Maria Paszkiewicz-Idzik

arXiv2024

A scalar product for the radiation of resonant modes

We introduce the conformally-invariant scalar product, originally devised for radiation fields, to the study of the modes of optical resonators. This scalar product allows one to normalize and compare resonant modes using their corresponding radiation fields. Such fields are polychromatic fields free of divergences, which are determined from the complex frequencies and the modal fields on the surface of the resonator. The scalar product is expressed as surface integrals involving the modal fields, multiplied by closed-form factors incorporating the complex frequencies. In a practical application, we study the modes of disk-shaped whispering gallery resonators, and show that the proposed scalar product accurately predicts the geometry-dependent crossings and anti-crossings between modes.

physics.optics↗

arXiv2024

Enhancement of the photon pair generation rate by spontaneous four-wave mixing in bent waveguides

Enhancing nonlinear optical effects is critical to improving the performance of many functional devices for nonlinear and quantum optical applications. Here we study the possibility of bending a waveguide to enhance the photon pair generation rate in a spontaneous four-wave mixing process. Whereas intuition might suggest that bending makes the process less efficient, because the waveguides are more lossy when bent, we show that the increase in the effective nonlinearity outperforms the disadvantage for moderate bending radii. That can be explained by a better localization of the guided eigenmodes, leading to a reduced mode area. By studying selected waveguide devices with a fixed length, we demonstrate an optimal improvement between 5 % and 270 % in the photon pair generation rate for an optimal bending radius. These findings have implications for the future design of integrated photonic devices for quantum optical applications, especially in cases where the chip estate tends to be a limiting factor.

physics.optics↗