Near-Field Imaging of Magnetic Complex Mode Volume

Abstract

The non-Hermitian nature of confined photonic modes is described by the electric complex modal volume, V E , which represents a key parameter that leads to counterintuitive effects, such as negative modal contribution to the local density of states and non-Lorentzian lineshapes. Here, we address the magnetic counterpart of V E by means of near-field perturbation experiments in a photonic crystal slab cavity. We study the relevant role played by the imaginary part of the magnetic modal volume, V H , which can increase the quality factor of the confined modes by means of a local external magnetic perturbation. We show how a mapping of the spatial distribution of both the real and imaginary parts of V H can be inferred by near-field experiments employing Al-covered near-field tips. Our findings deepen the role of the magnetic component of light and could open a new route in employing metamaterials, magnetic quantum emitters, and topological photonics.

Nanoscale Light Confinement: the Q’s and V’s

“…Here, our analysis of the mode volume refers to electric interaction. A magnetic mode volume can be analogously defined for the study of interaction between matter and the magnetic component of the electrometric field . 1/ V E plays the same role as the probability density function |ψ­( r )| 2 in quantum mechanics and may be interpreted as a density probability of having large vacuum electric field fluctuation in the selected point r .…”

“…It can be easily generalized to describe other kinds of interactions, for instance, with an unpolarized dipole, see eq 7.4 in ref . Just by exchanging the permittivity and permeability and the magnetic and electric fields, a mode volume for magnetic-dipole transitions, as would be required to interpret the original Purcell effect experiment at microwave frequencies, could be further defined . The notion of complex mode volumes can be further extended to high-order electric multipole transitions, see the Appendix B.…”

“…A magnetic mode volume can be analogously defined for the study of interaction between matter and the magnetic component of the electrometric field. 39 1/V E plays the same role as the probability density function |ψ(r)| 2 in quantum mechanics and may be interpreted as a density probability of having large vacuum electric field fluctuation in the selected point r. Alternatively, using the photonics language in quantum mechanics, we may also say that 1/|ψ(r)| 2 is the mode volume of the electron state at point r. The energy-based definition suggests that the strongest interaction is implemented at the field-intensity maximum. 40 It is quite intuitive and has been widely and successfully used to test the functionalities of microwave circuit components 41 to help interpret biosensing 42 or cQED solid-state experiments.…”

“…A similar expression of holds for M1 transitions, with and . The electric quadrupole and magnetic mode volumes are defined as and û Q and u being defined such that, Q̅ = qû Q and m = μ u , with ∑ ij | û Qij | 2 = 1, ∑ i | u i | 2 = 1 û Qij and .…”

“… and û Q and u being defined such that, Q̅ = qû Q and m = μ u , with ∑ ij | û Qij | 2 = 1, ∑ i | u i | 2 = 1 û Qij and .…”