Refractive index contrast: Difference between revisions
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'''Refractive index contrast''', in an [[optical waveguide]], such as an [[optical fiber]], is a measure of the relative difference in [[refractive index]] of the [[Fiber optics#Principle of operation|core]] and [[Cladding (fiber optics)|cladding]]. The refractive index contrast, Δ, is often given by <math>\Delta={n_1^2-n_2^2 \over 2 n_1^2}</math>, where ''n''<sub>1</sub> is the maximum refractive index in the core (or simply the core index for a [[step-index profile]]) and ''n''<sub>2</sub> is the refractive index of the [[Cladding (fiber optics)|cladding]].<ref>{{cite web |title=Definition: refractive index contrast |url=https://www.its.bldrdoc.gov/fs-1037/dir-031/_4507.htm |website=www.its.bldrdoc.gov}}</ref> The criterion ''n''<sub>2</sub> < ''n''<sub>1</sub> must be satisfied in order to sustain a [[Transverse mode|guided mode]] by [[total internal reflection]]. Alternative formulations include <math>\Delta=\sqrt{n_1^2-n_2^2}</math> <ref>{{Cite journal|last=Snyder|first=A.W.|date=1981|title=Understanding monomode optical fibers | '''Refractive index contrast''', in an [[optical waveguide]], such as an [[optical fiber]], is a measure of the relative difference in [[refractive index]] of the [[Fiber optics#Principle of operation|core]] and [[Cladding (fiber optics)|cladding]]. The refractive index contrast, Δ, is often given by <math>\Delta={n_1^2-n_2^2 \over 2 n_1^2}</math>, where ''n''<sub>1</sub> is the maximum refractive index in the core (or simply the core index for a [[step-index profile]]) and ''n''<sub>2</sub> is the refractive index of the [[Cladding (fiber optics)|cladding]].<ref>{{cite web |title=Definition: refractive index contrast |url=https://www.its.bldrdoc.gov/fs-1037/dir-031/_4507.htm |website=www.its.bldrdoc.gov}}</ref> The criterion ''n''<sub>2</sub> < ''n''<sub>1</sub> must be satisfied in order to sustain a [[Transverse mode|guided mode]] by [[total internal reflection]]. Alternative formulations include <math>\Delta=\sqrt{n_1^2-n_2^2}</math> <ref>{{Cite journal|last=Snyder|first=A.W.|date=1981|title=Understanding monomode optical fibers|journal=Proceedings of the IEEE|volume=69|issue=1|pages=6–13|doi=10.1109/PROC.1981.11917|s2cid=29679745 |issn=0018-9219}}</ref> and <math>\Delta = {n_1-n_2 \over n_1}</math>.<ref>{{Cite book|chapter-url=https://www.sciencedirect.com/science/article/pii/B9780125250962500027|chapter=Wave theory of optical waveguides|date=2006-01-01|publisher=Academic Press|isbn=978-0-12-525096-2|language=en|doi=10.1016/b978-012525096-2/50002-7|title=Fundamentals of Optical Waveguides |last1=Okamoto |first1=Katsunari |pages=1–12 |s2cid=123835110 }}</ref><ref>{{Cite journal|last1=Zhou|first1=J|last2=Ngo|first2=N Q|last3=Ho|first3=C|last4=Petti|first4=L|last5=Mormile|first5=P|date=2007-07-01|title=Design of low-loss and low crosstalk arrayed waveguide grating through Fraunhofer diffraction analysis and beam propagation method|url=https://iopscience.iop.org/article/10.1088/1464-4258/9/7/024|journal=Journal of Optics A: Pure and Applied Optics|volume=9|issue=7|pages=709–715|doi=10.1088/1464-4258/9/7/024|bibcode=2007JOptA...9..709Z|issn=1464-4258|url-access=subscription}}</ref> Normal optical fibers, constructed of different [[glass]]es, have very low refractive index contrast (Δ<<1) and hence are weakly-guiding. The weak guiding will cause a greater portion of the cross-sectional [[Electric field]] profile to reside within the cladding (as evanescent tails of the guided mode) as compared to strongly-guided waveguides.<ref>{{Cite book|last=Marcuse|first=Dietrich |title=Light transmission optics |date=1982 |publisher=Van Nostrand Reinhold |isbn=0-442-26309-0 |edition=2nd |location=New York |oclc=7998201}}</ref> [[Integrated optics]] can make use of higher core index to obtain Δ>1 <ref>{{Cite book|last1=Melloni|first1=A.|last2=Costa|first2=R.|last3=Cusmai|first3=G.|last4=Morichetti|first4=F.|last5=Martinelli|first5=M.|title=Proceedings of 2005 IEEE/LEOS Workshop on Fibres and Optical Passive Components, 2005 |chapter=Waveguide index contrast: Implications for passive integrated optical components |date=2005|location=Mondello, Italy|publisher=IEEE|pages=246–253|doi=10.1109/WFOPC.2005.1462134|isbn=978-0-7803-8949-6|s2cid=25058825 }}</ref> allowing light to be efficiently guided around corners on the micro-scale, where popular high-Δ material platform is [[Silicon on insulator|silicon-on-insulator]].<ref name=":0">{{Cite journal|last1=Melati|first1=Daniele|last2=Melloni|first2=Andrea|last3=Morichetti|first3=Francesco|date=2014-06-30|title=Real photonic waveguides: guiding light through imperfections|url=https://www.osapublishing.org/aop/abstract.cfm?uri=aop-6-2-156|journal=Advances in Optics and Photonics|language=en|volume=6|issue=2|pages=156|doi=10.1364/AOP.6.000156|bibcode=2014AdOP....6..156M |issn=1943-8206|hdl=11311/863356|hdl-access=free}}</ref> High-Δ allows sub-wavelength core dimensions and so greater control over the size of the evanescent tails. The most efficient low-loss optical fibers require low Δ to minimise losses to light scattered outwards.<ref name=":0" /><ref>{{Cite book|last=Snyder|first=Allan W. |title=Optical waveguide theory |date=1983 |publisher=Chapman and Hall |author2=J. D. Love |isbn=0-412-09950-0 |location=London |oclc=9557214}}</ref> | ||
==References== | ==References== | ||
Latest revision as of 07:38, 27 August 2025
Refractive index contrast, in an optical waveguide, such as an optical fiber, is a measure of the relative difference in refractive index of the core and cladding. The refractive index contrast, Δ, is often given by , where n1 is the maximum refractive index in the core (or simply the core index for a step-index profile) and n2 is the refractive index of the cladding.[1] The criterion n2 < n1 must be satisfied in order to sustain a guided mode by total internal reflection. Alternative formulations include [2] and .[3][4] Normal optical fibers, constructed of different glasses, have very low refractive index contrast (Δ<<1) and hence are weakly-guiding. The weak guiding will cause a greater portion of the cross-sectional Electric field profile to reside within the cladding (as evanescent tails of the guided mode) as compared to strongly-guided waveguides.[5] Integrated optics can make use of higher core index to obtain Δ>1 [6] allowing light to be efficiently guided around corners on the micro-scale, where popular high-Δ material platform is silicon-on-insulator.[7] High-Δ allows sub-wavelength core dimensions and so greater control over the size of the evanescent tails. The most efficient low-loss optical fibers require low Δ to minimise losses to light scattered outwards.[7][8]
References
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