Optical constants

Refractive index of H₂ (Hydrogen)

Peck and Hung 1977: n 0.168–1.695 µm

Data: formula 6
Range: 0.168–1.694 µm
Temperature: 273.15 K
Licence: CC0-1.0

Axis Log x Log y

Click the plot to set the calculator wavelength.

At one wavelength

Refractive index n: 1.00014
Extinction coefficient k: 0

Permittivity ε₁: 1.00028
Permittivity ε₂: 0

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

Abbe number V_d: 66.309
Chromatic dispersion dn/dλ: -1.07333e-05 µm⁻¹

Group index n_g: 1.00015
Group velocity dispersion: 0.0203569 fs²/mm

Dispersion parameter D: -0.111058 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

# H2 (Hydrogen): Peck and Hung 1977: n 0.168–1.695 µm
h2 = ls.fetch_refractiveindex("main", "H2", "Peck", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(h2.range_nm)  # (168, 1694.5) nm
eps = h2.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_07bf1fd1623a/lightsmith"
h2 = ls.Tabulated.model_validate(json.load(urllib.request.urlopen(url)))
print(h2.source)  # citation and provenance travel with the data

Any dataset here, as the library's Tabulated material (h2/peck-hung-1977).

# ... load h2 as above, then:
sim = ls.Simulation(
    particles=[ls.Particle(shape=ls.Sphere(radius_nm=50), material=h2)],
    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

Gases (formula 6), λ in µm

n - 1 = \frac{0.0148956}{180.7 - λ^{−2}} + \frac{0.0049037}{92.0 - λ^{−2}}

Valid from 0.168 to 1.6945 µm.

Coefficients as stored

C_i	Value
C1	0.0
C2	0.0148956
C3	180.7
C4	0.0049037
C5	92.0

Comments and conditions

Standard conditions. 0 °C, 760 torr (101.325 kPa).

Conditions

temperature: 273.15 K
pressure: 101325

References

E. R. Peck and S. Hung. Refractivity and dispersion of hydrogen in the visible and near infrared. J. Opt. Soc. Am. 67, 1550-1554 (1977)

doi:10.1364/josa.67.001550 Refractivity and dispersion of hydrogen in the visible and near infrared, Journal of the Optical Society of America (1977)

Cite

Edson R. Peck and Shiezen Huang. Refractivity and dispersion of hydrogen in the visible and near infrared. Journal of the Optical Society of America, 67, 1550 (1977), doi:10.1364/josa.67.001550; 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

H2 (Hydrogen), Peck and Hung 1977: n 0.168–1.695 µm: n and k versus wavelength
λ (µm)	n
0.168	1.000189
0.168976	1.000188
0.169958	1.000187
0.170945	1.000187
0.171938	1.000186
0.172937	1.000185
0.173941	1.000184
0.174952	1.000183
0.175968	1.000183
0.17699	1.000182
0.178019	1.000181
0.179053	1.00018
0.180093	1.00018
0.181139	1.000179
0.182191	1.000178
0.18325	1.000178
0.184314	1.000177
0.185385	1.000176
0.186462	1.000176
0.187545	1.000175
0.188635	1.000174
0.189731	1.000174
0.190833	1.000173
0.191941	1.000173
0.193056	1.000172
0.194178	1.000172
0.195306	1.000171
0.19644	1.00017
0.197582	1.00017
0.198729	1.000169
0.199884	1.000169
0.201045	1.000168
0.202213	1.000168
0.203388	1.000167
0.204569	1.000167
0.205758	1.000167
0.206953	1.000166
0.208155	1.000166
0.209364	1.000165
0.210581	1.000165
0.211804	1.000164
0.213034	1.000164
0.214272	1.000164
0.215517	1.000163
0.216769	1.000163
0.218028	1.000162
0.219295	1.000162
0.220568	1.000162
0.22185	1.000161
0.223139	1.000161
0.224435	1.000161
0.225739	1.00016
0.22705	1.00016
0.228369	1.00016
0.229696	1.000159
0.23103	1.000159
0.232372	1.000159
0.233722	1.000158
0.23508	1.000158
0.236445	1.000158
0.237819	1.000157
0.239201	1.000157
0.24059	1.000157
0.241988	1.000156
0.243393	1.000156
0.244807	1.000156
0.24623	1.000156
0.24766	1.000155
0.249099	1.000155
0.250546	1.000155
0.252001	1.000155
0.253465	1.000154
0.254938	1.000154
0.256419	1.000154
0.257908	1.000154
0.259406	1.000153
0.260913	1.000153
0.262429	1.000153
0.263954	1.000153
0.265487	1.000152
0.267029	1.000152
0.268581	1.000152
0.270141	1.000152
0.27171	1.000152
0.273288	1.000151
0.274876	1.000151
0.276473	1.000151
0.278079	1.000151
0.279694	1.000151
0.281319	1.00015
0.282953	1.00015
0.284597	1.00015
0.286251	1.00015
0.287913	1.00015
0.289586	1.000149
0.291268	1.000149
0.29296	1.000149
0.294662	1.000149
0.296374	1.000149
0.298096	1.000149
0.299827	1.000148
0.301569	1.000148
0.303321	1.000148
0.305083	1.000148
0.306855	1.000148
0.308638	1.000148
0.310431	1.000148
0.312234	1.000147
0.314048	1.000147
0.315873	1.000147
0.317707	1.000147
0.319553	1.000147
0.321409	1.000147
0.323277	1.000147
0.325155	1.000146
0.327044	1.000146
0.328943	1.000146
0.330854	1.000146
0.332776	1.000146
0.334709	1.000146
0.336654	1.000146
0.33861	1.000145
0.340577	1.000145
0.342555	1.000145
0.344545	1.000145
0.346547	1.000145
0.34856	1.000145
0.350585	1.000145
0.352621	1.000145
0.35467	1.000145
0.35673	1.000144
0.358803	1.000144
0.360887	1.000144
0.362983	1.000144
0.365092	1.000144
0.367213	1.000144
0.369346	1.000144
0.371492	1.000144
0.37365	1.000144
0.37582	1.000144
0.378004	1.000143
0.3802	1.000143
0.382408	1.000143
0.38463	1.000143
0.386864	1.000143
0.389112	1.000143
0.391372	1.000143
0.393646	1.000143
0.395932	1.000143
0.398232	1.000143
0.400546	1.000143
0.402873	1.000142
0.405213	1.000142
0.407567	1.000142
0.409935	1.000142
0.412316	1.000142
0.414711	1.000142
0.417121	1.000142
0.419544	1.000142
0.421981	1.000142
0.424432	1.000142
0.426898	1.000142
0.429378	1.000142
0.431872	1.000142
0.434381	1.000141
0.436905	1.000141
0.439443	1.000141
0.441995	1.000141
0.444563	1.000141
0.447146	1.000141
0.449743	1.000141
0.452356	1.000141
0.454984	1.000141
0.457627	1.000141
0.460285	1.000141
0.462959	1.000141
0.465649	1.000141
0.468354	1.000141
0.471075	1.000141
0.473811	1.000141
0.476564	1.00014
0.479332	1.00014
0.482117	1.00014
0.484917	1.00014
0.487734	1.00014
0.490568	1.00014
0.493418	1.00014
0.496284	1.00014
0.499167	1.00014
0.502067	1.00014
0.504983	1.00014
0.507917	1.00014
0.510868	1.00014
0.513835	1.00014
0.51682	1.00014
0.519823	1.00014
0.522842	1.00014
0.52588	1.00014
0.528935	1.00014
0.532007	1.00014
0.535098	1.000139
0.538206	1.000139
0.541333	1.000139
0.544478	1.000139
0.547641	1.000139
0.550822	1.000139
0.554022	1.000139
0.55724	1.000139
0.560478	1.000139
0.563733	1.000139
0.567008	1.000139
0.570302	1.000139
0.573615	1.000139
0.576947	1.000139
0.580299	1.000139
0.58367	1.000139
0.587061	1.000139
0.590471	1.000139
0.593901	1.000139
0.597352	1.000139
0.600822	1.000139
0.604312	1.000139
0.607823	1.000139
0.611354	1.000139
0.614905	1.000139
0.618477	1.000139
0.62207	1.000138
0.625684	1.000138
0.629319	1.000138
0.632974	1.000138
0.636652	1.000138
0.64035	1.000138
0.64407	1.000138
0.647812	1.000138
0.651575	1.000138
0.65536	1.000138
0.659167	1.000138
0.662996	1.000138
0.666848	1.000138
0.670722	1.000138
0.674618	1.000138
0.678537	1.000138
0.682479	1.000138
0.686444	1.000138
0.690431	1.000138
0.694442	1.000138
0.698476	1.000138
0.702534	1.000138
0.706615	1.000138
0.71072	1.000138
0.714849	1.000138
0.719002	1.000138
0.723178	1.000138
0.72738	1.000138
0.731605	1.000138
0.735855	1.000138
0.74013	1.000138
0.744429	1.000138
0.748754	1.000138
0.753104	1.000138
0.757479	1.000138
0.761879	1.000138
0.766305	1.000138
0.770757	1.000138
0.775234	1.000137
0.779738	1.000137
0.784267	1.000137
0.788823	1.000137
0.793406	1.000137
0.798015	1.000137
0.802651	1.000137
0.807314	1.000137
0.812003	1.000137
0.816721	1.000137
0.821465	1.000137
0.826237	1.000137
0.831037	1.000137
0.835865	1.000137
0.84072	1.000137
0.845604	1.000137
0.850517	1.000137
0.855458	1.000137
0.860427	1.000137
0.865425	1.000137
0.870453	1.000137
0.87551	1.000137
0.880596	1.000137
0.885711	1.000137
0.890857	1.000137
0.896032	1.000137
0.901237	1.000137
0.906473	1.000137
0.911738	1.000137
0.917035	1.000137
0.922362	1.000137
0.92772	1.000137
0.93311	1.000137
0.93853	1.000137
0.943983	1.000137
0.949466	1.000137
0.954982	1.000137
0.96053	1.000137
0.96611	1.000137
0.971722	1.000137
0.977367	1.000137
0.983045	1.000137
0.988756	1.000137
0.994499	1.000137
1.00028	1.000137
1.00609	1.000137
1.01193	1.000137
1.01781	1.000137
1.02372	1.000137
1.02967	1.000137
1.03565	1.000137
1.04167	1.000137
1.04772	1.000137
1.05381	1.000137
1.05993	1.000137
1.06609	1.000137
1.07228	1.000137
1.07851	1.000137
1.08477	1.000137
1.09107	1.000137
1.09741	1.000137
1.10379	1.000137
1.1102	1.000137
1.11665	1.000137
1.12314	1.000137
1.12966	1.000137
1.13622	1.000137
1.14282	1.000137
1.14946	1.000137
1.15614	1.000137
1.16286	1.000137
1.16961	1.000136
1.17641	1.000136
1.18324	1.000136
1.19011	1.000136
1.19703	1.000136
1.20398	1.000136
1.21098	1.000136
1.21801	1.000136
1.22509	1.000136
1.2322	1.000136
1.23936	1.000136
1.24656	1.000136
1.2538	1.000136
1.26109	1.000136
1.26841	1.000136
1.27578	1.000136
1.28319	1.000136
1.29065	1.000136
1.29814	1.000136
1.30569	1.000136
1.31327	1.000136
1.3209	1.000136
1.32857	1.000136
1.33629	1.000136
1.34405	1.000136
1.35186	1.000136
1.35972	1.000136
1.36761	1.000136
1.37556	1.000136
1.38355	1.000136
1.39159	1.000136
1.39967	1.000136
1.4078	1.000136
1.41598	1.000136
1.42421	1.000136
1.43248	1.000136
1.4408	1.000136
1.44917	1.000136
1.45759	1.000136
1.46606	1.000136
1.47457	1.000136
1.48314	1.000136
1.49176	1.000136
1.50042	1.000136
1.50914	1.000136
1.51791	1.000136
1.52672	1.000136
1.53559	1.000136
1.54451	1.000136
1.55349	1.000136
1.56251	1.000136
1.57159	1.000136
1.58072	1.000136
1.5899	1.000136
1.59914	1.000136
1.60843	1.000136
1.61777	1.000136
1.62717	1.000136
1.63662	1.000136
1.64613	1.000136
1.65569	1.000136
1.66531	1.000136
1.67498	1.000136
1.68471	1.000136
1.6945	1.000136

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: —

H₂ (Hydrogen): all datasets

About H2 (Hydrogen)

Hydrogen (H₂) is the most abundant element in the universe and forms diatomic molecules under standard conditions. In the realm of optics, hydrogen is commonly encountered in the form of gas cells that are used for Raman spectroscopy and as a reference in various types of spectroscopic analysis. Hydrogen's transparency over a broad range of wavelengths makes it useful in applications that require minimal interaction with light, although it's generally not used in its elemental form for robust optical components due to its reactivity and the challenges associated with containing it. Hydrogen gas cells can also serve as frequency standards in metrology.

More about H2 (Hydrogen) →

Provenance

Version: 1 (snapshot c5c2f18)
Source page: refractiveindex.info
Original file: database/data/main/H2/nk/Peck.yml
ID: ds_07bf1fd1623a
API: /v1/datasets/ds_07bf1fd1623a

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