Summary

Nicolaas Bloembergen's 1965 monograph establishes the theoretical foundation for nonlinear optics, arguing that intense electromagnetic fields (from lasers) induce a nonlinear polarization response in materials, enabling frequency mixing, parametric amplification, and other effects absent in linear optics. The book systematically derives the wave equation for nonlinear media, introduces the nonlinear susceptibility tensor, and covers three-wave mixing processes like second-harmonic generation and sum-frequency generation. It also addresses parametric oscillators, stimulated Raman scattering, and the Manley-Rowe relations governing energy conservation in nonlinear interactions. A reader gains a rigorous, quantum-mechanical understanding of how laser light can alter a medium's optical properties, enabling technologies from frequency doublers to optical parametric amplifiers.

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Key concepts

Nonlinear polarization — The dipole moment per unit volume induced in a material that depends nonlinearly on the applied electric field, expressed as a power series in the field strength.
Second-harmonic generation — A nonlinear process where two photons at frequency ω combine in a noncentrosymmetric crystal to produce one photon at frequency 2ω.
Phase matching — The condition that the wave vectors of interacting beams satisfy momentum conservation (Δk=0) for efficient energy transfer in nonlinear mixing.
Manley-Rowe relations — Energy conservation laws for parametric processes, stating that the sum of photon numbers in coupled modes remains constant.
Parametric amplification — A process where a pump photon splits into signal and idler photons in a nonlinear crystal, amplifying the signal wave.
Nonlinear susceptibility tensor — A rank-3 (or higher) tensor describing the material's anisotropic response to intense fields, with symmetry constraints from crystal structure.