(45-3) 07 * << * >> * Russian * English * Content * All Issues

Optical differentiator based on a trilayer metal-dielectric structure
A.I. Kashapov 1,2, L.L. Doskolovich 1,2, D.A. Bykov 1,2, E.A. Bezus 1,2, D.V. Nesterenko 1,2

IPSI RAS – Branch of the FSRC "Crystallography and Photonics" RAS,
443001, Samara, Russia, Molodogvardeyskaya st. 151,
Samara National Research University, 443086, Samara, Russia, Moskovskoye Shosse 34

 PDF, 1252 kB

DOI: 10.18287/2412-6179-CO-824

Pages: 356-363.

Full text of article: Russian language.

Optical properties of a resonant trilayer metal-dielectric-metal (MDM) structure that consists of an upper metal layer, a dielectric layer, and a metal substrate are investigated. Using a multiple wave interference model, we prove that the reflection coefficient of the MDM structure may strictly vanish. The existence of a reflectance zero makes it possible to use the MDM structure as an optical differentiator. The numerical simulation results presented demonstrate the possibility of optical computation of the first derivative with respect to either time or spatial variable. The obtained results may find application in novel analog optical computing and optical information processing systems.

resonant structure, metal-dielectric multilayer, optical differentiation.

Kashapov AI, Doskolovich LL, Bykov DA, Bezus EA, Nesterenko DV. Optical differentiator based on a trilayer metal-dielectric structure. Computer Optics 2021; 45(3): 356-363. DOI: 10.18287/2412-6179-CO-824.

This work was funded by the Russian Science Foundation (project № 19-19-00514) (investigation of the optical properties of the MDM structure, Sections 1 and 2), Russian Foundation for Basic Research (project 18-07-00613) (investigation of the MDM differentiators), and by the RF Ministry of Science and Higher Education within the State assignment to the FSRC "Crystallography and Photonics" RAS (development of the software for simulating MDM differentiators, Section 3).


  1. Silva A, Monticone F, Castaldi G, Galdi V, Alù A, Engheta N. Performing mathematical operations with metamaterials. Science 2014; 343(6167): 160-163.
  2. Solli DR, Jalali B. Analog optical computing. Nat Photon 2015; 9(11): 704-706.
  3. Bykov DA, Doskolovich LL, Soifer VA. Temporal differentiation of optical signals using resonant gratings. Opt Lett 2011; 36(17): 3509-3511. DOI: 10.1364/OL.36.003509.
  4. Bykov DA, Doskolovich LL, Soifer VA. Single-resonance diffraction gratings for time-domain pulse transformations: integration of optical signals. J Opt Soc Am A 2012; 29(8): 1734-1740. DOI: 10.1364/JOSAA.29.001734.
  5. Doskolovich LL, Bykov DA, Bezus EA, Soifer VA. Spatial differentiation of optical beams using phase-shifted Bragg grating. Opt Lett 2014; 39(5): 1278-1281.– DOI: 10.1364/OL.39.001278.
  6. Bykov DA, Doskolovich LL, Bezus EA, Soifer VA. Optical computation of the Laplace operator using phase-shifted Bragg grating. Opt Express 2014; 22(21): 25084-25092. DOI: 10.1364/OE.22.025084.
  7. Rivas LM, Boudreau S, Park Y, Slavík R, LaRochelle S, Carballar A, Azaña J. Experimental demonstration of ultrafast all-fiber high-order photonic temporal differentiators. Opt Lett 2009; 34(12): 1792-1794.
  8. Berger NK, Levit B, Fischer B, Kulishov M, Plant DV, Azaña J. Temporal differentiation of optical signals using a phase-shifted fiber Bragg grating. Opt Express 2007; 15(2): 371-381.
  9. Kulishov M, Azaña J. Design of high-order all-optical temporal differentiators based on multiple-phase-shifted fiber Bragg gratings. Opt Express 2007; 15(10): 6152-6166.
  10. Golovastikov NV, Doskolovich LL, Bezus EA, Bykov DA, Soifer VA. An optical differentiator based on a three-layer structure with a W-shaped refractive index profile. J Exp Theor Phys 2018; 127(2): 202-209. DOI: 10.1134/S1063776118080174.
  11. Zhu T, Zhou Y, Lou Y, Ye H, Qiu M, Ruan Z, Fan S. Plasmonic computing of spatial differentiation. Nat Commun 2017; 8(1): 1-6.
  12. Ruan Z. Spatial mode control of surface plasmon polariton excitation with gain medium: from spatial differentiator to integrator. Opt Lett 2015; 40(4): 601-604.
  13. Bykov DA, Doskolovich LL, Morozov AA, Podlipnov VV, Bezus EA, Verma P, Soifer VA. First-order optical spatial differentiator based on a guided-mode resonant grating. Opt Express 2018; 26(8): 10997-11006. DOI: 10.1364/OE.26.010997.
  14. Dong Z, Si J, Yu X, Deng X. Optical spatial differentiator based on subwavelength high-contrast gratings. Appl Phys Lett 2018; 112(18): 181102.
  15. Bykov DA, Doskolovich LL, Golovastikov NV, Soifer VA. Time-domain differentiation of optical pulses in reflection and in transmission using the same resonant grating. J Opt 2013; 15(10): 105703. DOI: 10.1088/2040-8978/15/10/105703.
  16. Golovastikov NV, Bykov DA, Doskolovich LL. Resonant diffraction gratings for spatial differentiation of optical beams. Quantum Electron 2014; 44(10): 984. DOI: 10.1070/QE2014v044n10ABEH015477.
  17. Youssefi A, Zangeneh-Nejad F, Abdollahramezani S, Khavasi A. Analog computing by Brewster effect. Opt Lett 2016; 41(15): 3467. DOI: 10.1364/OL.41.003467.
  18. Nesterenko DV, Kolesnikova MD, Lyubarskaya AV. Optical differentiation based on the Brewster effect. Computer Optics 2018; 42(5): 758-763. DOI: 10.18287/2412-6179-2018-42-5-758-763.
  19. Nesterenko DV, Lyubarskaya AV, Kolesnikova MD, Soifer VA. The dependence of the image edge detection directivity by Brewster effect on the gradient of inhomogeneities of objects. J Phys Conf Ser 2019; 1368: 022066. DOI: 10.1088/1742-6596/1368/2/022066.
  20. Kolesnikova MD, Lyubarskaya AV, Nesterenko DV, Soifer VA. The resolution of optical image edge detection based on Brewster effect. J Phys Conf Ser 2019; 1368: 022016. DOI: 10.1088/1742-6596/1368/2/022016.
  21. Nesterenko DV, Kolesnikova MD, Lyubarskaya AV, Soifer VA. The dependence of the image edge detection directivity by Brewster effect on the gradient of inhomogeneities of objects. J Phys Conf Ser 2020; 1461: 012116. DOI: 10.1088/1742-6596/1461/1/012116.
  22. Pors A, Nielsen MG, Bozhevolnyi SI. Analog computing using reflective plasmonic metasurfaces. Nano Lett 2015; 15(1): 791-797.
  23. Pors A, Bozhevolnyi SI. Plasmonic metasurfaces for efficient phase control in reflection. Opt Express 2013; 21(22): 27438-27451.
  24. Chizari A, Abdollahramezani S, Jamali MV, Salehi JA. Analog optical computing based on a dielectric meta-reflect array. Opt Lett 2016; 41(15): 3451-3454.
  25. Shu S, Li Z, Li YY. Triple-layer Fabry-Perot absorber with near-perfect absorption in visible and near-infrared regime. Opt Express 2013; 21(21): 25307-25315.
  26. Yan M. Metal–insulator–metal light absorber: a continuous structure. J Opt 2013; 15(2): 025006.
  27. Cui Y, He Y, Jin Y, Ding F, Yang L, Ye Y, He S. Plasmonic and metamaterial structures as electromagnetic absorbers. Laser & Photonics Reviews 2014; 8(4): 495-520.
  28. Ng C, Wesemann L, Panchenko E, Song J, Davis TJ, Roberts A, Gómez DE. Plasmonic near-complete optical absorption and its applications. Adv Opt Mater 2019; 7(14): 1801660.
  29. Li Z, Butun S, Aydin K. Large-area, lithography-free super absorbers and color filters at visible frequencies using ultrathin metallic films. ACS Photon 2015; 2(2): 183-188.
  30. Wesemann L, Panchenko E, Singh K, Della Gaspera E, Gómez DE, Davis TJ, Roberts A. Selective near-perfect absorbing mirror as a spatial frequency filter for optical image processing. APL Photon 2019; 4(10): 100801.
  31. Born M, Wolf E. Principles of optics. Electromagnetic theory of propagation, interference and diffraction of light. 7th ed. Cambridge: Cambridge University Press; 1999.
  32. Li L. Formulation and comparison of two recursive matrix algorithms for modeling layered diffraction gratings. J Opt Soc Am A 1996; 13(5): 1024-1035.
  33. Doskolovich LL, Golovastikov NV, Bykov DA, Bezus EA. Analytical design of flat-top transmission filters composed of several resonant structures. Opt Express 2019; 27(19): 26786-26798. DOI: 10.1364/OE.27.026786.
  34. Bykov DA, Bezus EA, Doskolovich LL. Coupled-wave formalism for bound states in the continuum in guided-mode resonant gratings. Phys Rev A 2019; 99(6): 063805. DOI: 10.1103/PhysRevA.99.063805.
  35. Refractive index database. Source: <https://refractiveindex.info/>.
  36. Moharam MG, Pommet DA, Grann EB, Gaylord TK. Stable implementation of the rigorous coupled-wave analysis for surface-relief gratings: enhanced transmittance matrix approach. J Opt Soc Am A 1995; 12(5): 1077-1086.

© 2009, IPSI RAS
151, Molodogvardeiskaya str., Samara, 443001, Russia; E-mail: ko@smr.ru ; Tel: +7 (846) 242-41-24 (Executive secretary), +7 (846) 332-56-22 (Issuing editor), Fax: +7 (846) 332-56-20