Fabry-Pérot Visualizer

Explore single-layer thin-film interference with a phasor diagram showing how multiple reflected beams combine to determine reflectance and transmittance.

Fabry-Perot Thin Film Interference

Visualize multiple reflections and phasor interference in a single thin film on a substrate.

Film index n₂: 2.00

Substrate index n₃: 3.50

Film thickness: 100 nm

Wavelength: 550 nm

16.2%

83.8%

Phase delta

4.570 rad

Quarter-wave d

68.8 nm

Model scope

Use this browser tool for intuition, relative trends, and design-space exploration. Its local simplified model is not a substitute for RCWA/FDTD sign-off, silicon calibration, or vendor process data.

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Thin Film Optics

Physics Notes

Single-Layer Interference

Plain-English Intuition

A single thin transparent film acts as a tiny resonator: light bounces back and forth between its two surfaces, and depending on the thickness, certain wavelengths come out strong (transmission peaks) while others are reflected. This is the same effect that paints rainbow colours on soap films and oily puddles, and it is the basic building block of nearly every thin-film optical filter.

Fabry-Perot behavior comes from repeated internal reflections whose phase can add constructively or destructively.

Assumptions

The cavity is represented as a single coherent thin film between two reflecting interfaces.
Surface roughness, finite aperture averaging, absorption dispersion, and lateral patterning are omitted unless approximated by input parameters.
The phasor diagram is an explanatory model for phase addition, not a complete multilayer solver.

Outputs

Round-trip phase, constructive/destructive interference condition, phasor geometry, and resonance shift with thickness or angle.
A compact intuition for why BARL, CFA, and cavity-like stacks move spectral peaks with angle and thickness.

Validation Example

Increasing film thickness should move a fixed interference order toward longer wavelength.
At oblique incidence, the effective phase term should change through $\cos\theta$ and shift the resonance condition.

Core Equations

Round-trip phase

$$\delta = \frac{4\pi n d \cos(\theta)}{\lambda}$$

$\delta$: Phase change for one round trip
$n$: Refractive index of the film
$d$: Physical thickness

A small thickness or angle change can move the film between reflection peaks and valleys.

Constructive condition

$$2nd \cos(\theta) = m\lambda$$

$m$: Integer order of interference

Integer round-trip phase gives resonant transmission or reflection depending on the stack.

Quarter-wave AR

$$d = \frac{\lambda_0}{4n}$$

$\lambda_0$: Reference design wavelength

The common AR seed thickness creates destructive interference for front-surface reflection.

Model Interpretation

A single layer is the simplest case of the full TMM stack.
Angle and spectral bandwidth broaden or shift interference features.
Real color filters and BARL stacks require multiple materials and absorbing films.

Resonance Reading

A peak or valley appears when the round-trip phase $\delta$ lines up reflected waves constructively or destructively.
Increasing thickness $d$ shifts the same interference order toward longer wavelength.
Increasing angle reduces $\cos\theta$ and therefore shifts the resonance condition.

Connection To TMM

The single-film equation is the one-layer limit of the characteristic-matrix method.
Absorbing films require complex $\tilde{n}=n+ik$, so resonance strength and loss must be interpreted together.
Real BARL or color-filter stacks superpose multiple such resonances across many interfaces.

Known Missing Physics

The compact equations omit finite aperture averaging, roughness scattering, and lateral patterning.
A single layer cannot model broadband color filters or multi-material anti-reflection coatings.
For high angles, s/p polarization split should be treated explicitly.