Linear optics

Linear optics is a sub-field of optics, consisting of linear systems, and is the opposite of nonlinear optics. Linear optics includes most applications of lenses, mirrors, waveplates, diffraction gratings, and many other common optical components and systems.

If an optical system is linear, it has the following properties (among others):

These properties are violated in nonlinear optics, which frequently involves high-power pulsed lasers. Also, many material interactions including absorption and fluorescence are not part of linear optics.

As an example, and using the Dirac bracket notations (see bra-ket notations), the transformation ${\displaystyle |k\rangle \rightarrow e^{ik\theta }|k\rangle }$ is linear, while the transformation ${\displaystyle \alpha _{0}|0\rangle +\alpha _{1}|1\rangle +\alpha _{2}|2\rangle \rightarrow \alpha _{0}|0\rangle +\alpha _{1}|1\rangle -\alpha _{2}|2\rangle }$ is non-linear. In the above examples, ${\displaystyle k=0,1,\ldots }$ is an integer representing the number of photons. The transformation in the first example is linear in the number of photons, while in the second example it is not.

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