Optical constants
Refractive index of H2O, D2O (Water, heavy water, ice)
Daimon and Masumura 2007: Water; n 0.18–1.13 µm; 21.5 °C
- Data
- formula 2
- Range
- 0.182–1.129 µm
- Temperature
- 294.65 K
- State
- liquid
- Licence
- CC0-1.0
Plot
Click the plot to set the calculator wavelength.
At one wavelength
- Refractive index n
- 1.33326
- Extinction coefficient k
- 0
- Permittivity ε1
- 1.77759
- Permittivity ε2
- 0
- Absorption coefficient α
- 0 cm⁻¹
- Penetration depth δ = λ/(2πk)
- — nm
- Abbe number Vd
- 55.78
- Chromatic dispersion dn/dλ
- -0.0313079 µm⁻¹
- Group index ng
- 1.35166
- Group velocity dispersion
- 47.2817 fs²/mm
- Dispersion parameter D
- -257.947 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): Daimon and Masumura 2007: Water; n 0.18–1.13 µm; 21.5 °C
h2o_d2o = ls.fetch_refractiveindex("main", "H2O", "Daimon-21.5C", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(h2o_d2o.range_nm) # (182, 1129) nm
eps = h2o_d2o.eps([633]) # complex permittivity
Downloads the original record once (pinned to the imported snapshot) and caches it.
import json, urllib.request
import lightsmith as ls
url = "https://materials.lightsmith.dev/v1/datasets/ds_b976f784a0eb/lightsmith"
h2o_d2o = ls.Tabulated.model_validate(json.load(urllib.request.urlopen(url)))
print(h2o_d2o.source) # citation and provenance travel with the data
Any dataset here, as the library's Tabulated material (h2o/daimon-masumura-2007-21-5c).
# ... load h2o_d2o as above, then:
sim = ls.Simulation(
particles=[ls.Particle(shape=ls.Sphere(radius_nm=50), material=h2o_d2o)],
medium_index=1.0,
wavelengths=ls.WavelengthRange(start_nm=400, stop_nm=1000, num=81),
)
res = ls.solve(sim) # exact Mie for a sphere
print(res.q_ext) # extinction efficiency at each wavelength
Same spec runs with DDA, FDTD, BEM or T-matrix: ls.compare(sim, ["mie", "dda"]).
import json, urllib.request
import lightsmith as ls
url = "https://materials.lightsmith.dev/v1/datasets/ds_b976f784a0eb/lightsmith?model=drude_lorentz"
h2o_d2o_dl = ls.DrudeLorentz.model_validate(json.load(urllib.request.urlopen(url)))
A dispersive Drude–Lorentz model for time-domain solvers.
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 µmValid from 0.182 to 1.129 µm.
Coefficients as stored
| Ci | Value |
|---|---|
| C1 | 0.0 |
| C2 | 0.5689093832 |
| C3 | 0.005110301794 |
| C4 | 0.1719708856 |
| C5 | 0.01825180155 |
| C6 | 0.02062501582 |
| C7 | 0.02624158904 |
| C8 | 0.1123965424 |
| C9 | 10.67505178 |
Comments and conditions
Conditions
- temperature
- 294.65 K
References
- doi:10.1364/ao.46.003811 Measurement of the refractive index of distilled water from the near-infrared region to the ultraviolet region, Applied Optics (2007)
Cite
Masahiko Daimon and Akira Masumura. Measurement of the refractive index of distilled water from the near-infrared region to the ultraviolet region. Applied Optics, 46, 3811 (2007), doi:10.1364/ao.46.003811; 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| λ (µm) | n |
|---|---|
| 0.182 | 1.467865 |
| 0.182834 | 1.464904 |
| 0.183673 | 1.46207 |
| 0.184515 | 1.459352 |
| 0.185361 | 1.456741 |
| 0.18621 | 1.454231 |
| 0.187064 | 1.451813 |
| 0.187922 | 1.449481 |
| 0.188783 | 1.44723 |
| 0.189649 | 1.445054 |
| 0.190518 | 1.44295 |
| 0.191392 | 1.440913 |
| 0.192269 | 1.438939 |
| 0.193151 | 1.437024 |
| 0.194036 | 1.435166 |
| 0.194926 | 1.433362 |
| 0.195819 | 1.431608 |
| 0.196717 | 1.429903 |
| 0.197619 | 1.428244 |
| 0.198525 | 1.426629 |
| 0.199435 | 1.425057 |
| 0.20035 | 1.423524 |
| 0.201268 | 1.422029 |
| 0.202191 | 1.420572 |
| 0.203118 | 1.419149 |
| 0.204049 | 1.417761 |
| 0.204984 | 1.416405 |
| 0.205924 | 1.41508 |
| 0.206868 | 1.413786 |
| 0.207817 | 1.41252 |
| 0.20877 | 1.411282 |
| 0.209727 | 1.410072 |
| 0.210688 | 1.408887 |
| 0.211654 | 1.407727 |
| 0.212624 | 1.406592 |
| 0.213599 | 1.40548 |
| 0.214578 | 1.40439 |
| 0.215562 | 1.403323 |
| 0.216551 | 1.402277 |
| 0.217543 | 1.401251 |
| 0.218541 | 1.400246 |
| 0.219543 | 1.39926 |
| 0.220549 | 1.398292 |
| 0.22156 | 1.397343 |
| 0.222576 | 1.396412 |
| 0.223596 | 1.395497 |
| 0.224622 | 1.3946 |
| 0.225651 | 1.393718 |
| 0.226686 | 1.392853 |
| 0.227725 | 1.392003 |
| 0.228769 | 1.391167 |
| 0.229818 | 1.390347 |
| 0.230872 | 1.38954 |
| 0.23193 | 1.388748 |
| 0.232993 | 1.387968 |
| 0.234062 | 1.387202 |
| 0.235135 | 1.386449 |
| 0.236213 | 1.385708 |
| 0.237296 | 1.38498 |
| 0.238384 | 1.384263 |
| 0.239476 | 1.383558 |
| 0.240574 | 1.382864 |
| 0.241677 | 1.382182 |
| 0.242785 | 1.38151 |
| 0.243898 | 1.380848 |
| 0.245017 | 1.380197 |
| 0.24614 | 1.379556 |
| 0.247268 | 1.378925 |
| 0.248402 | 1.378304 |
| 0.249541 | 1.377692 |
| 0.250685 | 1.377089 |
| 0.251834 | 1.376496 |
| 0.252989 | 1.375911 |
| 0.254148 | 1.375335 |
| 0.255314 | 1.374767 |
| 0.256484 | 1.374208 |
| 0.25766 | 1.373657 |
| 0.258841 | 1.373113 |
| 0.260028 | 1.372578 |
| 0.26122 | 1.37205 |
| 0.262418 | 1.37153 |
| 0.263621 | 1.371017 |
| 0.264829 | 1.370511 |
| 0.266044 | 1.370013 |
| 0.267263 | 1.369521 |
| 0.268489 | 1.369036 |
| 0.269719 | 1.368558 |
| 0.270956 | 1.368086 |
| 0.272198 | 1.367621 |
| 0.273446 | 1.367162 |
| 0.2747 | 1.366709 |
| 0.275959 | 1.366262 |
| 0.277224 | 1.365822 |
| 0.278495 | 1.365387 |
| 0.279772 | 1.364958 |
| 0.281055 | 1.364534 |
| 0.282343 | 1.364117 |
| 0.283638 | 1.363704 |
| 0.284938 | 1.363297 |
| 0.286244 | 1.362895 |
| 0.287557 | 1.362499 |
| 0.288875 | 1.362107 |
| 0.2902 | 1.36172 |
| 0.29153 | 1.361339 |
| 0.292867 | 1.360962 |
| 0.294209 | 1.36059 |
| 0.295558 | 1.360223 |
| 0.296913 | 1.35986 |
| 0.298274 | 1.359502 |
| 0.299642 | 1.359148 |
| 0.301016 | 1.358798 |
| 0.302396 | 1.358453 |
| 0.303782 | 1.358112 |
| 0.305175 | 1.357776 |
| 0.306574 | 1.357443 |
| 0.307979 | 1.357114 |
| 0.309391 | 1.35679 |
| 0.31081 | 1.356469 |
| 0.312235 | 1.356152 |
| 0.313666 | 1.355839 |
| 0.315104 | 1.35553 |
| 0.316549 | 1.355224 |
| 0.318 | 1.354922 |
| 0.319458 | 1.354623 |
| 0.320923 | 1.354328 |
| 0.322394 | 1.354037 |
| 0.323872 | 1.353748 |
| 0.325357 | 1.353464 |
| 0.326848 | 1.353182 |
| 0.328347 | 1.352904 |
| 0.329852 | 1.352629 |
| 0.331364 | 1.352357 |
| 0.332884 | 1.352088 |
| 0.33441 | 1.351822 |
| 0.335943 | 1.351559 |
| 0.337483 | 1.3513 |
| 0.33903 | 1.351043 |
| 0.340585 | 1.350789 |
| 0.342146 | 1.350538 |
| 0.343715 | 1.350289 |
| 0.34529 | 1.350044 |
| 0.346873 | 1.349801 |
| 0.348464 | 1.349561 |
| 0.350061 | 1.349323 |
| 0.351666 | 1.349089 |
| 0.353278 | 1.348856 |
| 0.354898 | 1.348626 |
| 0.356525 | 1.348399 |
| 0.35816 | 1.348174 |
| 0.359802 | 1.347952 |
| 0.361451 | 1.347732 |
| 0.363108 | 1.347515 |
| 0.364773 | 1.347299 |
| 0.366445 | 1.347086 |
| 0.368125 | 1.346876 |
| 0.369813 | 1.346667 |
| 0.371509 | 1.346461 |
| 0.373212 | 1.346257 |
| 0.374923 | 1.346055 |
| 0.376642 | 1.345855 |
| 0.378369 | 1.345657 |
| 0.380103 | 1.345462 |
| 0.381846 | 1.345268 |
| 0.383596 | 1.345077 |
| 0.385355 | 1.344887 |
| 0.387122 | 1.344699 |
| 0.388897 | 1.344514 |
| 0.39068 | 1.34433 |
| 0.392471 | 1.344148 |
| 0.39427 | 1.343968 |
| 0.396078 | 1.34379 |
| 0.397893 | 1.343613 |
| 0.399718 | 1.343438 |
| 0.40155 | 1.343266 |
| 0.403391 | 1.343094 |
| 0.405241 | 1.342925 |
| 0.407098 | 1.342757 |
| 0.408965 | 1.342591 |
| 0.41084 | 1.342427 |
| 0.412723 | 1.342264 |
| 0.414615 | 1.342103 |
| 0.416516 | 1.341943 |
| 0.418426 | 1.341785 |
| 0.420344 | 1.341628 |
| 0.422271 | 1.341473 |
| 0.424207 | 1.34132 |
| 0.426152 | 1.341168 |
| 0.428106 | 1.341017 |
| 0.430069 | 1.340868 |
| 0.43204 | 1.34072 |
| 0.434021 | 1.340574 |
| 0.436011 | 1.340429 |
| 0.43801 | 1.340286 |
| 0.440018 | 1.340143 |
| 0.442035 | 1.340003 |
| 0.444062 | 1.339863 |
| 0.446098 | 1.339725 |
| 0.448143 | 1.339588 |
| 0.450197 | 1.339452 |
| 0.452261 | 1.339318 |
| 0.454335 | 1.339185 |
| 0.456418 | 1.339053 |
| 0.45851 | 1.338922 |
| 0.460612 | 1.338792 |
| 0.462724 | 1.338664 |
| 0.464845 | 1.338537 |
| 0.466977 | 1.338411 |
| 0.469117 | 1.338286 |
| 0.471268 | 1.338162 |
| 0.473429 | 1.338039 |
| 0.475599 | 1.337918 |
| 0.47778 | 1.337797 |
| 0.47997 | 1.337678 |
| 0.482171 | 1.337559 |
| 0.484381 | 1.337442 |
| 0.486602 | 1.337325 |
| 0.488833 | 1.33721 |
| 0.491074 | 1.337095 |
| 0.493325 | 1.336982 |
| 0.495587 | 1.33687 |
| 0.497859 | 1.336758 |
| 0.500142 | 1.336647 |
| 0.502434 | 1.336538 |
| 0.504738 | 1.336429 |
| 0.507052 | 1.336321 |
| 0.509377 | 1.336214 |
| 0.511712 | 1.336108 |
| 0.514058 | 1.336003 |
| 0.516415 | 1.335899 |
| 0.518782 | 1.335795 |
| 0.521161 | 1.335693 |
| 0.52355 | 1.335591 |
| 0.52595 | 1.33549 |
| 0.528362 | 1.33539 |
| 0.530784 | 1.33529 |
| 0.533217 | 1.335192 |
| 0.535662 | 1.335094 |
| 0.538118 | 1.334997 |
| 0.540585 | 1.3349 |
| 0.543063 | 1.334805 |
| 0.545553 | 1.33471 |
| 0.548054 | 1.334615 |
| 0.550567 | 1.334522 |
| 0.553091 | 1.334429 |
| 0.555626 | 1.334337 |
| 0.558174 | 1.334246 |
| 0.560733 | 1.334155 |
| 0.563304 | 1.334065 |
| 0.565886 | 1.333976 |
| 0.56848 | 1.333887 |
| 0.571087 | 1.333799 |
| 0.573705 | 1.333711 |
| 0.576335 | 1.333624 |
| 0.578977 | 1.333538 |
| 0.581632 | 1.333452 |
| 0.584298 | 1.333367 |
| 0.586977 | 1.333282 |
| 0.589668 | 1.333198 |
| 0.592372 | 1.333115 |
| 0.595087 | 1.333032 |
| 0.597816 | 1.33295 |
| 0.600556 | 1.332868 |
| 0.60331 | 1.332787 |
| 0.606076 | 1.332706 |
| 0.608854 | 1.332626 |
| 0.611646 | 1.332546 |
| 0.61445 | 1.332467 |
| 0.617267 | 1.332388 |
| 0.620097 | 1.332309 |
| 0.62294 | 1.332232 |
| 0.625796 | 1.332154 |
| 0.628665 | 1.332077 |
| 0.631547 | 1.332001 |
| 0.634442 | 1.331925 |
| 0.637351 | 1.331849 |
| 0.640273 | 1.331774 |
| 0.643208 | 1.331699 |
| 0.646157 | 1.331625 |
| 0.64912 | 1.331551 |
| 0.652096 | 1.331477 |
| 0.655085 | 1.331404 |
| 0.658088 | 1.331331 |
| 0.661106 | 1.331259 |
| 0.664136 | 1.331187 |
| 0.667181 | 1.331115 |
| 0.67024 | 1.331043 |
| 0.673313 | 1.330972 |
| 0.6764 | 1.330902 |
| 0.679501 | 1.330831 |
| 0.682616 | 1.330761 |
| 0.685746 | 1.330691 |
| 0.688889 | 1.330622 |
| 0.692048 | 1.330553 |
| 0.69522 | 1.330484 |
| 0.698408 | 1.330415 |
| 0.70161 | 1.330347 |
| 0.704826 | 1.330279 |
| 0.708058 | 1.330211 |
| 0.711304 | 1.330144 |
| 0.714565 | 1.330076 |
| 0.717841 | 1.330009 |
| 0.721132 | 1.329942 |
| 0.724438 | 1.329876 |
| 0.727759 | 1.32981 |
| 0.731096 | 1.329743 |
| 0.734448 | 1.329677 |
| 0.737815 | 1.329612 |
| 0.741197 | 1.329546 |
| 0.744595 | 1.329481 |
| 0.748009 | 1.329416 |
| 0.751438 | 1.329351 |
| 0.754884 | 1.329286 |
| 0.758344 | 1.329221 |
| 0.761821 | 1.329157 |
| 0.765314 | 1.329092 |
| 0.768822 | 1.329028 |
| 0.772347 | 1.328964 |
| 0.775888 | 1.3289 |
| 0.779445 | 1.328836 |
| 0.783019 | 1.328773 |
| 0.786609 | 1.328709 |
| 0.790215 | 1.328646 |
| 0.793838 | 1.328582 |
| 0.797477 | 1.328519 |
| 0.801133 | 1.328456 |
| 0.804806 | 1.328393 |
| 0.808496 | 1.328329 |
| 0.812202 | 1.328266 |
| 0.815926 | 1.328203 |
| 0.819667 | 1.328141 |
| 0.823425 | 1.328078 |
| 0.8272 | 1.328015 |
| 0.830992 | 1.327952 |
| 0.834802 | 1.327889 |
| 0.838629 | 1.327827 |
| 0.842474 | 1.327764 |
| 0.846336 | 1.327701 |
| 0.850217 | 1.327638 |
| 0.854114 | 1.327576 |
| 0.85803 | 1.327513 |
| 0.861964 | 1.32745 |
| 0.865916 | 1.327387 |
| 0.869886 | 1.327324 |
| 0.873874 | 1.327261 |
| 0.87788 | 1.327198 |
| 0.881905 | 1.327135 |
| 0.885948 | 1.327072 |
| 0.89001 | 1.327009 |
| 0.89409 | 1.326946 |
| 0.898189 | 1.326883 |
| 0.902307 | 1.326819 |
| 0.906444 | 1.326756 |
| 0.910599 | 1.326692 |
| 0.914774 | 1.326628 |
| 0.918968 | 1.326565 |
| 0.923181 | 1.326501 |
| 0.927414 | 1.326436 |
| 0.931665 | 1.326372 |
| 0.935937 | 1.326308 |
| 0.940228 | 1.326243 |
| 0.944538 | 1.326179 |
| 0.948869 | 1.326114 |
| 0.953219 | 1.326049 |
| 0.957589 | 1.325983 |
| 0.961979 | 1.325918 |
| 0.966389 | 1.325852 |
| 0.97082 | 1.325786 |
| 0.975271 | 1.32572 |
| 0.979742 | 1.325654 |
| 0.984234 | 1.325587 |
| 0.988746 | 1.32552 |
| 0.993279 | 1.325453 |
| 0.997833 | 1.325386 |
| 1.00241 | 1.325318 |
| 1.007 | 1.325251 |
| 1.01162 | 1.325182 |
| 1.01626 | 1.325114 |
| 1.02092 | 1.325045 |
| 1.0256 | 1.324976 |
| 1.0303 | 1.324907 |
| 1.03502 | 1.324837 |
| 1.03977 | 1.324767 |
| 1.04454 | 1.324697 |
| 1.04932 | 1.324626 |
| 1.05413 | 1.324555 |
| 1.05897 | 1.324483 |
| 1.06382 | 1.324411 |
| 1.0687 | 1.324339 |
| 1.0736 | 1.324266 |
| 1.07852 | 1.324193 |
| 1.08347 | 1.32412 |
| 1.08843 | 1.324046 |
| 1.09342 | 1.323972 |
| 1.09844 | 1.323897 |
| 1.10347 | 1.323821 |
| 1.10853 | 1.323746 |
| 1.11361 | 1.323669 |
| 1.11872 | 1.323593 |
| 1.12385 | 1.323515 |
| 1.129 | 1.323438 |
Optical transmission calculator
Free-standing sample in vacuum, normal incidence- Transmittance T
- —
- Reflectance R
- —
Fresnel reflection calculator
- Rp
- —
- Rs
- —
- R = (Rp+Rs)/2
- —
- Phase φp
- —
- Phase φs
- —
- Brewster angle θB
- —
- Critical angle θC
- —
High performance liquid chromatography (HPLC) distilled water at 21.5 °C.