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The dispersion of the fundamental super mode confined along the boundary between a multilayer metal-insulator (MMI) stack and a dielectric coating is theoretically analyzed and compared to the dispersion of surface waves on a single metal-insulator (MI) boundary. Based on the classical Kretschmann setup, the MMI system is experimentally tested as an anisotropic material to exhibit plasmonic behavior and a candidate of “metametal” to engineer the preset surface plasmon frequency of conventional metals for optical sensing applications. The conditions to obtain artificial surface plasmon frequency are thoroughly studied, and the tuning of surface plasmon frequency is verified by electromagnetic modeling and experiments. The design rules drawn in this paper would bring important insights into applications such as optical lithography, nano-sensing and imaging.

The multilayer metal-insulator (MMI) stack system (also termed as metal-dielectric composite or MDC) has been widely used as an optically-anisotropic composite [

As a promising approach towards deep subwavelength optics, plasmonics have attracted great research interests for optical sensing and imaging in recent years. However, plasmonic materials are generally scarce in variety plus the working frequency is limited because of the preset plasma frequency of each plasmonic metal. This problem is worse off in optical frequency, as almost no substitutions (mostly doped semiconductor compounds) can be chosen to replace the overwhelmingly used metals such as aluminum (for DUV), silver and gold (for visible and NIR) due to high loss. It would therefore be significant for optical sensing or imaging applications to explore stratified medium as a plasmonic material or “metametal” and understand how its plasmonic features could be controlled, so as to broaden the frequency window for imaging or sensing applications [

Starting from the anisotropy of MMI structure, the effective permittivity tensor is obtained as [

where _{2}/_{1}, and the axes are setup in _{1} as the insulator and _{2} as the metal. Regarded as a single anisotropic medium, it can be placed next to the semi-space of a dielectric material (_{d}) and form a boundary as host of surface waves. Assuming a fundamental TM-polarized surface wave (super mode) propagating along this boundary and applying proper boundary conditions, the MMI-insulator boundary supports a propagation surface mode with the dispersion relation obtained as

To ensure this wave is confined to the boundary, an additional condition is applied as _{x} < 0, or

When

which is exactly the well-known dispersion relation for a metal-insulator (MI) boundary. When

which is the lightline of the dielectric coating.

(_{d}.

The similarity of the dispersion between MMI-insulator and MI-insulator structure revealed in Equations (4) and (5) gives a possibility to develop a concept of effective surface plasmon frequency (ESPF), especially when MMI is placed inside (or neighbored to) a dielectric semi-space to act just like a uniform metal (metametal). Firstly, we try to derive the value of the ESPF of MMI structure. Similar to the case of MI-insulator, the surface plasmon resonance (SPR) happens at the pole of the _{2}. The solution can be expressed by _{d}, _{1} and the filling ratio

while the positive root should be discarded based on the preconditions _{x} < 0 applied in the related section of Equation (3). Based on Equation (1), at least one of the two materials in the multilayered medium needs to have negative permittivity to make _{x} < 0. The negative root from Equation 6 gives the largest dielectric constant the metametal could reach at

To study the plasmonic property of the metametal, it is convenient to start from the Drude model of the filling metal _{p} is the plasmonic frequency of the filling metal. Here a characteristic frequency for the metametal can be defined as equal to ESPF (_{d} describes the dielectric half space. It would be interesting to study the relation between _{2}(–) and _{d}. For simplicity, we introduced a new term _{1}/_{d}, and another term _{2}(–) and –_{d}. From Equation (7), the factor

The observation indicates that the ratio

When

This case (_{d}) will not be able to decrease the free electron oscillation down to

To verify the existence of this super resonance mode and better explain the tuning of effective surface plasmon frequency (ESPF), we introduce a specific case for an identical substrate material under uniform gold and two types of MMIs. In _{d} = 2.5 (which can be regarded as a polymer-based photoresist). We then apply gold-SiO_{2} (_{2 }at 633 nm) and gold-Al_{2}O_{3} (_{2}O_{3} at 633 nm) multilayer stacks respectively to this substrate. It is obvious that the filling insulators have been chosen to make sure the ratio _{insulator}/_{d} can be less than unity for one case, and larger than unity for the other. Using the Equation (2) and the mode matching condition, we predicted the shifts of ESPF and SPR angle towards different directions (prism _{p} = 2.6). In _{2} and gold-Al_{2}O_{3} case respectively.

(_{2}O_{3} MMI (green) and gold-SiO_{2} MMI (red); (_{2}O_{3} MMI (green) and gold-SiO_{2} MMI (red). All three curves are on top of the same

The FDTD modeling of these 3 structures under a Kretschmann setup is shown in

To verify the tuning of surface plasma frequency, we have modeled a Kretschmann prism-coupling process (_{p} = 2.6) to excite the surface waves when the plasmons are neighbored to silicon dioxide (

Experimental setup for studying multilayer metal-insulator stacks and the cross-sectional view of the fabricated multilayer sample (SEM). Each individual layer is 10 nm and there are 10 layers (5 pairs) in total.

Note that for Kretschmann setup and the calculation from Equation (10), the mode of greatest interest here is the confined fundamental TM mode. Although MMI could support more complex modes [

Measured reflected power from a Kretschmann setup with a ZnSe (_{2} and Si_{3}N_{4} substrates are deposited via plasma-enhanced chemical vapor deposition (PECVD), while the gold single-layer and gold-alumina multilayer are deposited via e-beam evaporation (

Numerical and experimental results of reflection _{2} substrate and (_{3}N_{4} substrate. Red and blue lines describe the simulation results for single-layer and multilayer respectively. Red crosses and blue triangles denote the measured results.

The results shown in

As an example, in _{d} = 2.5, and the MMI system consists of 20 pairs of thin layers (_{1} = 1.25 and _{2} = −1.8) for a filling ratio _{0} (_{2} = 0.03 _{0}, _{2}/_{1} = 3), and the EMT theory could well approximate the behavior of the super surface mode. The mesh-size is small enough to resolve the finest layer _{1}.

H field distribution for: (

_{d} = 1.0, and the MMI system consists of 35 pairs of thin layers (_{1} = 3.1 and _{2} = −1.6) for a filling ratio _{0}, as can also be calculated from Equation 4. When the uniform metal is replaced by “metametal”, the dispersion curve will bend faster away from lightline (_{0}) is expected. According to the dispersion relation, this trend will also shrink the length of the exponential tail in the dielectric side, as can be clearly seen comparing the _{d} = 1.0 region of

We have theoretically and experimentally investigated the MMI stack as a plasmonic metametal and studied its capability of supporting surface waves and engineering surface plasmon frequency. The analysis proposes a concept of effective surface plasma frequency that can be effectively controlled, and provides new insight into using MMI stacks to accomplish deep subwavelength imaging and artificial dispersion of electromagnetic waves. The outlined design rules would empower researchers to excite confined surface waves more freely from a limited pool of plasmonic materials for optical lithography and subwavelength imaging, and to envision and demonstrate novel detecting/sensing scheme.

This material is based upon work supported in part by the US Army under Award No. W911NF-10-1-0153 and the National Science Foundation under Award No. ECCS-1057381. Acknowledgement is made to the Donors of the American Chemical Society Petroleum Research Fund for partial support of this research.