The waveguideLight in a thin film
Focal molography starts with light guided along a thin film. Part of the optical field extends into the sample and weights molecules near the surface more strongly than molecules farther away. Learn how the film, mode, and evanescent field set that weighting.
Objective. Understand how a thin film guides light and how far the evanescent field reaches.
Recommended first: The whole light path.
Total internal reflection traps the light
Light passing from a higher-index medium into a lower-index medium bends away from the surface normal, toward the interface. Above the critical angle, measured from the surface normal, total internal reflection occurs. An evanescent field still extends across the interface. The illustrative stack below places a 300 nm tantalum pentoxide (Ta2O5) film between glass and water. The refractive indices are about 2.1, 1.52, and 1.33, respectively. Light launched into the film at a shallow enough angle reflects at both faces and is trapped, bouncing along the film instead of escaping.
Change the angle of the ray inside the film. Above the critical angle it reflects at both faces and travels along the film, trapped. Below it, part of the light transmits into the glass. This ray schematic shows the transmitted path and omits partial reflection; the mode model below treats the wave conditions.
Guided modes: only certain angles survive
A guided mode must satisfy the wave equation and boundary conditions at both film interfaces. Only discrete field patterns satisfy these conditions for a given wavelength and polarization. A suitable film thickness supports one mode of the selected polarization. The 2019 research setup used the fundamental transverse-electric (TE) mode, with an effective index of about 1.81. Increasing thickness or refractive index can allow additional modes. A sufficiently thin asymmetric film can also fall below the guided-mode cutoff.
Change the film thickness and index. The profile is the fundamental mode's field across the stack. The readouts show how many modes the film supports, and the fraction of integrated |E|² inside the film. This is a lossless TE slab model; it excludes transverse-magnetic (TM) modes. Near cutoff, substantial field also extends into the glass.
Illustrative model inputs: 785 nm wavelength, 300 nm film thickness, film index 2.09, glass 1.521 and water 1.33. These yield Neff ≈ 1.92 and one TE mode; they are not a product specification. The 2019 research setup used 632.8 nm and reported Neff ≈ 1.81. Frutiger 2019, §III.
TE and TM polarization
Polarization describes the field orientation. In transverse-electric (TE) modes, the electric field lies parallel to the film and perpendicular to propagation. In transverse-magnetic (TM) modes, the magnetic field has that orientation; the electric field includes a component normal to the film. The two polarizations generally have different effective indices and evanescent decay lengths. The model uses the fundamental TE mode at 785 nm and gives an amplitude decay length in water of about 90 nm.
Effective index: how fast the mode travels
A guided mode travels along the film at a speed set by an effective refractive index, Neff. For a bound mode, it exceeds both surrounding indices and remains below the film index. It captures the fact that the mode is partly in the high-index film and partly in the lower-index surroundings. Neff matters for two reasons that come later. It decides the angle at which light is fed into the film, and how far the evanescent field reaches.
The evanescent field weights the surface region
In the sample, electric-field amplitude decays as E(z) = E(0) exp(−z/δE), where δE = λ0 / [2π√(Neff² − nc²)]. With λ0 = 785 nm, Neff ≈ 1.92 and nc = 1.33, δE ≈ 90 nm. Optical intensity decays twice as fast: I(z)/I(0) = exp(−2z/δE).
This is a continuous weighting, not a hard sensing boundary. Scattered amplitude is driven by the local field; conversion to a mass response also depends on the collection geometry and calibration. Bulk refractive-index changes within the evanescent region still affect the guided mode, which is why the refractometric mass-density readout (MD) can detect sample arrival. Frutiger 2019.
Change the amplitude decay length. Orange shows field amplitude and turquoise shows intensity at height z. Both decrease continuously; neither has a hard cutoff.
Worked example. Guided light illuminates the surface-bound recognition sites through its evanescent field. The 90 nm example is a field-weighting scale, not a streptavidin detection boundary.
Predict before revealing the explanation. Does a 90 nm amplitude decay length mean molecules at 180 nm are invisible?
Reveal the explanation
No. At twice the amplitude decay length, the field is exp(−2), about 14% of its surface value. Intensity is about 2%. The weighting decays continuously.