Kosmas L. Tsakmakidis

Quantum Condensed Matter Photonics @ NKUA

Complex frequencies

Complex-frequency excitations [1–4] have recently been exploited for a range of unexpected and exciting applications in photonics, from compensating losses in metamaterials, superlenses and polaritonic propagation, to enabling virtual absorption, virtual critical coupling, virtual optical pulling forces, virtual parity-time symmetry, and diverse other functionalities beyond the usual bounds on light scattering. These excitations open a completely new perspective to the optical world, primarily because they can make a lossy (e.g., plasmonic) structure behave as if it was completely lossless (while still plasmonic, i.e., with Re{ε} < 0) – without any violation of the conservation of energy.

We were the first group (back in 2014) to show how these solutions can be excited in the time domain (i.e., in realistic experimental setups) [1], and more recently we proposed the first fully-analytic closed-form description of these excitations in the context of attaining ‘virtual absorption’ [2]. We have also recently introduced the concepts of anisotropic virtual gain and oblique Kerker effect [3], where a lossy anisotropic medium behaves exactly as its anisotropic gain counterpart upon excitation by a synthetic complex-frequency wave. That strategy allowed one to largely tune the magnitude and angle of a particle’s scattering simply by changing the shape (envelope) of the incoming radiation, rather than by an involved medium- tuning mechanism. The so-attained anisotropic virtual gain enabled directional super-scattering at an oblique direction with fine-management of the scattering angle. We are currently exploring further consequences of and phenomena arising from these fascinating excitations. Our monograph on ‘Metamaterials and Nanophotonics’ [4] is the first book to detail these complex excitations.

  1. K. L. Tsakmakidis, T. W. Pickering, J. M. Hamm, A. F. Page, and O. Hess, "Completely stopped and dispersionless light in plasmonic waveguides", Phys. Rev. Lett. 112, 167401 (2014) ['Focus' story in APS Physics 7, 44 (2014)]. [PDF]
  2. I. Loulas, E.-C. Psychogiou, K. L. Tsakmakidis, and N. Stefanou, “Analytic theory of complex-frequency-aided virtual absorption,” Opt. Express 33, 28333 (2025). [PDF]
  3. G. P. Zouros, I. Loulas, E. Almpanis, A. Krasnok, and K. L. Tsakmakidis, “Anisotropic virtual gain and large tuning of particles’ scattering by complex- frequency excitations,” Comm. Phys. 7, 283 (2024) (Nature Publishing Group), https://doi.org/10.1038/s42005-024-01772-w. [open access: https://rdcu.be/dRBEL]
  4. (monograph) K. L. Tsakmakidis, K. G. Baskourelos, and M. S. Wartak, Metamaterials and Nanophotonics: Principles, Techniques and Applications (World Scientific, Sept. 2022, Singapore), DOI: https://doi.org/10.1142/13010.