Plasmon polaritons of the TE and TM types in a metal film bordering a superlattice. III. Plasmon polaritons in bilayer superlattices

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Abstract

The paper theoretically investigates TE and TM polarized surface plasmon polaritons in a metal film in contact with a semi-infinite periodic superlattice formed by alternating layers of two materials. It is shown that in a certain case, the frequency dependence of the impedances of such a bilayer superlattice can be of only two types out of three possible types of dependencies. The dispersion curves TE and TM of surface plasmon polaritons in a silver film have been calculated for a number of structures consisting of various combinations of bilayer superlattices containing layers of quartz and titanium oxide. The calculation results are compared with the conclusions of the general theory on the maximum number of surface plasmon polaritons. The effect of the absorption of electromagnetic waves in the film on the characteristics of surface plasmon polaritons is analyzed.

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About the authors

A. N. Darinskii

National Research Complex “Kurchatov Institute”

Author for correspondence.
Email: Alexandre_Dar@mail.ru

Shubnikov Institute of Crystallography, Kurchatov Complex of Crystallography and Photonics

Russian Federation, Leninskii prospekt 59, Moscow 119333

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Supplementary files

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2. Fig. 1. TE-SPP in the second upper band gap of the SiO2/TiO2 SL. Lines 1 and 2 are two branches of TE-SPP in the Ag film placed between the SL with an outer TiO2 layer 0.4 μm thick and the SL with an outer SiO2 layer 0.04 μm thick. Line 3, passing just below line 2, is a branch of TE-SPP in the Ag film at the boundary between the SL with an outer SiO2 layer 0.4 μm thick and vacuum. Lines 4 and 5 are the band boundaries. Gray areas are other zones.

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3. Fig. 2. TM-SPP in the lower and first upper band gaps of the SiO2/TiO2 SL. The Ag film is located between the SL with the outer TiO2 layer of 0.4 μm thickness and the SL with the outer SiO2 layer of 0.04 μm thickness. Lines 1 and 2 are two branches of TM-SPP in the lower band gap. Lines 3 and 4 are two branches of TM-SPP in the first upper band gap. The upper boundary of the lower and the lower boundary of the first upper band gaps practically coincide (line 5). Line 6 is the upper boundary of the first upper band gap. Gray areas are other bands.

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4. Fig. 3. The ratio of the imaginary part k'' of the wavenumber to its real part k' for the TE-SPP in the second upper band gap (a) and for the TM-SPP in the lower and first upper band gaps (b) of the SiO2/TiO2 SL taking into account the absorption in the Ag film. Lines 1–3 in Fig. 3a are the frequency dependence of the attenuation of the TE-SPP of branches 1–3 in Fig. 1, respectively. Lines 1–4 in Fig. 3b are the frequency dependence of the attenuation of the TM-SPP of branches 1–4 in Fig. 2, respectively.

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5. Fig. 4. The fraction of energy concentrated in the Ag film, depending on the frequency of the TM-PPP, the dispersion curves of which are shown in Fig. 2. The numbering of the curves is the same as in Fig. 2.

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6. Fig. 5. Dependence of the electric field Ex of the slow and fast TM-SPP on the distance z to the boundary with the film in the lower forbidden zone (lines 1 and 2). In Fig. 2, these SPPs correspond to dispersion curves 1 and 2. We assume that z = 0 is the boundary of both CPs.

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7. Fig. 6. Frequency dependence of approximate values ​​of k''/k' for TM-PPP, the dispersion curves of which are shown in Fig. 2. The numbering of the curves is the same as in Fig. 2.

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8. Fig. 7. TE-SPP in the second forbidden band of the SiO2/TiO2 SL. In both SLs, between which the Ag film is located, the outer layer is a 0.08 μm thick TiO2 layer. The film thickness is 25 nm. Line 1 is the upper boundary of the band, 2 and 3 are the dispersion dependences of the slow and fast TE-SPP, respectively. The lower boundary of the band is not shown.

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