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Optical properties of multilayer metal-dielectric nanofilms with all-evanescent modes

Simin Feng, J. Merle Elson, and Pamela L. Overfelt

Open Access Open Access

Abstract

We present a systematic study of mode characteristics of multilayer metal-dielectric (M-D) nanofilm structures. This structure can be described as a coupled-plasmon-resonantwaveguide (CPRW), a special case of coupled-resonator optical waveguide (CROW). Similar to a photonic crystal, the M-D is periodic, but there is a major difference in that the fields are evanescent everywhere in the M-D structure as in a nanoplasmonic structure. The transmission coefficient exhibits periodic oscillation with increasing number of periods. As a result of surface-plasmon-enhanced resonant tunneling, a 100% transmission occurs periodically at certain thicknesses of the M-D structure, depending on the wavelength, lattice constants, and excitation conditions. This structure indicates that a transparent material can be composed from non-transparent materials by alternatively stacking different materials of thin layers. The general properties of the CPRW and resonant tunneling phenomena are discussed.

©2005 Optical Society of America

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Figures (12)
Fig. 1.
Fig. 1. One-dimensional periodic structure with alternating layers of dielectric (subscript 1) and metallic materials (subscript 2). The thicknesses of the dielectric and metallic material layers are d 1 and d 2, respectively, with period d=d 1+d 2. The plasma wave vector K P=x̂KP and the Bloch wave vector K B=ẑKB . The thicknesses of the layers are sufficiently thin such that the surface plasmon fields are evanescently coupled along the ẑ direction throughout the multilayer structure.

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Fig. 2.
Fig. 2. Band structure of the evanescent fields of TM modes at different thickness of the layers. The blue zones represent the transmission pass bands of the evanescent fields, i.e. Bloch evanescent bands. The white areas are either stop bands or pass bands of traveling waves. The band diagram can be scaled by the lattice constants. In the plots, the values of the relative permittivity and permeability are ε1=2.66, µ 1=1, µ 2=1, and the effective plasmon frequency ωp =1.2×1016 s-1 with ε2=1-(ωp /ω)2.

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Fig. 3.
Fig. 3. Bloch evanescent bands of TM modes at different thickness of the layers for specially designed electron plasma frequency given by Eq.(8). The blue zones are the transmission bands of the evanescent fields. The white areas are either stop bands or pass bands of traveling waves. In the plots, the values of the relative permittivity and permeability are ε 1=2.66, µ 1=1, µ 2=1. Note that each value of Kp requires a different effective plasma frequency ωp . For a fixed value of Kp , there is a band of frequencies over which resonant modes can exist.

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Fig. 4.
Fig. 4. Bloch mode dispersion for the lower and upper bands at different thicknesses of the layers. The plasmon wave number Kp =1.5π/d for (a), (b), and (c), and Kp =1.36π/d for (d). The other parameters are the same as those in Fig. 2.

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Fig. 5.
Fig. 5. Plasmon mode dispersion of the lower and upper bands when (a) KB =0.25π/d and (b) KB =0.5π/d. The dashed red line represents the light line of the dielectric medium. In the plots d 1=120 nm and d 2=30 nm. The other parameters are the same as those in Fig. 2.

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Fig. 6.
Fig. 6. Transmission coefficient in the evanescent ẑ direction versus the number of periods of the structure. The wavelengths 375 and 495 nm are in the pass bands. The wavelength 430 nm is in the stop band. The parameters Kp =1.5π/d, d=d 1+d 2, d 1=120 nm, and d 2=30 nm. The other parameters are the same as those in Fig. 2.

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Fig. 7.
Fig. 7. Bloch wavevector KB versus the number of the periods for the three wavelengths in Fig. 6.

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Fig. 8.
Fig. 8. Transmission coefficient versus frequency showing the effects of defects in the MD structure with Kp =1.53π/d. Top: Six period M-D structure without defects with d=d 1+d 2 (d 1=120 nm and d 2=30 nm). In this case, there are 5 transmission resonances inside each pass band. The area in between is the stop band. Bottom: Six periods plus an extra metal layer at the dielectric end of the structure. In addition to the extra metal layer, the thickness of the third and the fifth metal layers is doubled while the thickness of the other layers are unchanged. There are three defect modes inside the stop band: one broadband with bandwidth 20 THz and two narrow transmission peaks.

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Fig. 9.
Fig. 9. Top: Dispersion of the defect modes represented by the red solid lines inside the bandgap. As a reference, the dashed blue curves shows the dispersion of the corresponding infinte periodic structure without defects. Bottom: Group velocities of the defect modes versus frequency. The ratio vg /c shows the group velocity vg relative to the speed of light, c, in vacuum. The parameters are the same as those in Fig. 8.

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Fig. 10.
Fig. 10. A DWDM filter of 100 GHz channel spacing using reflection mode of the CPRW structure that contains 140 periods. In the plots Kp =0.514π/d, d 1=150 nm, and d 2=60 nm. The plot shows part of the spectrum.

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Fig. 11.
Fig. 11. Schematic of a tunable nanoplasmonic filter. The metal/dielectric multilayer stack is placed between the prisms. The prisms on the top and bottom of the filter are used to couple light into and out of the filter. The plasmon frequency of the metal is ωp =1.2×1016 s -1. The refractive index is 1.75 for the prisms, and 1.63 for the dielectric material. To ensure the evanescent wave inside all the layers, the incident angle must be larger than the total interal reflection angle from the prism to the dielectric medium.

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Fig. 12.
Fig. 12. Transmission spectrum of the tunable filter shown in Fig. 11 when the applied voltage is zero (solid blue curve) volt and 1 volt (dashed green curve). The filter is composed of interleaved 8 nonlinear optical (NLO) polymer and 9 silver layers. The thickness of the polymer and the metal layer is 200 nm and 60 nm, respectively. The electro-optical (EO) coefficients of the NLO polymer are r 33=300 pm/V and r 13=100 pm/V. The index of refraction of the polymer is 1.63.

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Equations (8)

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K p = ω c ε 1 ε 2 ( ε 1 μ 2 − ε 2 μ 1 ) ε 1 2 − ε 2 2
ε 1 ε 2 < 0 , ε 1 μ 2 − ε 2 μ 1 ε 1 2 − ε 2 2 < 0 .
ε 2 ( ω ) = 1 − ω p 2 ω 2
∇ 2 E ( r ) + k 0 2 ε i μ i E ( r ) = 0 , i = 1 , 2
𝓔 n ( z ) = { a n exp [ − α 1 z n ] + b n exp [ α 1 ( z n − d 1 ) ] , 0 ≤ z n < d 1 c n exp [ − α 2 ( z n − d 1 ) ] + d n exp [ α 2 ( z z − d ) ] , d 1 < z n ≤ d .
α i = K p 2 − k 0 2 ε i μ i > 0 i = 1 , 2 .
cos ( K B d ) = cosh ( α 1 d 1 ) cosh ( α 2 d 2 ) + α 1 2 ε 2 2 + α 2 2 ε 1 2 2 α 1 α 2 ε 1 ε 2 sinh ( α 1 d 1 ) sinh ( α 2 d 2 ) ,
K p = ω p c ε 1 μ 1 ,
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