Optical constants

Refractive index of N₂ (Nitrogen)

Börzsönyi et al. 2008: n 0.4–1.0 µm; 0 °C

Data: formula 2
Range: 0.4–1 µm
Temperature: 273 K
Licence: CC0-1.0

Axis Log x Log y

Click the plot to set the calculator wavelength.

At one wavelength

Refractive index n: 1.00029
Extinction coefficient k: 0

Permittivity ε₁: 1.00059
Permittivity ε₂: 0

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

Abbe number V_d: 95.604
Chromatic dispersion dn/dλ: -1.57525e-05 µm⁻¹

Group index n_g: 1.0003
Group velocity dispersion: 0.0302557 fs²/mm

Dispersion parameter D: -0.165061 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

# N2 (Nitrogen): Börzsönyi et al. 2008: n 0.4–1.0 µm; 0 °C
n2 = ls.fetch_refractiveindex("main", "N2", "Borzsonyi", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(n2.range_nm)  # (400, 1000) nm
eps = n2.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_b7c7b1804745/lightsmith"
n2 = ls.Tabulated.model_validate(json.load(urllib.request.urlopen(url)))
print(n2.source)  # citation and provenance travel with the data

Any dataset here, as the library's Tabulated material (n2/borzsonyi-2008).

# ... load n2 as above, then:
sim = ls.Simulation(
    particles=[ls.Particle(shape=ls.Sphere(radius_nm=50), material=n2)],
    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_b7c7b1804745/lightsmith?model=drude_lorentz"
n2_dl = ls.DrudeLorentz.model_validate(json.load(urllib.request.urlopen(url)))

A dispersive Drude–Lorentz model for time-domain solvers.

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

Sellmeier (C in µm²) (formula 2), λ in µm

n^{2} - 1 = \frac{0.0003920995 λ^{2}}{λ^{2} - 0.00114624} + \frac{0.0001880648 λ^{2}}{λ^{2} - 0.013476}

Valid from 0.4 to 1.0 µm.

Coefficients as stored

C_i	Value
C1	0.0
C2	0.0003920995
C3	0.00114624
C4	0.0001880648
C5	0.013476

Comments and conditions

273 K (0 °C), 1000 mbar.
Dispersion formula may be usable down to ~0.2 µm.

Conditions

temperature: 273 K
pressure: 100000

References

A. Börzsönyi, Z. Heiner, M. P. Kalashnikov, A. P. Kovács, K. Osvay. Dispersion measurement of inert gases and gas mixtures at 800 nm. Appl. Opt. 47, 4856-4863 (2008)

doi:10.1364/ao.47.004856 Dispersion measurement of inert gases and gas mixtures at 800 nm, Applied Optics (2008)

Cite

A. Börzsönyi, Z. Heiner, M. P. Kalashnikov, A. P. Kovács and K. Osvay. Dispersion measurement of inert gases and gas mixtures at 800 nm. Applied Optics, 47, 4856 (2008), doi:10.1364/ao.47.004856; 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

N2 (Nitrogen), Börzsönyi et al. 2008: n 0.4–1.0 µm; 0 °C: n and k versus wavelength
λ (µm)	n
0.4	1.0003
0.40092	1.0003
0.401841	1.0003
0.402765	1.0003
0.403691	1.0003
0.404619	1.0003
0.40555	1.0003
0.406482	1.0003
0.407417	1.0003
0.408353	1.0003
0.409292	1.0003
0.410233	1.0003
0.411176	1.0003
0.412122	1.000299
0.413069	1.000299
0.414019	1.000299
0.414971	1.000299
0.415925	1.000299
0.416881	1.000299
0.41784	1.000299
0.4188	1.000299
0.419763	1.000299
0.420728	1.000299
0.421695	1.000299
0.422665	1.000299
0.423637	1.000299
0.424611	1.000299
0.425587	1.000299
0.426565	1.000299
0.427546	1.000299
0.428529	1.000299
0.429514	1.000299
0.430502	1.000299
0.431492	1.000299
0.432484	1.000299
0.433478	1.000299
0.434475	1.000298
0.435473	1.000298
0.436475	1.000298
0.437478	1.000298
0.438484	1.000298
0.439492	1.000298
0.440503	1.000298
0.441515	1.000298
0.44253	1.000298
0.443548	1.000298
0.444568	1.000298
0.44559	1.000298
0.446614	1.000298
0.447641	1.000298
0.44867	1.000298
0.449702	1.000298
0.450736	1.000298
0.451772	1.000298
0.452811	1.000298
0.453852	1.000298
0.454895	1.000298
0.455941	1.000298
0.456989	1.000298
0.45804	1.000298
0.459093	1.000298
0.460148	1.000297
0.461206	1.000297
0.462267	1.000297
0.46333	1.000297
0.464395	1.000297
0.465462	1.000297
0.466533	1.000297
0.467605	1.000297
0.46868	1.000297
0.469758	1.000297
0.470838	1.000297
0.47192	1.000297
0.473005	1.000297
0.474093	1.000297
0.475183	1.000297
0.476275	1.000297
0.47737	1.000297
0.478468	1.000297
0.479568	1.000297
0.48067	1.000297
0.481776	1.000297
0.482883	1.000297
0.483993	1.000297
0.485106	1.000297
0.486222	1.000297
0.487339	1.000297
0.48846	1.000297
0.489583	1.000297
0.490708	1.000297
0.491837	1.000297
0.492967	1.000296
0.494101	1.000296
0.495237	1.000296
0.496375	1.000296
0.497517	1.000296
0.49866	1.000296
0.499807	1.000296
0.500956	1.000296
0.502108	1.000296
0.503262	1.000296
0.504419	1.000296
0.505579	1.000296
0.506741	1.000296
0.507906	1.000296
0.509074	1.000296
0.510245	1.000296
0.511418	1.000296
0.512593	1.000296
0.513772	1.000296
0.514953	1.000296
0.516137	1.000296
0.517324	1.000296
0.518513	1.000296
0.519705	1.000296
0.5209	1.000296
0.522098	1.000296
0.523298	1.000296
0.524501	1.000296
0.525707	1.000296
0.526916	1.000296
0.528127	1.000296
0.529341	1.000296
0.530558	1.000296
0.531778	1.000296
0.533001	1.000296
0.534226	1.000295
0.535455	1.000295
0.536686	1.000295
0.537919	1.000295
0.539156	1.000295
0.540396	1.000295
0.541638	1.000295
0.542884	1.000295
0.544132	1.000295
0.545383	1.000295
0.546637	1.000295
0.547893	1.000295
0.549153	1.000295
0.550416	1.000295
0.551681	1.000295
0.552949	1.000295
0.554221	1.000295
0.555495	1.000295
0.556772	1.000295
0.558052	1.000295
0.559335	1.000295
0.560621	1.000295
0.56191	1.000295
0.563202	1.000295
0.564497	1.000295
0.565795	1.000295
0.567095	1.000295
0.568399	1.000295
0.569706	1.000295
0.571016	1.000295
0.572329	1.000295
0.573645	1.000295
0.574963	1.000295
0.576285	1.000295
0.57761	1.000295
0.578938	1.000295
0.580269	1.000295
0.581603	1.000295
0.582941	1.000295
0.584281	1.000295
0.585624	1.000295
0.586971	1.000295
0.58832	1.000294
0.589673	1.000294
0.591028	1.000294
0.592387	1.000294
0.593749	1.000294
0.595114	1.000294
0.596483	1.000294
0.597854	1.000294
0.599228	1.000294
0.600606	1.000294
0.601987	1.000294
0.603371	1.000294
0.604758	1.000294
0.606149	1.000294
0.607542	1.000294
0.608939	1.000294
0.610339	1.000294
0.611742	1.000294
0.613149	1.000294
0.614558	1.000294
0.615971	1.000294
0.617388	1.000294
0.618807	1.000294
0.62023	1.000294
0.621656	1.000294
0.623085	1.000294
0.624517	1.000294
0.625953	1.000294
0.627392	1.000294
0.628835	1.000294
0.630281	1.000294
0.63173	1.000294
0.633182	1.000294
0.634638	1.000294
0.636097	1.000294
0.637559	1.000294
0.639025	1.000294
0.640494	1.000294
0.641967	1.000294
0.643443	1.000294
0.644922	1.000294
0.646405	1.000294
0.647891	1.000294
0.649381	1.000294
0.650874	1.000294
0.65237	1.000294
0.65387	1.000294
0.655373	1.000294
0.65688	1.000294
0.65839	1.000294
0.659904	1.000294
0.661421	1.000294
0.662942	1.000294
0.664466	1.000294
0.665994	1.000293
0.667525	1.000293
0.66906	1.000293
0.670598	1.000293
0.67214	1.000293
0.673685	1.000293
0.675234	1.000293
0.676786	1.000293
0.678342	1.000293
0.679902	1.000293
0.681465	1.000293
0.683032	1.000293
0.684602	1.000293
0.686176	1.000293
0.687754	1.000293
0.689335	1.000293
0.69092	1.000293
0.692508	1.000293
0.694101	1.000293
0.695696	1.000293
0.697296	1.000293
0.698899	1.000293
0.700506	1.000293
0.702116	1.000293
0.703731	1.000293
0.705349	1.000293
0.70697	1.000293
0.708596	1.000293
0.710225	1.000293
0.711858	1.000293
0.713494	1.000293
0.715135	1.000293
0.716779	1.000293
0.718427	1.000293
0.720079	1.000293
0.721734	1.000293
0.723393	1.000293
0.725057	1.000293
0.726724	1.000293
0.728394	1.000293
0.730069	1.000293
0.731748	1.000293
0.73343	1.000293
0.735116	1.000293
0.736806	1.000293
0.7385	1.000293
0.740198	1.000293
0.7419	1.000293
0.743606	1.000293
0.745315	1.000293
0.747029	1.000293
0.748746	1.000293
0.750468	1.000293
0.752193	1.000293
0.753923	1.000293
0.755656	1.000293
0.757393	1.000293
0.759135	1.000293
0.76088	1.000293
0.762629	1.000293
0.764383	1.000293
0.76614	1.000293
0.767901	1.000293
0.769667	1.000293
0.771437	1.000293
0.77321	1.000293
0.774988	1.000293
0.77677	1.000293
0.778555	1.000293
0.780345	1.000293
0.78214	1.000293
0.783938	1.000293
0.78574	1.000293
0.787547	1.000292
0.789357	1.000292
0.791172	1.000292
0.792991	1.000292
0.794814	1.000292
0.796642	1.000292
0.798473	1.000292
0.800309	1.000292
0.802149	1.000292
0.803993	1.000292
0.805842	1.000292
0.807694	1.000292
0.809551	1.000292
0.811413	1.000292
0.813278	1.000292
0.815148	1.000292
0.817022	1.000292
0.8189	1.000292
0.820783	1.000292
0.82267	1.000292
0.824562	1.000292
0.826457	1.000292
0.828358	1.000292
0.830262	1.000292
0.832171	1.000292
0.834084	1.000292
0.836002	1.000292
0.837924	1.000292
0.83985	1.000292
0.841781	1.000292
0.843717	1.000292
0.845656	1.000292
0.847601	1.000292
0.849549	1.000292
0.851503	1.000292
0.85346	1.000292
0.855422	1.000292
0.857389	1.000292
0.85936	1.000292
0.861336	1.000292
0.863316	1.000292
0.865301	1.000292
0.867291	1.000292
0.869285	1.000292
0.871283	1.000292
0.873286	1.000292
0.875294	1.000292
0.877307	1.000292
0.879324	1.000292
0.881345	1.000292
0.883372	1.000292
0.885403	1.000292
0.887438	1.000292
0.889479	1.000292
0.891524	1.000292
0.893573	1.000292
0.895628	1.000292
0.897687	1.000292
0.899751	1.000292
0.901819	1.000292
0.903893	1.000292
0.905971	1.000292
0.908054	1.000292
0.910142	1.000292
0.912234	1.000292
0.914331	1.000292
0.916433	1.000292
0.91854	1.000292
0.920652	1.000292
0.922769	1.000292
0.924891	1.000292
0.927017	1.000292
0.929148	1.000292
0.931284	1.000292
0.933426	1.000292
0.935572	1.000292
0.937723	1.000292
0.939879	1.000292
0.942039	1.000292
0.944205	1.000292
0.946376	1.000292
0.948552	1.000292
0.950733	1.000292
0.952919	1.000292
0.955109	1.000292
0.957305	1.000292
0.959506	1.000292
0.961712	1.000292
0.963923	1.000292
0.96614	1.000292
0.968361	1.000292
0.970587	1.000292
0.972819	1.000292
0.975055	1.000292
0.977297	1.000292
0.979544	1.000292
0.981796	1.000292
0.984053	1.000292
0.986316	1.000292
0.988583	1.000292
0.990856	1.000292
0.993134	1.000292
0.995418	1.000292
0.997706	1.000292
1	1.000292

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: —

N₂ (Nitrogen): all datasets

About N2 (Nitrogen)

Nitrogen (N₂) is a diatomic gas that makes up approximately 78% of the Earth's atmosphere by volume. It is a colorless, odorless, and tasteless gas that is largely inert under standard conditions, resulting in its use as an unreactive blanket in many industrial applications. In the context of optics, nitrogen is commonly used as a purge gas to displace air and prevent condensation or contamination in high-power laser systems, optical instruments, and other sensitive equipment. Liquid nitrogen, which is nitrogen in its cryogenic liquid state, is employed as a coolant for infrared detectors and other electronic components. Its transparency in the visible and infrared regions makes it an ideal medium for certain optical experiments and applications.

More about N2 (Nitrogen) →

Provenance

Version: 1 (snapshot c5c2f18)
Source page: refractiveindex.info
Original file: database/data/main/N2/nk/Borzsonyi.yml
ID: ds_b7c7b1804745
API: /v1/datasets/ds_b7c7b1804745

Plot