Study of the Resonance Diffraction Phenomena on Gratings by the Rigorous Coupled Wave Method with Modified Equation System

Authors V. Fitio1, I. Yaremchuk1, A. Bendziak1, Y. Bobitski1,2

1Lviv Polytechnic National University, 12, S. Bandera St., 79013 Lviv, Ukraine

2University of Rzeszow, 16b, T. Rejtana St., 35959 Rzeszow, Poland

Issue Volume 12, Year 2020, Number 5
Dates Received 05 May 2020; revised manuscript received 15 October 2020; published online 25 October 2020
Citation V. Fitio, I. Yaremchuk, A. Bendziak, Y. Bobitski, J. Nano- Electron. Phys. 12 No 5, 05007 (2020)
PACS Number(s) 42.25.Bs, 42.79.Dj
Keywords Rigorous coupled wave analysis, Localized plasmon resonance, Diffraction gratings.

Results of a numerical analysis of the diffraction of optical waves of transverse magnetic (TM) polarization on gratings under the electromagnetic field resonance conditions are presented. Rigorous coupled wave analysis (RCWA) with modified equation system has been used. Modification is in change of the Toeplitz matrices in differential equation systems. These matrices are formed by complex Fourier series of a periodic function of the dielectric permittivity and its inversed function. Rectangular function of the dielectric permittivity per one period is changed by trapezoidal function; however, grating relief remains rectangular. Such replacement of the dielectric permittivity function more precisely corresponds to actual gratings. Oscillations of the reflectance and transmittance depending on the number of used coupled waves were reduced using modified equation system. Moreover, there is better convergence, especially in case of metallic gratings on the dielectric substrates, in which the localized plasmon resonance or the electromagnetic field resonance can occur in the grating slit. Any changes of the convergence with the use of modified systems of equations are not present in the case of dielectric gratings on the metallic substrates in comparison to the traditional expansion of the dielectric constant into a Fourier series. Surface plasmon-polariton resonance of a metal grating on metal substrate in case of which the reflectance from the grating is equal to zero was researched. There is a particularly complicated dependence of the reflectance on the number of coupled waves used in the analysis for both modifications of the equation system. Strong oscillations of the reflection coefficient from the grating are observed at certain values of coupled waves, which decrease with their growth.

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