Modal Purcell factor in $\mathcal{P}\mathcal{T}$-symmetric waveguides

Abstract

We study the spontaneous emission rate of a dipole emitter in $\mathcal{P}\mathcal{T}$-symmetric environment of two coupled waveguides using the reciprocity approach generalized to non-orthogonal eigenmodes of non-Hermitian systems. Considering emission to the guided modes, we define and calculate the modal Purcell factor composed of contributions of independent and interfering non-orthogonal modes leading to the emergence of cross-mode terms in the Purcell factor. We reveal that the closed-form expression for the modal Purcell factor within the coupled mode theory slightly alters for the non-Hermitian coupled waveguide compared to the Hermitian case. It is true even near the exceptional point, where the eigenmodes coalesce and the Petermann factor goes to infinity. This result is fully confirmed by the numerical simulations of active and passive $\mathcal{P}\mathcal{T}$-symmetric systems being the consequence of the mode non-orthogonality.

arXiv comment11 pages, 12 figures

References in corpus (8)

• Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
• Pseudo-Hermitian Representation of Quantum Mechanics
• General Theory of Spontaneous Emission Near Exceptional Points
• Consistency of PT-symmetric quantum mechanics
• Quantum noise and mode nonorthogonality in nonhermitian PT-symmetric optical resonators
• Completeness and Orthonormality in PT-symmetric Quantum Systems
• Reciprocity approach for calculating the Purcell effect for emission into an open optical system
• Reciprocity and the scattering matrix of waveguide modes

Cited by in corpus (4)

• Quasinormal modes and Purcell factors of coupled loss-gain resonators and index-modulated ring resonators near exceptional points
• Fermi's golden rule for spontaneous emission in absorptive and amplifying media
• Quasinormal mode analysis of chiral power flow from linearly polarized dipole emitters coupled to index-modulated microring resonators close to an exceptional point
• Extraction of power transmission parameters from PT-symmetric waveguides