Spontaneous Emission and Resonant Scattering in Transition from Type I to Type II Photonic Weyl Systems

Spontaneous emission and scattering behavior of an emitter or a resonant scatterer strongly depend on the density of states of the surrounding medium. It has been shown that the resonant scattering cross section (RSC) may diverge at the Weyl frequency of a type I Weyl system due to the diminishing density of states. Here we study the spontaneous emission (SE) and RSC in a photonic metacrystal across the critical transition between type I and type II Weyl systems. Theoretical results show that the SE rate of an emitter in a type I Weyl system diminishes to zero at the Weyl frequency. When the system is tuned towards the transition point between type I and type II Weyl point, the dip in the SE spectrum at the Weyl frequency becomes infinitely sharp. The dip vanishes at the critical transition, and transforms into a peak when the system changes into a type II Weyl system. We further show that the resonant scattering cross section also exhibits dramatically different spectral features across the transition. Our study demonstrates the ability to tune SE and RSC through altering the dispersion of the Weyl medium between type I and type II, which provides a fundamentally new route in manipulating light-matter interactions.

Figure 1

Transformation of the isofrequency surface of a type I (a) and type II (b) Weyl point according to a different Weyl parameter ${\alpha }_{\text{Weyl}}$ in the $k_x\text{−}{k}_y$ plane. (c) and (d) The transformation of density of states in type I and type II Weyl systems with different ${\alpha }_{\text{Weyl}}$, respectively.

Figure 2

(a) Schematic of a unit cell of saddle-shaped metallic inclusion, which has $D_{2d}$ point group symmetry, embedded in a background medium with a dielectric constant of 2.2 at 10 GHz. The metallic coil rotates with an angle of 45° along the $z$ direction. (b) Four type I Weyl points in the ideal photonic Weyl metacrystal reside on the same energy with respect of $k_z=0$ (purple plane). (c) Variation of the Weyl parameter ${\alpha }_{\text{Weyl}}$ with rotation angle; the critical transition of the Weyl point from type I to type II occurs at a rotation angle of about 34.1°. (d)–(f) Dispersions of the Weyl metacrystal along the Weyl vector with different rotation angles 0°, 45°, and 34° representing the type I Weyl point, type II Weyl point, and the critical transition of the Weyl point, respectively.

Figure 3

Transformation of the SE rate of the ideal Weyl metacrystal. Rotation angle: (a) 30°–34° (type I), (b) 35°–39° (type II), respectively. (c) Transformation of the SE rate across the critical transition between the type I and type II Weyl system.

Figure 4

Resonant scattering cross sections of type I (a) and type II (b) Weyl metacrystals, respectively. Rotation angle range: 30°–39°.