Ab initio nonlinear optics in solids: linear electro-optic effect and electric-field induced second-harmonic generation
Laboratoire des Solides Irradiés, CNRS, CEA/DRF/IRAMIS, École Polytechnique, Institut Polytechnique de Paris, 91128, Palaiseau, France
2 European Theoretical Spectroscopy Facility (ETSF), Palaiseau, France
3 Dipartimento di Scienze e Metodi dell’Ingegneria, Università di Modena e Reggio Emilia, Via Amendola 2 Padiglione Tamburini, 42122, Reggio Emilia, Italy
4 Dipartimento di Scienze e Metodi dell’Ingegneria, Università di Modena e Reggio Emilia and Centro Interdipartimentale En &Tech, Via Amendola 2 Padiglione Morselli, 42122, Reggio Emilia, Italy
5 Centro S3, Istituto Nanoscienze-Consiglio Nazionale delle Ricerche (CNR-NANO), Via Campi 213/A, 41125, Modena, Italy
6 Centro Interdipartimentale di Ricerca e per i Servizi nel Settore della Produzione, Stoccaggio ed Utilizzo dell’Idrogeno H2-MO.RE, Via Università 4, 41121, Modena, Italy
7 Laboratoire de Chimie Théorique, Sorbonne Université and CNRS, 75005, Paris, France
Accepted: 20 September 2022
Published online: 24 November 2022
Second-harmonic generation (SHG), linear electro-optic effect (LEO) and electric-field induced second-harmonic generation (EFISH) are nonlinear optical processes with important applications in optoelectronics and photovoltaics. SHG and LEO are second-order nonlinear optical processes described by second-order susceptibility. Instead, EFISH is a third-order nonlinear optical process described by third-order susceptibility. LEO and EFISH are only observed in the presence of a static electric field. These nonlinear processes are very sensitive to the symmetry of the systems. In particular, LEO is usually observed through a change in the dielectric properties of the material while EFISH can be used to generate a “second harmonic” response in centrosymmetric material. In this work, we present a first-principle formalism to calculate second- and third-order susceptibility for LEO and EFISH. LEO is studied for GaAs semiconductor and compared with the dielectric properties of this material. We also present how it is possible for LEO to include the ionic contribution to the second-order macroscopic susceptibility. Concerning EFISH we present for the first time the theory we developed in the framework of TDDFT to calculate this nonlinear optical process. Our approach permits to obtain an expression for EFISH which does not contain the mathematical divergences in the frequency-dependent second-order susceptibility that caused until now many difficulties for numerical calculations.
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