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Bulk quadrupole contribution to second harmonic generation from classical oscillator model in silicon.

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    We quantitatively predict the bulk quadrupole contribution to second harmonic generation in silicon using classical models. The (111) surface shows the main contribution, demonstrating the method's viability for other semiconductors.

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    Area of Science:

    • Condensed matter physics
    • Nonlinear optics
    • Materials science

    Background:

    • Second harmonic generation (SHG) is a key nonlinear optical process.
    • Understanding surface and bulk contributions in SHG is crucial for material characterization.
    • Silicon's optical properties are of significant interest for photonic applications.

    Purpose of the Study:

    • To quantitatively predict the frequency-dependent bulk quadrupole contribution to SHG in silicon.
    • To compare the quadrupole contribution with the dipole contribution.
    • To validate the developed models using literature data for other semiconductors.

    Main Methods:

    • Utilizing a generalized classical anharmonic oscillator model.
    • Employing a simplified bond hyperpolarizability model.
    • Calculating frequency-dependent linear susceptibility.

    Main Results:

    • The (111) silicon surface exhibits the dominant bulk quadrupole contribution to SHG in single-beam setups.
    • The (001) and (011) silicon facets show only minor contributions.
    • The model's dipole contribution predictions align with literature values for SiC, AlAs, and GaAs.

    Conclusions:

    • The generalized classical anharmonic oscillator and simplified bond hyperpolarizability models accurately predict SHG contributions in silicon.
    • Surface orientation significantly impacts the bulk quadrupole contribution to SHG in silicon.
    • The developed methodology is viable for predicting SHG in various semiconductor materials.