linearoptical

Linear optics, sometimes written as linear-optical or linearoptical in the literature, is the branch of optics that studies light propagation and interaction under the assumption that the material response is linear with respect to the electric field. In this regime, the output of an optical system is proportional to its input, and the principle of superposition applies.

When a medium is linear, the polarization P responds as P = χ^(1) E, and higher-order terms are negligible at moderate intensities. This leads to phenomena such as interference, diffraction, and polarization effects, where optical fields add coherently and detectors respond to the resulting intensity. Frequencies are not generated or mixed by the medium in linear optics.

Common linear-optical components include beam splitters, mirrors, lenses, phase shifters, and waveplates. Paraxial ray tracing uses transfer matrices (ABCD) for focusing systems, while polarization states are treated with Jones calculus (2x2 matrices) or Mueller calculus for partially polarized light.

Linear optics is contrasted with nonlinear optics, where the medium’s response contains higher-order terms that produce new frequencies or self-field effects. In quantum information, linear optics provides the toolkit for linear-optical quantum computing and photonic circuits, relying on beam splitters, phase shifters, and projective measurements; scalability often requires additional resources due to probabilistic gates.

Applications span interferometry, holography, fiber communications, optical imaging, spectroscopy, and precision metrology. The field underpins many everyday technologies, from imaging systems to metrological standards, and continues to evolve with integrated photonics and advanced materials that preserve linear response while enhancing performance.