Optical constants
Refractive index of Air
Mathar 2007: n 4.35–5.2 µm
- Data
- tabulated n
- Range
- 4.35–5.2 µm
- Points
- 86
- Temperature
- 288.15 K
- Licence
- CC0-1.0
Plot
Click the plot to set the calculator wavelength.
At one wavelength
- Refractive index n
- 1.00027
- Extinction coefficient k
- 0
- Permittivity ε1
- 1.00055
- Permittivity ε2
- 0
- Absorption coefficient α
- 0 cm⁻¹
- Penetration depth δ = λ/(2πk)
- — nm
- Abbe number Vd
- —
- Chromatic dispersion dn/dλ
- -1.22650e-07 µm⁻¹
- Group index ng
- 1.00027
- Group velocity dispersion
- — fs²/mm
- Dispersion parameter D
- — ps/(nm·km)
- Photon energy
- 0.260471 eV
ε = (n + ik)², α = 4πk/λ, ng = 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
# Air: Mathar 2007: n 4.35–5.2 µm
air = ls.fetch_refractiveindex("other", "air", "Mathar-4.35", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(air.range_nm) # (4350, 5200) nm
eps = air.eps([4760]) # complex permittivityDownloads 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_fbc013d9cee3/lightsmith"
air = ls.Tabulated.model_validate(json.load(urllib.request.urlopen(url)))
print(air.source) # citation and provenance travel with the dataAny dataset here, as the library's Tabulated material (air/mathar-2007-4-35).
# ... load air as above, then:
sim = ls.Simulation(
particles=[ls.Particle(shape=ls.Sphere(radius_nm=50), material=air)],
medium_index=1.0,
wavelengths=ls.WavelengthRange(start_nm=4350, stop_nm=5200, num=81),
)
res = ls.solve(sim) # exact Mie for a sphere
print(res.q_ext) # extinction efficiency at each wavelengthSame spec runs with DDA, FDTD, BEM or T-matrix: ls.compare(sim, ["mie", "dda"]).
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
Conditions
- temperature
- 288.15 K
- pressure
- 101325
References
[Calculation script (Python) - can be used to calculate the refractive index of air for specific values of humidity, temperature, and pressure]
- doi:10.1088/1464-4258/9/5/008 Refractive index of humid air in the infrared: model fits, Journal of Optics A: Pure and Applied Optics (2007)
Cite
Richard J Mathar. Refractive index of humid air in the infrared: model fits. Journal of Optics A: Pure and Applied Optics, 9, 470-476 (2007), doi:10.1088/1464-4258/9/5/008; [Calculation script (Python) - can be used to calculate the refractive index of air for specific values of humidity, temperature, and pressure]; Data from the refractiveindex.info database (M. N. Polyanskiy, Sci. Data 11, 94 (2024), doi:10.1038/s41597-023-02898-2)
Data
86 rows as published| λ (µm) | n |
|---|---|
| 4.35 | 1.000273011293 |
| 4.36 | 1.00027298824 |
| 4.37 | 1.000272967424 |
| 4.38 | 1.000272948658 |
| 4.39 | 1.000272931765 |
| 4.4 | 1.000272916582 |
| 4.41 | 1.000272902955 |
| 4.42 | 1.000272890743 |
| 4.43 | 1.000272879814 |
| 4.44 | 1.000272870046 |
| 4.45 | 1.000272861325 |
| 4.46 | 1.000272853547 |
| 4.47 | 1.000272846616 |
| 4.48 | 1.000272840441 |
| 4.49 | 1.000272834942 |
| 4.5 | 1.000272830043 |
| 4.51 | 1.000272825675 |
| 4.52 | 1.000272821776 |
| 4.53 | 1.000272818288 |
| 4.54 | 1.000272815159 |
| 4.55 | 1.000272812343 |
| 4.56 | 1.000272809798 |
| 4.57 | 1.000272807484 |
| 4.58 | 1.000272805367 |
| 4.59 | 1.000272803419 |
| 4.6 | 1.000272801611 |
| 4.61 | 1.00027279992 |
| 4.62 | 1.000272798325 |
| 4.63 | 1.000272796808 |
| 4.64 | 1.000272795355 |
| 4.65 | 1.000272793951 |
| 4.66 | 1.000272792586 |
| 4.67 | 1.000272791251 |
| 4.68 | 1.000272789939 |
| 4.69 | 1.000272788643 |
| 4.7 | 1.000272787361 |
| 4.71 | 1.000272786088 |
| 4.72 | 1.000272784824 |
| 4.73 | 1.000272783566 |
| 4.74 | 1.000272782316 |
| 4.75 | 1.000272781075 |
| 4.76 | 1.000272779843 |
| 4.77 | 1.000272778622 |
| 4.78 | 1.000272777416 |
| 4.79 | 1.000272776226 |
| 4.8 | 1.000272775056 |
| 4.81 | 1.000272773908 |
| 4.82 | 1.000272772786 |
| 4.83 | 1.000272771693 |
| 4.84 | 1.000272770631 |
| 4.85 | 1.000272769604 |
| 4.86 | 1.000272768614 |
| 4.87 | 1.000272767664 |
| 4.88 | 1.000272766754 |
| 4.89 | 1.000272765888 |
| 4.9 | 1.000272765065 |
| 4.91 | 1.000272764287 |
| 4.92 | 1.000272763553 |
| 4.93 | 1.000272762864 |
| 4.94 | 1.000272762217 |
| 4.95 | 1.000272761611 |
| 4.96 | 1.000272761044 |
| 4.97 | 1.000272760512 |
| 4.98 | 1.000272760012 |
| 4.99 | 1.000272759539 |
| 5.0 | 1.000272759087 |
| 5.01 | 1.00027275865 |
| 5.02 | 1.000272758222 |
| 5.03 | 1.000272757794 |
| 5.04 | 1.000272757358 |
| 5.05 | 1.000272756904 |
| 5.06 | 1.000272756422 |
| 5.07 | 1.0002727559 |
| 5.08 | 1.000272755328 |
| 5.09 | 1.00027275469 |
| 5.1 | 1.000272753975 |
| 5.11 | 1.000272753167 |
| 5.12 | 1.00027275225 |
| 5.13 | 1.000272751209 |
| 5.14 | 1.000272750025 |
| 5.15 | 1.00027274868 |
| 5.16 | 1.000272747157 |
| 5.17 | 1.000272745433 |
| 5.18 | 1.00027274349 |
| 5.19 | 1.000272741304 |
| 5.2 | 1.000272738855 |
Optical transmission calculator
Free-standing sample in vacuum, normal incidence- Transmittance T
- —
- Reflectance R
- —
Fresnel reflection calculator
- Rp
- —
- Rs
- —
- R = (Rp+Rs)/2
- —
- Phase φp
- —
- Phase φs
- —
- Brewster angle θB
- —
- Critical angle θC
- —
Dry air at 15 °C, 101.325 kPa, 370 ppm CO2 content.