My work focuses on the theoretical study of the interaction of light with matter using computational tools. By describing the field dynamics using Maxwell's equations, and the matter quantum dynamically within TDDFT, we can propagate light and matter simultaneously in time. With this powerful tool we can simulate the ultra-strong confinement of light in the nanoscale by plasmonic nanostructures, and enhance techniques such as high-resolution tip-enhanced Raman spectromicroscopy and attosecond streaking experiments.
To achieve this goal, Maxwell's equations are rewritten in the Riemann-Silberstein form, where the real electric and magnetic field are combined in a complex vector (eq. (1)). Now the four Maxwell's equations can be rewritten as two equations (eqs. (2)), one representing the Gauß laws and one combining the Faraday and Ampere laws. The latter can be written in Schrödinger form, where the vector plays the role of the wavefunction and the curl acts as a Hamiltonian, and the current density as an inhomogeneity (eq. (3)). In this form, this equation can be solved numerically in discretized time and space, using a proper computational code. Moreover, it can be fully coupled with the quantum dynamics of matter, accounting not only on the effects of light on matter, but also the back-reaction of the currents and charge density of the matter that shape the electromagnetic fields.
The Maxwell-TDDFT method is being implemented in the Octopus code, and the theory behind it can be found in this publication. This implementation enables the propagation of highly localized and spatially shaped fields and its interaction with matter both as a continuum or in its atomistic description. Among the relevant applications, we can mention: plasmonic shaping of twisted light (carrying orbital angular momentum) by chiral metal nanostructures; near-field effects in metallic junctions and its effect in near-field sensing and tip-enhanced Raman scattering of molecules (breaking of selection rules by non-uniform fields); local field effects in attosecond streaking spectroscopy and transfer or orbital angular momentum by twisted XUV light pulses when exciting core electrons.
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