The decays D → K−π+π+π− and D → K−π+π0 are studied in a sample of quantum-correlated $$ D\overline{D} $$ D D ¯ pairs produced through the process e+e− → ψ(3770) → $$ D\overline{D} $$ D D ¯ , exploiting a data set collected by the BESIII experiment that corresponds to an integrated luminosity of 2.93 fb−1. Here D indicates a quantum superposition of a D0 and a $$ {\overline{D}}^0 $$ D ¯ 0 meson. By reconstructing one neutral charm meson in a signal decay, and the other in the same or a different final state, observables are measured that contain information on the coherence factors and average strong-phase differences of each of the signal modes. These parameters are critical inputs in the measurement of the angle γ of the Unitarity Triangle in B− → DK− decays at the LHCb and Belle II experiments. The coherence factors are determined to be RK3π = $$ {0.52}_{-0.10}^{+0.12} $$ 0.52 − 0.10 + 0.12 and $$ {R}_{K{\pi \pi}^0} $$ R K ππ 0 = 0.78 ± 0.04, with values for the average strong-phase differences that are $$ {\delta}_D^{K3\pi }=\left({167}_{-19}^{+31}\right){}^{\circ} $$ δ D K 3 π = 167 − 19 + 31 ° and $$ {\delta}_D^{K{\pi \pi}^0}=\left({196}_{-15}^{+14}\right){}^{\circ} $$ δ D K ππ 0 = 196 − 15 + 14 ° , where the uncertainties include both statistical and systematic contributions. The analysis is re-performed in four bins of the phase-space of the D → K−π+π+π− to yield results that will allow for a more sensitive measurement of γ with this mode, to which the BESIII inputs will contribute an uncertainty of around 6°.

This paper considers multiple structural designs for photonic crystal surface emitting lasers operating at key wavelengths. Initially a structure from Williams et al. is modelled, the structure is modified to include an additional GaAs waveguide layer (termed ballast layer) and to include an additional PC layer (termed double decker). These structures are modelled by a combination of coupling calculation and waveguide modelling and are compared to the original structure. We show that both of these schemes give an increase in coupling, but present fabrication challenges. Next, we model standard laser structures operating at key wavelengths (400 nm, 1.3 and 10 lm) where a photonic crystal is located above the active region and explore the effect of increasing thickness of photonic crystal. We find that increasing the thickness increases the coupling coefficient but not true for the full range of thicknesses considered. This study allows a more universal comparison of the use of all-semiconductor, or void containing PCSELs to be conducted and we find that the realisation of all semiconductor PCSELs covering a wide range of material and wavelengths are possible.

This paper analyzes 2D photonic crystal surface-emitting laser diodes with void-containing and all-semiconductor structures by comparing their simulated mode distribution, band structure, and coupling coefficients. A photonic crystal design with a square lattice and circle atoms is considered.

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