A comparison of optical sensors’ characteristics based on guided-mode resonance has been carried out. It was considered a prism structure with a metal film, a metal grating on a metal substrate and a dielectric grating on a dielectric substrate. It is shown that the main characteristics are determined by the sensitivity of the constant propagation of the respective waveguides on a change in wavelength and a change in the refractive index of the tested medium. In addition, they depend on the full width at half maximum of the spectral or angular reflectance dependence. The corresponding analytical relationships obtained for the three types of sensors are almost the same. It is demonstrated that the ratio of the sensor spectral sensitivity on the resonance curve spectral width is equal to the ratio of the angular sensitivity on the angular width of the corresponding resonance curve for all three types of sensors.
In this work, the diffraction of a Gaussian beam on a volume phase grating was researched theoretically and numerically. The proposed method is based on rigorous coupled-wave analysis (RCWA) and Fourier transform. The Gaussian beam is decomposed into plane waves using the Fourier transform. The number of plane waves is determined using the sampling theorem. The complex reflected and transmitted amplitudes are calculated for each RCWA plane wave. The distribution of the fields along the grating for the reflected and transmitted waves is determined using inverse Fourier transform. The powers of the reflected and transmitted waves are determined based on these distributions. Our method shows that the energy conservation law is satisfied for the phase grating. That is, the power of the incident Gaussian beam is equal to the sum of the powers of the reflected and transmitted beams. It is demonstration of our approach correctness. The numerous studies have shown that the spatial shapes of the reflected and transmitted beams differ from the Gaussian beam under resonance. In additional, the waveguide mode appears also in the grating. The spatial forms of the reflected and transmitted beams are Gaussian in the absence of resonance. It was found that the width of the resonance curves is wider for the Gaussian beam than for the plane wave. However, the spectral and angular sensitivities are the same as for the plane wave. The resonant wavelengths are slightly different for the plane wave and the Gaussian beam. Numerical calculations for four refractive index modulation coefficients of the grating medium were carried out by the proposed method. The widths of the resonance curves decrease with the increasing in the refractive index modulation. Moreover, the reflection coefficient also increases.
The resonant excitation of surface plasmon–polariton waves in metal gratings with rectangular and sinusoidal relief was studied. The main characteristics of the resonant excitation of a surface plasmon–polariton wave were obtained using analytical methods due to the fact that the resonance is excited at a grating thickness much smaller than a wavelength (1.064 µm). It is shown that the obtained results are very close to those calculated using numerical methods, e.g., Rigorous Coupled Wave Approach (RCWA). There is a small difference in the numerical data defined by both methods. The difference between the parameters for the two types of gratings is small. New analytical relationships of angular and spectral sensitivities with the change of the refractive index of the medium were obtained, depending on the grating period and the angle of incidence of the light beam. An analytical relationship between the spectral and angular widths of the resonant curves, at full width at half maximum, was determined.
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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