secondharmonic

Second harmonic refers to a frequency component at twice the fundamental frequency. In signal processing and physics, the term is used in two related contexts: general nonlinear response of a system to a periodic drive, and a specific nonlinear optical process known as second harmonic generation.

In nonlinear optics, second harmonic generation (SHG) arises when an electromagnetic wave propagates through a noncentrosymmetric medium whose polarization responds nonlinearly to the electric field. The second-order polarization term P(2)(t) ∝ χ(2) E(t)E(t) produces radiation at twice the input frequency (2ω). The efficiency of SHG depends on the nonlinear susceptibility χ(2), the intensity of the fundamental, and the phase-matching condition, which ensures constructive interference of the generated 2ω waves along the propagation direction. In bulk centrosymmetric materials, χ(2) vanishes, so SHG is weak or forbidden; it can occur at surfaces or interfaces where symmetry is broken, or in noncentrosymmetric crystals.

Phase matching can be achieved by birefringent phase matching or quasi-phase matching using periodically poled crystals (for example, PPLN, PPKTP). Common SHG materials include BBO, LBO, KDP, and lithium niobate. A typical application is frequency doubling of infrared lasers, such as converting 1064 nm light to 532 nm green light in Nd:YAG laser systems.

Second harmonic phenomena also appear in electronics and acoustics as nonlinear distortion, where a circuit or medium generates a 2f component from a fundamental signal; such harmonics are often filtered and suppressed in precision systems. SHG remains a valuable tool for spectroscopy and microscopy, providing surface sensitivity and insights into material symmetry.