Communications: <i>Ab initio</i> second-order nonlinear optics in solids

Luppi, E.; Hübener, Hannes; Véniard, Valérie

doi:10.1063/1.3457671

Cited by 26 publications

(34 citation statements)

References 34 publications

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“…The prospect of controlling second-order nonlinear phenomena in Si by means of strain is very intriguing. In this work we provide the first quantitative demonstration of second-order nonlinearities in strained Si through both ab initio calculations and SHG experiments in suitably engineered Si waveguides.Second-order nonlinear optical response from strained bulk Si is computed by time-dependent density-functional theory in a supercell approximation with periodic boundary conditions [16][17][18] . All the studied strained Si structures were obtained using a unit cell of 16 Si atoms (Fig.…”

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confidence: 99%

Second-harmonic generation in silicon waveguides strained by silicon nitride

et al. 2011

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Silicon photonics meets the electronics requirement of increased speed and bandwidth with on-chip optical networks. All-optical data management requires nonlinear silicon photonics. In silicon only third-order optical nonlinearities are present owing to its crystalline inversion symmetry. Introducing a second-order nonlinearity into silicon photonics by proper material engineering would be highly desirable. It would enable devices for wideband wavelength conversion operating at relatively low optical powers. Here we show that a sizeable second-order nonlinearity at optical wavelengths is induced in a silicon waveguide by using a stressing silicon nitride overlayer. We carried out second-harmonic-generation experiments and first-principle calculations, which both yield large values of strain-induced bulk second-order nonlinear susceptibility, up to 40 pm V −1 at 2,300 nm. We envisage that nonlinear strained silicon could provide a competing platform for a new class of integrated light sources spanning the near-to mid-infrared spectrum from 1.2 to 10 µm. When a crystal possesses a significant second-order nonlinear optical susceptibility, χ (2) , it can produce a wide variety of wavelengths from an optical pump 1 . In fact, a second-order crystal generates shorter wavelengths by second-harmonic generation or longer wavelengths by spontaneous parametric down-conversion of a single pump beam. Such a crystal can also nonlinearly mix two different beams, thus generating other wavelengths by sum-frequency or difference-frequency generation. These possibilities are much more intriguing whenever the crystal can be used in integrated optical circuits because, on the one hand, light confinement reduces the average optical power needed to trigger nonlinear processes and, on the other hand, relatively long effective interaction lengths can be exploited.Si photonics has demonstrated the integration of multiple optical functionalities with microelectronic devices 2,3 . On the basis of the third-or higher-order nonlinearities of Si (ref. 4), functions such as amplification and lasing, wavelength conversion and optical processing have all been demonstrated in recent years 5 . However, third-order refractive nonlinearities require relatively high optical powers, and compete with nonlinear-loss mechanisms such as two-photon absorption and two-photon induced freecarrier absorption. Yet, the second-order term of the nonlinear susceptibility tensor cannot be exploited in Si simply because χ (2) vanishes in the dipole approximation owing to the crystal centrosymmetry: the residual χ (2) , which is due to higher-multipole processes, is too weak to be exploited in optical devices 6 .Second-harmonic generation (SHG) was observed in reflection from Si surfaces 7-11 or in diffusion from Si photonic crystal nanocavities 12 . This indicates that the reduction of the Si symmetry may indeed induce a significant χ (2) . In these cases, the Si symmetry was broken by the presence of a surface. Several groups have pointed out that the surface cont...

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confidence: 99%

Second-harmonic generation in silicon waveguides strained by silicon nitride

et al. 2011

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“…We have shown [18] that it is indeed sufficient to include only the linear f xc in our calculation and let g xc ¼ 0 when we want to achieve satisfying comparison with experimental data. We note, however, that the actual importance of g xc , as well as the limitations of the ''g xc ¼ 0''-approximation are still open questions.…”

Section: Excitonic Effectsmentioning

confidence: 95%

“…[18]. In Section 2 we show how to obtain the microscopic second order response in the framework of time dependent density functional theory (TDDFT) [19,20].…”

Section: P ð2þmentioning

confidence: 99%

Ab initio calculation of second harmonic generation in solids

Hübener

Luppi

Véniard

2010

Physica Status Solidi (b)

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An ab initio formalism for the calculation of macroscopic second order responses within the time dependent density functional theory (TDDFT) framework is presented. The linear Dyson-like equation of TDDFT is generalized to second order and the resulting microscopic response is related to the macroscopic non-linear susceptibility. The macroscopic relations are obtained considering Maxwell's equations and the non-linear relation between the microscopic and macroscopic field. Some approximations have to be made to account for many body effects. The impact of the several levels of approximation on the second harmonic spectrum is illustrated for the example of bulk AlAs in the zincblende structure. This success motivates expectations for an equally successful first principles description of non-linear optical processes. However, the basic requirement of such a description, is a comprehensive understanding of the non-linear microscopic physical mechanisms in the second order response function, and how they are related to the macroscopic quantities. This is a formidable task and considerable difficulties have delayed accurate calculations for many years [4-8], even for the lowest level of approximation: independent particle approximation (IPA) [9]. Within IPA, the absolute value of the second order susceptibility does not at all agree with the experimental measurements [10]. To go beyond the independent particle description, we need to carefully consider the second order susceptibility x ð2Þ defined as

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“…This IPA formalism has hence been further developed by V. Véniard [72] improving the accuracy of the response and the possibility of introducing straightforwardly many-body effects as crystal local fields and excitons in the macroscopic χ (2) . Starting from previous studies on semiconductors where the formalism and the code have been successfully applied to bulk cubic materials (GaAs, AlAs, SiC [72][73][74][75]) or deformed centrosymmetric materials (strained Si [13]), I have extended its application to the study of complex systems as the interfaces and surfaces, studying its accuracy and capabilities. This is the first time the theory and the code are applied to these kinds of systems and non-trivial problems have been encountered both of theoretical and numerical nature.…”

Section: Shg Theoretical Descriptionmentioning

confidence: 99%

“…Only bulk systems with a limited amount of atoms were studied before [13,[72][73][74][75]. As a consequence, the comparison with the experiment represent an ideal test for the accuracy of the method once applied to complex materials.…”

Section: The Si/caf 2 Interfacementioning

confidence: 99%

Second-Harmonic Generation

Powers¹

Field Guide to Nonlinear Optics

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Communications: Ab initio second-order nonlinear optics in solids

Cited by 26 publications

References 34 publications

Second-harmonic generation in silicon waveguides strained by silicon nitride

Second-harmonic generation in silicon waveguides strained by silicon nitride

Ab initio calculation of second harmonic generation in solids

Second-Harmonic Generation

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