Tamm Plasmon at a Metal-DBR Interface

This case targets the Tamm-plasmon mode at a metal-dielectric Bragg reflector interface. Unlike the omnidirectional-reflector example, the objective here is not broadband high reflectance. The relevant signature is a narrow resonance dip embedded in an otherwise high-reflectance spectral region.

The geometry is still a one-dimensional stratified stack, so TMM remains the correct solver class. What changes is the sensitivity to boundary phase. In practical terms, the question is no longer "does the multilayer interfere," but "does the interface support the specific resonant feature reported in the paper."

Research Context

A Tamm plasmon is a localized optical state supported at the boundary between a metal and a periodic dielectric reflector. The DBR supplies a stop-band background, while the metal boundary supplies the additional phase condition required for a localized interface mode.

This is a natural TMM problem because the structure is still purely layered. The two observables that matter are the narrow resonance in Reflection and the depth-resolved field profile in Depth Distribution. Both are already available in Dreapex TMM without introducing any lateral patterning or grating coupling.

Paper Information and Comparison Target

• Paper: Tamm plasmon-polaritons: Possible electromagnetic states at the interface of a metal and a dielectric Bragg mirror
• Authors: M. Kaliteevski, I. Iorsh, S. Brand, R. Abram, J. Chamberlain, A. Kavokin, I. Shelykh
• Journal: Physical Review B 76, 165415 (2007)
• DOI: 10.1103/PhysRevB.76.165415
• Comparison target: Figure 3 in the paper

Figure 3 is plotted against photon energy. Dreapex TMM uses wavelength. This case therefore maps the paper's 0.94-1.00 eV window to 1240-1320 nm through

lambda (nm) ~= 1240 / E (eV).

Mapping the Paper to a Dreapex TMM Model

This reconstruction is performed through the live app, not by writing internal state. The structure, run sequence, and screenshots are all produced by Playwright operating the actual front end, with the Footer checked before each run to confirm that no blocking validation errors remain.

That distinction matters: this is not an offline curve injected into the result page. The run goes through the real Structure -> Optics -> Run -> Results flow, and the screenshots preserve the app's own model configuration and validation state.

Modeling Workflow in the App

The build sequence is:

1. Create a Layer Group in Structure.
2. Define the repeated unit as GaAs / AlAs, with 14 periods.
3. Set the metal side to Au-backing, using gold optical data sourced from the built-in database.
4. Check the Footer and confirm that the status reads Parameter validation passed.
5. In Optics, set the wavelength window to 1240-1320 nm so the scan matches the paper's Figure 3 axis.

Reproduction Target and Acceptance Criteria

For Figure 3, the evaluation criteria are:

1. A clear narrow reflectance dip must appear inside the 1240-1320 nm window.
2. With increasing incident angle, the dip should shift toward shorter wavelength rather than collapse into a flat high-reflectance plateau.
3. At the resonant wavelength, the depth-resolved field should preferentially strengthen near the metal-DBR boundary instead of behaving like a generic standing wave distributed through the entire stack.

In a first-pass reconstruction, satisfying the first condition places the model in the correct spectral neighborhood. Failing the second or third condition means the paper's full Tamm-plasmon branch has not yet been reproduced and should not be claimed as such.

Simulation Results vs. Paper Figure 3

In the current live-app model, normal incidence already produces a distinct resonance dip. The minimum occurs at approximately 1286 nm, which corresponds to about 0.964 eV. That places the result in the same spectral neighborhood as the normal-incidence branch in the paper, which sits near ~0.956 eV.

In practical terms:

• the current normal-incidence minimum reflectance is about 0.18
• the resonant wavelength differs from the paper's normal branch by roughly 11 nm
• the model is therefore operating in the correct frequency region, even though the full angular branch is not yet matched

At 60 deg, however, the current model returns to an almost flat near-unity reflectance across the same 1240-1320 nm window. The high-angle resonance branch visible in the paper does not reappear within the comparison window. This means:

• the present implementation does not yet recover the full angular dispersion branch reported in Figure 3
• the oblique-angle branches are more sensitive to termination, outer-medium definition, and metal-interface phase than the normal-incidence branch
• the current state should be described as a successful normal-incidence resonance reconstruction, not a full angle-dispersion reproduction

The preset also captures 30 deg and 45 deg results for both TE and TM. In this first pass they behave similarly to the 60 deg case within the selected window, so they are not presented here as matched results.

Depth-Resolved Field Check

At normal incidence and 1286 nm, the Electric Field page shows a strong depth-selective response, but the dominant peaks are still distributed through the stack rather than pinned tightly to the first metal-DBR boundary. That is an important distinction.

It means:

• the model is exciting a strong resonance in the correct spectral neighborhood
• the resonance is not yet a clean reproduction of the ideal interface-localized Tamm-plasmon field pattern
• further tightening of the termination condition is still required before claiming full modal agreement

Deviation Analysis

The current mismatch is mainly driven by the following factors:

• the paper discusses an idealized metal-DBR boundary condition, while this case uses dispersive database materials through the real front-end solver path
• the incidence side is kept as default Air so the UI angle control retains a direct external-angle meaning; that is not strictly identical to the boundary treatment in the analytical derivation
• the 14-period LayerGroup reproduces the base periodic stack, but the exact metal-side termination has not yet been tuned beyond the first canonical configuration
• the metal side uses Johnson gold, and different gold datasets can shift the interface phase substantially
• the current wavelength step is 1 nm, which is sufficient to locate the resonance region but not to characterize a meV-scale linewidth precisely

The correct technical conclusion for this version is therefore: the live front-end workflow reproduces the normal-incidence resonance in the target spectral neighborhood, but it does not yet fully recover the angular branches or the ideal interface-localized field pattern reported in Figure 3.

Further Experiments

1. Keep the same database materials and scan the metal-side termination order to test whether the oblique branches return to the 1240-1320 nm window.
2. Hold the Figure 3 window fixed and repeat the case with a different built-in gold dataset such as Rakic-BB.
3. Refine the wavelength step below 1 nm once the branch position is stabilized, then revisit resonance depth and linewidth.
4. Build a separate 30 nm finite-gold-film version and compare it to Figure 1 / Figure 4, where the finite-thickness metal configuration is closer to the paper's illustrated field profiles.