shi, H. Enomoto, and A. Matsushima, "Improvement of resolution of liquid refractive index measurement using metallic grating," Progress In Electromagnetics Research M, Vol. 85, 29-38, 2019.
doi:10.2528/PIERM19060304

15. Xu, X., Y. Okuno, and T. Suyama, "Analysis of plasmon resonance in a multilayer-coated bigrating," PIERS Proceedings, 1318-1322, Guangzhou, China, Aug. 25–28, 2014.

16. Gong, R., B. W. Chen, X. Xu, and Y. Okuno, "Resolution of a grating-based plasmon index sensor with efficiency-alone interrogation," 2016 Progress In Electromagnetic Research Symposium (PIERS), 4062-4066, Shanghai, China, Aug. 8–11, 2016.

17. Zheng, M., X. Xu, R. Gong, and Y. Okuno, "A grating-based plasmon index sensor: performance simulation in the presence of noise," 2017 Progress In Electromagnetics Research Symposium — Fall (PIERS — FALL), 2193-2198, Singapore, Nov. 19–22, 2017.

18. Matsuda, T., X. Xu, and Y. Okuno, "A couple of topics in numerical analysis of diffraction by a metal grating using Yasuura's method of modal expansion," PIERS Proceedings, 1930-1934, Prague, Chez Republic, 2015.

19. Hass, G. and L. Hardy, "Optical properties of metals," American Inst. Phys. Handbook, D. G. Gray (ed.), 2nd Edition, 6–107, McGraw-Hill, NY, 1963.

20. Palik, E. D., Handbook of Optical Constants of Solids, Academic Press, 1998.

21. Johnson, P. B. and R. W. Christy, "Optical constants of the noble metals," Phys. Rev. B, Vol. 6, 4370, Published Dec. 15, 1972.

22. Rakik, A. D., A. B. Djurisic, J. M. Elazar, and M. L. Majewski, "Optical properties of metallic films for vertical-cavity optoelectronic devices," App. Opt., Vol. 37, 5271-5283, 1998.
doi:10.1364/AO.37.005271

23. Bryan-Brown, G. P., J. R. Sambles, and M. C. Hutley, "Polarization conversion through the excitation of surface plasmons on a metallic grating," J. Modern Opt., Vol. 37, 1227-1232, 1990.
doi:10.1080/09500349014551301

24. Matsuda, T., D. Zhou, and Y. Okuno, "Numerical analysis of TE-TM mode conversion in a metal grating placed in conical mounting," IEICE Trans. Electron., Vol. J82-C-I, 42-49, 1999 (in Japanese)(in.

Dr. Xun Xu

Mr. Miaoning Zheng

Dr. Yoichi Okuno