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<math display="block">\underline{n} = n - i\kappa.</math>
The real and imaginary part of this refractive index are not independent, and are connected through the [[Kramers–Kronig relations]], i.e. the complex refractive index is a [[linear response function]], ensuring causality. <ref name=lightmatterinteractionbook>{{cite book |last= Stenzel|first=Olaf |date=2022 |title=Light–Matter Interaction |series=UNITEXT for Physics |url=https://link.springer.com/book/10.1007/978-3-030-87144-4 |___location= |publisher=Springer, Cham |page=386 |doi=10.1007/978-3-030-87144-4 |isbn=978-3-030-87144-4 }}</ref> Here, the real part {{mvar|n}} is the refractive index and indicates the [[phase velocity]], while the imaginary part {{mvar|κ}} is called the '''extinction coefficient'''<ref name=DresselhausMITCourse>{{cite web
|url = http://web.mit.edu/course/6/6.732/www/6.732-pt2.pdf
|title = Solid State Physics Part II Optical Properties of Solids
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=== Bandgap ===
[[File:Annotated Eg vs n.png|thumb|A scatter plot of bandgap energy versus optical refractive index for many common IV, III-V, and II-VI semiconducting elements / compounds. ]]
The optical refractive index of a semiconductor tends to increase as the [[Band gap|bandgap energy]] decreases. Many attempts<ref>{{Cite journal |last1=Gomaa |first1=Hosam M. |last2=Yahia |first2=I. S. |last3=Zahran |first3=H. Y. |date=2021-11-01 |title=Correlation between the static refractive index and the optical bandgap: Review and new empirical approach |url=https://www.sciencedirect.com/science/article/abs/pii/S0921452621004208 |journal=Physica B: Condensed Matter |volume=620 |pages=413246 |doi=10.1016/j.physb.2021.413246 |bibcode=2021PhyB..62013246G |issn=0921-4526}}</ref> have been made to model this relationship beginning with T. S. Moses in 1949.<ref>{{Cite journal |last=Moss |first=T S |date=1950-03-01 |title=A Relationship between the Refractive Index and the Infra-Red Threshold of Sensitivity for Photoconductors |url= |journal=Proceedings of the Physical Society. Section B |volume=63 |issue=3 |pages=167–176 |doi=10.1088/0370-1301/63/3/302 |bibcode=1950PPSB...63..167M |issn=0370-1301}}</ref> Empirical models can match experimental data over a wide range of materials and yet fail for important cases like InSb, PbS, and Ge.<ref>{{Cite book |last=Moss |first=T. S. |title=October 1 |chapter-url=https://www.degruyter.com/document/doi/10.1515/9783112495384-003/html |chapter=Relations between the Refractive Index and Energy Gap oi Semiconductors |date=1985-12-31 |publisher=De Gruyter |isbn=978-3-11-249538-4 |pages=415–428 |doi=10.1515/9783112495384-003}}</ref>
This negative correlation between refractive index and bandgap energy, along with a negative correlation between bandgap and temperature, means that many semiconductors exhibit a positive correlation between refractive index and temperature.<ref>{{Cite journal |last1=Bertolotti |first1=Mario |last2=Bogdanov |first2=Victor |last3=Ferrari |first3=Aldo |last4=Jascow |first4=Andrei |last5=Nazorova |first5=Natalia |last6=Pikhtin |first6=Alexander |last7=Schirone |first7=Luigi |date=1990-06-01 |title=Temperature dependence of the refractive index in semiconductors |url=https://opg.optica.org/josab/abstract.cfm?uri=josab-7-6-918 |journal=JOSA B |language=EN |volume=7 |issue=6 |pages=918–922 |doi=10.1364/JOSAB.7.000918 |bibcode=1990JOSAB...7..918B |issn=1520-8540}}</ref> This is the opposite of most materials, where the refractive index decreases with temperature as a result of a decreasing material density.
===Group index===
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