Over the past several decades, the research field of optics at the nanoscale, i.e., nano-optics, has flourished alongside the development of concepts and techniques to shrink light to scales well below the limit imposed by the law of diffraction. In particular, recent progress in nanotechnology has allowed structuring materials at the deep nanoscale and even subnanometer scale, pushing the research field of nano-optics into extreme, or nano-optics version 2.0. In spectroscopic experiments, scientists have observed phenomena such as tip-enhanced Raman scattering and fluorescence phenomena that cannot be explained by classical local electromagnetic theory, posing a difficult challenge in interpreting the underlying physics. Now publishing in Physical Review Letters, Prof. Chen Xuewen and his team members (including PhD student Zhou Qiang and Assoc. Prof. Zhang Pu) report an important advance in the frontier of nano-optics to resolve the theoretical challenge.
In the context of extreme nano-optics, correct characterization of the nonlocal and quantum effects in nanostructured materials is the important starting point for quantitative studies, and then the development of a quasinormal mode theory is the key to gain physical insights into optical responses. Currently, for extreme nano-optics, the description of the nonlocal and quantum effects treats certain particular effects with the corresponding phenomenological nonlocal models, resulting in various specialized ad hoc theoretical models. Moreover, under these models the electromagnetic interactions and energies in materials manifest in complex forms, making it intricate to define the eigenmodes of the optical system, let alone to derive the orthonormalization relation of the modes.
In this work, titled “General framework of canonical quasinormal mode analysis for extreme nano-optics”, the authors recognize the essence of electron nonlocality, spillover and other quantum effects as the interaction between charged particles, and innovatively propose a generalized Lorentz model (GLM). The GLM abstracts the nonlocality related to the gradient of the charged particles’ spatial distributions as differential operators, and formulate the dynamic equation for the charged particles interacting with the optical field through the basic Newton's second law. Therefore, our GLM constitutes a general framework model, covering all the mainstream nonlocal models in the community. Our GLM description of the nonlocal and quantum effects in nanostructured material is in parallel to the usual textbook-level permittivity descriptions as given in Electrodynamics of continuous media by Landau, Lifshitz and Pitaevskii, but it is more mathematically concrete, and thus more operational, than the conventional textbook treatment. The GLM enables the authors to correctly formulate the linear eigenvalue problem for non-Hermitian systems showing complex nonlocal effects, leading to the definition of the eigenmodes. Furthermore, based on GLM the authors derive the electromagnetic theorems, e.g. Poynting and reciprocity theorems, of the non-Hermitian systems. Thereupon, the eigenmodes can be successfully orthonormalized. Overall, a canonical and general quasinormal mode framework suitable for extreme nano-optics is established, filling a gap in the research area of quasinormal mode.
As applications of the above quasinormal mode framework, the authors reported, for the first time, the GLM realizations of the quantum hydrodynamic model for electrons in metal and the nonlocal model for lattice vibrations in polar dielectrics. In sequence, they give the explicit orthonormalization relations for the corresponding quasinormal modes. As a concrete example, the authors investigated the modal evolution of a metallic dimer in the quantum tunneling regime. In comparison with conventional characterizations based on scattering or absorption spectra, the quasinormal mode analysis is capable of directly revealing the intrinsic physics.
The present research finding represents one of the recent important achievements in advancing the frontier of optical science by Prof. Chen Xuewen's group. Earlier in 2021, they reported a work dedicated to a fundamental problem of optical physics: how small a room optical field can be compressed into and whether light can exist almost as a "point" like an electron. As a result, the research group discovered a new mechanism of extreme light confinement, and reported the discovery as a Letter entitled Bright Optical Eigenmode of 1 nm3 Mode Volume in the authoritative physics journal Physical Review Letters (Phys. Rev. Lett. 126, 257401 (2021)). The Letter points out that there exists a kind of optical modes with mode volumes as small as 1 cubic nanometer in the visible frequency range, and leveraging optical antenna effect such modes can be efficiently excited by light from far-field region.
Link: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.127.267401
