Heterostructures

Selected layer branch: TM surface-plasmon pole. The plotted branch is the real, lossless single-interface mode for the currently selected adjacent layers.

Symmetric DMD and MDM presets use the coupled thin-film branches when the whole film layer is displayed. DMD means Dielectric-Metal-Dielectric; MDM means Metal-Dielectric-Metal.

• Build a stack of homogeneous layers between a semi-infinite substrate (incidence side) and cladding (exit side). The spectrum shows reflectance and transmittance versus wavelength; the field view reconstructs the standing-wave amplitude through the structure at a single wavelength.
• Editing layers. Set each layer's thickness, n and κ in its box. The + button adds a copy directly below, the ↑/↓ buttons reorder it, and × removes it.
• Layer groups. Layers that share the same thickness, n and κ form a group with the same colour. Click a layer's colour circle to lock the whole group — a black ring marks every member — so any edit to one entry applies to all of them at once. Click the same circle again to unlock, or click a different group's circle to switch the selection.

Method. The transfer-matrix method propagates the tangential field through each homogeneous layer. The scalar field F is the in-plane field component that stays continuous across interfaces: F = E_y for TE (s) polarization and F = H_y for TM (p). Each layer uses ε = (n + iκ)² and a normal wavevector k_z = √(k₀²ε − k_x²), with k₀ = 2π/λ and the transverse wavevector k_x = n_s k₀ sinθ conserved across the stack. The angle of incidence θ is measured inside the incidence (substrate) medium n_s. The 2×2 stack matrix M = m_N···m₁ yields the amplitude coefficients R, T and the powers ρ = |R|² and τ. For a lossless stack τ + ρ = 1.

• Place a point dipole at height z in a stratified stack and read out its local density of optical states (LDOS) — the normalized spontaneous-emission / decay rate relative to vacuum (the Purcell factor). The LDOS vs position view sweeps the emitter through the structure; the k∥ map resolves the emission over in-plane momentum, exposing radiative, evanescent and guided/plasmonic channels (guided modes appear as bright poles).
• Editing layers. Set each layer's thickness, n and κ. + duplicates a layer below, ↑/↓ reorder it, × removes it. Click a layer's colour circle to lock its group so edits apply to all members at once. The semi-infinite substrate (below, z<0) and superstrate (above) may be absorbing (e.g. a metal mirror); the emitting medium itself must be transparent.
• Near an absorber. The emitter is held 1 nm clear of any absorbing interface, and the sweep leaves that band blank rather than plotting through it. Approaching an absorber the LDOS diverges as 1/d³ — almost all of it non-radiative quenching into the metal, not useful emission — so the numbers there grow without bound and the momentum integral behind them stops converging. A local, macroscopic description is in any case the wrong model at that range: below roughly a nanometre nonlocal and quantum corrections dominate, and this model overestimates the quenching.
• Method. Electric, magnetic and magnetoelectric LDOS from a stable S-matrix (Redheffer star product) with a contour integral of the dyadic Green tensor over in-plane momentum, following Amos & Barnes. This is an in-browser TypeScript port of PyRAMIDS, validated against it to <1×10⁻³.