Crossing of manifolds leads to flat dispersion: Blazed Littrow waveguides

Abstract

International audienceWe display a photonic embodiment of the Demkov-Ostrovsky solution to the crossing of two manifolds made of equidistant modes thanks to broad periodic waveguides. We find clearly narrowing resonances that signal the singular, flat dispersion case that we had termed "critical coupling." The reconciliation of band-edge confinement and cavity confinement, two pillars of photonics, appear from the guide length dependence of spectra. We suggest the generality of the Demkov-Ostrovsky or critical coupling flat dispersion across all kinds of waves, e. g., electronic and acoustic

Mastered dispersion of material resonators: Broad corrugated waveguides working under the Littrow regime

“…The devices analysed here have better couplers than those used in Ref. 15, but are fully similar in other respects. Thus, we could get a spectrally extended set of resonances, and unambiguously assess the increasing FSR trend, given the well-known modal þ chromatic dispersion of n z (x), @n z (x)/@x > 0.…”

“…The BCW length is denoted by Tq, q being an even integer, since ray optics grants that tiling q triangles allows developing (q À 2)/2 coupled resonances in the actual folded resonator. 15 T4 devices with a single resonance are most exemplary of our proposal, but devices with several split resonances like T6 reported here are also of interest to accommodate richer dispersion features.…”

“…[11][12][13][14] These slow modes arise at the crossings of equidistant branches of two dispersion manifolds of opposite slopes. 15 Coupling of modes with proper amounts of transverse and longitudinal momentum 4 thus appears as a generic enabler for dispersion compensation strategies. The control of special electromagnetic features in highly multimode waveguides could also benefit from knowledge of the quasi-optics community.…”

“…x ¼ Àk x [2p/a], is thus obviously obeyed at k x ¼ p/a. 10,15 Whatever the details of coupling among the crossing manifolds, the resulting stationary frequencies (weakly curved dotted hyperbola of Fig. 1(b)) are known to be constrained by these crossings, and thus their FSR essentially follows the "Littrowian" FSR, FSR L ¼ Dx =2p, which derives from the intervals of the series…”

“…The width w of the BCWs corresponds to a resonator order m ¼ 75. 15 We have m ¼ 2p, a factor of 2 coming from the degeneracy lifting of the crossing (another factor would come from operating near h L ¼ 45 , k x p/a ¼ pp/wk y , but it is compensated by the unfolding, doubling w and m). We contact them by broad access guides tilted at h L ¼ 45 .…”