Optical constants

Refractive index of H2O, D2O (Water, heavy water, ice)

Kofman et al. 2019: Amorphous ice; n 0.210–0.757 µm; 90 K

Data
formula 1
Range
0.21–0.757 µm
Temperature
90 K
State
amorphous
Licence
CC0-1.0

Plot

Click the plot to set the calculator wavelength.

At one wavelength

Range 0.21–0.757 µm
Refractive index n
1.26139
Extinction coefficient k
0
Permittivity ε1
1.59111
Permittivity ε2
0
Absorption coefficient α
0 cm⁻¹
Penetration depth δ = λ/(2πk)
— nm
Abbe number Vd
46.96
Chromatic dispersion dn/dλ
-0.0283994 µm⁻¹
Group index ng
1.27808
Group velocity dispersion
55.1164 fs²/mm
Dispersion parameter D
-300.689 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

# H2O, D2O (Water, heavy water, ice): Kofman et al. 2019: Amorphous ice; n 0.210–0.757 µm; 90 K
h2o_d2o = ls.fetch_refractiveindex("main", "H2O", "Kofman-90K", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(h2o_d2o.range_nm)  # (210, 757) nm
eps = h2o_d2o.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.

Dispersion formula

Sellmeier (formula 1), λ in µm
n2−1=0.28λ2λ2−0.0712+0.291λ2λ2−0.1342

Valid from 0.21 to 0.757 µm.

Coefficients as stored
CiValue
C10.0
C20.28
C30.071
C40.291
C50.134

Comments and conditions

Amorphous water ice at 90 K.

Conditions

temperature
90 K

References

V. Kofman, J. He, I. L. ten Kate, H. Linnartz. The refractive index of amorphous and crystalline water ice in the UV–vis. Astrophys. J. 875, 131 (2019)

Cite

Vincent Kofman, Jiao He, Inge Loes ten Kate and Harold Linnartz. The Refractive Index of Amorphous and Crystalline Water Ice in the UV–vis. The Astrophysical Journal, 875, 131 (2019), doi:10.3847/1538-4357/ab0d89; Data from the refractiveindex.info database (M. N. Polyanskiy, Sci. Data 11, 94 (2024), doi:10.1038/s41597-023-02898-2)

Data

Computed on 400 wavelengths, the same grid as the API and the library
H2O, D2O (Water, heavy water, ice), Kofman et al. 2019: Amorphous ice; n 0.210–0.757 µm; 90 K: n and k versus wavelength
λ (µm)n
0.211.344247
0.2106761.343349
0.2113541.342464
0.2120341.341591
0.2127171.34073
0.2134021.33988
0.2140891.339042
0.2147781.338214
0.2154691.337398
0.2161631.336592
0.2168581.335797
0.2175561.335012
0.2182571.334237
0.2189591.333472
0.2196641.332717
0.2203711.331971
0.221081.331235
0.2217921.330508
0.2225061.329791
0.2232221.329082
0.2239411.328381
0.2246611.32769
0.2253851.327007
0.226111.326332
0.2268381.325665
0.2275681.325007
0.2283011.324356
0.2290351.323713
0.2297731.323078
0.2305121.322451
0.2312541.32183
0.2319991.321217
0.2327451.320612
0.2334951.320013
0.2342461.319421
0.2351.318836
0.2357571.318258
0.2365151.317686
0.2372771.317121
0.238041.316562
0.2388071.316009
0.2395751.315463
0.2403471.314923
0.241121.314389
0.2418961.313861
0.2426751.313338
0.2434561.312822
0.244241.312311
0.2450261.311805
0.2458151.311305
0.2466061.310811
0.24741.310322
0.2481961.309838
0.2489951.309359
0.2497961.308886
0.25061.308417
0.2514071.307953
0.2522161.307495
0.2530281.307041
0.2538431.306592
0.254661.306147
0.2554791.305708
0.2563021.305272
0.2571271.304842
0.2579541.304416
0.2587851.303994
0.2596181.303576
0.2604531.303163
0.2612921.302754
0.2621331.302349
0.2629771.301948
0.2638231.301551
0.2646721.301158
0.2655241.300769
0.2663791.300384
0.2672361.300003
0.2680961.299625
0.2689591.299252
0.2698251.298882
0.2706941.298515
0.2715651.298152
0.2724391.297793
0.2733161.297437
0.2741961.297085
0.2750781.296736
0.2759641.29639
0.2768521.296048
0.2777431.295709
0.2786371.295373
0.2795341.295041
0.2804341.294711
0.2813371.294385
0.2822421.294062
0.2831511.293742
0.2840621.293425
0.2849761.293111
0.2858941.292799
0.2868141.292491
0.2877371.292186
0.2886631.291883
0.2895931.291583
0.2905251.291286
0.291461.290992
0.2923981.2907
0.2933391.290411
0.2942831.290125
0.2952311.289841
0.2961811.28956
0.2971341.289282
0.2980911.289006
0.299051.288732
0.3000131.288461
0.3009791.288193
0.3019471.287926
0.3029191.287662
0.3038941.287401
0.3048721.287142
0.3058541.286885
0.3068381.28663
0.3078261.286378
0.3088171.286128
0.3098111.28588
0.3108081.285634
0.3118091.285391
0.3128121.285149
0.3138191.28491
0.3148291.284673
0.3158431.284437
0.3168591.284204
0.3178791.283973
0.3189021.283744
0.3199291.283517
0.3209591.283292
0.3219921.283068
0.3230281.282847
0.3240681.282627
0.3251111.28241
0.3261581.282194
0.3272071.28198
0.3282611.281768
0.3293171.281558
0.3303771.281349
0.3314411.281142
0.3325081.280937
0.3335781.280734
0.3346521.280533
0.3357291.280333
0.336811.280134
0.3378941.279938
0.3389811.279743
0.3400721.279549
0.3411671.279358
0.3422651.279168
0.3433671.278979
0.3444721.278792
0.3455811.278607
0.3466931.278423
0.3478091.27824
0.3489291.278059
0.3500521.27788
0.3511791.277702
0.3523091.277525
0.3534431.27735
0.3545811.277176
0.3557221.277004
0.3568671.276833
0.3580161.276664
0.3591681.276496
0.3603241.276329
0.3614841.276163
0.3626481.275999
0.3638151.275836
0.3649861.275675
0.3661611.275515
0.367341.275356
0.3685221.275198
0.3697081.275042
0.3708981.274887
0.3720921.274733
0.373291.27458
0.3744911.274429
0.3756971.274278
0.3769061.274129
0.3781191.273981
0.3793361.273835
0.3805571.273689
0.3817821.273545
0.3830111.273401
0.3842441.273259
0.3854811.273118
0.3867221.272978
0.3879671.272839
0.3892151.272701
0.3904681.272565
0.3917251.272429
0.3929861.272294
0.3942511.272161
0.395521.272028
0.3967931.271897
0.398071.271766
0.3993521.271637
0.4006371.271508
0.4019271.271381
0.403221.271254
0.4045181.271129
0.405821.271004
0.4071271.27088
0.4084371.270758
0.4097521.270636
0.4110711.270515
0.4123941.270395
0.4137211.270276
0.4150531.270158
0.4163891.270041
0.4177291.269925
0.4190741.269809
0.4204231.269695
0.4217761.269581
0.4231341.269468
0.4244961.269356
0.4258621.269245
0.4272331.269135
0.4286081.269025
0.4299881.268917
0.4313721.268809
0.432761.268702
0.4341531.268595
0.4355511.26849
0.4369531.268385
0.4383591.268282
0.439771.268179
0.4411861.268076
0.4426061.267975
0.4440311.267874
0.445461.267774
0.4468941.267674
0.4483321.267576
0.4497751.267478
0.4512231.267381
0.4526751.267285
0.4541331.267189
0.4555941.267094
0.4570611.267
0.4585321.266906
0.4600081.266813
0.4614891.266721
0.4629741.266629
0.4644641.266539
0.4659591.266448
0.4674591.266359
0.4689641.26627
0.4704731.266182
0.4719881.266094
0.4735071.266007
0.4750311.265921
0.476561.265835
0.4780941.26575
0.4796331.265666
0.4811771.265582
0.4827261.265499
0.484281.265416
0.4858391.265334
0.4874021.265253
0.4889711.265172
0.4905451.265091
0.4921241.265012
0.4937081.264933
0.4952971.264854
0.4968921.264776
0.4984911.264699
0.5000961.264622
0.5017051.264546
0.503321.26447
0.504941.264395
0.5065661.26432
0.5081961.264246
0.5098321.264172
0.5114731.264099
0.5131191.264027
0.5147711.263955
0.5164281.263883
0.518091.263812
0.5197581.263742
0.5214311.263672
0.5231091.263602
0.5247931.263533
0.5264831.263465
0.5281771.263397
0.5298771.263329
0.5315831.263262
0.5332941.263196
0.5350111.26313
0.5367331.263064
0.538461.262999
0.5401941.262934
0.5419321.26287
0.5436771.262806
0.5454271.262743
0.5471821.26268
0.5489441.262617
0.5507111.262555
0.5524831.262494
0.5542621.262433
0.5560461.262372
0.5578361.262312
0.5596311.262252
0.5614331.262192
0.563241.262133
0.5650531.262075
0.5668711.262016
0.5686961.261959
0.5705271.261901
0.5723631.261844
0.5742051.261788
0.5760541.261731
0.5779081.261676
0.5797681.26162
0.5816341.261565
0.5835071.261511
0.5853851.261456
0.5872691.261402
0.5891591.261349
0.5910561.261296
0.5929581.261243
0.5948671.261191
0.5967821.261139
0.5987031.261087
0.600631.261036
0.6025631.260985
0.6045031.260934
0.6064481.260884
0.6084011.260834
0.6103591.260784
0.6123241.260735
0.6142951.260686
0.6162721.260638
0.6182561.260589
0.6202461.260542
0.6222421.260494
0.6242451.260447
0.6262541.2604
0.628271.260353
0.6302921.260307
0.6323211.260261
0.6343571.260216
0.6363981.26017
0.6384471.260125
0.6405021.260081
0.6425641.260036
0.6446321.259992
0.6467071.259948
0.6487891.259905
0.6508771.259862
0.6529721.259819
0.6550741.259776
0.6571821.259734
0.6592981.259692
0.661421.25965
0.6635491.259609
0.6656851.259568
0.6678281.259527
0.6699771.259486
0.6721341.259446
0.6742971.259406
0.6764681.259366
0.6786451.259327
0.680831.259288
0.6830211.259249
0.685221.25921
0.6874251.259172
0.6896381.259133
0.6918581.259096
0.6940851.259058
0.6963191.259021
0.698561.258983
0.7008091.258947
0.7030651.25891
0.7053281.258874
0.7075981.258837
0.7098761.258802
0.7121611.258766
0.7144531.258731
0.7167531.258695
0.719061.25866
0.7213741.258626
0.7236961.258591
0.7260261.258557
0.7283631.258523
0.7307071.258489
0.7330591.258456
0.7354191.258423
0.7377861.258389
0.7401611.258357
0.7425431.258324
0.7449331.258292
0.7473311.258259
0.7497371.258227
0.752151.258196
0.7545711.258164
0.7571.258133

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
—