banner image
No data available.
Please log in to see this content.
You have no subscription access to this content.
No metrics data to plot.
The attempt to load metrics for this article has failed.
The attempt to plot a graph for these metrics has failed.
Mastered dispersion of material resonators: Broad corrugated waveguides working under the Littrow regime
Rent this article for
View: Figures


Image of FIG. 1.
FIG. 1.

(a) Scheme of a resonator formed by a broad waveguide section in the Littrow regime. The dashed-dotted line is a mirror plane. The actual devices are folded on this plane and have a single grating (Ref. 15 ). (b) Dispersion of a broad waveguide (solid line) with the effect of periodicity (folding at kx  = π/a). Coupled modes are dashed lines, and follow, modulo the splitting, the net of crossings of basic modes [dotted hyperbola ωH(kx ) and black circles]. They have increasing FSR at kx  = π/a (dots). The excitation along a light line, associated to a given angle in practice, hits the indicated points of the coupled modes in a way that further increases the FSR dispersion.

Image of FIG. 2.
FIG. 2.

(a) Raw collected spectrum of a T6 device, twice the length of Fig. 1(a) . (b) Raw spectrum of a T4 device, and same spectrum squared and with overall compensated profile, suited for automated FSR determination. (c) Calculated FSR for the kx  = π/a case (dots and full line) and the 45° light line case (dots and dotted line) and for the experimental T4 data (grey dots and correlation account by the local centroid of Δωc(ω) of C(ω,Δω)s with s = 4) and T6 (large crosses).

Image of FIG. 3.
FIG. 3.

Plot of the frequencies of zero dispersion (dots merging to solid lines) for initial silicon waveguide slabs of different thicknesses (from bottom to top, d = 200, 240, 300, 360, 420, 500, and 600 nm), as a function of the Littrow grating period a. The assumption is here the band edge one, kx  = π/a for the resonances cf. Fig. 1(b) , which can be made by feeding the resonator through a double period grating on a mirror (bottom left inset); The dotted lines represent the Littrow angle at the zero dispersion situation thus realised, labelled from 10° to 24° by 2° steps. The top right inset represents the dispersion of resonators made in bulk silicon (middle line), in a 200 nm silicon slab, and that of the Littrow resonator (d = 200 nm, a ∼ 1 μm, ν ∼ 150 THz, and θL ∼ 24°).


Article metrics loading...


Full text loading...

This is a required field
Please enter a valid email address
752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Mastered dispersion of material resonators: Broad corrugated waveguides working under the Littrow regime