Optical constants

Refractive index of Ag (Silver)

Rakić et al. 1998: Brendel-Bormann model; n,k 0.248–12.4 µm

Data
tabulated nk
Range
0.248–12.4 µm
Points
200
Licence
CC0-1.0

Plot

Click the plot to set the calculator wavelength.

At one wavelength

Range 0.248–12.4 µm
Refractive index n
0.150158
Extinction coefficient k
3.47275
Permittivity ε1
-12.0374
Permittivity ε2
1.04292
Absorption coefficient α
742679 cm⁻¹
Penetration depth δ = λ/(2πk)
26.9295 nm
Abbe number Vd
—
Chromatic dispersion dn/dλ
0.138622 µm⁻¹
Group index ng
0.0687038
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): Rakić et al. 1998: Brendel-Bormann model; n,k 0.248–12.4 µm
ag = ls.fetch_refractiveindex("main", "Ag", "Rakic-BB", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(ag.range_nm)  # (247.97, 12398) 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

Fit of experimental data from several sources to Brendel-Bormann (BB) model

References

A. D. Rakić, A. B. Djurišic, J. M. Elazar, M. L. Majewski. Optical properties of metallic films for vertical-cavity optoelectronic devices. Appl. Opt. 37, 5271-5283 (1998)
[Calculation script (Python)]
  • doi:10.1364/ao.37.005271 Optical properties of metallic films for vertical-cavity optoelectronic devices, Applied Optics (1998)

Cite

Aleksandar D. Rakić, Aleksandra B. Djurišić, Jovan M. Elazar and Marian L. Majewski. Optical properties of metallic films for vertical-cavity optoelectronic devices. Applied Optics, 37, 5271 (1998), doi:10.1364/ao.37.005271; [Calculation script (Python)]; Data from the refractiveindex.info database (M. N. Polyanskiy, Sci. Data 11, 94 (2024), doi:10.1038/s41597-023-02898-2)

Data

200 rows as published
Ag (Silver), Rakić et al. 1998: Brendel-Bormann model; n,k 0.248–12.4 µm: n and k versus wavelength
λ (µm)nk
0.247970.848631.192
0.252890.824931.2193
0.257910.796991.2844
0.263030.800091.3955
0.268250.875361.5246
0.273581.0321.6142
0.279011.23511.6125
0.284551.42451.5017
0.29021.54241.3028
0.295961.55491.0631
0.301841.45940.83581
0.307831.27670.66203
0.313941.03610.56621
0.320170.767830.56549
0.326530.522130.67421
0.333010.363780.84735
0.339620.27961.0142
0.346370.231781.1589
0.353240.201721.286
0.360250.181511.4005
0.367410.167411.5059
0.37470.157391.6045
0.382140.150211.6979
0.389730.145061.7873
0.397460.141411.8736
0.405350.138871.9574
0.41340.137162.0394
0.421610.136092.12
0.429980.13552.1995
0.438520.135292.2782
0.447220.135372.3564
0.45610.135692.4344
0.465150.136212.5122
0.474390.136872.5901
0.483810.137672.6682
0.493410.138572.7466
0.503210.139582.8254
0.51320.140672.9048
0.523390.141842.9848
0.533780.143083.0656
0.544370.14443.1471
0.555180.145783.2295
0.56620.147233.3128
0.577440.148753.3971
0.588910.150343.4825
0.60060.1523.569
0.612520.153733.6567
0.624680.155543.7455
0.637090.157423.8357
0.649730.159393.9272
0.662630.161434.02
0.675790.163564.1143
0.68920.165794.21
0.702890.16814.3072
0.716840.170514.4061
0.731070.173034.5065
0.745590.175654.6085
0.760390.178384.7123
0.775490.181234.8178
0.790880.18424.9251
0.806580.187295.0343
0.82260.190515.1453
0.838930.193875.2583
0.855580.197375.3732
0.872570.201025.4902
0.889890.204825.6093
0.907560.208785.7304
0.925570.212915.8538
0.943950.217215.9793
0.962690.221696.1072
0.98180.226366.2373
1.00130.231226.3699
1.02120.236286.5048
1.04140.241556.6423
1.06210.247056.7823
1.08320.252776.9248
1.10470.258727.07
1.12660.264937.2179
1.1490.271387.3686
1.17180.278117.5221
1.19510.285117.6785
1.21880.292397.8378
1.2430.299988.0001
1.26770.307888.1654
1.29290.316098.3339
1.31850.324658.5056
1.34470.333558.6805
1.37140.342818.8587
1.39860.352459.0403
1.42640.362499.2254
1.45470.372929.414
1.48360.383799.6062
1.5130.395099.8021
1.54310.4068410.002
1.57370.4190810.205
1.6050.431810.412
1.63680.4450410.624
1.66930.4588210.839
1.70250.4731411.059
1.73630.4880511.282
1.77070.5035511.51
1.80590.5196711.743
1.84170.5364411.979
1.87830.5538912.221
1.91560.5720312.467
1.95360.590912.718
1.99240.6105312.973
2.03190.6309413.234
2.07230.6521613.499
2.11340.6742413.77
2.15540.6971914.046
2.19820.7210614.327
2.24180.7458814.614
2.28630.771714.906
2.33170.7985415.203
2.3780.8264515.507
2.42520.8554615.816
2.47340.8856416.131
2.52250.9170116.453
2.57250.9496216.78
2.62360.9835317.114
2.67571.018817.454
2.72881.055417.801
2.7831.093518.154
2.83831.133218.514
2.89461.174318.881
2.95211.217119.255
3.01071.261619.636
3.07041.307920.025
3.13141.35620.421
3.19361.40620.824
3.2571.457921.235
3.32161.511921.654
3.38761.56822.081
3.45481.626322.516
3.52341.686922.959
3.59341.749923.41
3.66471.815323.87
3.73751.883324.339
3.81171.95424.817
3.88732.027425.303
3.96452.103625.799
4.04322.182926.304
4.12352.265226.818
4.20532.350727.342
4.28882.439627.876
4.3742.531928.419
4.46082.627728.973
4.54942.727329.537
4.63972.830730.111
4.73182.938130.696
4.82573.049631.291
4.92163.165431.898
5.01933.285632.515
5.11893.410433.143
5.22053.5433.783
5.32423.674534.435
5.42993.814135.098
5.53773.959135.773
5.64764.109536.46
5.75974.265637.159
5.87414.427537.87
5.99074.595638.594
6.10964.769939.331
6.23094.950840.08
6.35465.138440.842
6.48085.332941.618
6.60945.534742.407
6.74075.743943.209
6.87455.960944.025
7.0116.185744.854
7.15026.418845.697
7.29216.660446.555
7.43696.910747.426
7.58457.170148.312
7.73517.438949.212
7.88877.717250.126
8.04538.005551.055
8.2058.30451.999
8.36798.613152.958
8.5348.93353.931
8.70349.264254.92
8.87629.606855.923
9.05249.961456.942
9.232210.32857.976
9.415410.70759.025
9.602411.160.09
9.79311.50561.17
9.987411.92462.265
10.18612.35763.376
10.38812.80564.502
10.59413.26765.643
10.80413.74466.8
11.01914.23767.973
11.23814.74669.16
11.46115.2770.363
11.68815.81271.581
11.9216.3772.814
12.15716.94674.063
12.39817.5475.326

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
—