Optical constants
Refractive index of H2O, D2O (Water, heavy water, ice)
Daimon and Masumura 2007: Water; n 0.18–1.13 µm; 19.0 °C
- Data
- formula 2
- Range
- 0.182–1.129 µm
- Temperature
- 292.15 K
- State
- liquid
- Licence
- CC0-1.0
Plot
Click the plot to set the calculator wavelength.
At one wavelength
- Refractive index n
- 1.33349
- Extinction coefficient k
- 0
- Permittivity ε1
- 1.7782
- Permittivity ε2
- 0
- Absorption coefficient α
- 0 cm⁻¹
- Penetration depth δ = λ/(2πk)
- — nm
- Abbe number Vd
- 55.746
- Chromatic dispersion dn/dλ
- -0.0313526 µm⁻¹
- Group index ng
- 1.35191
- Group velocity dispersion
- 47.2869 fs²/mm
- Dispersion parameter D
- -257.975 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; 19.0 °C
h2o_d2o = ls.fetch_refractiveindex("main", "H2O", "Daimon-19.0C", 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_8bf4d95d4f4d/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-2007-19-0c).
# ... 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_8bf4d95d4f4d/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 | 0.5672526103 |
| C3 | 0.005085550461 |
| C4 | 0.1736581125 |
| C5 | 0.01814938654 |
| C6 | 0.02121531502 |
| C7 | 0.02617260739 |
| C8 | 0.1138493213 |
| C9 | 10.73888649 |
Comments and conditions
Conditions
- temperature
- 292.15 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 | 1.467997 |
| 0.182834 | 1.465046 |
| 0.183673 | 1.462221 |
| 0.184515 | 1.459512 |
| 0.185361 | 1.456909 |
| 0.18621 | 1.454405 |
| 0.187064 | 1.451993 |
| 0.187922 | 1.449667 |
| 0.188783 | 1.447421 |
| 0.189649 | 1.44525 |
| 0.190518 | 1.44315 |
| 0.191392 | 1.441117 |
| 0.192269 | 1.439146 |
| 0.193151 | 1.437235 |
| 0.194036 | 1.43538 |
| 0.194926 | 1.433578 |
| 0.195819 | 1.431828 |
| 0.196717 | 1.430125 |
| 0.197619 | 1.428468 |
| 0.198525 | 1.426855 |
| 0.199435 | 1.425284 |
| 0.20035 | 1.423753 |
| 0.201268 | 1.42226 |
| 0.202191 | 1.420804 |
| 0.203118 | 1.419383 |
| 0.204049 | 1.417996 |
| 0.204984 | 1.416641 |
| 0.205924 | 1.415318 |
| 0.206868 | 1.414024 |
| 0.207817 | 1.41276 |
| 0.20877 | 1.411523 |
| 0.209727 | 1.410313 |
| 0.210688 | 1.409129 |
| 0.211654 | 1.40797 |
| 0.212624 | 1.406835 |
| 0.213599 | 1.405724 |
| 0.214578 | 1.404635 |
| 0.215562 | 1.403568 |
| 0.216551 | 1.402523 |
| 0.217543 | 1.401498 |
| 0.218541 | 1.400493 |
| 0.219543 | 1.399507 |
| 0.220549 | 1.39854 |
| 0.22156 | 1.397591 |
| 0.222576 | 1.39666 |
| 0.223596 | 1.395746 |
| 0.224622 | 1.394848 |
| 0.225651 | 1.393967 |
| 0.226686 | 1.393102 |
| 0.227725 | 1.392252 |
| 0.228769 | 1.391417 |
| 0.229818 | 1.390597 |
| 0.230872 | 1.38979 |
| 0.23193 | 1.388998 |
| 0.232993 | 1.388219 |
| 0.234062 | 1.387453 |
| 0.235135 | 1.386699 |
| 0.236213 | 1.385959 |
| 0.237296 | 1.38523 |
| 0.238384 | 1.384514 |
| 0.239476 | 1.383808 |
| 0.240574 | 1.383115 |
| 0.241677 | 1.382432 |
| 0.242785 | 1.38176 |
| 0.243898 | 1.381099 |
| 0.245017 | 1.380448 |
| 0.24614 | 1.379807 |
| 0.247268 | 1.379176 |
| 0.248402 | 1.378554 |
| 0.249541 | 1.377942 |
| 0.250685 | 1.37734 |
| 0.251834 | 1.376746 |
| 0.252989 | 1.376161 |
| 0.254148 | 1.375585 |
| 0.255314 | 1.375017 |
| 0.256484 | 1.374458 |
| 0.25766 | 1.373906 |
| 0.258841 | 1.373363 |
| 0.260028 | 1.372828 |
| 0.26122 | 1.3723 |
| 0.262418 | 1.371779 |
| 0.263621 | 1.371266 |
| 0.264829 | 1.370761 |
| 0.266044 | 1.370262 |
| 0.267263 | 1.36977 |
| 0.268489 | 1.369285 |
| 0.269719 | 1.368807 |
| 0.270956 | 1.368335 |
| 0.272198 | 1.36787 |
| 0.273446 | 1.36741 |
| 0.2747 | 1.366958 |
| 0.275959 | 1.366511 |
| 0.277224 | 1.36607 |
| 0.278495 | 1.365635 |
| 0.279772 | 1.365206 |
| 0.281055 | 1.364782 |
| 0.282343 | 1.364364 |
| 0.283638 | 1.363952 |
| 0.284938 | 1.363544 |
| 0.286244 | 1.363142 |
| 0.287557 | 1.362746 |
| 0.288875 | 1.362354 |
| 0.2902 | 1.361967 |
| 0.29153 | 1.361586 |
| 0.292867 | 1.361209 |
| 0.294209 | 1.360837 |
| 0.295558 | 1.360469 |
| 0.296913 | 1.360106 |
| 0.298274 | 1.359748 |
| 0.299642 | 1.359394 |
| 0.301016 | 1.359044 |
| 0.302396 | 1.358699 |
| 0.303782 | 1.358358 |
| 0.305175 | 1.358021 |
| 0.306574 | 1.357688 |
| 0.307979 | 1.357359 |
| 0.309391 | 1.357035 |
| 0.31081 | 1.356714 |
| 0.312235 | 1.356397 |
| 0.313666 | 1.356084 |
| 0.315104 | 1.355774 |
| 0.316549 | 1.355468 |
| 0.318 | 1.355166 |
| 0.319458 | 1.354867 |
| 0.320923 | 1.354572 |
| 0.322394 | 1.35428 |
| 0.323872 | 1.353992 |
| 0.325357 | 1.353707 |
| 0.326848 | 1.353426 |
| 0.328347 | 1.353147 |
| 0.329852 | 1.352872 |
| 0.331364 | 1.3526 |
| 0.332884 | 1.352331 |
| 0.33441 | 1.352065 |
| 0.335943 | 1.351802 |
| 0.337483 | 1.351542 |
| 0.33903 | 1.351285 |
| 0.340585 | 1.351031 |
| 0.342146 | 1.35078 |
| 0.343715 | 1.350531 |
| 0.34529 | 1.350286 |
| 0.346873 | 1.350043 |
| 0.348464 | 1.349802 |
| 0.350061 | 1.349565 |
| 0.351666 | 1.34933 |
| 0.353278 | 1.349097 |
| 0.354898 | 1.348868 |
| 0.356525 | 1.34864 |
| 0.35816 | 1.348415 |
| 0.359802 | 1.348193 |
| 0.361451 | 1.347973 |
| 0.363108 | 1.347755 |
| 0.364773 | 1.34754 |
| 0.366445 | 1.347326 |
| 0.368125 | 1.347116 |
| 0.369813 | 1.346907 |
| 0.371509 | 1.346701 |
| 0.373212 | 1.346497 |
| 0.374923 | 1.346295 |
| 0.376642 | 1.346095 |
| 0.378369 | 1.345897 |
| 0.380103 | 1.345701 |
| 0.381846 | 1.345507 |
| 0.383596 | 1.345316 |
| 0.385355 | 1.345126 |
| 0.387122 | 1.344938 |
| 0.388897 | 1.344752 |
| 0.39068 | 1.344568 |
| 0.392471 | 1.344386 |
| 0.39427 | 1.344206 |
| 0.396078 | 1.344028 |
| 0.397893 | 1.343851 |
| 0.399718 | 1.343676 |
| 0.40155 | 1.343503 |
| 0.403391 | 1.343332 |
| 0.405241 | 1.343162 |
| 0.407098 | 1.342995 |
| 0.408965 | 1.342828 |
| 0.41084 | 1.342664 |
| 0.412723 | 1.342501 |
| 0.414615 | 1.34234 |
| 0.416516 | 1.34218 |
| 0.418426 | 1.342022 |
| 0.420344 | 1.341865 |
| 0.422271 | 1.34171 |
| 0.424207 | 1.341556 |
| 0.426152 | 1.341404 |
| 0.428106 | 1.341253 |
| 0.430069 | 1.341104 |
| 0.43204 | 1.340956 |
| 0.434021 | 1.34081 |
| 0.436011 | 1.340665 |
| 0.43801 | 1.340521 |
| 0.440018 | 1.340379 |
| 0.442035 | 1.340238 |
| 0.444062 | 1.340098 |
| 0.446098 | 1.33996 |
| 0.448143 | 1.339823 |
| 0.450197 | 1.339687 |
| 0.452261 | 1.339553 |
| 0.454335 | 1.339419 |
| 0.456418 | 1.339287 |
| 0.45851 | 1.339157 |
| 0.460612 | 1.339027 |
| 0.462724 | 1.338898 |
| 0.464845 | 1.338771 |
| 0.466977 | 1.338645 |
| 0.469117 | 1.33852 |
| 0.471268 | 1.338396 |
| 0.473429 | 1.338273 |
| 0.475599 | 1.338151 |
| 0.47778 | 1.338031 |
| 0.47997 | 1.337911 |
| 0.482171 | 1.337792 |
| 0.484381 | 1.337675 |
| 0.486602 | 1.337558 |
| 0.488833 | 1.337443 |
| 0.491074 | 1.337328 |
| 0.493325 | 1.337215 |
| 0.495587 | 1.337102 |
| 0.497859 | 1.336991 |
| 0.500142 | 1.33688 |
| 0.502434 | 1.33677 |
| 0.504738 | 1.336661 |
| 0.507052 | 1.336553 |
| 0.509377 | 1.336446 |
| 0.511712 | 1.33634 |
| 0.514058 | 1.336235 |
| 0.516415 | 1.33613 |
| 0.518782 | 1.336027 |
| 0.521161 | 1.335924 |
| 0.52355 | 1.335822 |
| 0.52595 | 1.335721 |
| 0.528362 | 1.335621 |
| 0.530784 | 1.335521 |
| 0.533217 | 1.335422 |
| 0.535662 | 1.335324 |
| 0.538118 | 1.335227 |
| 0.540585 | 1.335131 |
| 0.543063 | 1.335035 |
| 0.545553 | 1.33494 |
| 0.548054 | 1.334846 |
| 0.550567 | 1.334752 |
| 0.553091 | 1.334659 |
| 0.555626 | 1.334567 |
| 0.558174 | 1.334475 |
| 0.560733 | 1.334385 |
| 0.563304 | 1.334294 |
| 0.565886 | 1.334205 |
| 0.56848 | 1.334116 |
| 0.571087 | 1.334028 |
| 0.573705 | 1.33394 |
| 0.576335 | 1.333853 |
| 0.578977 | 1.333767 |
| 0.581632 | 1.333681 |
| 0.584298 | 1.333595 |
| 0.586977 | 1.333511 |
| 0.589668 | 1.333427 |
| 0.592372 | 1.333343 |
| 0.595087 | 1.33326 |
| 0.597816 | 1.333178 |
| 0.600556 | 1.333096 |
| 0.60331 | 1.333014 |
| 0.606076 | 1.332933 |
| 0.608854 | 1.332853 |
| 0.611646 | 1.332773 |
| 0.61445 | 1.332694 |
| 0.617267 | 1.332615 |
| 0.620097 | 1.332536 |
| 0.62294 | 1.332458 |
| 0.625796 | 1.332381 |
| 0.628665 | 1.332304 |
| 0.631547 | 1.332227 |
| 0.634442 | 1.332151 |
| 0.637351 | 1.332075 |
| 0.640273 | 1.332 |
| 0.643208 | 1.331925 |
| 0.646157 | 1.331851 |
| 0.64912 | 1.331776 |
| 0.652096 | 1.331703 |
| 0.655085 | 1.331629 |
| 0.658088 | 1.331556 |
| 0.661106 | 1.331484 |
| 0.664136 | 1.331412 |
| 0.667181 | 1.33134 |
| 0.67024 | 1.331268 |
| 0.673313 | 1.331197 |
| 0.6764 | 1.331126 |
| 0.679501 | 1.331056 |
| 0.682616 | 1.330985 |
| 0.685746 | 1.330915 |
| 0.688889 | 1.330846 |
| 0.692048 | 1.330777 |
| 0.69522 | 1.330708 |
| 0.698408 | 1.330639 |
| 0.70161 | 1.33057 |
| 0.704826 | 1.330502 |
| 0.708058 | 1.330434 |
| 0.711304 | 1.330366 |
| 0.714565 | 1.330299 |
| 0.717841 | 1.330232 |
| 0.721132 | 1.330165 |
| 0.724438 | 1.330098 |
| 0.727759 | 1.330032 |
| 0.731096 | 1.329965 |
| 0.734448 | 1.329899 |
| 0.737815 | 1.329833 |
| 0.741197 | 1.329768 |
| 0.744595 | 1.329702 |
| 0.748009 | 1.329637 |
| 0.751438 | 1.329572 |
| 0.754884 | 1.329507 |
| 0.758344 | 1.329442 |
| 0.761821 | 1.329377 |
| 0.765314 | 1.329313 |
| 0.768822 | 1.329248 |
| 0.772347 | 1.329184 |
| 0.775888 | 1.32912 |
| 0.779445 | 1.329056 |
| 0.783019 | 1.328992 |
| 0.786609 | 1.328928 |
| 0.790215 | 1.328865 |
| 0.793838 | 1.328801 |
| 0.797477 | 1.328738 |
| 0.801133 | 1.328674 |
| 0.804806 | 1.328611 |
| 0.808496 | 1.328548 |
| 0.812202 | 1.328485 |
| 0.815926 | 1.328421 |
| 0.819667 | 1.328358 |
| 0.823425 | 1.328295 |
| 0.8272 | 1.328232 |
| 0.830992 | 1.328169 |
| 0.834802 | 1.328106 |
| 0.838629 | 1.328043 |
| 0.842474 | 1.32798 |
| 0.846336 | 1.327918 |
| 0.850217 | 1.327855 |
| 0.854114 | 1.327792 |
| 0.85803 | 1.327729 |
| 0.861964 | 1.327666 |
| 0.865916 | 1.327603 |
| 0.869886 | 1.32754 |
| 0.873874 | 1.327476 |
| 0.87788 | 1.327413 |
| 0.881905 | 1.32735 |
| 0.885948 | 1.327287 |
| 0.89001 | 1.327223 |
| 0.89409 | 1.32716 |
| 0.898189 | 1.327097 |
| 0.902307 | 1.327033 |
| 0.906444 | 1.326969 |
| 0.910599 | 1.326905 |
| 0.914774 | 1.326841 |
| 0.918968 | 1.326777 |
| 0.923181 | 1.326713 |
| 0.927414 | 1.326649 |
| 0.931665 | 1.326584 |
| 0.935937 | 1.32652 |
| 0.940228 | 1.326455 |
| 0.944538 | 1.32639 |
| 0.948869 | 1.326325 |
| 0.953219 | 1.326259 |
| 0.957589 | 1.326194 |
| 0.961979 | 1.326128 |
| 0.966389 | 1.326062 |
| 0.97082 | 1.325996 |
| 0.975271 | 1.32593 |
| 0.979742 | 1.325863 |
| 0.984234 | 1.325796 |
| 0.988746 | 1.325729 |
| 0.993279 | 1.325662 |
| 0.997833 | 1.325595 |
| 1.00241 | 1.325527 |
| 1.007 | 1.325459 |
| 1.01162 | 1.32539 |
| 1.01626 | 1.325321 |
| 1.02092 | 1.325252 |
| 1.0256 | 1.325183 |
| 1.0303 | 1.325113 |
| 1.03502 | 1.325043 |
| 1.03977 | 1.324973 |
| 1.04454 | 1.324902 |
| 1.04932 | 1.324831 |
| 1.05413 | 1.32476 |
| 1.05897 | 1.324688 |
| 1.06382 | 1.324616 |
| 1.0687 | 1.324544 |
| 1.0736 | 1.324471 |
| 1.07852 | 1.324397 |
| 1.08347 | 1.324323 |
| 1.08843 | 1.324249 |
| 1.09342 | 1.324174 |
| 1.09844 | 1.324099 |
| 1.10347 | 1.324024 |
| 1.10853 | 1.323948 |
| 1.11361 | 1.323871 |
| 1.11872 | 1.323794 |
| 1.12385 | 1.323716 |
| 1.129 | 1.323638 |
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 19.0 °C.