“Nanooptics and nanophotonics”

Express algorithm for calculating the sensory effect of a three-layer optical circuit in comparison with the transfer matrix method
A.D. Suprun, L.V. Shmeleva
 Department of Theoretical Physics, Faculty of Physics, Taras Shevchenko National University of Kyiv. Volodymyrska Street, 64/13, Kyiv-01601, Ukraine. 
E-mail: lshmel@univ.kiev.ua 

Usually, the matrix transfer (MT) method is used to calculate complex optical systems. This method, on the one hand, makes it possible to calculate quite complex (multilayer) systems, although it is several approximate. And, on the other hand, it is quite accurate and allows practically modulate a real experiment.
But a significant flaw of the MT method is that it requires significant computer power. Moreover, the more complex the system in terms of the number of layers, the more unwieldy its numerical realization. This always leaves open the question of finding less unwieldy, but at the same time sufficiently accurate express algorithms (EA) for finding the sensor values of the resonant wavelength and the resonant angle of incidence. 
Three-layer scheme (Kretschman) "prism - gold nano layer - dielectric" was considered, as having the simplest structure and, at the same time, for it the EA are known to calculate the resonant wavelength and resonant angle of incidence. The results of direct calculation using MT and the results of calculation using EA are compared. The optimal mode in calculations by the TM method was chosen from the condition of the maximum relation of the depth of the minimum of the reflection coefficient to its half-width.
Comparison of the results of calculations by both methods showed the coincidence of the values of the resonant wavelength and the resonant angle of incidence for the three-layer scheme.
This allows us to talk about the search for similar algorithms for more complex systems, for example, for four-layer schemes often used in today’s investigates using a graphene layer.