Optical constants

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

Kedenburg et al. 2012: Water; n 0.5–1.6 µm, k 0.5–1.75 µm; 20.0 °C

Data
formula 2 + tabulated k
Range
0.5–1.6 µm
Temperature
293 K
State
liquid
Licence
CC0-1.0

Plot

Click the plot to set the calculator wavelength.

At one wavelength

Range 0.5–1.6 µm
Refractive index n
1.33329
Extinction coefficient k
7.00476e-09
Permittivity ε1
1.77767
Permittivity ε2
1.86788e-08
Absorption coefficient α
0.00149803 cm⁻¹
Penetration depth δ = λ/(2πk)
1.33508e+10 nm
Abbe number Vd
—
Chromatic dispersion dn/dλ
-0.0344967 µm⁻¹
Group index ng
1.35356
Group velocity dispersion
53.5915 fs²/mm
Dispersion parameter D
-292.37 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): Kedenburg et al. 2012: Water; n 0.5–1.6 µm, k 0.5–1.75 µm; 20.0 °C
h2o_d2o = ls.fetch_refractiveindex("main", "H2O", "Kedenburg", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(h2o_d2o.range_nm)  # (500, 1600) 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 (C in µm²) (formula 2), λ in µm
n2−1=0.75831λ2λ2−0.01007+0.08495λ2λ2−8.91377

Valid from 0.5 to 1.6 µm.

Coefficients as stored
CiValue
C10.0
C20.75831
C30.01007
C40.08495
C58.91377

Comments and conditions

Distilled water at 20 °C.

Conditions

temperature
293 K

References

S. Kedenburg, M. Vieweg, T. Gissibl, H. Giessen. Linear refractive index and absorption measurements of nonlinear optical liquids in the visible and near-infrared spectral region. Opt. Mater. Express 2, 1588-1611 (2012)
  • doi:10.1364/ome.2.001588 Linear refractive index and absorption measurements of nonlinear optical liquids in the visible and near-infrared spectral region, Optical Materials Express (2012)

Cite

S. Kedenburg, M. Vieweg, T. Gissibl and H. Giessen. Linear refractive index and absorption measurements of nonlinear optical liquids in the visible and near-infrared spectral region. Optical Materials Express, 2, 1588 (2012), doi:10.1364/ome.2.001588; Data from the refractiveindex.info database (M. N. Polyanskiy, Sci. Data 11, 94 (2024), doi:10.1038/s41597-023-02898-2)

Data

Computed on 1409 wavelengths, the same grid as the API and the library
H2O, D2O (Water, heavy water, ice), Kedenburg et al. 2012: Water; n 0.5–1.6 µm, k 0.5–1.75 µm; 20.0 °C: n and k versus wavelength
λ (µm)nk
0.51.3370441.893940e-09
0.5011.336992.013350e-09
0.501461.3369661.950922e-09
0.5021.3369371.877550e-09
0.5029241.3368891.951250e-09
0.5031.3368851.957340e-09
0.5041.3368321.897060e-09
0.5043921.3368121.868610e-09
0.5051.336781.824470e-09
0.5058641.3367361.897214e-09
0.5061.3367291.908620e-09
0.5071.3366772.081840e-09
0.5073411.336662.087382e-09
0.5081.3366262.098080e-09
0.5088221.3365842.211402e-09
0.5091.3365752.235870e-09
0.511.3365252.321430e-09
0.5103081.3365092.325337e-09
0.5111.3364742.334120e-09
0.5117981.3364342.435268e-09
0.5121.3364242.460920e-09
0.5131.3363742.510630e-09
0.5132921.336362.479829e-09
0.5141.3363252.405090e-09
0.514791.3362862.454132e-09
0.5151.3362762.467140e-09
0.5161.3362272.480140e-09
0.5162931.3362122.498442e-09
0.5171.3361782.542550e-09
0.5178011.3361392.529990e-09
0.5181.3361292.526860e-09
0.5191.3360812.560640e-09
0.5193121.3360662.585435e-09
0.521.3360332.640060e-09
0.5208281.3359942.627097e-09
0.5211.3359862.624410e-09
0.5221.3359382.687600e-09
0.5223491.3359222.679236e-09
0.5231.3358912.663620e-09
0.5238741.335852.507759e-09
0.5241.3358442.485240e-09
0.5251.3357982.552650e-09
0.5254031.3357792.591737e-09
0.5261.3357512.649600e-09
0.5269371.3357082.497125e-09
0.5271.3357052.486880e-09
0.5281.3356592.584040e-09
0.5284751.3356372.656408e-09
0.5291.3356132.736270e-09
0.531.3355682.699270e-09
0.5300181.3355672.699286e-09
0.5311.3355232.700140e-09
0.5315661.3354972.674282e-09
0.5321.3354782.654420e-09
0.5331.3354332.930860e-09
0.5331171.3354282.903560e-09
0.5341.3353882.698390e-09
0.5346741.3353582.733355e-09
0.5351.3353442.750280e-09
0.5361.33532.844990e-09
0.5362351.335292.803099e-09
0.5371.3352562.666550e-09
0.53781.3352212.725337e-09
0.5381.3352122.740010e-09
0.5391.3351692.800860e-09
0.539371.3351532.839388e-09
0.541.3351262.904900e-09
0.5409451.3350852.909984e-09
0.5411.3350832.910280e-09
0.5421.335042.872520e-09
0.5425241.3350182.947787e-09
0.5431.3349973.016100e-09
0.5441.3349553.264080e-09
0.5441081.3349513.274570e-09
0.5451.3349133.361150e-09
0.5456971.3348843.247418e-09
0.5461.3348713.197870e-09
0.5471.3348293.430080e-09
0.547291.3348173.440737e-09
0.5481.3347883.466870e-09
0.5488871.3347513.627566e-09
0.5491.3347473.647950e-09
0.551.3347053.794650e-09
0.550491.3346853.729297e-09
0.5511.3346653.661240e-09
0.5521.3346243.681060e-09
0.5520971.334623.675306e-09
0.5531.3345833.621720e-09
0.5537091.3345553.657612e-09
0.5541.3345433.672360e-09
0.5551.3345033.727570e-09
0.5553251.334493.742705e-09
0.5561.3344633.774100e-09
0.5569471.3344253.767948e-09
0.5571.3344233.767600e-09
0.5581.3343843.934210e-09
0.5585721.3343613.851666e-09
0.5591.3343443.790020e-09
0.561.3343053.912670e-09
0.5602031.3342973.901390e-09
0.5611.3342663.857150e-09
0.5618391.3342343.930431e-09
0.5621.3342273.944530e-09
0.5631.3341893.902260e-09
0.5634791.334173.914179e-09
0.5641.334153.927150e-09
0.5651.3341124.037520e-09
0.5651241.3341074.014965e-09
0.5661.3340743.855500e-09
0.5667741.3340453.982960e-09
0.5671.3340364.020230e-09
0.5681.3339984.171960e-09
0.5684281.3339824.196443e-09
0.5691.3339614.229110e-09
0.571.3339234.268300e-09
0.5700881.333924.268958e-09
0.5711.3338864.275790e-09
0.5717521.3338584.360172e-09
0.5721.3338494.387970e-09
0.5731.3338124.527870e-09
0.5734211.3337974.583169e-09
0.5741.3337754.659100e-09
0.5751.3337394.758730e-09
0.5750951.3337354.763895e-09
0.5761.3337034.812850e-09
0.5767741.3336744.961548e-09
0.5771.3336665.004870e-09
0.5781.333634.967540e-09
0.5784581.3336145.055933e-09
0.5791.3335945.160440e-09
0.581.3335595.400130e-09
0.5801471.3335535.435479e-09
0.5811.3335235.640610e-09
0.5818411.3334935.843451e-09
0.5821.3334885.881890e-09
0.5831.3334525.984780e-09
0.5835391.3334336.040443e-09
0.5841.3334176.087990e-09
0.5851.3333826.517390e-09
0.5852431.3333746.542753e-09
0.5861.3333476.621800e-09
0.5869511.3333146.765893e-09
0.5871.3333136.773240e-09
0.5881.3332787.159110e-09
0.5886651.3332557.291893e-09
0.5891.3332447.358770e-09
0.591.333217.699920e-09
0.5903841.3331977.849253e-09
0.5911.3331768.089210e-09
0.5921.3331428.338450e-09
0.5921071.3331388.365248e-09
0.5931.3331088.588480e-09
0.5938361.333088.798121e-09
0.5941.3330748.839310e-09
0.5951.3330419.138280e-09
0.5955691.3330229.471119e-09
0.5961.3330079.722780e-09
0.5971.3329741.045170e-08
0.5973081.3329641.057441e-08
0.5981.3329411.084990e-08
0.5991.3329081.144010e-08
0.5990521.3329061.149318e-08
0.61.3328751.246180e-08
0.6008011.3328491.289978e-08
0.6011.3328431.300870e-08
0.6021.332811.322200e-08
0.6025551.3327921.347378e-08
0.6031.3327781.367580e-08
0.6041.3327461.379460e-08
0.6043141.3327351.386222e-08
0.6051.3327131.401000e-08
0.6061.3326811.437070e-08
0.6060781.3326791.436500e-08
0.6071.332651.429780e-08
0.6078481.3326231.435883e-08
0.6081.3326181.436980e-08
0.6091.3325861.449030e-08
0.6096221.3325671.456552e-08
0.611.3325551.461120e-08
0.6111.3325231.473240e-08
0.6114021.3325111.472251e-08
0.6121.3324921.470780e-08
0.6131.3324611.468310e-08
0.6131871.3324551.471495e-08
0.6141.332431.485360e-08
0.6149771.33241.502066e-08
0.6151.3323991.502460e-08
0.6161.3323681.490200e-08
0.6167721.3323451.507238e-08
0.6171.3323381.512260e-08
0.6181.3323071.514710e-08
0.6185731.332291.521757e-08
0.6191.3322771.527010e-08
0.621.3322471.534410e-08
0.6203791.3322351.539092e-08
0.6211.3322161.546770e-08
0.6221.3321861.554210e-08
0.622191.3321811.557510e-08
0.6231.3321571.571580e-08
0.6241.3321271.569140e-08
0.6240061.3321271.569220e-08
0.6251.3320971.581600e-08
0.6258281.3320731.587819e-08
0.6261.3320671.589110e-08
0.6271.3320381.591650e-08
0.6276551.3320191.606412e-08
0.6281.3320091.614180e-08
0.6291.3319791.626760e-08
0.6294881.3319651.630466e-08
0.631.331951.634360e-08
0.6311.3319211.636960e-08
0.6313251.3319121.641075e-08
0.6321.3318921.649610e-08
0.6331.3318641.657260e-08
0.6331681.3318591.660250e-08
0.6341.3318351.675010e-08
0.6351.3318061.677650e-08
0.6350171.3318061.677695e-08
0.6361.3317781.680290e-08
0.6368711.3317531.704663e-08
0.6371.3317491.708280e-08
0.6381.3317211.716040e-08
0.638731.3317011.714295e-08
0.6391.3316931.713650e-08
0.641.3316651.736700e-08
0.6405951.3316481.735278e-08
0.6411.3316371.734310e-08
0.6421.3316091.757450e-08
0.6424651.3315961.761105e-08
0.6431.3315811.765310e-08
0.6441.3315541.783430e-08
0.6443411.3315441.786121e-08
0.6451.3315261.791330e-08
0.6461.3314991.783820e-08
0.6462221.3314921.791282e-08
0.6471.3314711.817480e-08
0.6481.3314441.835760e-08
0.6481081.3314411.838862e-08
0.6491.3314171.864410e-08
0.651.331391.872460e-08
0.651.331391.872467e-08
0.6511.3313631.890880e-08
0.6518981.3313381.912127e-08
0.6521.3313361.914540e-08
0.6531.3313091.938260e-08
0.6538011.3312871.965652e-08
0.6541.3312821.972450e-08
0.6551.3312562.006740e-08
0.655711.3312372.023742e-08
0.6561.3312292.030690e-08
0.6571.3312032.080840e-08
0.6576241.3311862.105695e-08
0.6581.3311762.120660e-08
0.6591.331152.134370e-08
0.6595441.3311362.158994e-08
0.661.3311242.179630e-08
0.6611.3310982.188190e-08
0.661471.3310852.194693e-08
0.6621.3310722.202040e-08
0.6631.3310462.237020e-08
0.6634011.3310352.246840e-08
0.6641.331022.261530e-08
0.6651.3309942.259640e-08
0.6653371.3309862.258999e-08
0.6661.3309692.257740e-08
0.6671.3309432.266440e-08
0.667281.3309362.273340e-08
0.6681.3309172.291100e-08
0.6691.3308922.294530e-08
0.6692281.3308862.295312e-08
0.671.3308672.297960e-08
0.6711.3308412.301390e-08
0.6711821.3308372.303954e-08
0.6721.3308162.315510e-08
0.6731.3307912.329670e-08
0.6731411.3307882.328644e-08
0.6741.3307662.322400e-08
0.6751.3307412.341960e-08
0.6751061.3307392.345187e-08
0.6761.3307162.372330e-08
0.6771.3306922.381230e-08
0.6770771.330692.383167e-08
0.6781.3306672.406330e-08
0.6791.3306422.415280e-08
0.6790541.3306412.416637e-08
0.681.3306182.440480e-08
0.6811.3305932.460330e-08
0.6810361.3305932.461249e-08
0.6821.3305692.485650e-08
0.6831.3305452.505600e-08
0.6830251.3305442.506357e-08
0.6841.3305212.536480e-08
0.6851.3304962.551090e-08
0.6850191.3304962.551463e-08
0.6861.3304722.571200e-08
0.6871.3304482.629610e-08
0.6870181.3304482.630184e-08
0.6881.3304242.660820e-08
0.6891.3304012.714030e-08
0.6890241.33042.715051e-08
0.691.3303772.756400e-08
0.6911.3303532.809890e-08
0.6910361.3303522.811213e-08
0.6921.3303292.847000e-08
0.6931.3303062.895230e-08
0.6930531.3303052.898675e-08
0.6941.3302822.960150e-08
0.6951.3302593.025260e-08
0.6950761.3302573.030245e-08
0.6961.3302353.090530e-08
0.6971.3302123.167080e-08
0.6971061.330213.174598e-08
0.6981.3301893.238280e-08
0.6991.3301663.315230e-08
0.6991411.3301633.326873e-08
0.71.3301433.397960e-08
0.7011.330123.497640e-08
0.7011821.3301153.513784e-08
0.7021.3300973.586430e-08
0.7031.3300743.681050e-08
0.7032291.3300693.702763e-08
0.7041.3300513.775920e-08
0.7051.3300283.910320e-08
0.7052821.3300223.940389e-08
0.7061.3300064.016990e-08
0.7071.3299834.146460e-08
0.7073411.3299754.194554e-08
0.7081.329964.287540e-08
0.7091.3299384.434650e-08
0.7094061.3299294.501404e-08
0.711.3299154.599100e-08
0.7111.3298934.786630e-08
0.7114771.3298824.879025e-08
0.7121.3298714.980340e-08
0.7131.3298485.168900e-08
0.7135541.3298365.292547e-08
0.7141.3298265.392060e-08
0.7151.3298045.610130e-08
0.7156371.329795.774888e-08
0.7161.3297825.868680e-08
0.7171.329766.162160e-08
0.7177261.3297446.375949e-08
0.7181.3297386.456440e-08
0.7191.3297166.694300e-08
0.7198221.3296986.937387e-08
0.721.3296946.990090e-08
0.7211.3296727.286670e-08
0.7219231.3296527.614289e-08
0.7221.3296517.641510e-08
0.7231.3296297.939760e-08
0.7241.3296078.354040e-08
0.7240311.3296078.365086e-08
0.7251.3295868.711740e-08
0.7261.3295649.128170e-08
0.7261451.3295619.188560e-08
0.7271.3295439.545720e-08
0.7281.3295211.008020e-07
0.7282651.3295161.022200e-07
0.7291.32951.061620e-07
0.731.3294791.115360e-07
0.7303911.3294711.140952e-07
0.7311.3294581.180870e-07
0.7321.3294361.240740e-07
0.7325231.3294251.275183e-07
0.7331.3294151.306600e-07
0.7341.3293941.366790e-07
0.7346621.329381.398973e-07
0.7351.3293731.415440e-07
0.7361.3293521.464230e-07
0.7368061.3293351.494200e-07
0.7371.3293311.501400e-07
0.7381.329311.532810e-07
0.7389571.3292911.557318e-07
0.7391.329291.558410e-07
0.741.3292691.578180e-07
0.7411.3292481.598000e-07
0.7411151.3292461.598924e-07
0.7421.3292281.606060e-07
0.7431.3292071.614140e-07
0.7432781.3292011.616391e-07
0.7441.3291861.622230e-07
0.7451.3291661.630340e-07
0.7454481.3291571.631322e-07
0.7461.3291451.632530e-07
0.7471.3291251.640660e-07
0.7476251.3291121.642034e-07
0.7481.3291051.642860e-07
0.7491.3290841.645060e-07
0.7498071.3290681.646828e-07
0.751.3290641.647250e-07
0.7511.3290441.649450e-07
0.7519961.3290241.657598e-07
0.7521.3290241.657630e-07
0.7531.3290031.659830e-07
0.7541.3289831.662040e-07
0.7541921.328981.662461e-07
0.7551.3289631.664240e-07
0.7561.3289431.666450e-07
0.7563931.3289351.667315e-07
0.7571.3289231.668650e-07
0.7581.3289031.670860e-07
0.7586021.3288921.672183e-07
0.7591.3288841.673060e-07
0.761.3288641.669220e-07
0.7608161.3288481.671008e-07
0.7611.3288441.671410e-07
0.7621.3288241.673610e-07
0.7631.3288051.675810e-07
0.7630371.3288041.675665e-07
0.7641.3287851.671920e-07
0.7651.3287651.674110e-07
0.7652651.328761.673074e-07
0.7661.3287461.670200e-07
0.7671.3287261.672380e-07
0.7674991.3287171.670418e-07
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1.246251.3211111.120660e-05
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1.261.3208871.092920e-05
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1.311.320051.594970e-05
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1.31251.3200071.660680e-05
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1.319961.3198791.910429e-05
1.321.3198781.911770e-05
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1.323821.3198122.056993e-05
1.3251.3197912.108800e-05
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1.328751.3197262.273380e-05
1.331.3197052.339020e-05
1.331251.3196832.415380e-05
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1.33251.3196612.481270e-05
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1.3351.3196172.602780e-05
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1.338751.3195512.801850e-05
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1.391.3186260.000101764
1.391071.3186060.0001103988
1.391251.3186030.000111819
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1.41.3184390.000170455
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1.4651.3171730.000320598
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1.46751.3171220.000318809
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1.471.3170710.000317013
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1.47251.317020.000315208
1.473751.3169950.00031313
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1.478751.3168920.000305955
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1.481251.316840.000301758
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1.591.3144240.000103753
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1.596251.3142740.000100096
1.59751.3142449.928460e-05
1.598751.3142139.859900e-05
1.61.3141839.791210e-05

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
—