Axis Log x Log y

Click the plot to set the calculator wavelength.

At one wavelength

Refractive index n: 1.30977
Extinction coefficient k: 4.74496e-09

Permittivity ε₁: 1.7155
Permittivity ε₂: 1.24296e-08

Absorption coefficient α: 0.00101475 cm⁻¹
Penetration depth δ = λ/(2πk): 1.97092e+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 and Brandt 2008: Ice; n,k 0.00443–2e6 µm
h2o_d2o = ls.fetch_refractiveindex("main", "H2O", "Warren-2008", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(h2o_d2o.range_nm)  # (44.3, 2e+09) 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_98429ce1ac7e/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-brandt-2008).

# ... 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 and R. E. Brandt. Optical constants of ice from the ultraviolet to the microwave: A revised compilation. J. Geophys. Res. 113, D14220 (2008)
Optical constants available online at https://atmos.washington.edu/ice_optical_constants/

doi:10.1029/2007jd009744 Optical constants of ice from the ultraviolet to the microwave: A revised compilation, Journal of Geophysical Research: Atmospheres (2008)

Cite

Stephen G. Warren and Richard E. Brandt. Optical constants of ice from the ultraviolet to the microwave: A revised compilation. Journal of Geophysical Research: Atmospheres, 113, 2007JD009744 (2008), doi:10.1029/2007jd009744; Optical constants available online at https://atmos.washington.edu/ice_optical_constants/; Data from the refractiveindex.info database (M. N. Polyanskiy, Sci. Data 11, 94 (2024), doi:10.1038/s41597-023-02898-2)

Data

486 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 and Brandt 2008: Ice; n,k 0.00443–2e6 µm: n and k versus wavelength
λ (µm)	n	k
0.0443	0.8228	0.164
0.0451	0.825	0.173
0.0459	0.8255	0.183
0.0468	0.8258	0.195
0.0477	0.8263	0.208
0.0486	0.8281	0.223
0.0496	0.8347	0.24
0.0506	0.8428	0.25
0.0517	0.8483	0.259
0.0528	0.8505	0.268
0.0539	0.8497	0.279
0.0551	0.8489	0.297
0.0564	0.8519	0.319
0.0577	0.8566	0.34
0.059	0.8647	0.366
0.0605	0.8797	0.392
0.062	0.897	0.416
0.0636	0.9173	0.44
0.0653	0.94	0.464
0.067	0.9679	0.492
0.0689	1.0093	0.517
0.0708	1.0536	0.528
0.0729	1.0986	0.533
0.0738	1.1183	0.534
0.0751	1.1449	0.531
0.0775	1.1885	0.524
0.08	1.2273	0.51
0.0827	1.2629	0.5
0.0855	1.3117	0.499
0.0886	1.3807	0.468
0.0918	1.4091	0.38
0.093	1.4028	0.36
0.0954	1.3948	0.339
0.0992	1.3964	0.318
0.1033	1.4047	0.291
0.1078	1.3981	0.251
0.11	1.3886	0.244
0.1127	1.3806	0.239
0.114	1.3772	0.239
0.1181	1.3783	0.244
0.121	1.3929	0.247
0.124	1.4061	0.224
0.1272	1.3999	0.195
0.1295	1.3777	0.174
0.1305	1.3607	0.172
0.1319	1.3389	0.18
0.1333	1.321	0.194
0.1348	1.303	0.213
0.1362	1.2871	0.243
0.137	1.2849	0.271
0.1378	1.2851	0.289
0.1387	1.297	0.334
0.1393	1.3151	0.344
0.1409	1.3575	0.382
0.1425	1.413	0.401
0.1435	1.4525	0.4065
0.1442	1.4845	0.405
0.145	1.5157	0.389
0.1459	1.5484	0.377
0.1468	1.5729	0.345
0.1476	1.5915	0.332
0.148	1.6021	0.315
0.1485	1.6077	0.298
0.1494	1.6156	0.274
0.1512	1.622	0.228
0.1531	1.6311	0.198
0.154	1.6345	0.172
0.155	1.6363	0.156
0.1569	1.6353	0.11
0.158	1.6309	0.083
0.1589	1.6214	0.058
0.161	1.5818	0.022
0.163	1.5482	0.008473
0.165	1.5225	0.003263
0.167	1.5027	0.001256
0.169	1.487	0.0004837
0.171	1.4743	0.0001862
0.173	1.4635	7.165e-05
0.175	1.4543	2.757e-05
0.177	1.4462	1.061e-05
0.179	1.439	4.081e-06
0.181	1.4326	1.57e-06
0.183	1.4268	5.403e-07
0.185	1.4215	1.829e-07
0.187	1.4167	6.218e-08
0.189	1.4122	2.113e-08
0.191	1.4081	7.181e-09
0.193	1.4043	2.44e-09
0.195	1.4007	8.289e-10
0.197	1.3974	2.816e-10
0.199	1.3943	9.565e-11
0.201	1.3914	3.249e-11
0.2019	1.3901	2e-11
0.21	1.3801	2e-11
0.25	1.3509	2e-11
0.3	1.3339	2e-11
0.35	1.3249	2e-11
0.39	1.3203	2e-11
0.4	1.3194	2.365e-11
0.41	1.3185	2.669e-11
0.42	1.3177	3.135e-11
0.43	1.317	4.14e-11
0.44	1.3163	6.268e-11
0.45	1.3157	9.239e-11
0.46	1.3151	1.325e-10
0.47	1.3145	1.956e-10
0.48	1.314	2.861e-10
0.49	1.3135	4.172e-10
0.5	1.313	5.889e-10
0.51	1.3126	8.036e-10
0.52	1.3121	1.076e-09
0.53	1.3117	1.409e-09
0.54	1.3114	1.813e-09
0.55	1.311	2.289e-09
0.56	1.3106	2.839e-09
0.57	1.3103	3.461e-09
0.58	1.31	4.159e-09
0.59	1.3097	4.93e-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	1.3059	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	1.3046	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	1.3039	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	1.3019	1.12e-06
0.99	1.3017	1.33e-06
1.0	1.3015	1.62e-06
1.01	1.3014	2e-06
1.02	1.3012	2.25e-06
1.03	1.301	2.33e-06
1.04	1.3009	2.33e-06
1.05	1.3007	2.17e-06
1.06	1.3005	1.96e-06
1.07	1.3003	1.81e-06
1.08	1.3002	1.74e-06
1.09	1.3	1.73e-06
1.1	1.2998	1.7e-06
1.11	1.2997	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	1.299	2.29e-06
1.16	1.2988	3.04e-06
1.17	1.2986	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	1.2979	8.66e-06
1.22	1.2977	1.02e-05
1.23	1.2975	1.13e-05
1.24	1.2973	1.22e-05
1.25	1.2971	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	1.2959	1.31e-05
1.32	1.2957	1.32e-05
1.33	1.2955	1.32e-05
1.34	1.2953	1.34e-05
1.35	1.2951	1.39e-05
1.36	1.2949	1.42e-05
1.37	1.2946	1.48e-05
1.38	1.2944	1.58e-05
1.39	1.2941	1.74e-05
1.4	1.2939	1.98e-05
1.41	1.2937	3.442e-05
1.42	1.2934	5.959e-05
1.43	1.2931	0.0001028
1.44	1.2929	0.0001516
1.449	1.2927	0.000203
1.46	1.2924	0.0002942
1.471	1.2921	0.0003987
1.481	1.292	0.0004941
1.493	1.2918	0.0005532
1.504	1.2916	0.0005373
1.515	1.2914	0.0005143
1.527	1.2912	0.0004908
1.538	1.2909	0.0004594
1.563	1.2903	0.0003858
1.587	1.2897	0.0003105
1.613	1.289	0.0002659
1.65	1.2879	0.0002361
1.68	1.287	0.0002046
1.7	1.2863	0.0001875
1.73	1.2853	0.000165
1.76	1.2843	0.0001522
1.8	1.2828	0.0001411
1.83	1.2816	0.0001302
1.84	1.2811	0.000131
1.85	1.2807	0.0001339
1.855	1.2805	0.0001377
1.86	1.2802	0.0001432
1.87	1.2797	0.0001632
1.89	1.2788	0.0002566
1.905	1.278	0.0004081
1.923	1.2771	0.000706
1.942	1.2762	0.001108
1.961	1.2756	0.001442
1.98	1.275	0.001614
2.0	1.2744	0.00164
2.02	1.2736	0.001566
2.041	1.2728	0.001458
2.062	1.2718	0.001267
2.083	1.2707	0.001023
2.105	1.2694	0.0007586
2.13	1.2677	0.0005255
2.15	1.2663	0.0004025
2.17	1.2648	0.0003235
2.19	1.2633	0.0002707
2.22	1.2609	0.0002228
2.24	1.2591	0.0002037
2.245	1.2587	0.0002026
2.25	1.2582	0.0002035
2.26	1.2573	0.0002078
2.27	1.2564	0.0002171
2.29	1.2545	0.0002538
2.31	1.2525	0.0003138
2.33	1.2504	0.0003858
2.35	1.2482	0.0004591
2.37	1.2459	0.0005187
2.39	1.2435	0.0005605
2.41	1.2409	0.0005956
2.43	1.2382	0.0006259
2.46	1.2337	0.000682
2.5	1.227	0.000753
2.52	1.2232	0.0007685
2.55	1.2169	0.0007647
2.565	1.2135	0.0007473
2.58	1.2097	0.0007392
2.59	1.2071	0.0007437
2.6	1.2043	0.0007543
2.62	1.1983	0.0008059
2.675	1.1776	0.001367
2.725	1.1507	0.003508
2.778	1.1083	0.01346
2.817	1.0657	0.03245
2.833	1.0453	0.04572
2.849	1.0236	0.06287
2.865	1.0001	0.08548
2.882	0.9747	0.1198
2.899	0.9563	0.169
2.915	0.9538	0.221
2.933	0.9678	0.276
2.95	0.9873	0.312
2.967	1.0026	0.347
2.985	1.018	0.388
3.003	1.039	0.438
3.021	1.0722	0.493
3.04	1.1259	0.554
3.058	1.2089	0.612
3.077	1.3215	0.625
3.096	1.4225	0.593
3.115	1.4933	0.539
3.135	1.5478	0.491
3.155	1.597	0.438
3.175	1.6336	0.372
3.195	1.6477	0.3
3.215	1.6405	0.238
3.236	1.6248	0.193
3.257	1.6108	0.158
3.279	1.5905	0.121
3.3	1.5714	0.103
3.322	1.5559	0.0836
3.345	1.5396	0.0668
3.367	1.5241	0.05312
3.39	1.5086	0.04286
3.413	1.4949	0.03523
3.436	1.4827	0.02887
3.46	1.471	0.02347
3.484	1.4604	0.01921
3.509	1.4502	0.01586
3.534	1.4411	0.01326
3.559	1.4328	0.0113
3.624	1.4146	0.008146
3.732	1.3924	0.006672
3.775	1.385	0.006966
3.847	1.375	0.008248
3.969	1.3623	0.01112
4.099	1.3526	0.01471
4.239	1.3447	0.01867
4.348	1.3406	0.02411
4.387	1.3401	0.02656
4.444	1.3412	0.0299
4.505	1.3444	0.03179
4.547	1.3473	0.0309
4.56	1.3482	0.03007
4.58	1.3491	0.02883
4.719	1.347	0.0194
4.904	1.3379	0.01347
5.0	1.3325	0.0124
5.1	1.3268	0.0122
5.2	1.3212	0.01302
5.263	1.3176	0.0138
5.4	1.31	0.01683
5.556	1.3013	0.02232
5.714	1.2933	0.03256
5.747	1.2917	0.03539
5.78	1.2906	0.03883
5.814	1.2902	0.0427
5.848	1.2904	0.04643
5.882	1.2915	0.05045
6.061	1.3015	0.06439
6.135	1.3083	0.0656
6.25	1.3152	0.0636
6.289	1.3167	0.06265
6.329	1.3178	0.0617
6.369	1.3187	0.06101
6.41	1.3194	0.06031
6.452	1.3201	0.05964
6.494	1.3207	0.05899
6.579	1.3214	0.0578
6.667	1.3219	0.057
6.757	1.3229	0.0568
6.897	1.3242	0.05428
7.042	1.3244	0.05161
7.143	1.3236	0.0494
7.246	1.3229	0.0484
7.353	1.3218	0.046
7.463	1.32	0.0444
7.576	1.3183	0.0429
7.692	1.3158	0.04041
7.812	1.3123	0.03911
7.937	1.3086	0.03819
8.065	1.3047	0.0376
8.197	1.3007	0.03724
8.333	1.2964	0.037
8.475	1.2917	0.03677
8.696	1.2835	0.03654
8.929	1.2735	0.03664
9.091	1.2655	0.03706
9.259	1.2561	0.03789
9.524	1.2387	0.04026
9.804	1.2151	0.0445
10.0	1.1926	0.05008
10.2	1.1659	0.06461
10.31	1.1501	0.075
10.42	1.1323	0.088
10.53	1.1136	0.108
10.64	1.0971	0.134
10.75	1.0867	0.168
10.87	1.0833	0.204
11.0	1.0886	0.248
11.11	1.1023	0.28
11.36	1.1439	0.341
11.63	1.1983	0.379
11.9	1.2546	0.409
12.2	1.3194	0.422
12.5	1.3822	0.422
12.82	1.4412	0.403
12.99	1.4683	0.389
13.16	1.4928	0.374
13.33	1.5132	0.354
13.51	1.53	0.335
13.7	1.5458	0.315
13.89	1.5596	0.294
14.08	1.5701	0.271
14.29	1.5775	0.246
14.71	1.5762	0.198
15.15	1.5637	0.164
15.38	1.5559	0.152
15.63	1.5481	0.142
16.13	1.5353	0.128
16.39	1.5302	0.125
16.67	1.5294	0.123
16.95	1.5306	0.116
17.24	1.5303	0.107
18.18	1.5141	0.079
18.32	1.5104	0.07752
18.61	1.5043	0.07455
18.87	1.4982	0.072
19.23	1.4939	0.076
19.61	1.4963	0.075
20.0	1.4986	0.067
20.41	1.4956	0.055
20.83	1.4877	0.045
22.22	1.4575	0.029
22.6	1.4486	0.0275
23.05	1.439	0.027
23.6	1.4282	0.0273
24.6	1.4102	0.0289
25.0	1.403	0.03
26.0	1.3854	0.034
28.57	1.3404	0.05122
31.0	1.2969	0.08615
33.33	1.2641	0.1348
34.48	1.253	0.1615
35.64	1.2445	0.1895
37.0	1.2371	0.2227
38.24	1.2317	0.2528
39.6	1.2243	0.2853
41.14	1.2054	0.324
42.76	1.1742	0.3945
43.58	1.1549	0.4521
44.58	1.1496	0.5535
45.5	1.1853	0.6782
46.15	1.2543	0.7684
46.71	1.3474	0.8254
47.36	1.4725	0.8458
48.0	1.5874	0.8158
48.78	1.6841	0.7414
50.03	1.7505	0.6191
51.28	1.7649	0.5353
52.75	1.7668	0.478
53.5	1.7687	0.4599
54.24	1.7792	0.4468
55.0	1.7955	0.4214
55.74	1.8052	0.386
56.4	1.8041	0.3508
57.0	1.794	0.3196
57.46	1.7805	0.2981
58.4	1.741	0.2659
59.29	1.693	0.2569
60.0	1.661	0.2785
61.0	1.6419	0.3076
61.25	1.6396	0.3146
62.5	1.6372	0.3471
63.78	1.6471	0.3748
64.67	1.6596	0.3902
65.58	1.6754	0.4024
66.55	1.6945	0.4115
67.6	1.7167	0.4167
69.0	1.7466	0.4167
70.53	1.778	0.4089
73.0	1.8185	0.383
75.0	1.8419	0.3543
76.29	1.8504	0.334
80.0	1.8617	0.2944
82.97	1.8669	0.2679
85.0	1.8688	0.2519
86.8	1.8699	0.239
90.8	1.8698	0.214
95.17	1.8681	0.1913
100.0	1.8654	0.1706
120.0	1.8499	0.1151
160.0	1.8268	0.06684
210.0	1.8114	0.04282
300.0	1.7989	0.02549
500.0	1.7908	0.01405
1300.0	1.7868	0.005173
5000.0	1.7861	0.001337
19000.0	1.7861	0.0003574
39000.0	1.7861	0.0001839
61000.0	1.7861	0.0001294
86000.0	1.7861	0.0001058
110000.0	1.7861	9.675e-05
140000.0	1.7861	9.36e-05
180000.0	1.7861	9.613e-05
240000.0	1.7861	0.0001066
340000.0	1.7861	0.0001312
540000.0	1.7861	0.0001895
1000000.0	1.7861	0.0003348
2000000.0	1.7861	0.0006596

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