Dirac energy dispersions are responsible for the extraordinary transport properties of graphene. This motivated the quest for engineering such energy dispersions also in photonics, where they have been predicted to lead to many exciting phenomena. One paradigmatic example is the possibility of obtaining power-law, decoherence-free, photon-mediated interactions between quantum emitters when they interact with such photonic baths. This prediction, however, has been obtained either by using toy-model baths, which neglect polarization effects, or by restricting the emitter position to high-symmetry points of the unit cell in the case of realistic structures. Here, we develop a semianalytical theory of dipole radiation near photonic Dirac points in realistic structures that allows us to compute the effective photonmediated interactions along the whole unit cell. Using this theory, we are able to find the positions that maximize the emitter interactions and their range, finding a trade-off between them. Besides, using the polarization degree of freedom, we also find positions where the nature of the collective interactions changes from being coherent to dissipative ones. Thus, our results significantly improve the knowledge of Dirac light−matter interfaces and can serve as a guidance for future experimental designs.
The plane wave expansion method was used to calculate the photonic band structure of a hexagonal lattice in which the triangular GaAs scatterers have a Sierpinski structure. In triangles with lengths of less than 0.6 a, in the photonic band structure for low frequencies, the photonic band gaps appear mainly in the transverse-magnetic polarization, as shown by the results. Nevertheless, when the size of triangles increases above 0.8 a, an overlap of the photonic band gap in the transverse-electric and transverse-magnetic polarizations occurs. Hence, a complete photonic band gap is produced, where the photonic modes cannot propagate in either direction. In addition, we detected that another optimal condition for creating a complete photonic band gap is that the dielectric contrast should be greater than 12. Likewise, the pressure and temperature dependence of the GaAs dielectric constant are considered, detecting a higher frequency shift of the photonic band structure, when the temperature remains constant at 4 K and the pressure increases from 0 to 70 kbar.
Dirac energy-dispersions are responsible of the extraordinary transport properties of graphene. This motivated the quest for engineering such energy dispersions also in photonics, where they have been predicted to lead to many exciting phenomena. One paradigmatic example is the possibility of obtaining power-law, decoherence-free, photon-mediated interactions between quantum emitters when they interact with such photonic baths. This prediction, however, has been obtained either by using toy-model baths, which neglect polarization effects, or by restricting the emitter position to high-symmetry points of the unit cell in the case of realistic structures. Here, we develop a semianalytical theory of dipole radiation near photonic Dirac points in realistic structures that allows us to compute the effective photon-mediated interactions along the whole unit cell. Using this theory, we are able to find the positions that maximize the emitter interactions and their range, finding a trade-off between them. Besides, using the polarization degree of freedom, we also find positions where the nature of the collective interactions change from being coherent to dissipative ones. Thus, our results significantly improve the knowledge of Dirac light-matter interfaces, and can serve as a guidance for future experimental designs.
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