Axis Log x Log y

Click the plot to set the calculator wavelength.

At one wavelength

Refractive index n: 1.30977
Extinction coefficient k: 4.67840e-09

Permittivity ε₁: 1.7155
Permittivity ε₂: 1.22553e-08

Absorption coefficient α: 0.00100052 cm⁻¹
Penetration depth δ = λ/(2πk): 1.99896e+10 nm

Abbe number V_d: —
Chromatic dispersion dn/dλ: -0.03 µm⁻¹

Group index n_g: 1.3274
Group velocity dispersion: — fs²/mm

Dispersion parameter D: — 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): Warren 1984: Ice; n,k 0.00443–167 µm
h2o_d2o = ls.fetch_refractiveindex("main", "H2O", "Warren-1984", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(h2o_d2o.range_nm)  # (44.3, 167000) 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_189e7ac1f99f/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/warren-1984).

# ... 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.

Comments and conditions

Water ice (solid H₂O) at -7 °C

Conditions

temperature: 266.15 K

References

S. G. Warren. Optical constants of ice from the ultraviolet to the microwave. Appl. Opt. 23, 1206-1225 (1984)

doi:10.1364/ao.23.001206 Optical constants of ice from the ultraviolet to the microwave, Applied Optics (1984)

Cite

Stephen G. Warren. Optical constants of ice from the ultraviolet to the microwave. Applied Optics, 23, 1206 (1984), doi:10.1364/ao.23.001206; Data from the refractiveindex.info database (M. N. Polyanskiy, Sci. Data 11, 94 (2024), doi:10.1038/s41597-023-02898-2)

Data

468 rows as published

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), Warren 1984: Ice; n,k 0.00443–167 µm: n and k versus wavelength
λ (µm)	n	k
0.0443	0.8344	0.164
0.0451	0.8368	0.173
0.0459	0.8373	0.183
0.0468	0.8377	0.195
0.0477	0.8383	0.208
0.0486	0.8404	0.223
0.0496	0.8472	0.24
0.0506	0.8552	0.25
0.0517	0.8605	0.259
0.0528	0.8625	0.268
0.0539	0.8616	0.279
0.0551	0.8609	0.297
0.0564	0.8642	0.319
0.0577	0.8692	0.34
0.059	0.8776	0.366
0.0605	0.893	0.392
0.062	0.9104	0.416
0.0636	0.9309	0.44
0.0653	0.9537	0.464
0.067	0.9819	0.492
0.0689	1.0233	0.517
0.0708	1.0673	0.528
0.0729	1.112	0.533
0.0738	1.1313	0.534
0.0751	1.1575	0.531
0.0775	1.2004	0.524
0.08	1.2384	0.51
0.0827	1.2732	0.5
0.0855	1.3216	0.499
0.0886	1.3896	0.468
0.0918	1.4164	0.38
0.093	1.4091	0.36
0.0954	1.4006	0.339
0.0992	1.4017	0.318
0.1033	1.4093	0.291
0.1078	1.4022	0.251
0.11	1.3924	0.244
0.1127	1.3842	0.239
0.114	1.3807	0.239
0.1181	1.3819	0.244
0.121	1.3963	0.247
0.124	1.4092	0.224
0.1272	1.4026	0.195
0.1295	1.3801	0.174
0.1305	1.363	0.172
0.1319	1.3414	0.18
0.1333	1.3238	0.194
0.1348	1.306	0.213
0.1362	1.2905	0.243
0.137	1.2889	0.271
0.1378	1.2893	0.289
0.1387	1.3019	0.334
0.1393	1.3203	0.344
0.1409	1.363	0.382
0.1425	1.4187	0.401
0.1435	1.4583	0.4065
0.1442	1.4903	0.405
0.145	1.5213	0.389
0.1459	1.5538	0.377
0.1468	1.5778	0.345
0.1476	1.5964	0.332
0.148	1.6065	0.315
0.1485	1.6117	0.298
0.1494	1.6192	0.274
0.1512	1.6252	0.228
0.1531	1.634	0.198
0.154	1.6369	0.172
0.155	1.6383	0.156
0.1569	1.6372	0.11
0.158	1.6323	0.083
0.1589	1.6222	0.058
0.161	1.5827	0.022
0.1625	1.5564	0.01
0.1648	1.5245	0.003
0.1669	1.5032	0.001
0.1692	1.485	0.0003
0.1713	1.4723	0.00011
0.1737	1.4599	3e-05
0.1757	1.4511	1e-05
0.1779	1.4427	3e-06
0.1802	1.435	1e-06
0.1809	1.4328	7e-07
0.1821	1.4292	4e-07
0.1833	1.426	2e-07
0.1843	1.4232	1e-07
0.185	1.4214	6.377e-08
0.186	1.419	3.75e-08
0.187	1.4166	2.8e-08
0.188	1.4143	2.4e-08
0.189	1.4122	2.2e-08
0.19	1.4101	1.9e-08
0.191	1.4081	1.75e-08
0.193	1.4042	1.64e-08
0.195	1.4007	1.59e-08
0.21	1.38	1.325e-08
0.25	1.3509	8.623e-09
0.3	1.3339	5.504e-09
0.35	1.3249	3.765e-09
0.4	1.3194	2.71e-09
0.41	1.3185	2.51e-09
0.42	1.3177	2.26e-09
0.43	1.317	2.08e-09
0.44	1.3163	1.91e-09
0.45	1.3157	1.54e-09
0.46	1.3151	1.53e-09
0.47	1.3145	1.55e-09
0.48	1.314	1.64e-09
0.49	1.3135	1.78e-09
0.5	1.313	1.91e-09
0.51	1.3126	2.14e-09
0.52	1.3122	2.26e-09
0.53	1.3118	2.54e-09
0.54	1.3114	2.93e-09
0.55	1.311	3.11e-09
0.56	1.3106	3.29e-09
0.57	1.3103	3.52e-09
0.58	1.31	4.04e-09
0.59	1.3097	4.88e-09
0.6	1.3094	5.73e-09
0.61	1.3091	6.89e-09
0.62	1.3088	8.58e-09
0.63	1.3085	1.04e-08
0.64	1.3083	1.22e-08
0.65	1.308	1.43e-08
0.66	1.3078	1.66e-08
0.67	1.3076	1.89e-08
0.68	1.3073	2.09e-08
0.69	1.3071	2.4e-08
0.7	1.3069	2.9e-08
0.71	1.3067	3.44e-08
0.72	1.3065	4.03e-08
0.73	1.3062	4.3e-08
0.74	1.306	4.92e-08
0.75	1.3058	5.87e-08
0.76	1.3057	7.08e-08
0.77	1.3055	8.58e-08
0.78	1.3053	1.02e-07
0.79	1.3051	1.18e-07
0.8	1.3049	1.34e-07
0.81	1.3047	1.4e-07
0.82	1.3045	1.43e-07
0.83	1.3044	1.45e-07
0.84	1.3042	1.51e-07
0.85	1.304	1.83e-07
0.86	1.3038	2.15e-07
0.87	1.3037	2.65e-07
0.88	1.3035	3.35e-07
0.89	1.3033	3.92e-07
0.9	1.3032	4.2e-07
0.91	1.303	4.44e-07
0.92	1.3028	4.74e-07
0.93	1.3027	5.11e-07
0.94	1.3025	5.53e-07
0.95	1.3023	6.02e-07
0.96	1.3022	7.55e-07
0.97	1.302	9.26e-07
0.98	1.3018	1.12e-06
0.99	1.3017	1.33e-06
1.0	1.3015	1.62e-06
1.01	1.3013	2e-06
1.02	1.3012	2.25e-06
1.03	1.301	2.33e-06
1.04	1.3008	2.33e-06
1.05	1.3006	2.17e-06
1.06	1.3005	1.96e-06
1.07	1.3003	1.81e-06
1.08	1.3001	1.74e-06
1.09	1.3	1.73e-06
1.1	1.2998	1.7e-06
1.11	1.2996	1.76e-06
1.12	1.2995	1.82e-06
1.13	1.2993	2.04e-06
1.14	1.2991	2.25e-06
1.15	1.2989	2.29e-06
1.16	1.2987	3.04e-06
1.17	1.2985	3.84e-06
1.18	1.2984	4.77e-06
1.19	1.2982	5.76e-06
1.2	1.298	6.71e-06
1.21	1.2978	8.66e-06
1.22	1.2976	1.02e-05
1.23	1.2974	1.13e-05
1.24	1.2972	1.22e-05
1.25	1.297	1.29e-05
1.26	1.2969	1.32e-05
1.27	1.2967	1.35e-05
1.28	1.2965	1.33e-05
1.29	1.2963	1.32e-05
1.3	1.2961	1.32e-05
1.31	1.2958	1.31e-05
1.32	1.2956	1.32e-05
1.33	1.2954	1.32e-05
1.34	1.2952	1.34e-05
1.35	1.295	1.39e-05
1.36	1.2948	1.42e-05
1.37	1.2945	1.48e-05
1.38	1.2943	1.58e-05
1.39	1.2941	1.74e-05
1.4	1.2938	1.98e-05
1.41	1.2936	2.5e-05
1.42	1.2933	5.4e-05
1.43	1.293	0.000104
1.44	1.2927	0.000203
1.449	1.2925	0.0002708
1.46	1.2923	0.0003511
1.471	1.2921	0.0004299
1.481	1.2919	0.0005181
1.493	1.2917	0.0005855
1.504	1.2915	0.0005899
1.515	1.2913	0.0005635
1.527	1.2911	0.000548
1.538	1.2908	0.0005266
1.563	1.2903	0.0004394
1.587	1.2896	0.0003701
1.613	1.2889	0.0003372
1.65	1.2878	0.000241
1.68	1.2869	0.000189
1.7	1.2862	0.000166
1.73	1.2852	0.000145
1.76	1.2841	0.000128
1.8	1.2826	0.000103
1.83	1.2814	8.6e-05
1.84	1.2809	8.22e-05
1.85	1.2805	8.03e-05
1.855	1.2802	8.5e-05
1.86	1.28	9.9e-05
1.87	1.2795	0.00015
1.89	1.2785	0.000295
1.905	1.2777	0.0004687
1.923	1.2769	0.0007615
1.942	1.2761	0.00101
1.961	1.2754	0.001313
1.98	1.2747	0.001539
2.0	1.274	0.001588
2.02	1.2733	0.00154
2.041	1.2724	0.001412
2.062	1.2714	0.001244
2.083	1.2703	0.001068
2.105	1.269	0.0008414
2.13	1.2674	0.000565
2.15	1.2659	0.000432
2.17	1.2644	0.00035
2.19	1.2628	0.000287
2.22	1.2604	0.000221
2.24	1.2586	0.000203
2.245	1.2582	0.000201
2.25	1.2577	0.000203
2.26	1.2567	0.000214
2.27	1.2558	0.000232
2.29	1.2538	0.000289
2.31	1.2518	0.000381
2.33	1.2497	0.000462
2.35	1.2475	0.000548
2.37	1.2451	0.000618
2.39	1.2427	0.00068
2.41	1.24	0.00073
2.43	1.2373	0.000782
2.46	1.2327	0.000848
2.5	1.2258	0.000925
2.52	1.222	0.00092
2.55	1.2155	0.000892
2.565	1.2118	0.00087
2.58	1.2079	0.00089
2.59	1.2051	0.00093
2.6	1.2021	0.00101
2.62	1.1957	0.00135
2.675	1.1741	0.00342
2.725	1.1473	0.00792
2.778	1.1077	0.02
2.817	1.0674	0.038
2.833	1.0476	0.052
2.849	1.0265	0.068
2.865	1.0036	0.0923
2.882	0.982	0.127
2.899	0.965	0.169
2.915	0.9596	0.221
2.933	0.9727	0.276
2.95	0.9917	0.312
2.967	1.0067	0.347
2.985	1.0219	0.388
3.003	1.0427	0.438
3.021	1.076	0.493
3.04	1.1295	0.554
3.058	1.2127	0.612
3.077	1.3251	0.625
3.096	1.426	0.593
3.115	1.4966	0.539
3.135	1.551	0.491
3.155	1.5999	0.438
3.175	1.6363	0.372
3.195	1.6502	0.3
3.215	1.6428	0.238
3.236	1.6269	0.193
3.257	1.6128	0.158
3.279	1.5924	0.121
3.3	1.5733	0.103
3.322	1.5577	0.0836
3.345	1.5413	0.0668
3.367	1.5265	0.054
3.39	1.5114	0.0422
3.413	1.4973	0.0342
3.436	1.4845	0.0274
3.46	1.4721	0.022
3.484	1.4612	0.0186
3.509	1.4513	0.0152
3.534	1.4421	0.0126
3.559	1.4337	0.0106
3.624	1.4155	0.00802
3.732	1.3942	0.00685
3.775	1.3873	0.0066
3.847	1.3773	0.00696
3.969	1.3645	0.00916
4.099	1.3541	0.0111
4.239	1.3446	0.0145
4.348	1.3388	0.02
4.387	1.3381	0.023
4.444	1.3385	0.026
4.505	1.3405	0.029
4.547	1.3429	0.0293
4.56	1.3442	0.03
4.58	1.3463	0.0285
4.719	1.3442	0.0173
4.904	1.3345	0.0129
5.0	1.329	0.012
5.1	1.3233	0.0125
5.2	1.318	0.0134
5.263	1.3143	0.014
5.4	1.3062	0.0175
5.556	1.2972	0.024
5.714	1.289	0.035
5.747	1.2873	0.038
5.78	1.286	0.042
5.814	1.2851	0.046
5.848	1.2854	0.052
5.882	1.2881	0.057
6.061	1.3016	0.069
6.135	1.309	0.07
6.25	1.3172	0.067
6.289	1.3189	0.065
6.329	1.3204	0.064
6.369	1.322	0.062
6.41	1.3224	0.059
6.452	1.3215	0.057
6.494	1.3204	0.056
6.579	1.3181	0.055
6.667	1.3171	0.057
6.757	1.3181	0.058
6.897	1.3195	0.057
7.042	1.3193	0.055
7.143	1.319	0.055
7.246	1.3191	0.054
7.353	1.318	0.052
7.463	1.3163	0.052
7.576	1.3154	0.052
7.692	1.3154	0.052
7.812	1.3155	0.05
7.937	1.3145	0.047
8.065	1.3119	0.043
8.197	1.3068	0.039
8.333	1.2993	0.037
8.475	1.2925	0.039
8.696	1.2839	0.04
8.929	1.274	0.042
9.091	1.2672	0.044
9.259	1.2599	0.045
9.524	1.2451	0.046
9.804	1.2224	0.047
10.0	1.1991	0.051
10.2	1.1715	0.065
10.31	1.1553	0.075
10.42	1.137	0.088
10.53	1.1181	0.108
10.64	1.1013	0.134
10.75	1.0908	0.168
10.87	1.0873	0.204
11.0	1.0925	0.248
11.11	1.1065	0.28
11.36	1.1478	0.341
11.63	1.202	0.379
11.9	1.2582	0.409
12.2	1.3231	0.422
12.5	1.3857	0.422
12.82	1.4448	0.403
12.99	1.4717	0.389
13.16	1.4962	0.374
13.33	1.5165	0.354
13.51	1.5333	0.335
13.7	1.549	0.315
13.89	1.5628	0.294
14.08	1.5732	0.271
14.29	1.5803	0.246
14.71	1.5792	0.198
15.15	1.5667	0.164
15.38	1.5587	0.152
15.63	1.5508	0.142
16.13	1.5381	0.128
16.39	1.533	0.125
16.67	1.5322	0.123
16.95	1.5334	0.116
17.24	1.5329	0.107
18.18	1.517	0.079
18.87	1.501	0.072
19.23	1.4968	0.076
19.61	1.4993	0.075
20.0	1.5015	0.067
20.41	1.4986	0.055
20.83	1.4905	0.045
22.22	1.4607	0.029
22.6	1.4512	0.0275
23.05	1.4422	0.027
23.6	1.4316	0.0273
24.6	1.4138	0.0289
25.0	1.4068	0.03
26.0	1.3895	0.034
28.57	1.3489	0.053
31.0	1.3104	0.0755
33.33	1.2642	0.106
34.48	1.2366	0.135
35.64	1.2166	0.1761
37.0	1.2023	0.2229
38.24	1.1964	0.2746
39.6	1.1997	0.328
41.14	1.2086	0.3906
42.76	1.2217	0.4642
43.58	1.2417	0.5247
44.58	1.2818	0.5731
45.5	1.3278	0.6362
46.15	1.3866	0.6839
46.71	1.4649	0.7091
47.36	1.5532	0.679
48.0	1.6038	0.625
48.78	1.6188	0.5654
50.03	1.6296	0.5433
51.28	1.6571	0.5292
52.75	1.6981	0.507
53.5	1.7206	0.4883
54.24	1.7486	0.4707
55.0	1.7674	0.4203
55.74	1.7648	0.3771
56.4	1.7501	0.3376
57.0	1.7233	0.3056
57.46	1.6849	0.2835
58.4	1.624	0.317
59.29	1.596	0.3517
60.0	1.5851	0.3902
61.0	1.5992	0.4509
61.25	1.614	0.4671
62.5	1.6662	0.4779
63.78	1.7066	0.489
64.67	1.7371	0.4899
65.58	1.7686	0.4873
66.55	1.8034	0.4766
67.6	1.833	0.4508
69.0	1.8568	0.4193
70.53	1.8741	0.388
73.0	1.8911	0.3433
75.0	1.8992	0.3118
76.29	1.9043	0.2935
80.0	1.9033	0.235
82.97	1.8874	0.1981
85.0	1.875	0.1865
86.8	1.867	0.1771
90.8	1.8536	0.162
95.17	1.8425	0.149
100.0	1.8323	0.139
120.0	1.8191	0.12
150.0	1.8227	0.0962
167.0	1.8296	0.083

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