CouplingGetting light in and out
Coupling light into a guided mode requires matching its momentum along the film. A grating supplies the difference between the incident beam and the mode. Its period, the wavelength, and the effective index determine the coupling angle.
Objective. Understand why a grating coupler is needed and what sets the coupling angle.
Recommended first: The waveguide.
Why a beam cannot just enter the film
The incident light and guided mode must have the same wavevector component along the surface. This component describes their spatial phase variation. The mode’s effective index, Neff, exceeds the refractive index of the surrounding medium. A beam incident on a smooth, uniform film cannot supply enough in-plane momentum to excite that bound mode directly.
A grating coupler supplies the missing momentum
A periodic grating supplies additional in-plane momentum in multiples of its grating vector, 2π/Λ. Coupling occurs when the combined beam and grating contributions match the guided mode. This is the phase-matching condition. It depends on incidence angle, wavelength, grating period, and effective index. The 2019 research setup coupled 632.8 nm light through a 318 nm grating at −10.6°. Frutiger 2019, §III.
Try an angle near −6° at a 380 nm period. This illustrative period is not a chip specification. The line shows in-plane wavevector divided by k₀ = 2π/λ₀. This teaching model assumes incidence from water (blue). The grating contribution is violet; the relation is nᵢ sin θ + λ₀/Λ = N_eff for the +1 order, with θ measured from the surface normal. Its water-side angle is not the external angle reported for the research apparatus.
The coupling angle depends on wavelength
For a selected mode and diffraction order, phase matching selects an incidence angle when a solution exists. Changing wavelength changes the propagation constants and therefore the required angle. The physical grating vector, 2π/Λ, remains fixed. Resonance width depends on coupler geometry and illumination. The lab uses an illustrative width, not an alignment tolerance.
Change wavelength and watch the phase-matched angle move. This model uses an illustrative 380 nm period, water-side incidence and fixed N_eff = 1.92; it neglects dispersion. The normalized peak shape and width are illustrative.
The same phase-matching principle governs out-coupling
Molecules bound to the mologram scatter guided light out of the film. Their positions account for both the illuminating mode’s phase and the path to the focus. At that focus, the selected scattered fields reinforce each other. The coupling grating supplies illumination; the mologram converts patterned binding into the measured optical signal.
Worked example. The coupling grating supplies illumination to the binding pattern. Its alignment affects the available light, which must be accounted for during optical normalization.
Predict before revealing the explanation. At fixed wavelength and effective index, what happens to the +1-order coupling angle when the grating period increases?
Reveal the explanation
For the convention shown here, the grating contribution λ/Λ decreases. The incidence angle must increase to restore phase matching.