{{Short description|Type of artificial sheet material}} {{context|date=May 2015}} [[File:Metasurface (5941035620).jpg|thumb|A liquid-tunable electromagnetic metasurface|275px]] An '''electromagnetic metasurface''' is an artificially engineered, two-dimensional material designed to control the behavior of electromagnetic waves through arrays of subwavelength features. Unlike bulk [[metamaterials]], which achieve unusual properties through three-dimensional structuring, metasurfaces manipulate waves at an interface by imposing abrupt changes in amplitude, phase, or polarization. Their thin, planar form factor allows them to perform functions traditionally requiring bulky optical components, such as lenses or polarizers, within a single ultrathin layer.<ref name="capasso2">{{cite journal|last1=Yu|first1=Nanfang|last2=Capasso|first2=Federico|title=Flat optics with designer metasurfaces|journal=Nat. Mater.|date=2014|volume=13|issue=2|pages=139–150|doi=10.1038/nmat3839|pmid=24452357|bibcode=2014NatMa..13..139Y}}</ref><ref name="Quevedo-teruel">{{cite journal|author=Quevedo-Teruel, O.|title=Roadmap on metasurfaces |journal=Journal of Optics|volume=21|year=2019|issue=7 |page=073002 |doi=10.1088/2040-8986/ab161d|bibcode=2019JOpt...21g3002Q |s2cid=198449951 |display-authors=etal|doi-access=free|hdl=10016/33235|hdl-access=free}}</ref>

Metasurfaces are typically constructed from periodic or aperiodic arrangements of resonant elements, such as metallic antennas, dielectric scatterers, or patterned films, that interact with incident waves. Depending on design, they can operate in reflective, transmissive, or absorbing modes, enabling applications in [[beam steering]], wavefront shaping, holography, and dispersion engineering. More advanced designs integrate tunable materials (e.g., [[Liquid crystal|liquid crystals]], [[graphene]], or phase-change compounds), creating ''reconfigurable intelligent surfaces'' that allow dynamic, programmable control of scattering and radiation patterns.<ref>{{cite journal |last1=Di Renzo |first1=Marco |last2=Zappone |first2=Antonio |last3=Debbah |first3=Mér |last4=Alouini |first4=Mohamed-Slim |title=Smart radio environments empowered by reconfigurable intelligent surfaces: How it works, state of research, and the road ahead |journal=IEEE Journal on Selected Areas in Communications |date=2020 |volume=38 |issue=11 |pages=2450–2525 |doi=10.1109/JSAC.2020.3007211 |arxiv=2004.09352 |bibcode=2020IJSAC..38.2450D |s2cid=219601556}}</ref>

Historically, metasurfaces build on early studies of anomalous diffraction in metallic gratings (''[[Wood's anomaly]]'', 1902) and the later development of [[surface plasmon polaritons]]. The field expanded significantly in the early 2000s with the advent of plasmonic nanostructures and in the 2010s with the demonstration of "flat optics" and planar holograms. Since then, metasurfaces have been developed for a wide range of wavelengths, from radio frequency (RF) and microwave to visible light, enabling research in stealth technology, communications, imaging, and biosensing.<ref name="ReferenceA">{{cite journal|author=Zeng, S.|title=Graphene-gold metasurface architectures for ultrasensitive plasmonic biosensing |journal=Advanced Materials|volume=27|pages=6163–6169 |year=2015|issue=40 |doi=10.1002/adma.201501754|url=https://www.researchgate.net/publication/281618671|display-authors=etal|pmid=26349431|bibcode=2015AdM....27.6163Z |hdl=20.500.12210/45908 |s2cid=205261271 |hdl-access=free}}</ref><ref name="capasso1" />

Metasurfaces are widely studied as a versatile platform for electromagnetic and optical engineering. They serve both as tools for exploring generalized laws of reflection and refraction, and as enabling technologies for compact optical systems, radar cross-section reduction, integrated photonics, and bioimaging. Their rapid development has established them as a significant topic in contemporary nanophotonics, antenna research, and materials science.<ref name="capasso2" /><ref name="Quevedo-teruel" /><ref name="ReferenceB" />

==Definition and categorization==

A metasurface is generally defined as an artificially structured, two-dimensional array of subwavelength elements that collectively control the properties of electromagnetic waves at an interface. Because their thickness is negligible compared to the wavelength of operation, metasurfaces can be treated as discontinuities that impose abrupt changes in the amplitude, phase, or polarization of incoming waves.<ref name="capasso2" /><ref name="Quevedo-teruel" />

Although various authors emphasize different aspects, such as arrays of nanoantennas,<ref name="ReferenceB">{{cite journal |last1=Kildishev |first1=A. V. |last2=Boltasseva |first2=A. |last3=Shalaev |first3=V. M. |year=2013 |title=Planar photonics with metasurfaces |journal=Science |volume=339 |issue=6125 |article-number=1232009 |doi=10.1126/science.1232009 |pmid=23493714 |s2cid=33896271 }}</ref> periodic scattering elements,<ref>{{cite journal|last1=Li|first1=Ping-Chun|last2=Zhao|first2=Yang|last3=Alu|first3=Andrea|last4=Yu|first4=Edward T.|title=Experimental realization and modeling of a subwavelength frequency-selective plasmonic metasurface|journal=Appl. Phys. Lett.|date=2011|volume=99|issue=3|page=221106|bibcode=2011ApPhL..99c1106B|doi=10.1063/1.3614557}}</ref> or ultrathin films with unusual absorption,<ref name=capasso2 /> the unifying concept is that metasurfaces derive their functionality from engineered two-dimensional structures rather than from bulk material composition.

Metasurfaces can be classified in several complementary ways, depending on their mode of interaction, functional intent, or implementation mechanism. These categories often overlap: a single device may be both reflective and reconfigurable, or simultaneously serve beam-steering and polarization-conversion purposes.

; By interaction * Reflective ([[Reflectarray antenna]]) – reshape incident waves by reflection, typically using a metallic ground plane.<ref name="ReferenceB" /> * Transmissive ([[Transmitarray antenna]]) – modify waves as they pass through, functioning as ultrathin lenses.<ref>{{cite journal|last1=Hum|first1=Stephen V.|last2=Pozar|first2=David M.|title=Recent advances in reflectarray antennas|journal=Proceedings of the IEEE|year=2014|volume=102|issue=1|pages=30–45 }}</ref> * Absorbing ([[Metamaterial absorber]]) –suppresses reflection and transmission to achieve near-perfect absorption.<ref name=thinfilmCPA />

; By functional intent * Beam steering and focusing – redirect or concentrate energy through phase-gradient control.<ref name="capasso1" /> * Wavefront shaping and holography – generate structured beams (holograms, vortex beams) using amplitude and phase control.<ref name="Metasurface holograms" /> * Dispersion engineering – design frequency/time response for filtering or chromatic correction.<ref name="Quevedo-teruel" /> * Polarization conversion – convert between linear and circular polarization states, often via geometric-phase (Pancharatnam–Berry) elements.<ref name="capasso1" />

; By mechanism * Passive metasurfaces – rely on fixed geometry to yield a static response (e.g., holographic or leaky-wave designs). * Reconfigurable metasurfaces (also called RIS or programmable metasurfaces) – incorporate tunable components such as MEMS, liquid crystals, or graphene to allow dynamic control of scattering and radiation patterns.<ref>{{cite journal|last1=Di Renzo|first1=Marco|last2=Zappone|first2=Antonio|last3=Debbah|first3=Mér|last4=Alouini|first4=Mohamed-Slim|title=Smart radio environments empowered by reconfigurable intelligent surfaces: How it works, state of research, and the road ahead|journal=IEEE Journal on Selected Areas in Communications|date=2020|volume=38|issue=11|pages=2450–2525|doi=10.1109/JSAC.2020.3007211 |arxiv=2004.09352 |bibcode=2020IJSAC..38.2450D|s2cid=219601556}}</ref>

==History== The research on electromagnetic metasurfaces has a long history. Early in 1902, [[Robert W. Wood]] found that the reflection spectra of subwavelength metallic grating had dark areas. This unusual phenomenon was named Wood's anomaly and led to the discovery of the surface plasmon polariton (SPP),<ref>{{cite journal|last1=Wood|first1=R. W.|title=On a remarkable case of uneven distribution of light in a diffraction grating spectrum|journal=Proc. Phys. Soc. Lond.|date=1902|volume=18|issue=1|pages=269–275|bibcode = 1902PPSL...18..269W |doi = 10.1088/1478-7814/18/1/325 |url=https://zenodo.org/record/1431485}}</ref> a particular electromagnetic wave excited at metal surfaces. Subsequently, another important phenomenon, the Levi-Civita relation,<ref>{{cite journal|last1=Senior|first1=T.|title=Approximate boundary conditions|journal=IEEE Trans. Antennas Propag.|date=1981|volume=29|issue=5|pages=826–829|doi=10.1109/TAP.1981.1142657|bibcode=1981ITAP...29..826S|hdl=2027.42/20954|hdl-access=free}}</ref> was introduced, which states that a subwavelength-thick film can result in a dramatic change in electromagnetic boundary conditions.

Generally speaking, metasurfaces could include some traditional concepts in the microwave spectrum, such as frequency-selective surfaces (FSS), impedance sheets, and even Ohmic sheets. In the microwave regime, the thickness of these metasurfaces can be much smaller than the wavelength of operation (for example, 1/1000 of the wavelength) since the skin depth could be minimal for highly conductive metals. Recently, some novel phenomena were demonstrated, such as ultra-broadband [[Coherent perfect absorber|coherent perfect absorption]]. The results showed that a 0.3&nbsp;nm thick film could absorb all electromagnetic waves across the RF, microwave, and terahertz frequencies.<ref name=thinfilmCPA>{{cite journal|last1=Pu|first1=M.|title=Ultrathin broadband nearly perfect absorber with symmetrical coherent illumination|journal=Optics Express|date=17 January 2012|volume=20|issue=3|pages=2246–2259|doi=10.1364/oe.20.002246|pmid=22330464|display-authors=etal|bibcode = 2012OExpr..20.2246P |doi-access=free}}</ref><ref>{{cite journal|last1=Li|first1=S.|title=Broadband Perfect Absorption of Ultrathin Conductive Films with Coherent Illumination: Super Performance of Electromagnetic Absorption|arxiv=1406.1847|display-authors=etal|doi=10.1103/PhysRevB.91.220301|volume=91|journal=Physical Review B|bibcode=2015PhRvB..91v0301L|year=2015|issue=22|article-number=220301|s2cid=118609773}}</ref><ref>{{cite journal|last1=Taghvaee|first1=H.R.|title=Circuit modeling of graphene absorber in terahertz band|display-authors=etal|doi=10.1016/j.optcom.2016.08.059|date=2017|volume=383|pages=11–16|journal=Optics Communications|bibcode=2017OptCo.383...11T |url=https://nottingham-repository.worktribe.com/output/13464303 }}</ref>

In optical applications, an [[anti-reflective coating]] could also be regarded as a simple metasurface, as first observed by Lord Rayleigh.

In recent years, several new metasurfaces have been developed, including [[plasmon]]ic metasurfaces,<ref>{{cite journal | last1 = Ni | first1 = X. | last2 = Emani | first2 = N. K. | last3 = Kildishev | first3 = A.V. | last4 = Boltasseva | first4 = A. | last5 = Shalaev | first5 = V.M. | year = 2012| title = Broadband light bending with plasmonic nanoantennas | journal = Science | volume = 335 | issue = 6067 | page = 427 | doi = 10.1126/science.1214686 | pmid = 22194414 | bibcode = 2012Sci...335..427N | s2cid = 18790738 | doi-access = free }}</ref><ref name="ReferenceA"/><ref name="ReferenceB"/><ref>{{cite journal|last1=Verslegers|first1=Lieven|last2=Fan|first2=Shanhui|title=Planar Lenses Based on Nanoscale Slit Arrays in a Metallic Film|journal=Nano Lett.|date=2009|volume=9|issue=1|pages=235–238|doi=10.1021/nl802830y|pmid=19053795|bibcode=2009NanoL...9..235V|s2cid=28741710}}</ref> metasurfaces based on geometric phases,<ref name="capasso1">{{cite journal|last1=Yu|first1=Nanfang|last2=Genevet|first2=Patrice|author3=[[Mikhail Kats]]|last4=Aieta|first4=Francesco|last5=Tetienne|first5=Jean-Philippe|last6=Capasso|first6=Federico|last7=Gaburro|first7=Zeno|title=Light Propagation with Phase Discontinuities: Generalized Laws of Reflection and Refraction|journal=Science|date=2011|volume=334|issue=6054|pages=333–337|bibcode = 2011Sci...334..333Y |doi = 10.1126/science.1210713|pmid=21885733|s2cid=10156200|doi-access=free}}</ref><ref name="hasman1">{{cite journal|last1=Lin|first1=Dianmin|last2=Fan|first2=Pengyu|last3=Hasman|first3=Erez|last4=Brongersma|first4=Mark L.|title=Dielectric gradient metasurface optical elements|journal=Science|date=2014|volume=345|issue=6194|pages=298–302|bibcode = 2014Sci...345..298L |doi = 10.1126/science.1253213|pmid=25035488|s2cid=29708554}}</ref> metasurfaces based on impedance sheets,<ref>{{cite journal|last1=Pfeiffer|first1=Carl|last2=Grbic|first2=Anthony|title=Metamaterial Huygens' Surfaces: Tailoring Wave Fronts with Reflectionless Sheets|journal=Phys. Rev. Lett.|date=2013|volume=110|issue=2|page=197401|arxiv = 1206.0852 |bibcode = 2013PhRvL.110b7401W |doi = 10.1103/PhysRevLett.110.027401 |pmid=23383937|s2cid=118458038 }}</ref><ref>{{cite journal|first1=Didier|last1=Felbacq|title=Impedance operator description of a metasurface|journal=Mathematical Problems in Engineering|date=2015|volume=2015|article-number=473079 |doi = 10.1155/2015/473079|doi-access=free|arxiv=1507.07736}}</ref> and glide-symmetric metasurfaces.<ref>{{cite journal|last1=Quevedo-Teruel|first1=Oscar|title=On the benefits of glide symmetries for microwave devices|journal=IEEE Journal of Microwaves|date=2021|volume=1|pages=457–469|doi =10.1109/JMW.2020.3033847|s2cid=231619012|display-authors=etal|issue=1 |bibcode=2021IJMic...1..457Q |doi-access=free}}</ref>

==Applications==

One of the most important applications of metasurfaces is to control a wavefront of electromagnetic waves by imparting local, gradient phase shifts to the incoming waves, which leads to a generalization of the ancient [[Snell's law|laws of reflection and refraction]].<ref name=capasso1 /> In this way, a metasurface can be used as a planar lens,<ref>{{cite journal|last1=Aieta|first1=Francesco|last2=Genevet|first2=Patrice|last3=Kats|first3=Mikhail|last4=Yu|first4=Nanfang|last5=Blanchard|first5=Romain|last6=Gaburro|first6=Zeno|last7=Capasso|first7=Federico| title=Aberration-free ultra-thin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces|journal=Nano Letters|date=2012|volume=12|issue=9|pages=4932–6|doi=10.1021/nl302516v|pmid=22894542|arxiv=1207.2194|bibcode=2012NanoL..12.4932A|s2cid=5412108}}</ref><ref name="Plasmonic Metalenses">{{cite journal | last1 = Ni | first1 = X. | last2 = Ishii | first2 = S. | last3 = Kildishev | first3 = A.V. | last4 = Shalaev | first4 = V.M. | year = 2013| title = Ultra-thin, planar, Babinet-inverted plasmonic metalenses | url = https://engineering.purdue.edu/~shalaev/Publication_list_files/LSA_Ni_2013.pdf | journal = Light: Science & Applications | volume = 2 | issue = 4 | page = e72 | doi = 10.1038/lsa.2013.28 | bibcode = 2013LSA.....2E..72N | s2cid = 8927737 }}</ref> illumination lens,<ref>I. Moreno, M. Avendaño-Alejo, and C. P. Castañeda-Almanza, "Nonimaging metaoptics," Opt. Lett. 45, 2744-2747 (2020). https://doi.org/10.1364/OL.391357</ref> planar [[hologram]],<ref name="Metasurface holograms">{{cite journal | last1 = Ni | first1 = X. | last2 = Kildishev | first2 = A.V. | last3 = Shalaev | first3 = V.M. | title = Metasurface holograms for visible light | url = https://engineering.purdue.edu/~shalaev/Publication_list_files/Metasurface%20holograms%20for%20visible%20light%20(2013).pdf | journal = Nature Communications | year = 2013 | volume = 4 | pages = 1–6 | article-number = 2807 | doi = 10.1038/ncomms3807 | bibcode = 2013NatCo...4.2807N | s2cid = 5550551 }}</ref> vortex generator,<ref>{{cite journal|last1=Genevet|first1=Patrice|last2=Yu|first2=Nanfang|last3=Aieta|first3=Francesco|last4=Lin|first4=Jiao|last5=Kats|first5=Mikhail|last6=Blanchard|first6=Romain|last7=Scully|first7=Marlan|last8=Gaburro|first8=Zeno|last9=Capasso|first9=Federico|title=Ultra-thin plasmonic optical vortex plate based on phase discontinuities|journal= Applied Physics Letters|date=2012|volume=100|issue=1|page=013101|doi = 10.1063/1.3673334|bibcode=2012ApPhL.100a3101G}}</ref> beam deflector, [[axicon]] and so on.<ref name=hasman1 /><ref>{{cite journal|last1=Xu|first1=T.|title=Plasmonic deflector|journal=Opt. Express|date=2008|volume=16|issue=7|pages=4753–4759|display-authors=etal|doi=10.1364/oe.16.004753|pmid=18542573|bibcode=2008OExpr..16.4753X|doi-access=free}}</ref>

Besides the gradient metasurface lenses, metasurface-based [[superlenses]] offer another degree of control of the wavefront by using evanescent waves. With surface plasmons in the ultrathin metallic layers, perfect imaging and super-resolution lithography could be possible, which breaks the common assumption that all optical lens systems are limited by diffraction, a phenomenon called the [[diffraction limit]].<ref>{{cite journal|last1=Luo|first1=Xiangang|last2=Ishihara|first2=Teruya|title=Surface plasmon resonant interference nanolithography technique|journal=Appl. Phys. Lett.|date=2004|volume=84|issue=23|page=4780|bibcode = 2004ApPhL..84.4780L |doi = 10.1063/1.1760221 }}</ref><ref>{{cite journal|last1=Fang|first1=Nicholas|last2=Lee|first2=Hyesog|last3=Sun|first3=Cheng|last4=Zhang|first4=Xiang|title=Sub-Diffraction-Limited Optical Imaging with a Silver Superlens|journal=Science|date=2005|volume=308|issue=5721|pages=534–7|bibcode = 2005Sci...308..534F |doi = 10.1126/science.1108759|pmid=15845849|s2cid=1085807}}</ref>

All-dielectric subwavelength metasurface focusing lens operating in the near infrared has been demonstrated by the Shalaev group in collaboration with the [[Raytheon]] team.<ref name="All-dielectric-lens">P. R. West, J. L. Stewart, A. V. Kildishev, V. M. Shalaev, V. M. Shkunov, F. Strohkendl, Y. A. Zakharenkov, R. K. Dodds, R. Byren, [https://opg.optica.org/oe/fulltext.cfm?uri=oe-22-21-26212 All-dielectric sub-wavelength metasurface focusing lens], Optics Express 22, 26212-26221 (2014)</ref> This lens is currently used in Raytheon defense system products.

Another promising application is in the field of [[stealth technology]]. A target's [[radar cross-section]] (RCS) has conventionally been reduced by either [[radiation-absorbent material]] (RAM) or by purpose shaping of the target such that the scattered energy can be redirected away from the source. Unfortunately, RAMs have narrow frequency-band functionality, and purpose shaping limits the aerodynamic performance of the target. Metasurfaces have been synthesized that redirect scattered energy away from the source using either array theory <ref name="A. Modi 19 2">{{cite journal | last1 = Modi | first1 = A. Y. | last2 = Alyahya | first2 = M. A. | last3 = Balanis | first3 = C. A. | last4 = Birtcher | first4 = C. R. | year = 2019| title = Metasurface-Based Method for Broadband RCS Reduction of Dihedral Corner Reflectors with Multiple Bounces | journal = IEEE Transactions on Antennas and Propagation | volume = 68 | issue = 3 | page = 1| doi = 10.1109/TAP.2019.2940494 | s2cid = 212649480 }}</ref><ref>{{cite journal | last1 = Modi | first1 = A. Y. | last2 = Balanis | first2 = C. A. | last3 = Birtcher | first3 = C. R. | last4 = Shaman | first4 = H. | year = 2019| title = New Class of RCS-Reduction Metasurfaces Based on Scattering Cancellation Using Array Theory | journal = IEEE Transactions on Antennas and Propagation | volume = 67 | issue = 1| pages = 298–308 | doi = 10.1109/TAP.2018.2878641 | bibcode = 2019ITAP...67..298M | s2cid = 58670543 }}</ref><ref>{{cite journal | last1 = Modi | first1 = A. Y. | last2 = Balanis | first2 = C. A. | last3 = Birtcher | first3 = C. R. | last4 = Shaman | first4 = H. | year = 2017| title = Novel Design of Ultrabroadband Radar Cross Section Reduction Surfaces using Artificial Magnetic Conductors | journal = IEEE Transactions on Antennas and Propagation | volume = 65 | issue = 10 | pages = 5406–5417 | doi = 10.1109/TAP.2017.2734069 | bibcode = 2017ITAP...65.5406M | s2cid = 20724998 }}</ref> or the generalized Snell's law.<ref>{{cite journal | doi = 10.1063/1.4881935 | volume=104 | title=Wideband radar cross section reduction using two-dimensional phase gradient metasurfaces | year=2014 | journal=Applied Physics Letters | page=221110 | last1 = Li | first1 = Yongfeng | last2 = Zhang | first2 = Jieqiu | last3 = Qu | first3 = Shaobo | last4 = Wang | first4 = Jiafu | last5 = Chen | first5 = Hongya | last6 = Xu | first6 = Zhuo | last7 = Zhang | first7 = Anxue | issue=22 | bibcode = 2014ApPhL.104v1110L}}</ref><ref name="capasso">{{cite journal |last1=Yu |first1=Nanfang |last2=Genevet |first2=Patrice |last3=Kats |first3=Mikhail A. |last4=Aieta |first4=Francesco |last5=Tetienne |first5=Jean-Philippe |last6=Capasso |first6=Federico |last7=Gaburro |first7=Zeno |date=October 2011 |title=Light Propagation with Phase Discontinuities: Generalized Laws of Reflection and Refraction |journal=Science |bibcode=2011Sci...334..333Y |doi=10.1126/science.1210713 |volume=334 |issue=6054 |pages=333–337 |pmid=21885733|s2cid=10156200 |doi-access=free }}</ref> This has led to aerodynamically favorable shapes for the targets with reduced RCS.

Metasurface can also be integrated with [[optical waveguides]] for controlling guided [[electromagnetic waves]].<ref>{{Cite journal |last1=Meng |first1=Yuan |last2=Chen |first2=Yizhen |last3=Lu |first3=Longhui |last4=Ding |first4=Yimin |last5=Cusano |first5=Andrea |last6=Fan |first6=Jonathan A. |last7=Hu |first7=Qiaomu |last8=Wang |first8=Kaiyuan |last9=Xie |first9=Zhenwei |last10=Liu |first10=Zhoutian |last11=Yang |first11=Yuanmu |date=2021-11-22 |title=Optical meta-waveguides for integrated photonics and beyond |journal=Light: Science & Applications |language=en |volume=10 |issue=1 |page=235 |doi=10.1038/s41377-021-00655-x |pmid=34811345 |pmc=8608813 |bibcode=2021LSA....10..235M |issn=2047-7538}}</ref><ref name=":0">{{Cite journal |last1=Li |first1=Zhaoyi |last2=Kim |first2=Myoung-Hwan |last3=Wang |first3=Cheng |last4=Han |first4=Zhaohong |last5=Shrestha |first5=Sajan |last6=Overvig |first6=Adam Christopher |last7=Lu |first7=Ming |last8=Stein |first8=Aaron |last9=Agarwal |first9=Anuradha Murthy|author9-link=Anu Agarwal |last10=Lončar |first10=Marko |last11=Yu |first11=Nanfang |date=July 2017 |title=Controlling propagation and coupling of waveguide modes using phase-gradient metasurfaces |url=https://www.nature.com/articles/nnano.2017.50 |journal=Nature Nanotechnology |language=en |volume=12 |issue=7 |pages=675–683 |doi=10.1038/nnano.2017.50 |pmid=28416817 |bibcode=2017NatNa..12..675L |osti=1412777 |issn=1748-3395}}</ref> Applications for [[meta-waveguide]]s such as integrated waveguide mode converters,<ref name=":0" /> structured-light generations,<ref>{{Cite journal |last1=Guo |first1=Xuexue |last2=Ding |first2=Yimin |last3=Chen |first3=Xi |last4=Duan |first4=Yao |last5=Ni |first5=Xingjie |date=2020-07-17 |title=Molding free-space light with guided wave–driven metasurfaces |journal=Science Advances |language=en |volume=6 |issue=29 |article-number=eabb4142 |doi=10.1126/sciadv.abb4142 |issn=2375-2548 |pmc=7439608 |pmid=32832643|arxiv=2001.03001 |bibcode=2020SciA....6.4142G }}</ref><ref>{{Cite journal |last1=He |first1=Tiantian |last2=Meng |first2=Yuan |last3=Liu |first3=Zhoutian |last4=Hu |first4=Futai |last5=Wang |first5=Rui |last6=Li |first6=Dan |last7=Yan |first7=Ping |last8=Liu |first8=Qiang |last9=Gong |first9=Mali |last10=Xiao |first10=Qirong |date=2021-11-22 |title=Guided mode meta-optics: metasurface-dressed waveguides for arbitrary mode couplers and on-chip OAM emitters with a configurable topological charge |url=https://opg.optica.org/abstract.cfm?URI=oe-29-24-39406 |journal=Optics Express |language=en |volume=29 |issue=24 |pages=39406–39418 |doi=10.1364/OE.443186 |pmid=34809306 |bibcode=2021OExpr..2939406H |s2cid=243813207 |issn=1094-4087|doi-access=free }}</ref> versatile multiplexers,<ref>{{Cite journal |last1=Cheben |first1=Pavel |last2=Halir |first2=Robert |last3=Schmid |first3=Jens H. |last4=Atwater |first4=Harry A. |last5=Smith |first5=David R. |date=August 2018 |title=Subwavelength integrated photonics |url=https://www.nature.com/articles/s41586-018-0421-7 |journal=Nature |language=en |volume=560 |issue=7720 |pages=565–572 |doi=10.1038/s41586-018-0421-7 |pmid=30158604 |bibcode=2018Natur.560..565C |s2cid=52117964 |issn=1476-4687|url-access=subscription }}</ref><ref>{{Cite journal |last1=Meng |first1=Yuan |last2=Liu |first2=Zhoutian |last3=Xie |first3=Zhenwei |last4=Wang |first4=Ride |last5=Qi |first5=Tiancheng |last6=Hu |first6=Futai |last7=Kim |first7=Hyunseok |last8=Xiao |first8=Qirong |last9=Fu |first9=Xing |last10=Wu |first10=Qiang |last11=Bae |first11=Sang-Hoon |last12=Gong |first12=Mali |last13=Yuan |first13=Xiaocong |date=2020-04-01 |title=Versatile on-chip light coupling and (de)multiplexing from arbitrary polarizations to controlled waveguide modes using an integrated dielectric metasurface |url=https://opg.optica.org/abstract.cfm?URI=prj-8-4-564 |journal=[[Photonics Research]] |language=en |volume=8 |issue=4 |page=564 |doi=10.1364/PRJ.384449 |s2cid=213576669 |issn=2327-9125|url-access=subscription }}</ref> and photonic neural networks<ref>{{Cite journal |last1=Wu |first1=Changming |last2=Yu |first2=Heshan |last3=Lee |first3=Seokhyeong |last4=Peng |first4=Ruoming |last5=Takeuchi |first5=Ichiro |last6=Li |first6=Mo |date=2021-01-04 |title=Programmable phase-change metasurfaces on waveguides for multimode photonic convolutional neural network |journal=Nature Communications |language=en |volume=12 |issue=1 |page=96 |doi=10.1038/s41467-020-20365-z |pmid=33398011 |pmc=7782756 |arxiv=2004.10651 |bibcode=2021NatCo..12...96W |issn=2041-1723}}</ref> can be enabled.

In addition, metasurfaces are also applied in electromagnetic absorbers, polarization converters, [[polarimeter]]s, and spectrum filters.<ref name="q967">{{cite journal | last1=Rubin | first1=Noah A. | last2=Zaidi | first2=Aun | last3=Juhl | first3=Michael | last4=Li | first4=Ruo Ping | last5=Mueller | first5=J.P. Balthasar | last6=Devlin | first6=Robert C. | last7=Leósson | first7=Kristján | last8=Capasso | first8=Federico | title=Polarization state generation and measurement with a single metasurface | journal=Optics Express | volume=26 | issue=17 | date=2018-08-20 | pages=21455–21478 | issn=1094-4087 | doi=10.1364/OE.26.021455 | pmid=30130853 | bibcode=2018OExpr..2621455R | doi-access=free }}</ref> Metasurface-empowered novel bioimaging and biosensing devices have also emerged and been reported recently.<ref>{{cite journal|author=A. Arbabi|title=Miniature optical planar camera based on a wide-angle metasurface doublet corrected for monochromatic aberrations |journal=Nature Communications|volume=7 |pages=13682–89 |date=2016|article-number=13682 |doi=10.1038/ncomms13682|pmid=27892454 |pmc=5133709 |arxiv=1604.06160 |bibcode=2016NatCo...713682A |url=}}</ref><ref>{{cite journal|author=W. Chen|title=A broadband achromatic metalens for focusing and imaging in the visible |journal=Nature Nanotechnology|volume=13 |pages=220–226 |date=2018|issue=3 |doi=10.1038/s41565-017-0034-6|pmid=29292382 |bibcode=2018NatNa..13..220C |s2cid=205567341 |url=https://www.nature.com/articles/s41565-017-0034-6 }}</ref><ref>{{cite journal|author=S. Zhang|title=Metasurfaces for biomedical applications: imaging and sensing from a nanophotonics perspective |journal=Nanophotonics|volume=10 |pages=259–293 |date=2020|issue=1 |doi=10.1515/nanoph-2020-0373|bibcode=2020Nanop..10..373Z |s2cid=225279574 |doi-access=free |hdl=10023/20902 |hdl-access=free }}</ref><ref>{{cite journal|author=L. Jiang|title=Multifunctional hyperbolic nanogroove metasurface for submolecular detection |journal=Small|volume=13 |pages=1700600–10 |date=2017|issue=30 |article-number=1700600 |doi=10.1002/smll.201700600|pmid=28597602 |bibcode=2017Small..1300600J |url=https://www.researchgate.net/publication/317501397 }}</ref> For many optically based bioimaging devices, their bulk footprint and heavy physical weight have limited their usage in clinical settings.<ref>{{cite journal|author=M. Beruete|title=Terahertz sensing based on metasurfaces |journal=Advanced Optical Materials|volume=8 |pages=1900721–28 |date=2019|issue=3 |article-number=1900721 |doi=10.1002/adom.201900721|s2cid=199649103 |url=https://onlinelibrary.wiley.com/doi/abs/10.1002/adom.201900721 |url-access=subscription }}</ref><ref>{{cite journal|author=R. Ahmed|title=Tunable Fano-resonant metasurfaces on a disposable plastic-template for multimodal and multiplex biosensing |journal=Advanced Materials|volume=32 |pages=1907160–78 |date=2020|issue=19 |article-number=1907160 |doi=10.1002/adma.201907160|pmid=32201997 |pmc=8713081 |bibcode=2020AdM....3207160A |hdl=11693/75646 }}</ref>

== Simulation and Artificial Intelligence == Various methods are available for simulating the interaction of [[electromagnetic wave]]s on metasurfaces, and to enable their design, such as [[finite-difference time-domain]] (FDTD), [[finite-element method]]s (FEM), and [[rigorous coupled-wave analysis]] (RCWA).

For planar optical metasurfaces, prism-based algorithms allow for triangular prismatic space discretization, which is optimal for planar geometries. The prism-based algorithm has fewer elements than conventional tetrahedral methods, bringing higher computational efficiency.<ref>{{Cite journal|last1=Mai|first1=Wending|last2=Campbell|first2=Sawyer D.|last3=Whiting|first3=Eric B.|last4=Kang|first4=Lei|last5=Werner|first5=Pingjuan L.|last6=Chen|first6=Yifan|author7-link=Douglas Werner|last7=Werner|first7=Douglas H.|date=2020-10-01|title=Prismatic discontinuous Galerkin time domain method with an integrated generalized dispersion model for efficient optical metasurface analysis|url=https://www.osapublishing.org/ome/abstract.cfm?uri=ome-10-10-2542|journal=Optical Materials Express|language=EN|volume=10|issue=10|pages=2542–2559|doi=10.1364/OME.399414|bibcode=2020OMExp..10.2542M |issn=2159-3930|doi-access=free}}</ref> A simulation toolkit has been released online, enabling users to efficiently analyze metasurfaces with customized pixel patterns.<ref>{{Cite web |last1=Mai |first1=Wending |last2=Werner |first2=Douglas H. |date=2020 |title=prism-DGTD with GDM to analyze pixelized metasurfaces |url=https://osf.io/2na4f/ |website=Open Science Framework |publisher=Center for Open Science |doi=10.17605/OSF.IO/2NA4F |access-date=17 August 2025 }}</ref>

Traditional simulation methods have historically been effective for modeling electromagnetic metasurfaces, providing valuable insights and reliable results. However, recent advancements in artificial intelligence (AI) and machine learning (ML) have revolutionized this field by offering significantly enhanced capabilities<ref>{{Cite journal |last=Al-Raeei |first=Marwan |date=2026-06-01 |title=Artificial intelligence driven design and fabrication of metamaterials and metasurfaces |url=https://www.sciencedirect.com/science/article/pii/S2590048X26000701 |journal=Results in Materials |volume=30 |article-number=100954 |doi=10.1016/j.rinma.2026.100954 |issn=2590-048X|doi-access=free }}</ref><ref>{{Cite journal |last1=Ma |first1=Qian |last2=Feng |first2=Zi Rui |last3=Hou |first3=Junming |last4=Liu |first4=Che |last5=Ning |first5=Yu Ming |last6=Li |first6=Rui Si |last7=Wu |first7=Qian Wen |last8=Huang |first8=Yi Su |last9=Zhang |first9=Yi |last10=Gu |first10=Ze |last11=You |first11=Jian Wei |last12=Cui |first12=Tie Jun |date=2026-04-03 |title=Artificial intelligence with metasurfaces: from intelligent design to intelligent computing |journal=PhotoniX |language=en |volume=7 |issue=1 |pages=23 |doi=10.1186/s43074-026-00239-1 |doi-access=free |issn=2662-1991}}</ref>. These modern techniques are not only faster but also more accurate, enabling researchers and engineers to perform complex simulations with greater precision and efficiency. AI and ML algorithms can analyze vast datasets, identify intricate patterns, and make predictions that would be computationally intensive or infeasible with conventional methods. As a result, the integration of AI and machine learning into electromagnetic metasurface simulations has opened new avenues for innovation, allowing for more rapid prototyping, optimization, and real-time analysis in various applications such as antenna design, radar systems, and electromagnetic compatibility testing.

== Optical characterization == Characterizing metasurfaces in the optical domain requires advanced imaging methods since the involved optical properties often include both [[Phase (waves)|phase]] and [[Polarization (waves)|polarization]] properties. Recent works suggest that vectorial [[ptychography]], a recently developed computational imaging method, can be of relevance. It combines the [[Jones matrix]] mapping with a microscopic lateral resolution, even on large specimens.<ref>{{Cite journal|last1=Song|first1=Qinghua|last2=Baroni|first2=Arthur|last3=Sawant|first3=Rajath|last4=Ni|first4=Peinan|last5=Brandli|first5=Virginie|last6=Chenot|first6=Sébastien|last7=Vézian|first7=Stéphane|last8=Damilano|first8=Benjamin|last9=de Mierry|first9=Philippe|last10=Khadir|first10=Samira|last11=Ferrand|first11=Patrick|date=December 2020|title=Ptychography retrieval of fully polarized holograms from geometric-phase metasurfaces|journal=Nature Communications|language=en|volume=11|issue=1|page=2651|doi=10.1038/s41467-020-16437-9|issn=2041-1723|pmc=7253437|pmid=32461637|bibcode=2020NatCo..11.2651S }}</ref>

==See also== *[[Kinoform]]

== References == {{reflist}}

[[Category:Photonics]] [[Category:Metamaterials]]