Computational Optics Group
We investigate fundamental concepts of light-matter interactions at nanoscale when classical and quantum approaches merge
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Adi Salomon [Bar-Ilan University, Israel]
Renaud Vallee [Centre de Recherche Paul Pascal, France]
Hayk Harutyunyan [Emory University]
Nien-Hui Ge [University of California, Irvine]
Abraham Nitzan [UPenn, Tel Aviv University]
Joseph Zyss [Ecole Normale Supérieure Paris Saclay]
Ruth Pachter [AFRL, WPAFB]
Andrei Piryatinski [LANL]
Joseph Subotnik [UPenn]
SHG by strongly coupled exciton-plasmons: the role of polaritonic states in nonlinear dynamics
Read our manuscript at arXiv:

In collaboration with Joseph Zyss and Adi Salomon we investigate second harmonic generation (SHG) from hexagonal periodic arrays of triangular nano-holes of aluminum using a self-consistent methodology based on the hydrodynamics-Maxwell-Bloch approach. It is shown that angular polarization patterns of the far-field second harmonic response abide to three-fold symmetry constraints on tensors. When a molecular layer is added to the system and its parameters are adjusted to achieve the strong coupling regime between a localized plasmon mode and molecular excitons, Rabi splitting is observed from occurrence of both single- and two-photon transition peaks within the SHG power spectrum. It is argued that the splitting observed for both transitions results from direct transitions between lower and upper polaritonic states of the strongly coupled system. This interpretation can be accounted by a tailored three-level quantum model, with results in agreement with the unbiased numerical approach. Our results suggest the hybrid states formed in strongly coupled systems directly contribute to the nonlinear dynamics. This opens new directions in designing THz sources and nonlinear frequency converters.
Second order susceptibility for metal only (black) and metal with molecules (blue) as a function of frequency. One can see the Rabi splitting for 1-photon (2.42 eV) and 2-photon peaks (1.21 eV).
Enhancing SHG in strongly coupled systems with optical gain
Read our JCP manuscript: paper
In collaboration with Andrei Piryatinski (LANL) and Oleksiy Roslyak (Fordham) we successfully applied laser theory and scrutinize a possibility to greatly enhance SHG efficiency in plasmonic systems. We generalized driven-dissipative Tavis-Cummings model by introducing anharmonic surface-plasmon mode coupled to QEs and examine physical properties of corresponding polariton modes. Calculations of the SHG efficiency for strong QE-plasmon coupling demonstrates orders of magnitude enhancement due to polariton gain. We further discussed time-domain numerical simulations of SHG in a square lattice comprised of Ag nanopillars coupled to QEs utilizing fully vectorial nonperturbative nonlinear hydrodynamic model for conduction electrons coupled to Maxwell-Bloch equations for QEs. The simulations supported the idea of gain enhanced SHG and show orders of magnitude increase in the SHG efficiency as the QEs were tuned in resonance with the lattice plasmon mode and brought above the population inversion threshold by incoherent pump. By varying pump frequency and tuning QEs to a localized plasmon mode, we demonstrated further enhancement of the SHG efficiency facilitated by strong local electric fields. The incident light polarization dependence of the SHG was examined. It was shown that the polarization was related to the symmetries of participating plasmon modes.
(a) weakly coupling regime (b) strong coupling regime—SHG efficiency conversion as a function of the pump frequency for different inversion parameters. Red color indicates material with optical gain.
SHG by a TMD monolayer coupled to a single plasmonic nanoparticle
Read our Nano Letters manuscript: paper
In collaboration with Hayk Harutyunyan (Emory) and Matt Pelton (UMBC) we successfully applied our theory to explain recent experiments performed by Hayk and his research group. For the first time it was shown that the SHG signal generated by WSe2 monolayer coupled to a single Au nanorod exhibits Rabi splitting opening up a new platform for investigating nonlinear optical processes at true nanoscale.
Angular properties of SHG by gold nanocrescents
Read our JPCC manuscript: paper
In collaboration with Nien-Hui Ge (UCI) we put our hydrodynamics model to the test directly comparing simulations with experiments on SHG by gold nanocrescents. Not only the comparison is good we were also able to explain several fascinating features including SPP multipole contribution to SHG and astonishing sensitivity of SHG to nanoparticle’s shape imperfections.
SHG by periodic arrays of nano-holes
Read our JCP manuscript: paper
Linear and nonlinear optical response of periodic arrays of nanoholes of triangular shape is examined using experimentally realizable parameters. Utilizing a three dimensional fully vectorial approach based on the nonlinear hydrodynamic model describing metal coupled to Maxwell’s equations and Bloch equations for molecular emitters we analyze linear transmission, reflection, and nonlinear power spectra. It is shown that both the Coulomb interaction of conduction electrons and the convective term contribute on equal footing to the nonlinear response of metal. When molecular emitters are placed on a surface of hole arrays calculated second harmonic response exhibits three peaks corresponding to second harmonics of hybrid exciton-plasmon states.
Field-testing nonlinear hydrodynamic model: direct comparison with experiments
In collaboration with the experimental group from Institute of d'Alembert (ENS Paris Saclay) we have recently completed studies of second-order nonlinear properties of triangular nanoprisms. We utlized our numerical hydrodynamic model for conduction electrons and computed second-order hyperpolarizability using experimental parameters. The direct comparison with experiments led to:

ß = 1.43 x 10-33 (SI units) --- THEORY
ß = 1.30 x 10-33 (SI units) --- EXPERIMENT

It should be noted that our model had no fitting parameters. Such a great aggrement betwen our theory and experiments reveals quantitative power of the hydrodynamic model when applied to nonlinear plasmonics. We also explored how hyperpolarizability varied with the sharpness of nanoprims. Our manuscript was submitted to Israel Journal of Chemistry.
TEM images of gold nanoprism used in experiments. Different pictures show nanoprisms with different edge length and curvature of the corners of the triangular cross section.
Fano plasmonics goes nonlinear
In collaboration with Dr. Ruth Pachter we we investigate the second order nonlinear response of a plasmonic nanosystem, namely nanodolmen that supports localized surface plasmon-polariton resonances with the so-called Fano profile. It has been shown by various researchers that such systems exhibit a wide variety of fascinating phenomena including strong local field enhancement and strong coupling between bright and dark modes. In our work we utilize the full machinery of hydrodynamics-Maxwell equations taking nonlinear response of metal directly into account and also propose a simple analytical toy model that explains our major findings, i.e., significant second harmonic enhancement at the frequency of a plasmon mode with the Fano profile. Manuscript has been recently submited to Journal of Chemical Physics. See its arxiv version at:
Second-order susceptibility (black) and the linear absorption (red) as functions of the pump frequency calculated for a periodic array of nanodolmens - one can see the enhancement of the second-order response near the frequency corresponding to the linear plasmon resonance with Fano profile. Simulations are performed utilzing fully vectorial three-dimensional hydrodynamics - Maxwell equations.