Saturable Lorentz model for fully explicit three-dimensional modeling of nonlinear optics

Area of Science:

• Computational Physics
• Nonlinear Optics
• Quantum Mechanics

Background:

• Simulating nonlinear optical phenomena like laser filamentation using the finite-difference time-domain (FDTD) method with instantaneous Kerr nonlinearity requires iterative solutions, which can be unstable for strong fields.
• Existing explicit integration methods using anharmonic oscillator equations are often unstable and unsuitable for strong-field laser-matter interactions.

Purpose of the Study:

• To develop a stable and explicit numerical method for simulating nonlinear optical phenomena.
• To accurately model strong-field interactions, including laser filamentation and high harmonic generation, by overcoming the limitations of iterative FDTD approaches.

Main Methods:

• A novel approach using a nonlinear force-driven harmonic oscillator model to represent nonlinear susceptibility.
• This model reproduces polarization from quantum mechanical two-level equations, enabling explicit integration.
• The saturable harmonic oscillator model is integrated using the stable leapfrog method.

Main Results:

• The developed saturable harmonic oscillator model quantitatively reproduces quantum mechanical solutions for harmonic generation up to the 9th harmonic in the under-resonant limit.
• The explicit leapfrog integration of this model demonstrates stability even under intense laser fields characteristic of laser filamentation and high harmonic generation.
• This method provides a stable and accurate alternative to iterative FDTD for strong-field nonlinear optics.

Conclusions:

• A stable, explicit numerical framework for simulating strong-field nonlinear optics has been established.
• The driven harmonic oscillator model offers a robust and accurate representation of nonlinear susceptibility for phenomena like laser filamentation and harmonic generation.
• This advancement facilitates more efficient and reliable simulations in ultrafast optics and strong-field physics.