nonlinearoptical

Nonlinear optics is the branch of optics that studies the behavior of light in media where the polarization responds nonlinearly to the electric field of the light. In most materials at moderate intensities the polarization P is proportional to the electric field E, P = ε0[χ^(1)E + χ^(2)E^2 + χ^(3)E^3 + …], but at higher field strengths higher-order terms become significant. In centrosymmetric media the second-order susceptibility χ^(2) vanishes, making χ^(3) the lowest-order nonlinear term.

Common nonlinear processes include second-harmonic generation (SHG), sum-frequency and difference-frequency generation, and optical parametric amplification, which enable frequency conversion and generation of new wavelengths. Third-order effects include the Kerr effect, self-phase and cross-phase modulation, and four-wave mixing, which can induce an intensity-dependent refractive index and support optical solitons. Efficient frequency conversion requires phase matching; techniques such as birefringent phase matching and quasi-phase matching using periodically poled crystals (e.g., PPLN) are widely used.

Nonlinear optics underpins many technologies, including laser frequency conversion, ultrafast spectroscopy, optical telecommunications, and the generation of entangled photons and terahertz waves. Materials commonly used include nonlinear crystals such as lithium niobate, beta barium borate, and potassium dihydrogen phosphate, as well as nonlinear optical fibers. Characterization methods include Z-scan for nonlinear refractive indices and Maker fringe measurements for χ^(2). The field continues to explore extreme regimes with ultrafast sources and nanostructured materials, aiming for higher efficiencies and novel quantum-optical applications.