Axis Log x Log y

Click the plot to set the calculator wavelength.

At one wavelength

Refractive index n: 1.33295
Extinction coefficient k: 0

Permittivity ε₁: 1.77676
Permittivity ε₂: 0

Absorption coefficient α: 0 cm⁻¹
Penetration depth δ = λ/(2πk): — nm

Abbe number V_d: 45.608
Chromatic dispersion dn/dλ: -0.0388706 µm⁻¹

Group index n_g: 1.35579
Group velocity dispersion: 59.1111 fs²/mm

Dispersion parameter D: -322.482 ps/(nm·km)
Photon energy: 2.11001 eV

ε = (n + ik)², α = 4πk/λ, n_g = 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): Bashkatov and Genina 2003: Water; n 0.225–1.14 µm; 20 °C
h2o_d2o = ls.fetch_refractiveindex("main", "H2O", "Bashkatov", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(h2o_d2o.range_nm)  # (225, 1140) 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_fe50ef8e6e54/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/bashkatov-genina-2003).

# ... 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"]).

Materials guide Open a sphere of it in Studio Quick start Ask the community

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

Cauchy (formula 5), λ in µm

n = 1.31984 + 0.005190553 λ^{- 2.0} - 0.000256169 λ^{- 4.0} + 9.39388 \times 10^{-6} λ^{- 6.0}

Valid from 0.225 to 1.14 µm.

Coefficients as stored

C_i	Value
C1	1.31984
C2	0.005190553
C3	-2.0
C4	-0.000256169
C5	-4.0
C6	9.39388e-06
C7	-6.0

Comments and conditions

High-performance liquid chromatography (HPLC) distilled water at 20.0 °C.

There are typesetting errors in the original paper: In Table 2, the coefficient C must be multiplied by 10⁸ (not 10⁻⁸) and the coefficient D must be multiplied by 10¹². Additionally, Equation (7) must be multiplied by 10¹². With these corrections, and after converting the wavelength to µm, the following expressions can be used to calculate the coefficients of the dispersion formula at any temperature in the 0–100 °C range:

A(t) = 1.3208 − 1.2325×10⁻⁵·t − 1.8674×10⁻⁶·t² + 5.0233×10⁻⁹·t³
B(t) = 5.2082413×10⁻³ − 5.179×10⁻⁷·t − 2.284×10⁻⁸·t² + 6.9608×10⁻¹¹·t³
C(t) = −2.5551×10⁻⁴ − 1.8341336×10⁻⁸·t − 9.172319×10⁻¹⁰·t² + 2.7729×10⁻¹²·t³
D(t) = 9.3495×10⁻⁶ + 1.7855×10⁻³·t + 3.6733×10⁻¹·t² − 1.2932×10¹·t³

Conditions

temperature: 293.15 K

References

A. N. Bashkatov and E. A. Genina. Water refractive index in dependence on temperature and wavelength: a simple approximation. Proc. SPIE 5068, 393-395 (2003)

doi:10.1117/12.518857 <title>Water refractive index in dependence on temperature and wavelength: a simple approximation</title>, SPIE Proceedings (2003)

Cite

Alexey N. Bashkatov and Elina A. Genina. <title>Water refractive index in dependence on temperature and wavelength: a simple approximation</title>. SPIE Proceedings, 393-395 (2003), doi:10.1117/12.518857; 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

CSV comma separated TXT tab separated YAML n, k Full database record original YAML All quantities CSV JSON metadata

H2O, D2O (Water, heavy water, ice), Bashkatov and Genina 2003: Water; n 0.225–1.14 µm; 20 °C: n and k versus wavelength
λ (µm)	n
0.225	1.394818
0.225917	1.393855
0.226838	1.392915
0.227762	1.391997
0.22869	1.3911
0.229622	1.390224
0.230558	1.389369
0.231497	1.388533
0.232441	1.387716
0.233388	1.386918
0.234339	1.386138
0.235294	1.385376
0.236253	1.384631
0.237216	1.383902
0.238182	1.383189
0.239153	1.382492
0.240128	1.38181
0.241106	1.381143
0.242089	1.38049
0.243075	1.379851
0.244066	1.379226
0.24506	1.378614
0.246059	1.378014
0.247062	1.377427
0.248069	1.376852
0.24908	1.376288
0.250095	1.375736
0.251114	1.375195
0.252137	1.374665
0.253165	1.374145
0.254196	1.373635
0.255232	1.373135
0.256272	1.372644
0.257317	1.372163
0.258365	1.37169
0.259418	1.371227
0.260475	1.370772
0.261537	1.370325
0.262603	1.369886
0.263673	1.369455
0.264747	1.369032
0.265826	1.368615
0.266909	1.368206
0.267997	1.367804
0.269089	1.367409
0.270186	1.36702
0.271287	1.366638
0.272392	1.366262
0.273502	1.365891
0.274617	1.365527
0.275736	1.365168
0.27686	1.364815
0.277988	1.364467
0.279121	1.364125
0.280258	1.363787
0.2814	1.363454
0.282547	1.363126
0.283699	1.362803
0.284855	1.362485
0.286016	1.36217
0.287181	1.36186
0.288351	1.361555
0.289526	1.361253
0.290706	1.360955
0.291891	1.360661
0.29308	1.360371
0.294275	1.360084
0.295474	1.359801
0.296678	1.359522
0.297887	1.359245
0.299101	1.358972
0.30032	1.358703
0.301544	1.358436
0.302773	1.358172
0.304007	1.357911
0.305245	1.357654
0.306489	1.357398
0.307738	1.357146
0.308992	1.356896
0.310252	1.356649
0.311516	1.356405
0.312785	1.356162
0.31406	1.355923
0.31534	1.355685
0.316625	1.35545
0.317915	1.355217
0.319211	1.354987
0.320512	1.354758
0.321818	1.354532
0.323129	1.354307
0.324446	1.354085
0.325768	1.353864
0.327096	1.353645
0.328429	1.353429
0.329767	1.353214
0.331111	1.353
0.33246	1.352789
0.333815	1.352579
0.335175	1.352371
0.336541	1.352165
0.337913	1.35196
0.33929	1.351756
0.340673	1.351555
0.342061	1.351354
0.343455	1.351155
0.344854	1.350958
0.34626	1.350762
0.347671	1.350568
0.349088	1.350375
0.35051	1.350183
0.351939	1.349992
0.353373	1.349803
0.354813	1.349615
0.356259	1.349428
0.357711	1.349243
0.359168	1.349059
0.360632	1.348876
0.362102	1.348694
0.363577	1.348513
0.365059	1.348333
0.366547	1.348155
0.36804	1.347978
0.36954	1.347801
0.371046	1.347626
0.372558	1.347452
0.374076	1.347279
0.375601	1.347107
0.377131	1.346936
0.378668	1.346766
0.380211	1.346597
0.381761	1.346429
0.383317	1.346262
0.384879	1.346096
0.386447	1.345931
0.388022	1.345767
0.389603	1.345603
0.391191	1.345441
0.392785	1.345279
0.394386	1.345119
0.395993	1.344959
0.397607	1.3448
0.399227	1.344643
0.400854	1.344486
0.402487	1.344329
0.404127	1.344174
0.405774	1.34402
0.407428	1.343866
0.409088	1.343713
0.410755	1.343561
0.412429	1.34341
0.41411	1.34326
0.415798	1.34311
0.417492	1.342961
0.419193	1.342813
0.420902	1.342666
0.422617	1.34252
0.424339	1.342374
0.426068	1.34223
0.427805	1.342086
0.429548	1.341942
0.431298	1.3418
0.433056	1.341658
0.434821	1.341517
0.436593	1.341377
0.438372	1.341237
0.440158	1.341098
0.441952	1.34096
0.443753	1.340823
0.445562	1.340686
0.447377	1.340551
0.4492	1.340415
0.451031	1.340281
0.452869	1.340147
0.454715	1.340014
0.456568	1.339882
0.458428	1.33975
0.460296	1.33962
0.462172	1.339489
0.464056	1.33936
0.465947	1.339231
0.467845	1.339103
0.469752	1.338976
0.471666	1.338849
0.473588	1.338723
0.475518	1.338597
0.477456	1.338473
0.479402	1.338349
0.481355	1.338225
0.483317	1.338103
0.485287	1.337981
0.487264	1.337859
0.48925	1.337739
0.491244	1.337619
0.493246	1.337499
0.495256	1.33738
0.497274	1.337262
0.4993	1.337145
0.501335	1.337028
0.503378	1.336912
0.505429	1.336797
0.507489	1.336682
0.509557	1.336568
0.511634	1.336454
0.513719	1.336341
0.515812	1.336229
0.517914	1.336117
0.520025	1.336006
0.522144	1.335896
0.524272	1.335786
0.526408	1.335677
0.528554	1.335568
0.530708	1.33546
0.53287	1.335353
0.535042	1.335246
0.537222	1.33514
0.539411	1.335035
0.54161	1.33493
0.543817	1.334825
0.546033	1.334722
0.548258	1.334619
0.550492	1.334516
0.552736	1.334414
0.554988	1.334313
0.55725	1.334212
0.559521	1.334112
0.561801	1.334013
0.56409	1.333914
0.566389	1.333816
0.568697	1.333718
0.571015	1.333621
0.573342	1.333524
0.575678	1.333428
0.578024	1.333332
0.58038	1.333238
0.582745	1.333143
0.585119	1.333049
0.587504	1.332956
0.589898	1.332864
0.592302	1.332772
0.594716	1.33268
0.597139	1.332589
0.599573	1.332499
0.602016	1.332409
0.604469	1.33232
0.606933	1.332231
0.609406	1.332143
0.611889	1.332055
0.614383	1.331968
0.616887	1.331881
0.619401	1.331795
0.621925	1.33171
0.624459	1.331625
0.627004	1.33154
0.629559	1.331456
0.632125	1.331373
0.634701	1.33129
0.637287	1.331208
0.639884	1.331126
0.642492	1.331044
0.64511	1.330964
0.647739	1.330883
0.650379	1.330803
0.653029	1.330724
0.65569	1.330645
0.658362	1.330567
0.661045	1.330489
0.663739	1.330412
0.666444	1.330335
0.66916	1.330259
0.671887	1.330183
0.674625	1.330108
0.677374	1.330033
0.680134	1.329959
0.682906	1.329885
0.685689	1.329811
0.688483	1.329738
0.691289	1.329666
0.694106	1.329594
0.696935	1.329523
0.699775	1.329451
0.702626	1.329381
0.70549	1.329311
0.708365	1.329241
0.711251	1.329172
0.71415	1.329103
0.71706	1.329035
0.719982	1.328967
0.722916	1.3289
0.725862	1.328833
0.72882	1.328767
0.73179	1.328701
0.734773	1.328635
0.737767	1.32857
0.740773	1.328505
0.743792	1.328441
0.746823	1.328377
0.749867	1.328314
0.752922	1.328251
0.755991	1.328188
0.759072	1.328126
0.762165	1.328064
0.765271	1.328003
0.768389	1.327942
0.771521	1.327882
0.774665	1.327822
0.777822	1.327762
0.780991	1.327703
0.784174	1.327644
0.78737	1.327585
0.790578	1.327527
0.7938	1.32747
0.797035	1.327413
0.800283	1.327356
0.803544	1.327299
0.806819	1.327243
0.810107	1.327188
0.813408	1.327132
0.816723	1.327077
0.820051	1.327023
0.823393	1.326969
0.826748	1.326915
0.830118	1.326862
0.8335	1.326809
0.836897	1.326756
0.840308	1.326704
0.843732	1.326652
0.84717	1.3266
0.850623	1.326549
0.854089	1.326498
0.85757	1.326448
0.861064	1.326398
0.864573	1.326348
0.868097	1.326299
0.871634	1.32625
0.875186	1.326201
0.878753	1.326153
0.882334	1.326105
0.885929	1.326057
0.88954	1.32601
0.893165	1.325963
0.896805	1.325916
0.900459	1.32587
0.904129	1.325824
0.907813	1.325778
0.911513	1.325733
0.915227	1.325688
0.918957	1.325643
0.922702	1.325598
0.926462	1.325554
0.930237	1.325511
0.934028	1.325467
0.937835	1.325424
0.941656	1.325381
0.945494	1.325339
0.949347	1.325297
0.953216	1.325255
0.9571	1.325213
0.961	1.325172
0.964917	1.325131
0.968849	1.32509
0.972797	1.32505
0.976761	1.32501
0.980742	1.32497
0.984738	1.324931
0.988751	1.324891
0.992781	1.324852
0.996826	1.324814
1.00089	1.324775
1.00497	1.324737
1.00906	1.3247
1.01317	1.324662
1.0173	1.324625
1.02145	1.324588
1.02561	1.324551
1.02979	1.324515
1.03399	1.324479
1.0382	1.324443
1.04243	1.324407
1.04668	1.324372
1.05095	1.324336
1.05523	1.324302
1.05953	1.324267
1.06385	1.324233
1.06818	1.324199
1.07254	1.324165
1.07691	1.324131
1.08129	1.324098
1.0857	1.324065
1.09013	1.324032
1.09457	1.323999
1.09903	1.323967
1.10351	1.323935
1.108	1.323903
1.11252	1.323871
1.11705	1.32384
1.12161	1.323809
1.12618	1.323778
1.13077	1.323747
1.13537	1.323717
1.14	1.323687

Optical transmission calculator

Free-standing sample in vacuum, normal incidence

Transmittance T: —
Reflectance R: —

Fresnel reflection calculator

R_p: —
R_s: —
R = (R_p+R_s)/2: —
Phase φ_p: —
Phase φ_s: —
Brewster angle θ_B: —
Critical angle θ_C: —

Plot