Sumfrequency

SumFrequency is a term used to describe the generation or observation of a signal whose frequency equals the sum of two input frequencies, f_out = f1 + f2, arising in systems with nonlinear response. In linear systems, frequencies pass independently, but in nonlinear media, frequency mixing produces additional spectral components, including sum and difference frequencies.

Mechanisms for sum-frequency generation occur in several domains. In electronic circuits, nonlinear devices such as diodes or transistors in mixers produce intermodulation products; the output includes components at f1+f2 and f1−f2. In optical systems, sum-frequency generation is a second-order nonlinear optical process in materials with nonzero second-order susceptibility, where photons at f1 and f2 combine to produce a photon at f_sum = f1+f2, subject to energy conservation and phase-matching conditions.

Applications of sum-frequency concepts span telecommunications, coherent optical communications, and spectroscopy. In communications, sum-frequency processes can be used for frequency shifting or conversion between bands. In optics, sum-frequency generation is employed for wavelength conversion and ultrafast spectroscopy. Sum-frequency generation spectroscopy (SFG) is used to probe surfaces and interfaces with broken inversion symmetry, providing information about molecular structure at boundaries.

Measurement and analysis typically involve spectral analysis to identify lines at f1+f2, with amplitude influenced by input amplitudes, nonlinear coefficients, interaction length, and phase matching. In digital or audio contexts, sum frequencies can be synthesized by mixing signals in nonlinear processors or specialized software.

See also: intermodulation distortion, mixers, sum-frequency generation, nonlinear optics.