Divergent Petermann factor of interacting resonances in a stadium-shaped microcavity

It is numerically shown that the Petermann excess noise factor diverges to infinity at an exceptional point (EP) found near an avoided resonance crossing in a stadium-shaped dielectric microcavity. Square-root singularity of eigenvalue at the EP is explicitly demonstrated in two-dimensional parameter space spanned by refractive index and deformation parameter. The results imply that mode-mode interaction makes the Petermann factor large.

Figure 1

(Color online) Avoided resonance crossing of real parts (a) and resonance crossing of imaginary parts (b) of eigenvalues. The variation of mode patterns (c) as $\epsilon$ increases with $n=2$.

Figure 2

(Color online) Topology of eigenvalue planes around the EP. (a) Real part and (b) imaginary part. The recent microcavity experiment of Ref. 23 demonstrated similar topological structures in a different 2D parameter space.

Figure 3

(Color online) Traces of eigenvalues near the EP. The lines denote eigenvalue traces under $\epsilon$ variation with $n$ fixed. The parameter point ${\lambda }_j$ are defined in the text. Modes denoted by $A$ and $B$ are the same as those in Fig. 2.

Figure 4

(Color online) (a) Approximate $⟨{\psi }^{*}\mid \psi ⟩$ near the EP. The lines correspond to the same $\epsilon$ variation as those in Fig. 3. Here the range of $n$ is $1.9896⩽n⩽1.9948$. (b),(c) Divergent Petermann factor $K$’s of two interacting modes around ${\lambda }_{\mathrm{EP}}\simeq (1.9922,0.5617)$.