Optical constants

Refractive index of Ag (Silver)

Ferrera et al. 2019: n,k 0.245–1.45 µm; 404 K

Data
tabulated nk
Range
0.2452–1.449 µm
Points
605
Temperature
404 K
State
polycrystalline
Licence
CC0-1.0

Plot

Click the plot to set the calculator wavelength.

At one wavelength

Range 0.2452–1.449 µm
Refractive index n
0.138499
Extinction coefficient k
3.83781
Permittivity ε1
-14.7096
Permittivity ε2
1.06306
Absorption coefficient α
820751 cm⁻¹
Penetration depth δ = λ/(2πk)
24.3679 nm
Abbe number Vd
—
Chromatic dispersion dn/dλ
0.207654 µm⁻¹
Group index ng
0.0164812
Group velocity dispersion
— fs²/mm
Dispersion parameter D
— ps/(nm·km)
Photon energy
2.11001 eV

ε = (n + ik)², α = 4πk/λ, ng = n − λ dn/dλ, GVD = λ³/(2πc²) d²n/dλ², D = −(λ/c) d²n/dλ². Group-velocity dispersion is given for formula data only.

Use it in Lightsmith

Load this data in Python, simulate in one more line

pip install lightsmith
import lightsmith as ls

# Ag (Silver): Ferrera et al. 2019: n,k 0.245–1.45 µm; 404 K
ag = ls.fetch_refractiveindex("main", "Ag", "Ferrera-404K", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(ag.range_nm)  # (245.202, 1449.25) nm
eps = ag.eps([633])  # complex permittivity

Downloads the original record once (pinned to the imported snapshot) and caches it.

Lightsmith is open source (MIT): Mie, T-matrix, BEM, DDA, FDTD, RCWA, TMM, mode solvers and inverse design behind one spec, on CPU or GPU. GitHub.

Comments and conditions

404 K (131 °C). Optically thick and morphologically flat polycrystalline Ag film, deposited by molecular beam epitaxy on a silicon wafer with a native oxide substrate.
The supplemental material of the original publication provides extra information by including additional data for 25 temperatures within the range of 298–600 K.

Conditions

temperature
404 K
substrate
Si/SiO2

References

M. Ferrera, M. Magnozzi, F. Bisio, M. Canepa. Temperature-dependent permittivity of silver and implications for thermoplasmonics. Phys. Rev. Mater., 3, 105201 (2019) (See Supplemental Material)

Cite

Marzia Ferrera, Michele Magnozzi, Francesco Bisio and Maurizio Canepa. Temperature-dependent permittivity of silver and implications for thermoplasmonics. Physical Review Materials, 3, 105201 (2019), doi:10.1103/physrevmaterials.3.105201; Data from the refractiveindex.info database (M. N. Polyanskiy, Sci. Data 11, 94 (2024), doi:10.1038/s41597-023-02898-2)

Data

605 rows as published
Ag (Silver), Ferrera et al. 2019: n,k 0.245–1.45 µm; 404 K: n and k versus wavelength
λ (µm)nk
0.2452021.1707191.352653
0.2467931.1775271.364364
0.2483841.1852191.374931
0.2499761.1951741.382817
0.2515671.2082061.387163
0.2531591.2229971.389606
0.2547511.2377141.392318
0.2563421.2517451.396027
0.2579341.2661921.399464
0.2595261.2810371.40243
0.2611181.2970671.403833
0.262711.3147321.403002
0.2643021.3318591.402067
0.2658941.34821.401078
0.2674861.3642981.399314
0.2690781.3805121.396278
0.2706711.3964261.392273
0.2722631.4116621.387544
0.2738561.4268961.381299
0.2754481.4422881.373282
0.2770411.4575331.363685
0.2786331.4723091.3527
0.2802261.4861941.340591
0.2818191.4996081.326858
0.2834121.5122821.311659
0.2850041.5239381.29515
0.2865971.5345241.277278
0.288191.5440481.25793
0.2897831.5525391.237002
0.2913771.5597241.21469
0.292971.5663041.190435
0.2945631.5714041.164894
0.2961561.5750421.137985
0.297751.5784961.108339
0.2993431.5789931.077091
0.3009361.5773541.042829
0.302531.5748711.005399
0.3041241.5685120.968655
0.3057171.5596510.929227
0.3073111.5468760.883277
0.3089051.5263980.838631
0.3104981.5038230.792353
0.3120921.4729790.744037
0.3136861.4342180.697517
0.315281.3925670.653469
0.3168741.3467640.608741
0.3184681.2889620.5634
0.3200621.2213940.518
0.3216561.1435420.475852
0.323251.0519440.440599
0.3248440.9474980.41439
0.3264390.8325530.400655
0.3280330.7115540.404397
0.3296270.588740.431218
0.3312220.4726450.485921
0.3328160.3770760.564485
0.3344110.3083230.652424
0.3360050.2599120.739957
0.33760.2241390.825244
0.3391940.1976190.905253
0.3407890.1791140.971387
0.3423840.1654981.02801
0.3439780.1538241.087072
0.3455730.1443931.143584
0.3471680.1374851.190996
0.3487630.1321081.233525
0.3503580.1275381.275337
0.3519520.1236131.31635
0.3535470.1202391.355916
0.3551420.1173271.393462
0.3567370.1147641.428813
0.3583320.1124611.462316
0.3599280.1103691.494331
0.3615230.1084511.525179
0.3631180.1066761.555156
0.3647130.1050211.584532
0.3663080.1034661.613554
0.3679030.1020041.642314
0.3694990.1006371.67075
0.3710940.0993681.698794
0.3726890.0982011.726383
0.3742850.0971361.753458
0.375880.0961751.779961
0.3774760.0953211.805841
0.3790710.0945741.831045
0.3806670.0939351.855537
0.3822620.0934021.879352
0.3838580.092971.902544
0.3854530.0926341.925166
0.3870490.0923841.947267
0.3886440.0922141.968895
0.390240.0921171.990092
0.3918360.0920862.010902
0.3934310.0921172.031364
0.3950270.0922022.051517
0.3966230.0923382.071398
0.3982190.0925182.091042
0.3998140.092742.110483
0.401410.0929982.129753
0.4030060.0932882.148884
0.4046020.0936072.167907
0.4061980.093952.18685
0.4077930.0943142.205742
0.4093890.0946962.22461
0.4109850.0950922.243468
0.4125810.0955012.262301
0.4141770.0959232.281091
0.4157730.0963552.299818
0.4173690.0967972.318465
0.4189650.0972472.337013
0.4205610.0977042.355448
0.4221570.0981682.373751
0.4237530.0986372.391908
0.4253490.0991092.409903
0.4269450.0995852.427722
0.4285410.1000632.445348
0.4301370.1005422.462769
0.4317330.1010212.479977
0.4333290.10152.49698
0.4349250.1019792.513787
0.4365210.1024582.53041
0.4381170.1029362.546856
0.4397130.1034132.563136
0.441310.1038892.579258
0.4429060.1043642.595231
0.4445020.1048372.611064
0.4460980.1053082.626764
0.4476940.1057782.642341
0.449290.1062462.657801
0.4508860.1067112.673152
0.4524820.1071742.688402
0.4540790.1076342.703558
0.4556750.1080922.718627
0.4572710.1085472.733615
0.4588670.1089992.74853
0.4604630.1094482.763379
0.4620590.1098942.778167
0.4636550.1103362.792901
0.4652510.1107742.807588
0.4668480.111212.822232
0.4684440.1116412.836835
0.470040.1120692.851398
0.4716360.1124942.86592
0.4732320.1129152.880404
0.4748280.1133342.894848
0.4764240.1137492.909253
0.478020.1141612.923621
0.4796160.114572.93795
0.4812120.1149762.952243
0.4828090.1153792.966499
0.4844050.115782.980718
0.4860010.1161782.994901
0.4875970.1165733.009049
0.4891930.1169663.023161
0.4907890.1173573.037239
0.4923850.1177453.051281
0.4939810.118133.06529
0.4955770.1185143.079265
0.4971730.1188953.093206
0.4987690.1192743.107114
0.5003650.1196513.12099
0.501960.1200263.134833
0.5035560.12043.148643
0.5051520.1207713.162422
0.5067480.121143.176169
0.5083440.1215083.189884
0.509940.1218743.203569
0.5115360.1222383.217223
0.5131310.1226013.230847
0.5147270.1229623.24444
0.5163230.1233213.258003
0.5179190.1236793.271537
0.5195150.1240363.285041
0.521110.1243913.298516
0.5227060.1247463.311962
0.5243020.1250983.32538
0.5258970.125453.338768
0.5274930.12583.352129
0.5290880.1261493.365462
0.5306840.1264983.378767
0.5322790.1268453.392044
0.5338750.1271913.405295
0.535470.1275363.418518
0.5370660.127883.431714
0.5386610.1282243.444885
0.5402570.1285663.45803
0.5418520.1289083.471149
0.5434470.1292493.484243
0.5450430.1295893.497312
0.5466380.1299283.510356
0.5482330.1302673.523376
0.5498290.1306053.536372
0.5514240.1309433.549344
0.5530190.131283.562293
0.5546140.1316163.575218
0.5562090.1319523.588121
0.5578040.1322873.601002
0.5593990.1326223.613859
0.5609940.1329563.626695
0.5625890.133293.639508
0.5641840.1336243.6523
0.5657790.1339573.665071
0.5673740.134293.677821
0.5689690.1346233.69055
0.5705630.1349563.703258
0.5721580.1352883.715945
0.5737530.135623.728613
0.5753470.1359523.741261
0.5769420.1362833.753889
0.5785360.1366153.766498
0.5801310.1369473.779087
0.5817250.1372783.791657
0.583320.1376093.804209
0.5849140.1379413.816741
0.5865090.1382723.829256
0.5881030.1386033.841752
0.5896970.1389353.85423
0.5912910.1392663.86669
0.5928860.1395983.879133
0.594480.139933.891558
0.5960740.1402613.903966
0.5976680.1405933.916358
0.5992620.1409263.928732
0.6008560.1412583.941092
0.6024490.1415913.953436
0.6040430.1419233.965766
0.6056370.1422563.978082
0.6072310.1425893.990385
0.6088240.1429234.002675
0.6104180.1432564.014954
0.6120120.1435894.02722
0.6136050.1439234.039477
0.6151990.1442574.051722
0.6167920.144594.063958
0.6183850.1449244.076185
0.6199790.1452584.088403
0.6215720.1455914.100612
0.6231650.1459254.112814
0.6247580.1462584.125009
0.6263510.1465924.137198
0.6279440.1469254.14938
0.6295370.1472584.161557
0.631130.1475914.173728
0.6327230.1479234.185896
0.6343160.1482554.198058
0.6359080.1485874.210217
0.6375010.1489194.222374
0.6390930.149254.234527
0.6406860.1495814.246678
0.6422780.1499124.258827
0.6438710.1502424.270975
0.6454630.1505724.283122
0.6470550.1509024.295268
0.6486480.1512314.307414
0.650240.1515594.319561
0.6518320.1518874.331709
0.6534240.1522154.343857
0.6550160.1525424.356008
0.6566080.1528684.36816
0.6581990.1531944.380315
0.6597910.1535194.392473
0.6613830.1538444.404634
0.6629740.1541684.416799
0.6645660.1544914.428967
0.6661570.1548144.44114
0.6677480.1551364.453318
0.669340.1554584.465501
0.6709310.1557784.477689
0.6725220.1560984.489883
0.6741130.1564174.502083
0.6757040.1567364.514287
0.6772950.1570544.526495
0.6788860.1573714.538708
0.6804770.1576874.550926
0.6820670.1580034.563147
0.6836580.1583184.575372
0.6852480.1586324.587601
0.6868390.1589464.599833
0.6884290.1592594.612068
0.690020.1595714.624305
0.691610.1598834.636545
0.69320.1601944.648788
0.694790.1605044.661032
0.696380.1608144.673279
0.697970.1611234.685527
0.699560.1614314.697776
0.7011490.1617394.710026
0.7027390.1620464.722278
0.7043280.1623524.73453
0.7059180.1626584.746783
0.7075070.1629634.759036
0.7090960.1632684.77129
0.7106860.1635724.783543
0.7122750.1638754.795796
0.7138640.1641784.808048
0.7154530.164484.8203
0.7170420.1647814.832551
0.718630.1650824.844801
0.7202190.1653824.85705
0.7218070.1656824.869297
0.7233960.1659814.881542
0.7249840.1662794.893786
0.7265730.1665774.906028
0.7281610.1668744.918268
0.7297490.1671714.930505
0.7313370.1674674.94274
0.7329250.1677634.954972
0.7345130.1680574.967201
0.73610.1683524.979427
0.7376880.1686464.99165
0.7392760.1689395.00387
0.7408630.1692315.016085
0.742450.1695235.028297
0.7440380.1698155.040506
0.7456250.1701065.052709
0.7472120.1703965.06491
0.7487990.1706865.077105
0.7503850.1709755.089296
0.7519720.1712645.101482
0.7535590.1715525.113664
0.7551450.1718395.12584
0.7567320.1721265.138011
0.7583180.1724135.150177
0.7599040.1726995.162338
0.761490.1729845.174493
0.7630760.1732695.186642
0.7646620.1735535.198785
0.7662480.1738375.210922
0.7678340.174125.223053
0.7694190.1744035.235177
0.7710050.1746855.247295
0.772590.1749675.259407
0.7741750.1752485.271512
0.775760.1755285.28361
0.7773450.1758085.295701
0.778930.1760885.307784
0.7805150.1763675.319861
0.78210.1766455.33193
0.7836840.1769235.343991
0.7852690.1772015.356045
0.7868530.1774785.36809
0.7884370.1777545.380128
0.7900220.178035.392158
0.7916060.1783055.40418
0.793190.178585.416194
0.7947730.1788555.428199
0.7963570.1791285.440195
0.797940.1794025.452183
0.7995240.1796755.464162
0.8011070.1799475.476132
0.802690.1802195.488093
0.8042730.180495.500045
0.8058560.1807615.511988
0.8074390.1810315.523921
0.8090220.1813015.535845
0.8106040.181575.547759
0.8121870.1818395.559664
0.8137690.1821075.571559
0.8153510.1823755.583444
0.8169330.1826425.595319
0.8185150.1829095.607183
0.8200970.1831765.619038
0.8216790.1834415.630882
0.8232610.1837075.642715
0.8248420.1839725.654538
0.8264230.1842365.666351
0.8280040.18455.678152
0.8295860.1847635.689943
0.8311670.1850265.701723
0.8327470.1852885.713491
0.8343280.185555.72525
0.8359080.1858125.736995
0.8374890.1860735.748731
0.8390690.1863335.760454
0.8406490.1865935.772166
0.8422290.1868535.783867
0.8438090.1871125.795555
0.8453890.187375.807232
0.8469690.1876285.818897
0.8485480.1878865.83055
0.8501270.1881435.842191
0.8517070.18845.853819
0.8532860.1886565.865436
0.8548650.1889125.87704
0.8564430.1891675.888631
0.8580220.1894225.90021
0.8596010.1896775.911776
0.8611790.1899315.92333
0.8627570.1901855.934871
0.8643350.1904385.946398
0.8659130.1906925.957913
0.8674910.1909455.969416
0.8690690.1911985.980905
0.8706460.1914515.99238
0.8722240.1917036.003843
0.8738010.1919566.015292
0.8753780.1922086.026727
0.8769550.192466.038149
0.8785320.1927126.049557
0.8801080.1929646.060952
0.8816850.1932156.072333
0.8832610.1934676.083699
0.8848370.1937196.095053
0.8864130.1939716.106392
0.8879890.1942226.117717
0.8895650.1944746.129028
0.8911410.1947266.140324
0.8927160.1949786.151607
0.8942920.195236.162875
0.8958670.1954826.174129
0.8974420.1957346.185368
0.8990170.1959866.196592
0.9005910.1962396.207802
0.9021660.1964916.218997
0.903740.1967446.230177
0.9053140.1969976.241343
0.9068880.197256.252494
0.9084620.1975046.263629
0.9100360.1977586.274749
0.911610.1980126.285855
0.9131830.1982666.296945
0.9147560.198526.308019
0.916330.1987756.319079
0.9179030.1990316.330123
0.9194750.1992866.341151
0.9210480.1995426.352165
0.9226210.1997996.363162
0.9241930.2000556.374144
0.9257650.2003136.38511
0.9273370.200576.39606
0.9289090.2008286.406994
0.930480.2010876.417913
0.9320520.2013466.428815
0.9336230.2016066.439702
0.9351950.2018666.450572
0.9367660.2021266.461426
0.9383360.2023876.472264
0.9399070.2026496.483085
0.9414780.2029116.493891
0.9430480.2031746.504679
0.9446180.2034376.515452
0.9461880.2037016.526208
0.9477580.2039666.536947
0.9493280.2042316.54767
0.9508970.2044976.558376
0.9524660.2047646.569065
0.9540360.2050316.579738
0.9556040.2052996.590393
0.9571730.2055686.601031
0.9587420.2058386.611653
0.960310.2061086.622257
0.9618790.2063796.632845
0.9634470.206656.643414
0.9650150.2069236.653968
0.9665820.2071966.664505
0.968150.207476.675026
0.9697170.2077456.685533
0.9712850.208026.696026
0.9728520.2082976.706504
0.9744180.2085746.716971
0.9759850.2088516.727424
0.9775520.2091296.737866
0.9791180.2094086.748297
0.9806840.2096886.758718
0.982250.2099686.769129
0.9838160.2102496.779532
0.9853810.2105316.789925
0.9869470.2108136.800311
0.9885120.2110966.81069
0.9900770.211386.821062
0.9916420.2116646.831427
0.9932060.2119496.841788
0.9947710.2122346.852144
0.9963350.212526.862495
0.9978990.2128076.872843
0.9994630.2130946.883188
1.0116630.2153546.963895
1.0150860.2159946.986562
1.0185090.2166377.009248
1.0219310.2172827.031958
1.0253520.2179297.054698
1.0287730.2185797.077473
1.0321940.2192317.10029
1.0356140.2198857.123153
1.0390340.2205417.146068
1.0424540.2211987.169041
1.0458730.2218587.192077
1.0492920.2225197.21518
1.0527110.2231817.238354
1.0561290.2238447.261596
1.0595470.2245097.284905
1.0629640.2251767.308278
1.0663820.2258447.331713
1.0697990.2265137.355207
1.0732150.2271847.37876
1.0766320.2278577.402368
1.0800480.2285317.426029
1.0834640.2292077.449741
1.0868790.2298847.473502
1.0902950.2305637.497311
1.093710.2312447.521165
1.0971250.2319277.545062
1.1005390.2326127.569001
1.1039540.2332987.592978
1.1073680.2339877.616994
1.1107820.2346777.641044
1.1141960.2353697.665129
1.1176090.2360647.689246
1.1210230.236767.713393
1.1244360.2374587.737568
1.1278490.2381597.76177
1.1312620.2388617.785997
1.1346750.2395667.810247
1.1380880.2402737.834518
1.14150.2409827.85881
1.1449130.2416937.88312
1.1483250.2424067.907446
1.1517380.2431227.931788
1.155150.243847.956142
1.1585620.2445617.980509
1.1619740.2452838.004887
1.1653860.2460088.029273
1.1687980.2467368.053666
1.172210.2474668.078065
1.1756220.2481988.10247
1.1790340.2489338.126876
1.1824460.249678.151285
1.1858580.250418.175694
1.189270.2511528.200102
1.1926820.2518978.224506
1.1960930.2526458.248907
1.1995050.2533958.273304
1.2029170.2541488.297693
1.2063290.2549038.322074
1.2097420.2556618.346447
1.2131540.2564228.370809
1.2165660.2571868.395159
1.2199780.2579528.419496
1.2233910.2587218.44382
1.2268030.2594938.468127
1.2302160.2602678.492419
1.2336290.2610458.516692
1.2370410.2618258.540947
1.2404540.2626088.565182
1.2438670.2633958.589395
1.2472810.2641848.613586
1.2506940.2649768.637754
1.2541080.265778.661898
1.2575220.2665688.686015
1.2609360.2673698.710106
1.264350.2681728.734169
1.2677640.2689798.758203
1.2711790.2697888.782207
1.2745940.27068.806181
1.2780090.2714168.830122
1.2814240.2722338.854031
1.284840.2730548.877905
1.2882550.2738788.901745
1.2916710.2747058.925548
1.2950880.2755348.949315
1.2985040.2763668.973043
1.3019210.2772018.996733
1.3053380.2780399.020384
1.3087560.278889.043992
1.3121740.2797239.06756
1.3155920.280579.091085
1.319010.2814199.114566
1.3224290.2822719.138003
1.3258490.2831269.161395
1.3292680.2839849.184741
1.3326880.2848449.208041
1.3361080.2857079.231297
1.3395290.2865739.254511
1.342950.2874419.277687
1.3463720.2883129.300825
1.3497940.2891859.323928
1.3532160.290069.346997
1.3566390.2909379.370035
1.3600620.2918179.393043
1.3634860.2926989.416024
1.366910.2935819.43898
1.3703340.2944669.461912
1.3737590.2953539.484821
1.3771850.2962419.507712
1.3806110.2971319.530585
1.3840380.2980229.553442
1.3874650.2989159.576284
1.3908920.2998089.599114
1.394320.3007049.621933
1.3977490.30169.644744
1.4011780.3024979.667547
1.4046080.3033959.690345
1.4080380.3042949.713141
1.4114690.3051949.735934
1.41490.3060959.758727
1.4183320.3069969.781521
1.4217650.3078989.804319
1.4251980.3088019.827123
1.4286320.3097039.849932
1.4320670.3106079.87275
1.4355020.311519.895579
1.4389380.3124149.918418
1.4423740.3133179.941272
1.4458110.3142219.96414
1.4492490.3151259.987024

Optical transmission calculator

Free-standing sample in vacuum, normal incidence
Method
Transmittance T
—
Reflectance R
—

Fresnel reflection calculator

Direction
Rp
—
Rs
—
R = (Rp+Rs)/2
—
Phase φp
—
Phase φs
—
Brewster angle θB
—
Critical angle θC
—