Optical constants
Refractive index of C (Carbon, diamond, graphite, graphene, carbon nanotubes)
Peter 1923: Diamond; n 0.226–0.760 µm
- Data
- formula 1
- Range
- 0.226–0.76 µm
- Licence
- CC0-1.0
Plot
Click the plot to set the calculator wavelength.
At one wavelength
- Refractive index n
- 2.41748
- Extinction coefficient k
- 0
- Permittivity ε1
- 5.84421
- Permittivity ε2
- 0
- Absorption coefficient α
- 0 cm⁻¹
- Penetration depth δ = λ/(2πk)
- — nm
- Abbe number Vd
- 55.301
- Chromatic dispersion dn/dλ
- -0.130975 µm⁻¹
- Group index ng
- 2.49444
- Group velocity dispersion
- 252.341 fs²/mm
- Dispersion parameter D
- -1376.65 ps/(nm·km)
- Photon energy
- 2.11001 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
# C (Carbon, diamond, graphite, graphene, carbon nanotubes): Peter 1923: Diamond; n 0.226–0.760 µm
c = ls.fetch_refractiveindex("main", "C", "Peter", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(c.range_nm) # (226, 760) nm
eps = c.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_d522dc77fdb1/lightsmith"
c = ls.Tabulated.model_validate(json.load(urllib.request.urlopen(url)))
print(c.source) # citation and provenance travel with the data
Any dataset here, as the library's Tabulated material (c/peter-1923).
# ... load c as above, then:
sim = ls.Simulation(
particles=[ls.Particle(shape=ls.Sphere(radius_nm=50), material=c)],
medium_index=1.0,
wavelengths=ls.WavelengthRange(start_nm=400, stop_nm=760, 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_d522dc77fdb1/lightsmith?model=drude_lorentz"
c_dl = ls.DrudeLorentz.model_validate(json.load(urllib.request.urlopen(url)))
A dispersive Drude–Lorentz model for time-domain solvers.
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 (formula 1), λ in µmValid from 0.226 to 0.76 µm.
Coefficients as stored
| Ci | Value |
|---|---|
| C1 | 0.0 |
| C2 | 0.3306 |
| C3 | 0.175 |
| C4 | 4.3356 |
| C5 | 0.106 |
Comments and conditions
References
- doi:10.1007/bf01330487 �ber Brechungsindizes und Absorptionskonstanten des Diamanten zwischen 644 und 226 m?, Zeitschrift f�r Physik (1923)
Cite
Fritz Peter. �ber Brechungsindizes und Absorptionskonstanten des Diamanten zwischen 644 und 226 m?. Zeitschrift f�r Physik, 15, 358-368 (1923), doi:10.1007/bf01330487; 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| λ (µm) | n |
|---|---|
| 0.226 | 2.717357 |
| 0.226688 | 2.714244 |
| 0.227378 | 2.711176 |
| 0.22807 | 2.708152 |
| 0.228765 | 2.705171 |
| 0.229461 | 2.702233 |
| 0.230159 | 2.699335 |
| 0.23086 | 2.696478 |
| 0.231563 | 2.693659 |
| 0.232268 | 2.690879 |
| 0.232975 | 2.688136 |
| 0.233684 | 2.68543 |
| 0.234395 | 2.682759 |
| 0.235109 | 2.680123 |
| 0.235825 | 2.677521 |
| 0.236543 | 2.674952 |
| 0.237263 | 2.672415 |
| 0.237985 | 2.669911 |
| 0.238709 | 2.667438 |
| 0.239436 | 2.664995 |
| 0.240165 | 2.662582 |
| 0.240896 | 2.660199 |
| 0.241629 | 2.657844 |
| 0.242365 | 2.655518 |
| 0.243103 | 2.653219 |
| 0.243843 | 2.650947 |
| 0.244585 | 2.648702 |
| 0.24533 | 2.646483 |
| 0.246077 | 2.64429 |
| 0.246826 | 2.642121 |
| 0.247577 | 2.639978 |
| 0.248331 | 2.637858 |
| 0.249087 | 2.635762 |
| 0.249845 | 2.63369 |
| 0.250605 | 2.63164 |
| 0.251368 | 2.629613 |
| 0.252134 | 2.627609 |
| 0.252901 | 2.625626 |
| 0.253671 | 2.623664 |
| 0.254443 | 2.621723 |
| 0.255218 | 2.619803 |
| 0.255995 | 2.617904 |
| 0.256774 | 2.616025 |
| 0.257556 | 2.614165 |
| 0.25834 | 2.612324 |
| 0.259126 | 2.610503 |
| 0.259915 | 2.608701 |
| 0.260706 | 2.606917 |
| 0.2615 | 2.605151 |
| 0.262296 | 2.603403 |
| 0.263094 | 2.601673 |
| 0.263895 | 2.59996 |
| 0.264699 | 2.598264 |
| 0.265504 | 2.596585 |
| 0.266313 | 2.594923 |
| 0.267123 | 2.593277 |
| 0.267937 | 2.591648 |
| 0.268752 | 2.590034 |
| 0.26957 | 2.588436 |
| 0.270391 | 2.586853 |
| 0.271214 | 2.585286 |
| 0.27204 | 2.583734 |
| 0.272868 | 2.582196 |
| 0.273698 | 2.580673 |
| 0.274532 | 2.579165 |
| 0.275367 | 2.577671 |
| 0.276206 | 2.576191 |
| 0.277046 | 2.574724 |
| 0.27789 | 2.573272 |
| 0.278736 | 2.571833 |
| 0.279584 | 2.570407 |
| 0.280435 | 2.568994 |
| 0.281289 | 2.567595 |
| 0.282145 | 2.566208 |
| 0.283004 | 2.564833 |
| 0.283866 | 2.563472 |
| 0.28473 | 2.562122 |
| 0.285597 | 2.560785 |
| 0.286466 | 2.55946 |
| 0.287338 | 2.558146 |
| 0.288213 | 2.556844 |
| 0.28909 | 2.555554 |
| 0.28997 | 2.554276 |
| 0.290853 | 2.553008 |
| 0.291738 | 2.551752 |
| 0.292627 | 2.550507 |
| 0.293517 | 2.549273 |
| 0.294411 | 2.548049 |
| 0.295307 | 2.546836 |
| 0.296206 | 2.545634 |
| 0.297108 | 2.544442 |
| 0.298012 | 2.54326 |
| 0.298919 | 2.542088 |
| 0.299829 | 2.540927 |
| 0.300742 | 2.539775 |
| 0.301658 | 2.538633 |
| 0.302576 | 2.537501 |
| 0.303497 | 2.536379 |
| 0.304421 | 2.535266 |
| 0.305348 | 2.534162 |
| 0.306277 | 2.533068 |
| 0.30721 | 2.531983 |
| 0.308145 | 2.530906 |
| 0.309083 | 2.529839 |
| 0.310024 | 2.528781 |
| 0.310968 | 2.527731 |
| 0.311914 | 2.52669 |
| 0.312864 | 2.525658 |
| 0.313816 | 2.524634 |
| 0.314771 | 2.523619 |
| 0.31573 | 2.522612 |
| 0.316691 | 2.521613 |
| 0.317655 | 2.520623 |
| 0.318622 | 2.51964 |
| 0.319592 | 2.518665 |
| 0.320565 | 2.517699 |
| 0.321541 | 2.51674 |
| 0.322519 | 2.515788 |
| 0.323501 | 2.514845 |
| 0.324486 | 2.513909 |
| 0.325474 | 2.51298 |
| 0.326465 | 2.512059 |
| 0.327458 | 2.511145 |
| 0.328455 | 2.510239 |
| 0.329455 | 2.50934 |
| 0.330458 | 2.508447 |
| 0.331464 | 2.507562 |
| 0.332473 | 2.506684 |
| 0.333485 | 2.505813 |
| 0.3345 | 2.504949 |
| 0.335519 | 2.504091 |
| 0.33654 | 2.50324 |
| 0.337564 | 2.502396 |
| 0.338592 | 2.501558 |
| 0.339623 | 2.500727 |
| 0.340657 | 2.499902 |
| 0.341694 | 2.499084 |
| 0.342734 | 2.498272 |
| 0.343777 | 2.497466 |
| 0.344824 | 2.496667 |
| 0.345873 | 2.495874 |
| 0.346926 | 2.495086 |
| 0.347982 | 2.494305 |
| 0.349042 | 2.49353 |
| 0.350104 | 2.492761 |
| 0.35117 | 2.491997 |
| 0.352239 | 2.49124 |
| 0.353311 | 2.490488 |
| 0.354387 | 2.489742 |
| 0.355466 | 2.489001 |
| 0.356548 | 2.488266 |
| 0.357633 | 2.487537 |
| 0.358722 | 2.486813 |
| 0.359814 | 2.486095 |
| 0.360909 | 2.485382 |
| 0.362008 | 2.484674 |
| 0.36311 | 2.483972 |
| 0.364215 | 2.483275 |
| 0.365324 | 2.482583 |
| 0.366436 | 2.481896 |
| 0.367552 | 2.481215 |
| 0.368671 | 2.480538 |
| 0.369793 | 2.479867 |
| 0.370919 | 2.4792 |
| 0.372048 | 2.478538 |
| 0.37318 | 2.477882 |
| 0.374316 | 2.47723 |
| 0.375456 | 2.476583 |
| 0.376599 | 2.475941 |
| 0.377745 | 2.475303 |
| 0.378895 | 2.47467 |
| 0.380049 | 2.474042 |
| 0.381206 | 2.473418 |
| 0.382366 | 2.472799 |
| 0.38353 | 2.472185 |
| 0.384698 | 2.471575 |
| 0.385869 | 2.470969 |
| 0.387043 | 2.470368 |
| 0.388222 | 2.469771 |
| 0.389403 | 2.469178 |
| 0.390589 | 2.46859 |
| 0.391778 | 2.468006 |
| 0.39297 | 2.467426 |
| 0.394167 | 2.466851 |
| 0.395367 | 2.466279 |
| 0.39657 | 2.465712 |
| 0.397777 | 2.465149 |
| 0.398988 | 2.46459 |
| 0.400203 | 2.464035 |
| 0.401421 | 2.463483 |
| 0.402643 | 2.462936 |
| 0.403869 | 2.462393 |
| 0.405098 | 2.461853 |
| 0.406332 | 2.461318 |
| 0.407569 | 2.460786 |
| 0.408809 | 2.460258 |
| 0.410054 | 2.459734 |
| 0.411302 | 2.459213 |
| 0.412554 | 2.458697 |
| 0.41381 | 2.458183 |
| 0.41507 | 2.457674 |
| 0.416333 | 2.457168 |
| 0.417601 | 2.456666 |
| 0.418872 | 2.456167 |
| 0.420147 | 2.455672 |
| 0.421426 | 2.45518 |
| 0.422709 | 2.454691 |
| 0.423996 | 2.454207 |
| 0.425286 | 2.453725 |
| 0.426581 | 2.453247 |
| 0.42788 | 2.452772 |
| 0.429182 | 2.452301 |
| 0.430489 | 2.451833 |
| 0.431799 | 2.451368 |
| 0.433114 | 2.450906 |
| 0.434432 | 2.450448 |
| 0.435755 | 2.449992 |
| 0.437081 | 2.44954 |
| 0.438412 | 2.449091 |
| 0.439746 | 2.448646 |
| 0.441085 | 2.448203 |
| 0.442428 | 2.447763 |
| 0.443775 | 2.447327 |
| 0.445126 | 2.446893 |
| 0.446481 | 2.446463 |
| 0.44784 | 2.446035 |
| 0.449203 | 2.445611 |
| 0.45057 | 2.445189 |
| 0.451942 | 2.44477 |
| 0.453318 | 2.444354 |
| 0.454698 | 2.443941 |
| 0.456082 | 2.443531 |
| 0.45747 | 2.443123 |
| 0.458863 | 2.442719 |
| 0.46026 | 2.442317 |
| 0.461661 | 2.441918 |
| 0.463066 | 2.441522 |
| 0.464476 | 2.441128 |
| 0.46589 | 2.440737 |
| 0.467308 | 2.440349 |
| 0.468731 | 2.439963 |
| 0.470158 | 2.43958 |
| 0.471589 | 2.4392 |
| 0.473025 | 2.438822 |
| 0.474465 | 2.438447 |
| 0.475909 | 2.438074 |
| 0.477358 | 2.437704 |
| 0.478811 | 2.437336 |
| 0.480268 | 2.436971 |
| 0.48173 | 2.436609 |
| 0.483197 | 2.436248 |
| 0.484668 | 2.435891 |
| 0.486143 | 2.435535 |
| 0.487623 | 2.435182 |
| 0.489108 | 2.434832 |
| 0.490597 | 2.434484 |
| 0.49209 | 2.434138 |
| 0.493588 | 2.433794 |
| 0.495091 | 2.433453 |
| 0.496598 | 2.433114 |
| 0.49811 | 2.432778 |
| 0.499626 | 2.432443 |
| 0.501147 | 2.432111 |
| 0.502672 | 2.431781 |
| 0.504203 | 2.431454 |
| 0.505737 | 2.431128 |
| 0.507277 | 2.430805 |
| 0.508821 | 2.430484 |
| 0.51037 | 2.430165 |
| 0.511924 | 2.429848 |
| 0.513482 | 2.429533 |
| 0.515045 | 2.42922 |
| 0.516613 | 2.42891 |
| 0.518186 | 2.428601 |
| 0.519763 | 2.428295 |
| 0.521346 | 2.427991 |
| 0.522933 | 2.427688 |
| 0.524525 | 2.427388 |
| 0.526121 | 2.42709 |
| 0.527723 | 2.426793 |
| 0.529329 | 2.426499 |
| 0.530941 | 2.426206 |
| 0.532557 | 2.425916 |
| 0.534178 | 2.425627 |
| 0.535804 | 2.425341 |
| 0.537436 | 2.425056 |
| 0.539072 | 2.424773 |
| 0.540713 | 2.424492 |
| 0.542359 | 2.424213 |
| 0.54401 | 2.423935 |
| 0.545666 | 2.42366 |
| 0.547327 | 2.423386 |
| 0.548993 | 2.423114 |
| 0.550664 | 2.422844 |
| 0.552341 | 2.422576 |
| 0.554022 | 2.422309 |
| 0.555709 | 2.422045 |
| 0.5574 | 2.421782 |
| 0.559097 | 2.42152 |
| 0.560799 | 2.421261 |
| 0.562506 | 2.421003 |
| 0.564219 | 2.420747 |
| 0.565936 | 2.420492 |
| 0.567659 | 2.420239 |
| 0.569387 | 2.419988 |
| 0.57112 | 2.419739 |
| 0.572859 | 2.419491 |
| 0.574603 | 2.419244 |
| 0.576352 | 2.419 |
| 0.578107 | 2.418757 |
| 0.579866 | 2.418515 |
| 0.581632 | 2.418275 |
| 0.583402 | 2.418037 |
| 0.585178 | 2.4178 |
| 0.58696 | 2.417565 |
| 0.588746 | 2.417331 |
| 0.590539 | 2.417099 |
| 0.592336 | 2.416868 |
| 0.59414 | 2.416639 |
| 0.595948 | 2.416411 |
| 0.597762 | 2.416185 |
| 0.599582 | 2.415961 |
| 0.601407 | 2.415737 |
| 0.603238 | 2.415515 |
| 0.605075 | 2.415295 |
| 0.606916 | 2.415076 |
| 0.608764 | 2.414859 |
| 0.610617 | 2.414642 |
| 0.612476 | 2.414428 |
| 0.614341 | 2.414214 |
| 0.616211 | 2.414002 |
| 0.618087 | 2.413792 |
| 0.619968 | 2.413583 |
| 0.621855 | 2.413375 |
| 0.623748 | 2.413168 |
| 0.625647 | 2.412963 |
| 0.627552 | 2.412759 |
| 0.629462 | 2.412557 |
| 0.631378 | 2.412355 |
| 0.6333 | 2.412155 |
| 0.635228 | 2.411957 |
| 0.637162 | 2.411759 |
| 0.639102 | 2.411563 |
| 0.641047 | 2.411369 |
| 0.642999 | 2.411175 |
| 0.644956 | 2.410983 |
| 0.64692 | 2.410792 |
| 0.648889 | 2.410602 |
| 0.650864 | 2.410413 |
| 0.652846 | 2.410226 |
| 0.654833 | 2.410039 |
| 0.656826 | 2.409854 |
| 0.658826 | 2.40967 |
| 0.660831 | 2.409488 |
| 0.662843 | 2.409306 |
| 0.664861 | 2.409126 |
| 0.666885 | 2.408947 |
| 0.668915 | 2.408769 |
| 0.670951 | 2.408592 |
| 0.672994 | 2.408416 |
| 0.675043 | 2.408242 |
| 0.677097 | 2.408068 |
| 0.679159 | 2.407896 |
| 0.681226 | 2.407724 |
| 0.6833 | 2.407554 |
| 0.68538 | 2.407385 |
| 0.687466 | 2.407217 |
| 0.689559 | 2.40705 |
| 0.691658 | 2.406884 |
| 0.693764 | 2.406719 |
| 0.695876 | 2.406555 |
| 0.697994 | 2.406393 |
| 0.700119 | 2.406231 |
| 0.70225 | 2.40607 |
| 0.704388 | 2.405911 |
| 0.706532 | 2.405752 |
| 0.708683 | 2.405594 |
| 0.710841 | 2.405438 |
| 0.713004 | 2.405282 |
| 0.715175 | 2.405128 |
| 0.717352 | 2.404974 |
| 0.719536 | 2.404821 |
| 0.721726 | 2.40467 |
| 0.723923 | 2.404519 |
| 0.726127 | 2.404369 |
| 0.728338 | 2.40422 |
| 0.730555 | 2.404072 |
| 0.732779 | 2.403925 |
| 0.735009 | 2.403779 |
| 0.737247 | 2.403634 |
| 0.739491 | 2.40349 |
| 0.741742 | 2.403347 |
| 0.744 | 2.403205 |
| 0.746265 | 2.403063 |
| 0.748537 | 2.402923 |
| 0.750816 | 2.402783 |
| 0.753101 | 2.402644 |
| 0.755394 | 2.402506 |
| 0.757693 | 2.402369 |
| 0.76 | 2.402233 |
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
- —
Cubic carbon (diamond). Room temperature; no temperature effect on refractive index was observed in the temperature interval 10 - 30 °C