Current Optics and Photonics

Optical Society of Korea (한국광학회)
권호 표지
DOI QR코드

DOI QR Code

Scalar Fourier Modal Method for Wave-optic Optical-element Modeling

  • Kim, Soobin (Department of Electronics and Information Engineering, Korea University Sejong Campus) ;
  • Hahn, Joonku (School of Electronic and Electrical Engineering, Kyungpook National University) ;
  • Kim, Hwi (Department of Electronics and Information Engineering, Korea University Sejong Campus)
  • Received : 2021.06.17
  • Accepted : 2021.08.18
  • Published : 2021.10.25
Download PDF
⟨ Previous Next ⟩

Abstract

A scalar Fourier modal method for the numerical analysis of the scalar wave equation in inhomogeneous space with an arbitrary permittivity profile, is proposed as a novel theoretical embodiment of Fourier optics. The modeling of devices and systems using conventional Fourier optics is based on the thin-element approximation, but this approach becomes less accurate with high numerical aperture or thick optical elements. The proposed scalar Fourier modal method describes the wave optical characteristics of optical structures in terms of the generalized transmittance function, which can readily overcome a current limitation of Fourier optics.

Keywords

Acknowledgement

This study was supported by the National Research Foundation of Korea (NRF) (NRF-2019R1A2C1010243).

References

  1. J. W. Goodman, Introduction to Fourier optics, 3rd ed. (Roberts and Company Publishers, CO, USA. 2004).
  2. H. Gross, Handbook of Optical Systems: Fundamentals of Technical Optics (Wiley-VCH, Darmstadt, Germany. 2005), Vol. 1.
  3. K.-H. Brenner and W. Singer, "Light-propagation through microlenses: a new simulation method," Appl. Opt. 32, 4984-4988 (1993). https://doi.org/10.1364/AO.32.004984
  4. M. D. Feit and J. A. Fleck, "Light propagation in graded-index optical fibers," Appl. Opt. 17, 3990-3998 (1978). https://doi.org/10.1364/AO.17.003990
  5. J. Van Roey, J. van der Donk, and P. E. Lagasse, "Beampropagation method: analysis and assessment," J. Opt. Soc. Am. 71, 803-810 (1981). https://doi.org/10.1364/JOSA.71.000803
  6. S. Schmidt, T. Tiess, S. Schroter, R. Hambach, M. Jager, H. Bartelt, A. Tunnermann, and H. Gross, "Wave-optical modeling beyond the thin-element-approximation," Opt. Express 24, 30188-30200 (2016). https://doi.org/10.1364/OE.24.030188
  7. T. D. Gerke and R. Piestun, "Aperiodic volume optics," Nat. Photonics 4, 188-193 (2010). https://doi.org/10.1038/nphoton.2009.290
  8. M. Kim, Y. Choi, C. Yoon, W. Choi, J. Kim, Q.-H. Park, and W. Choi, "Maximal energy transport through disordered media with the implementation of transmission eigenchannels," Nat. Photonics 6, 581-585 (2012). https://doi.org/10.1038/nphoton.2012.159
  9. Y. Choi, T. D. Yang, C. Fang-Yen, P. Kang, K. J. Lee, R. R. Dasari, M. S. Feld, and W. Choi, "Overcoming the diffraction limit using multiple light scattering in a highly disordered medium," Phys. Rev. Lett. 107, 023902 (2011). https://doi.org/10.1103/PhysRevLett.107.023902
  10. S. Y. Lee, K. Lee, S. Shin, and Y. K. Park, "Generalized image deconvolution by exploiting spatially variant point spread functions," arXiv:1703.08974 (2017).
  11. J. Chung, G. W. Martinez, K. C. Lencioni, S. R. Sadda, and C. Yang, "Computational aberration compensation by coded-aperture-based correction of aberration obtained from optical Fourier coding and blur estimation," Optica 6, 647-661 (2019). https://doi.org/10.1364/optica.6.000647
  12. C. Jang, K. Bang, S. Moon, J. Kim, S. Lee, and B. Lee, "Retinal 3D: augmented reality near-eye display via pupil-tracked light field projection on retina," ACM Trans. Graph. 36, 190 (2017).
  13. S. Lee, C. Jang, S. Moon, J. Cho, and B. Lee, "Additive light field displays: realization of augmented reality with holographic optical elements," ACM Trans. Graph. 35, 60 (2016).
  14. H. Kogelnik, "Coupled wave theory for thick hologram gratings," Bell Syst. Tech. J. 48, 2909-2947 (1969). https://doi.org/10.1002/j.1538-7305.1969.tb01198.x
  15. M. G. Moharam and T. K. Gaylord, "Rigorous coupled-wave analysis of planar-grating diffraction," J. Opt. Soc. Am. 71, 811-818 (1981). https://doi.org/10.1364/JOSA.71.000811
  16. H. Kim, J. Park, and B. Lee, Fourier Modal Method and Its Applications in Computational Nanophotonics (CRC Press, NY, USA. 2012).
  17. P. S. Carney, J. C. Schotland, and E. Wolf, "Generalized optical theorem for reflection, transmission, and extinction of power for scalar fields," Phys. Rev. E 70, 036611 (2004). https://doi.org/10.1103/physreve.70.036611