25:
823:
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1125:
1304:
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891:
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1849:
The transmission of an etalon as a function of wavelength. A high-finesse etalon (red line) shows sharper peaks and lower transmission minima than a low-finesse etalon (blue). The free spectral range is Δλ (shown above the
207:
552:
1191:
317:
986:
1608:
1055:
1840:
1588:
1546:
2013:
1864:
193:, but instead is sometimes represented by just the letters FSR. The reason is that these different terms often refer to the bandwidth or linewidth of an emitted source respectively.
454:
1846:
191:
477:
921:
168:
2212:"Fabry-Pérot resonator: spectral line shapes, generic and related Airy distributions, linewidths, finesses, and performance at low or frequency-dependent reflectivity"
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818:{\displaystyle \left|\left({\frac {\partial \beta }{\partial \lambda }}\right)\right|={\frac {2\pi }{\lambda ^{2}}}\left={\frac {2\pi }{\lambda ^{2}}}n_{g}}
1315:
831:
301:{\displaystyle \left|\Delta \lambda _{\text{FSR}}\right|={\frac {2\pi }{L}}\left|\left({\frac {\partial \beta }{\partial \lambda }}\right)^{-1}\right|}
482:
1136:
411:{\displaystyle \left|\Delta \nu _{\text{FSR}}\right|={\frac {2\pi }{L}}\left|\left({\frac {\partial \beta }{\partial \nu }}\right)^{-1}\right|}
1721:{\displaystyle \Delta \lambda ={\frac {\lambda _{0}^{2}}{2nl\cos \theta +\lambda _{0}}}\approx {\frac {\lambda _{0}^{2}}{2nl\cos \theta }},}
933:
1602:
or etalon, the wavelength separation between adjacent transmission peaks is called the free spectral range of the etalon and is given by
1017:
1789:
89:
61:
2183:
1554:
68:
42:
2150:
1485:
is the largest wavelength range for a given order that does not overlap the same range in an adjacent order. If the (
108:
75:
1599:
1946:{\displaystyle {\mathcal {F}}={\frac {\Delta \lambda }{\delta \lambda }}={\frac {\pi }{2\arcsin(1/{\sqrt {F}})}},}
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57:
1959:
46:
1854:
The FSR is related to the full-width half-maximum δλ of any one transmission band by a quantity known as the
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is the thickness of the cavity. More often FSR is quoted in frequency, rather than wavelength units:
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2264:
459:
899:
150:
82:
35:
2118:{\displaystyle {\mathcal {F}}\approx {\frac {\pi {\sqrt {F}}}{2}}={\frac {\pi R^{1/2}}{(1-R)}}.}
2211:
924:
1492:
1383:
584:
1746:
1196:
A simple intuitive interpretation of the FSR is that it is the inverse of the roundtrip time
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1407:
8:
1740:
1482:
1120:{\displaystyle \Delta \lambda _{\text{FSR}}\approx {\frac {\lambda ^{2}}{n(\lambda )L}},}
136:
between two successive reflected or transmitted optical intensity maxima or minima of an
2227:
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1456:
1436:
1299:{\displaystyle T_{R}={\frac {n_{\text{g}}L}{c}}={\frac {1}{\Delta \nu _{\text{FSR}}}}.}
994:
644:
624:
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2241:
2189:
2179:
2156:
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1370:{\displaystyle \Delta \lambda _{\text{FSR}}={\frac {\lambda ^{2}}{n_{\text{g}}L}},}
886:{\displaystyle \Delta \lambda _{\text{FSR}}={\frac {\lambda ^{2}}{n_{\text{g}}L}},}
1453:
is the distance travelled by light in one roundtrip around the closed cavity, and
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is the round trip length of the cavity (notice that for a standing-wave cavity,
137:
2258:
2193:
2160:
547:{\displaystyle \beta =k_{0}n(\lambda )={\frac {2\pi }{\lambda }}n(\lambda )}
2245:
1186:{\displaystyle \Delta \nu _{\text{FSR}}\approx {\frac {c}{n(\lambda )L}}.}
2236:
133:
129:
1400:
is the vacuum wavelength of light. For a linear cavity, such as the
981:{\displaystyle \Delta \nu _{\text{FSR}}={\frac {c}{n_{\text{g}}L}},}
24:
201:
The free spectral range (FSR) of a cavity in general is given by
1050:{\displaystyle {\frac {\partial n}{\partial \lambda }}\approx 0}
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These expressions can be derived from the resonance condition
1835:{\displaystyle \Delta f\approx {\frac {c}{2nl\cos \theta }}.}
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is the central wavelength of the nearest transmission peak,
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2210:
Ismail, N.; Kores, C. C.; Geskus, D.; Pollnau, M. (2016).
2209:
1583:{\displaystyle \Delta \lambda ={\frac {\lambda }{m}}.}
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If the dispersion of the material is negligible, i.e.
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is equal to twice the physical length of the cavity).
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1962:
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1749:
1611:
1557:
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1139:
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1020:
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834:
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153:
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927:of the media within the cavity. or, equivalently,
49:. Unsourced material may be challenged and removed.
2117:
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554:is the wavevector of the light inside the cavity,
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601:are the wavevector and wavelength in vacuum,
2019:, and R is the reflectivity of the mirrors.
1057:, then the two expressions above reduce to
1541:{\displaystyle (\lambda +\Delta \lambda )}
621:is the refractive index of the cavity and
2235:
2008:{\displaystyle F={\frac {4R}{(1-R)^{2}}}}
109:Learn how and when to remove this message
1844:
2145:(5th ed.). pp. 431–433, 614.
1476:
2257:
825:, the FSR (in wavelength) is given by
2173:
2140:
147:The FSR is not always represented by
449:{\displaystyle \Delta \beta L=2\pi }
47:adding citations to reliable sources
18:
2174:Rabus, Dominik.G. (26 April 2007).
2022:This is commonly approximated (for
1309:In wavelength, the FSR is given by
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1011:is the speed of light in vacuum.
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1763:is the angle of incidence, and
186:{\displaystyle \Delta \lambda }
34:needs additional citations for
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1:
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1548:lie at the same angle, then
1481:The free spectral range of a
1473:is the length of the cavity.
472:{\displaystyle \Delta \beta }
196:
1489: + 1)-th order of
916:{\displaystyle n_{\text{g}}}
128:) is the spacing in optical
7:
163:{\displaystyle \Delta \nu }
142:diffractive optical element
10:
2281:
2176:Integrated Ring Resonators
1600:Fabry–Pérot interferometer
1594:Fabry–Pérot interferometer
1402:Fabry-Pérot interferometer
1502:{\displaystyle \lambda }
1393:{\displaystyle \lambda }
594:{\displaystyle \lambda }
479:in Taylor series. Here,
1756:{\displaystyle \theta }
2141:Hecht, Eugene (2017).
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2017:coefficient of finesse
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1743:of the cavity medium,
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16:Concept in wave optics
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1216:{\displaystyle T_{R}}
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574:{\displaystyle k_{0}}
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58:"Free spectral range"
2237:10.1364/OE.24.016366
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1477:Diffraction gratings
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1426:{\displaystyle L=2l}
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43:improve this article
2228:2016OExpr..2416366I
2222:(15): 16366–16389.
1741:index of refraction
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1483:diffraction grating
122:Free spectral range
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311:or, equivalently,
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1776:{\displaystyle l}
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1466:{\displaystyle l}
1446:{\displaystyle L}
1404:discussed below,
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1004:{\displaystyle c}
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654:{\displaystyle L}
634:{\displaystyle L}
614:{\displaystyle n}
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2265:Physical optics
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2216:Optics Express
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255:
249:
245:
242:
236:
232:
222:
218:
214:
198:
195:
182:
179:
159:
156:
138:interferometer
117:
116:
31:
29:
22:
15:
9:
6:
4:
3:
2:
2277:
2266:
2263:
2262:
2260:
2247:
2243:
2238:
2233:
2229:
2225:
2221:
2217:
2213:
2206:
2204:
2195:
2191:
2187:
2181:
2177:
2170:
2162:
2158:
2154:
2152:9780133977226
2148:
2144:
2137:
2133:
2112:
2103:
2100:
2097:
2087:
2083:
2079:
2075:
2071:
2065:
2060:
2054:
2049:
2043:
2029:
2028:
2027:
2026:> 0.5) by
2025:
2020:
2018:
1997:
1989:
1986:
1983:
1975:
1972:
1966:
1963:
1940:
1929:
1923:
1919:
1913:
1910:
1907:
1903:
1898:
1892:
1889:
1884:
1875:
1861:
1860:
1859:
1857:
1847:
1829:
1823:
1820:
1817:
1814:
1811:
1808:
1804:
1799:
1796:
1786:
1785:
1784:
1770:
1750:
1742:
1738:
1715:
1709:
1706:
1703:
1700:
1697:
1694:
1688:
1683:
1679:
1673:
1665:
1661:
1657:
1654:
1651:
1648:
1645:
1642:
1639:
1633:
1628:
1624:
1618:
1615:
1605:
1604:
1603:
1601:
1577:
1572:
1569:
1564:
1561:
1551:
1550:
1549:
1532:
1526:
1523:
1513:-th order of
1512:
1496:
1488:
1484:
1474:
1460:
1440:
1420:
1417:
1414:
1411:
1403:
1387:
1364:
1358:
1349:
1342:
1338:
1332:
1323:
1312:
1311:
1310:
1293:
1281:
1273:
1268:
1263:
1259:
1250:
1243:
1238:
1234:
1226:
1225:
1224:
1208:
1204:
1180:
1174:
1168:
1162:
1158:
1153:
1144:
1133:
1132:
1131:
1114:
1108:
1102:
1096:
1090:
1086:
1080:
1071:
1060:
1059:
1058:
1044:
1041:
1035:
1027:
1012:
998:
975:
969:
960:
955:
950:
941:
930:
929:
928:
926:
904:
880:
874:
865:
858:
854:
848:
839:
828:
827:
826:
810:
806:
798:
794:
789:
786:
780:
776:
769:
761:
752:
749:
743:
737:
733:
725:
721:
716:
713:
707:
703:
699:
693:
685:
676:
672:
662:
648:
628:
608:
588:
566:
562:
538:
532:
527:
523:
520:
514:
508:
502:
497:
493:
489:
486:
466:
456:by expanding
443:
440:
437:
434:
431:
404:
399:
396:
391:
385:
377:
368:
363:
357:
353:
350:
344:
340:
330:
322:
314:
313:
312:
294:
289:
286:
281:
275:
267:
258:
253:
247:
243:
240:
234:
230:
220:
212:
204:
203:
202:
194:
180:
157:
145:
143:
139:
135:
131:
127:
123:
113:
110:
102:
91:
88:
84:
81:
77:
74:
70:
67:
63:
60: –
59:
55:
54:Find sources:
48:
44:
38:
37:
32:This article
30:
26:
21:
20:
2219:
2215:
2175:
2169:
2142:
2136:
2023:
2021:
2016:
1955:
1855:
1853:
1736:
1730:
1597:
1510:
1486:
1480:
1379:
1308:
1195:
1129:
1013:
990:
895:
663:
420:
310:
200:
146:
125:
121:
120:
105:
96:
86:
79:
72:
65:
53:
41:Please help
36:verification
33:
925:group index
664:Given that
99:August 2017
2129:References
197:In general
134:wavelength
69:newspapers
2194:123893382
2161:953709783
2101:−
2072:π
2050:π
2044:≈
1987:−
1914:
1904:π
1893:λ
1890:δ
1885:λ
1882:Δ
1824:θ
1821:
1800:≈
1794:Δ
1751:θ
1710:θ
1707:
1680:λ
1674:≈
1662:λ
1655:θ
1652:
1625:λ
1616:λ
1613:Δ
1570:λ
1562:λ
1559:Δ
1533:λ
1530:Δ
1524:λ
1497:λ
1388:λ
1339:λ
1324:λ
1320:Δ
1282:ν
1278:Δ
1169:λ
1154:≈
1145:ν
1141:Δ
1103:λ
1087:λ
1081:≈
1072:λ
1068:Δ
1042:≈
1036:λ
1033:∂
1025:∂
942:ν
938:Δ
855:λ
840:λ
836:Δ
795:λ
790:π
770:λ
767:∂
759:∂
753:λ
750:−
744:λ
722:λ
717:π
694:λ
691:∂
686:β
683:∂
589:λ
539:λ
528:λ
524:π
509:λ
487:β
467:β
464:Δ
444:π
432:β
429:Δ
397:−
386:ν
383:∂
378:β
375:∂
354:π
331:ν
327:Δ
287:−
276:λ
273:∂
268:β
265:∂
244:π
221:λ
217:Δ
181:λ
178:Δ
158:ν
155:Δ
130:frequency
2259:Category
2246:27464090
1433:, where
2224:Bibcode
2015:is the
1856:finesse
1850:graph).
1739:is the
1731:where λ
923:is the
83:scholar
2244:
2192:
2182:
2159:
2149:
2143:Optics
1956:where
1911:arcsin
1380:where
991:where
896:being
85:
78:
71:
64:
56:
1598:In a
1130:and
90:JSTOR
76:books
2242:PMID
2190:OCLC
2180:ISBN
2157:OCLC
2147:ISBN
1509:and
581:and
62:news
2232:doi
1818:cos
1704:cos
1649:cos
1328:FSR
1286:FSR
1149:FSR
1076:FSR
946:FSR
844:FSR
335:FSR
225:FSR
170:or
140:or
132:or
126:FSR
45:by
2261::
2240:.
2230:.
2220:24
2218:.
2214:.
2202:^
2188:.
2178:.
2155:.
1858::
1223::
144:.
2248:.
2234::
2226::
2196:.
2163:.
2113:.
2107:)
2104:R
2098:1
2095:(
2088:2
2084:/
2080:1
2076:R
2066:=
2061:2
2055:F
2039:F
2024:R
1998:2
1994:)
1990:R
1984:1
1981:(
1976:R
1973:4
1967:=
1964:F
1941:,
1935:)
1930:F
1924:/
1920:1
1917:(
1908:2
1899:=
1876:=
1871:F
1830:.
1815:l
1812:n
1809:2
1805:c
1797:f
1771:l
1737:n
1733:0
1716:,
1701:l
1698:n
1695:2
1689:2
1684:0
1666:0
1658:+
1646:l
1643:n
1640:2
1634:2
1629:0
1619:=
1578:.
1573:m
1565:=
1536:)
1527:+
1521:(
1511:m
1487:m
1461:l
1441:L
1421:l
1418:2
1415:=
1412:L
1365:,
1359:L
1354:g
1350:n
1343:2
1333:=
1294:.
1274:1
1269:=
1264:c
1260:L
1255:g
1251:n
1244:=
1239:R
1235:T
1209:R
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1181:.
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1166:(
1163:n
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1115:,
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1100:(
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1045:0
1028:n
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976:,
970:L
965:g
961:n
956:c
951:=
909:g
905:n
881:,
875:L
870:g
866:n
859:2
849:=
811:g
807:n
799:2
787:2
781:=
777:]
762:n
747:)
741:(
738:n
734:[
726:2
714:2
708:=
704:|
700:)
677:(
673:|
649:L
629:L
609:n
567:0
563:k
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536:(
533:n
521:2
515:=
512:)
506:(
503:n
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494:k
490:=
441:2
438:=
435:L
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400:1
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369:(
364:|
358:L
351:2
345:=
341:|
323:|
295:|
290:1
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259:(
254:|
248:L
241:2
235:=
231:|
213:|
124:(
112:)
106:(
101:)
97:(
87:·
80:·
73:·
66:·
39:.
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