Optical constants

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

Kofman et al. 2019: Amorphous ice; n 0.210–0.757 µm; 130 K

Data
formula 1
Range
0.21–0.757 µm
Temperature
130 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
1.30205
Extinction coefficient k
0
Permittivity ε1
1.69533
Permittivity ε2
0
Absorption coefficient α
0 cm⁻¹
Penetration depth δ = λ/(2πk)
— nm
Abbe number Vd
55.671
Chromatic dispersion dn/dλ
-0.027709 µm⁻¹
Group index ng
1.31833
Group velocity dispersion
53.5291 fs²/mm
Dispersion parameter D
-292.03 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; 130 K
h2o_d2o = ls.fetch_refractiveindex("main", "H2O", "Kofman-130K", 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=0.417λ2λ2−0.0712+0.258λ2λ2−0.1342

Valid from 0.21 to 0.757 µm.

Coefficients as stored
CiValue
C10.0
C20.417
C30.071
C40.258
C50.134

Comments and conditions

Amorphous water ice at 130 K.

Conditions

temperature
130 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; 130 K: n and k versus wavelength
λ (µm)n
0.211.380585
0.2106761.379754
0.2113541.378933
0.2120341.378123
0.2127171.377324
0.2134021.376536
0.2140891.375757
0.2147781.374989
0.2154691.37423
0.2161631.373481
0.2168581.372742
0.2175561.372011
0.2182571.37129
0.2189591.370579
0.2196641.369875
0.2203711.369181
0.221081.368495
0.2217921.367817
0.2225061.367148
0.2232221.366487
0.2239411.365834
0.2246611.365188
0.2253851.36455
0.226111.36392
0.2268381.363297
0.2275681.362682
0.2283011.362074
0.2290351.361473
0.2297731.360878
0.2305121.360291
0.2312541.35971
0.2319991.359136
0.2327451.358569
0.2334951.358008
0.2342461.357453
0.2351.356905
0.2357571.356362
0.2365151.355826
0.2372771.355296
0.238041.354771
0.2388071.354252
0.2395751.353739
0.2403471.353232
0.241121.35273
0.2418961.352233
0.2426751.351742
0.2434561.351256
0.244241.350775
0.2450261.3503
0.2458151.349829
0.2466061.349363
0.24741.348903
0.2481961.348447
0.2489951.347996
0.2497961.347549
0.25061.347107
0.2514071.34667
0.2522161.346237
0.2530281.345809
0.2538431.345385
0.254661.344966
0.2554791.34455
0.2563021.344139
0.2571271.343732
0.2579541.343329
0.2587851.34293
0.2596181.342535
0.2604531.342144
0.2612921.341757
0.2621331.341374
0.2629771.340995
0.2638231.340619
0.2646721.340247
0.2655241.339878
0.2663791.339513
0.2672361.339152
0.2680961.338794
0.2689591.33844
0.2698251.338089
0.2706941.337741
0.2715651.337397
0.2724391.337056
0.2733161.336718
0.2741961.336383
0.2750781.336052
0.2759641.335724
0.2768521.335398
0.2777431.335076
0.2786371.334757
0.2795341.334441
0.2804341.334128
0.2813371.333817
0.2822421.33351
0.2831511.333205
0.2840621.332903
0.2849761.332604
0.2858941.332308
0.2868141.332014
0.2877371.331723
0.2886631.331435
0.2895931.331149
0.2905251.330866
0.291461.330586
0.2923981.330307
0.2933391.330032
0.2942831.329759
0.2952311.329488
0.2961811.32922
0.2971341.328954
0.2980911.32869
0.299051.328429
0.3000131.32817
0.3009791.327914
0.3019471.327659
0.3029191.327407
0.3038941.327157
0.3048721.326909
0.3058541.326664
0.3068381.32642
0.3078261.326179
0.3088171.32594
0.3098111.325703
0.3108081.325467
0.3118091.325234
0.3128121.325003
0.3138191.324774
0.3148291.324547
0.3158431.324321
0.3168591.324098
0.3178791.323877
0.3189021.323657
0.3199291.323439
0.3209591.323223
0.3219921.323009
0.3230281.322797
0.3240681.322586
0.3251111.322378
0.3261581.322171
0.3272071.321965
0.3282611.321762
0.3293171.32156
0.3303771.32136
0.3314411.321161
0.3325081.320964
0.3335781.320769
0.3346521.320575
0.3357291.320383
0.336811.320193
0.3378941.320004
0.3389811.319817
0.3400721.319631
0.3411671.319446
0.3422651.319264
0.3433671.319082
0.3444721.318902
0.3455811.318724
0.3466931.318547
0.3478091.318371
0.3489291.318197
0.3500521.318024
0.3511791.317853
0.3523091.317683
0.3534431.317514
0.3545811.317347
0.3557221.317181
0.3568671.317017
0.3580161.316853
0.3591681.316691
0.3603241.316531
0.3614841.316371
0.3626481.316213
0.3638151.316056
0.3649861.3159
0.3661611.315746
0.367341.315593
0.3685221.315441
0.3697081.31529
0.3708981.31514
0.3720921.314992
0.373291.314844
0.3744911.314698
0.3756971.314553
0.3769061.314409
0.3781191.314266
0.3793361.314125
0.3805571.313984
0.3817821.313844
0.3830111.313706
0.3842441.313569
0.3854811.313432
0.3867221.313297
0.3879671.313163
0.3892151.31303
0.3904681.312898
0.3917251.312766
0.3929861.312636
0.3942511.312507
0.395521.312379
0.3967931.312252
0.398071.312126
0.3993521.312
0.4006371.311876
0.4019271.311753
0.403221.31163
0.4045181.311509
0.405821.311388
0.4071271.311268
0.4084371.31115
0.4097521.311032
0.4110711.310915
0.4123941.310799
0.4137211.310683
0.4150531.310569
0.4163891.310456
0.4177291.310343
0.4190741.310231
0.4204231.31012
0.4217761.31001
0.4231341.309901
0.4244961.309792
0.4258621.309684
0.4272331.309578
0.4286081.309471
0.4299881.309366
0.4313721.309262
0.432761.309158
0.4341531.309055
0.4355511.308953
0.4369531.308851
0.4383591.30875
0.439771.30865
0.4411861.308551
0.4426061.308453
0.4440311.308355
0.445461.308258
0.4468941.308161
0.4483321.308066
0.4497751.307971
0.4512231.307876
0.4526751.307783
0.4541331.30769
0.4555941.307598
0.4570611.307506
0.4585321.307415
0.4600081.307325
0.4614891.307236
0.4629741.307147
0.4644641.307058
0.4659591.306971
0.4674591.306884
0.4689641.306797
0.4704731.306712
0.4719881.306627
0.4735071.306542
0.4750311.306458
0.476561.306375
0.4780941.306292
0.4796331.30621
0.4811771.306129
0.4827261.306048
0.484281.305967
0.4858391.305888
0.4874021.305809
0.4889711.30573
0.4905451.305652
0.4921241.305574
0.4937081.305497
0.4952971.305421
0.4968921.305345
0.4984911.30527
0.5000961.305195
0.5017051.305121
0.503321.305047
0.504941.304974
0.5065661.304901
0.5081961.304829
0.5098321.304758
0.5114731.304687
0.5131191.304616
0.5147711.304546
0.5164281.304476
0.518091.304407
0.5197581.304338
0.5214311.30427
0.5231091.304203
0.5247931.304135
0.5264831.304069
0.5281771.304002
0.5298771.303937
0.5315831.303871
0.5332941.303807
0.5350111.303742
0.5367331.303678
0.538461.303615
0.5401941.303552
0.5419321.303489
0.5436771.303427
0.5454271.303365
0.5471821.303304
0.5489441.303243
0.5507111.303183
0.5524831.303122
0.5542621.303063
0.5560461.303004
0.5578361.302945
0.5596311.302887
0.5614331.302829
0.563241.302771
0.5650531.302714
0.5668711.302657
0.5686961.302601
0.5705271.302545
0.5723631.302489
0.5742051.302434
0.5760541.302379
0.5779081.302325
0.5797681.302271
0.5816341.302217
0.5835071.302164
0.5853851.302111
0.5872691.302058
0.5891591.302006
0.5910561.301954
0.5929581.301903
0.5948671.301852
0.5967821.301801
0.5987031.30175
0.600631.3017
0.6025631.301651
0.6045031.301601
0.6064481.301552
0.6084011.301503
0.6103591.301455
0.6123241.301407
0.6142951.301359
0.6162721.301312
0.6182561.301265
0.6202461.301218
0.6222421.301172
0.6242451.301126
0.6262541.30108
0.628271.301034
0.6302921.300989
0.6323211.300944
0.6343571.3009
0.6363981.300855
0.6384471.300812
0.6405021.300768
0.6425641.300725
0.6446321.300682
0.6467071.300639
0.6487891.300596
0.6508771.300554
0.6529721.300512
0.6550741.300471
0.6571821.300429
0.6592981.300388
0.661421.300348
0.6635491.300307
0.6656851.300267
0.6678281.300227
0.6699771.300187
0.6721341.300148
0.6742971.300109
0.6764681.30007
0.6786451.300031
0.680831.299993
0.6830211.299955
0.685221.299917
0.6874251.29988
0.6896381.299842
0.6918581.299805
0.6940851.299768
0.6963191.299732
0.698561.299696
0.7008091.29966
0.7030651.299624
0.7053281.299588
0.7075981.299553
0.7098761.299518
0.7121611.299483
0.7144531.299448
0.7167531.299414
0.719061.29938
0.7213741.299346
0.7236961.299312
0.7260261.299279
0.7283631.299245
0.7307071.299212
0.7330591.29918
0.7354191.299147
0.7377861.299115
0.7401611.299083
0.7425431.299051
0.7449331.299019
0.7473311.298987
0.7497371.298956
0.752151.298925
0.7545711.298894
0.7571.298864

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
—