Second-harmonic generation

Second-harmonic generation is a nonlinear optical process in which an intense light field induces a material to emit light at twice the incident frequency, halving its wavelength.

Nonlinear polarization: A material polarization that depends nonlinearly on the applied electric field. Its second-order term oscillates at twice the driving field's frequency.
Frequency: The number of cycles of a periodic signal completed per unit time. The generated wave has twice the pump's frequency.
Frequency-doubled laser: A laser system that uses nonlinear conversion to emit light at twice its fundamental frequency. It directly applies this process to produce a shorter-wavelength output.
Third-harmonic generation: A nonlinear optical process that generates light at three times the incident frequency. It produces a third harmonic through a third-order response rather than a second-order one.
Second-order nonlinear optical process: An optical process driven by the quadratic response of a material to an electric field. Second-harmonic generation is its characteristic frequency-doubling example.
Wavelength: The spatial period of a wave, measured between corresponding points in successive cycles. In the same medium, doubling frequency halves the generated light's wavelength.
Green laser pointer: A visible green laser device, commonly made by frequency-doubling infrared laser light. Many such pointers convert 1064-nanometer light into green light near 532 nanometers.
Sum-frequency generation: A nonlinear process in which two input frequencies combine to produce light at their sum. It shares second-order physics but need not use two photons of the same frequency.
Phase matching: A condition that aligns the propagation phases of interacting optical waves to sustain their energy transfer. It prevents the generated harmonic from falling out of step with the pump.
Electric susceptibility: A measure of how readily a material polarizes in response to an electric field. The linear response provides the baseline for the nonlinear polarization used here.

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