Limits of the Standard Model
The software never asks for light intensity, spot size, or beam divergence, because the standard model of thin film optics has no degrees of freedom for them. This chapter lists every idealized assumption the model relies on, the situations in which real samples and real illumination violate them, and the direction in which simulated results depart from measurement. The content follows the review by Stenzel and Wilbrandt, Theoretical Aspects of Thin Film Optical Spectra (Appl. Sci. 2025, 15, 2187, CC BY 4.0).
The Eight Assumptions Behind the Standard Model
| No. | Assumption | Corresponding input in the software |
|---|---|---|
| I | Stratified medium: optical properties vary with depth only, interfaces are ideal planes normal to the depth axis | Layer order and thickness in Structure |
| II | Every layer extends to infinity laterally | No input; implied by the model |
| III | All media are optically isotropic, magnetic response neglected | Isotropic materials are the default; Birefringent is a controlled relaxation |
| IV | Incidence and exit sides are semi-infinite homogeneous media, the incidence medium is non-absorbing | Incident and exit media under Surrounding Medium |
| V | The incident light is a plane monochromatic wave with a single wavevector | Wavelength and Incident Angle |
| VI | At oblique incidence the wavevector and the normal define a unique plane of incidence | The s / p definition in Polarization depends on this plane |
| VII | Three-wave scenario: one incident, one reflected, one transmitted wave | Reflection and Transmission detectors |
| VIII | Materials respond linearly | n and k are independent of intensity |
Nothing in this input list describes light intensity, spot size, beam divergence, or surface roughness. No real sample satisfies all eight, so deviations are the norm rather than the exception.
What Happens When the Assumptions Break
| Real condition | Assumption violated | Observable effect | Direction of the simulation error |
|---|---|---|---|
| Laterally restricted spot (slit, small spot, focused beam) | V | The outgoing beam is laterally displaced relative to the incident beam; sub-millimeter shifts have been measured on coatings | Spectral values remain valid, but the beam lands away from where the ideal model implies |
| Focused or defocused conical illumination | VI | Polarization leakage: p-components mix into nominally s-polarized light | Measured extinction ratio of thin film polarizers falls below the design value |
| Rough interfaces | I | Large-scale roughness causes scatter losses; small-scale roughness acts like an antireflection layer | Simulation overestimates specular reflectance and transmittance; no single accepted model exists |
| Layer thickness comparable to the coherence length (thick substrates, broadband sources, limited spectral resolution) | Coherent superposition | Interference fringe amplitude is damped; a single spectrum may contain both coherent and incoherent regions | The fully coherent model produces fringes that are too strong |
| Anisotropic materials (glancing-angle deposition, nanolaminates, stretched polymers) | III | s and p cannot share one refractive index | An isotropic n fit misses both polarizations at once |
| Spatial dispersion (metal island films, near strong resonances) | Local response | The dielectric function depends on the wavevector | n(λ) is insufficient to describe the material response |
| Time-varying material parameters | Time homogeneity | The light frequency is converted; at a temporal interface reflectance plus transmittance can exceed 1 | Outside the range the model can describe |
| High-intensity illumination (pulsed lasers) | VIII | Reflectance and transmittance depend on incident intensity | Linear n, k disagree with high-power measurements |
| Ultrathin films, metal island films, molecular monolayers | Separability of index and thickness | Effective optical constants vary with thickness | Bulk n, k introduce a systematic bias |
Restricted Spot Size: Displaced Exit Position
The displacement is set by the derivative of the complex reflection coefficient phase with respect to the incidence angle, so it varies with wavelength and with the coating design. The effect is not confined to total internal reflection: it has been observed near the Brewster angle in p-polarization, at interfaces between transparent and absorbing media, and at metal surfaces. TMM returns reflectance and transmittance values, not the spatial position of the beam; where the spot size and the displacement are comparable, this term has to be budgeted separately.
Conical Illumination: Polarization Leakage
The leakage grows with the cone half-angle and falls as the working incidence angle increases. It is set by the illumination geometry alone, which is why improving the coating design cannot remove it, and why thin film polarizers operating at high incidence angles were developed. When designing polarizing components, treat the simulated extinction ratio as a system upper bound; the achievable value depends on the cone half-angle and the working angle of the illumination system.
How Far the Software Goes
| Capability | Assumption relaxed | Covered | Not covered |
|---|---|---|---|
Cone Angle | V (single incidence angle) | Weighted average of R / T / A, incident-spectrum-weighted spectra, and color over the cone | Ellipsometry, Depth Distribution, and Dispersion still use a single incidence angle |
Incoherent layers | Coherent superposition | The fully incoherent limit, suitable for thick substrates | The partially coherent regime where thickness and coherence length are comparable |
Birefringent (nExt / kExt) | III (isotropy) | Uniaxially anisotropic materials | Mutually exclusive with Incoherent on the same layer |
Surface and interface roughness, scatter losses, spatial dispersion, non-linear response, time-varying materials, thickness-dependent effective optical constants, and lateral beam displacement are not modeled.
Judging Result Reliability
- When layer thicknesses are well below the source coherence length, interfaces are smooth, illumination is near-collimated, and intensity stays in the linear range, simulated spectra can be compared with measurement directly.
- When the stack includes a millimeter-scale substrate or a broadband source is used, mark that layer
Incoherent; otherwise the spectrum shows dense fringes that do not exist in measurement. - When the sample has measurable roughness or scatter, the simulated specular reflectance and transmittance are upper bounds and the difference goes into scatter loss.
- When evaluating the extinction ratio of a polarizing component, the simulated value is an upper bound set by the cone half-angle of the illumination system.
- When thicknesses reach the few-nanometer range, or metal island films and nanolaminates are used, measured
n,kfor that thickness are required; bulk data do not apply.
Next Steps
Read Transfer Matrix Method for how the model is solved internally, or Optical Parameters to configure cone angle and polarization. For a quantitative comparison against an independent reference under fixed inputs, see Algorithm Validation.
Reference
Stenzel, O.; Wilbrandt, S. Theoretical Aspects of Thin Film Optical Spectra: Underlying Models, Model Restrictions and Inadequacies, Algorithms, and Challenges. Appl. Sci. 2025, 15, 2187. https://doi.org/10.3390/app15042187 (CC BY 4.0)