Seminarium Fizyki Materii Skondensowanej

The typical description of a planar microcavity relies on two different approaches. The first is a fully numerical method, known as the Transfer Matrix Method (TMM), which is highly complex but accurately reproduces experimental observations, as it accounts for all interactions that are linear in the electric or magnetic field. The second approach is a semi-analytical method based on the diagonalization of a 2-mode Hamiltonian, which describes the interaction between two cavity modes with similar energy for a perpendicularly incident wave. While this second approach is significantly simpler, it has several limitations, such as being restricted to terms up to quadratic order and difficulties in determining the non-Hermitian part due to the complex relationship between the Stokes polarization pattern or energy dispersion and the coefficients of the 2-mode Hamiltonian. In some cases, higher-order terms are introduced into such Hamiltonians, but they are typically added in theoretical calculations as ad hoc terms.Here, we present new approaches for determining a 2-mode non-Hermitian Hamiltonian that accurately reproduces both energy and polarization dispersion for different types of cavities. The first method is based on the Green’s function and is limited to quadratic terms in the wavevector. The second method utilizes data obtained from the Transfer Matrix Method and, through symmetry-invariant considerations, enables the determination of a general 2-mode non-Hermitian Hamiltonian that fully captures both energy and polarization dispersion. These symmetry-based considerations predict the symmetry invariants for different types of cavities, ultimately allowing for the determination of symmetric polynomials fitted to the TMM results. Although this second approach is not derived from fundamental physical principles, it overcomes the limitations observed in the first method.This entirely new approach provides insight into non-Hermitian effects observed in birefringent microcavities. One example is the different number of polarization singularities (C-points – points where the light is purely circularly polarized) in the two photonic branches. Another example is the topological transition of the winding number of the exceptional point.