# Linear optics > Mediated Wiki article. Canonical URL: https://mediated.wiki/source/Linear_optics > Markdown URL: https://mediated.wiki/source/Linear_optics.md > Source: https://en.wikipedia.org/wiki/Linear_optics > Source revision: 1341152174 > License: Creative Commons Attribution-ShareAlike 4.0 International (https://creativecommons.org/licenses/by-sa/4.0/) {{Short description|Sub-field in optics consisting of lenses and mirrors}} {{More citations needed|date=March 2026}} '''Linear optics''' is a sub-field of [optics](/source/optics), consisting of [linear system](/source/linear_system)s, and is the opposite of [nonlinear optics](/source/nonlinear_optics). Linear optics includes most applications of lenses, mirrors, waveplates, diffraction gratings, and many other common optical components and systems.{{Cite web |last=Janaky |date=2024-09-05 |title=What Is the Difference Between Linear and Nonlinear Optics? |url=https://www.azooptics.com/Article.aspx?ArticleID=2668 |access-date=2026-03-01 |website=AZoOptics |language=en}} If an optical system is linear, it has the following properties (among others): * If [monochromatic light](/source/monochromatic_light) enters an unchanging linear-optical system, the output will be at the same frequency. For example, if red light enters a lens, it will still be red when it exits the lens. * The [superposition principle](/source/superposition_principle) is valid for linear-optical systems. For example, if a mirror transforms light input A into output B, and input C into output D, then an input consisting of A and C simultaneously give an output of B and D simultaneously. * Relatedly, if the input light is made more intense, then the output light is made more intense but otherwise unchanged. These properties are violated in nonlinear optics, which frequently involves high-power pulsed lasers. Also, many material interactions including absorption and [fluorescence](/source/fluorescence) are not part of linear optics. ==Linear versus non-linear transformations (examples)== As an example, and using the [Dirac bracket](/source/Dirac_bracket) notations (see [bra-ket notations](/source/bra-ket_notation)), the transformation |k\rangle \rightarrow e^{ik\theta}|k\rangle is linear, while the transformation \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, 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.{{clarify|reason=The second transformation is a linear operator, but why is this different from a nonlinear transformation?|date=January 2022}} This specific nonlinear transformation plays an important role in optical quantum computing. ==Linear versus nonlinear optical devices (examples)== Phase shifters and beam splitters are examples of devices commonly used in linear optics. In contrast, frequency-mixing processes, the optical Kerr effect, cross-phase modulation, and Raman amplification, are a few examples of nonlinear effects in optics. ==Connections to quantum computing== One currently active field of research is the use of linear optics versus the use of nonlinear optics in quantum [computing](/source/computing).{{Cite journal |last=Yildirim |first=Mustafa |last2=Dinc |first2=Niyazi Ulas |last3=Oguz |first3=Ilker |last4=Psaltis |first4=Demetri |last5=Moser |first5=Christophe |date=November 2024 |title=Nonlinear processing with linear optics |url=https://www.nature.com/articles/s41566-024-01494-z |journal=Nature Photonics |language=en |volume=18 |issue=10 |pages=1076–1082 |doi=10.1038/s41566-024-01494-z |issn=1749-4893}} For example, one model of [linear optical quantum computing](/source/linear_optical_quantum_computing), the [KLM model](/source/KLM_protocol), is universal for [quantum computing](/source/quantum_computing), and another model, the [boson sampling](/source/boson_sampling)-based model, is believed to be non-universal (for quantum computing) yet still seems to be able to solve some problems exponentially faster than a classical computer. The specific nonlinear transformation \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, (called "a gate" when using computer science terminology) presented above, plays an important role in optical quantum computing: on the one hand, it is useful for deriving a universal set of gates, and on the other hand, with (only) linear-optical devices and post-selection of specific outcomes plus a feed-forward process, it can be applied with high success probability, and be used for obtaining universal linear-optical quantum computing, as done in the [KLM model](/source/KLM_protocol).{{cite journal | title=A scheme for efficient quantum computation with linear optics | author1=Knill, E. | journal=Nature | year=2001 | volume=409 | pages=46–52 | author2=Laflamme, R. | author3=Milburn, G. J. | publisher=Nature Publishing Group | doi=10.1038/35051009 | pmid=11343107 | issue=6816|bibcode = 2001Natur.409...46K | s2cid=4362012 }} == See also == {{portal|Physics}} *[Optics](/source/Optics) *[Quantum optics](/source/Quantum_optics) *[Nonlinear optics](/source/Nonlinear_optics) *[Linear optical quantum computing](/source/Linear_optical_quantum_computing) (LOQC) *[KLM model](/source/KLM_protocol) for LOQC *[Optical phase space](/source/Optical_phase_space) *[Optical physics](/source/Optical_physics) *[Nonclassical light](/source/Nonclassical_light) ==References== {{Reflist}} Category:Optics --- Adapted from the Wikipedia article [Linear optics](https://en.wikipedia.org/wiki/Linear_optics) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/Linear_optics?action=history)). Available under [Creative Commons Attribution-ShareAlike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/). Changes may have been made.