Nonreciprocal

Nonreciprocal describes systems or components whose response to a stimulus depends on the direction of the stimulus or the path taken. In other words, the transmission from port A to port B is not the same as from port B to port A. Nonreciprocal behavior is the opposite of reciprocity, a property expected in many linear, passive, and time-invariant systems.

In physics, reciprocity is formalized by the Lorentz reciprocity theorem, which holds for linear, passive media with symmetric constitutive relations that do not break time-reversal symmetry. Nonreciprocity arises when this symmetry is broken. Common approaches include introducing a bias that distinguishes forward and backward directions (such as a magnetic field in magneto-optic materials), using moving media or spatiotemporal modulation, or employing active components or nonlinearities that differ for opposing waves.

Nonreciprocal devices are widely used in communications and signal processing. In the microwave and RF domain, isolators and circulators made from magnetized ferrites route signals while suppressing reflections. In optics, optical isolators and circulators rely on Faraday rotation combined with polarizers to achieve unidirectional transmission. Nonreciprocity is also studied in acoustics and mechanics, where time-varying media or nonlinear effects enable one-way transmission of sound or stress waves.

While nonreciprocal devices can be passive (for example, certain gyrators or ferrite-based components) they most commonly rely on some form of time-reversal symmetry breaking or amplification. The concept is essential for protecting sources from back-reflected power, enabling full-duplex communication in some systems, and supporting novel wave-control strategies in various physical platforms.