Optical constants
Refractive index of HgS (Mercury sulfide)
Bond et al. 1967: α-HgS; n(o) 0.62–11 µm
- Data
- formula 2
- Range
- 0.62–11 µm
- Optical axis
- o
- Licence
- CC0-1.0
Uniaxial crystal, axes: oe
Plot
Click the plot to set the calculator wavelength.
At one wavelength
- Refractive index n
- 2.64283
- Extinction coefficient k
- 0
- Permittivity ε1
- 6.98456
- Permittivity ε2
- 0
- Absorption coefficient α
- 0 cm⁻¹
- Penetration depth δ = λ/(2πk)
- — nm
- Abbe number Vd
- —
- Chromatic dispersion dn/dλ
- -0.00982577 µm⁻¹
- Group index ng
- 2.66848
- Group velocity dispersion
- 283.125 fs²/mm
- Dispersion parameter D
- -78.2885 ps/(nm·km)
- Photon energy
- 0.475035 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
# HgS (Mercury sulfide): Bond et al. 1967: α-HgS; n(o) 0.62–11 µm
hgs = ls.fetch_refractiveindex("main", "HgS", "Bond-o", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(hgs.range_nm) # (620, 11000) nm
eps = hgs.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_ecbf3f34e660/lightsmith"
hgs = ls.Tabulated.model_validate(json.load(urllib.request.urlopen(url)))
print(hgs.source) # citation and provenance travel with the data
Any dataset here, as the library's Tabulated material (hgs/bond-1967-o).
# ... load hgs as above, then:
sim = ls.Simulation(
particles=[ls.Particle(shape=ls.Sphere(radius_nm=50), material=hgs)],
medium_index=1.0,
wavelengths=ls.WavelengthRange(start_nm=620, 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_ecbf3f34e660/lightsmith?model=drude_lorentz"
hgs_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 (C in µm²) (formula 2), λ in µmValid from 0.62 to 11.0 µm.
Coefficients as stored
| Ci | Value |
|---|---|
| C1 | 3.1506 |
| C2 | 2.7896 |
| C3 | 0.1328 |
| C4 | 1.1378 |
| C5 | 705.0 |
Comments and conditions
Conditions
- direction
- o
References
2) G. C. Bhar. Refractive index interpolation in phase-matching. Appl. Opt. 15, 305-307 (1976)
* Ref. 2 provides a dispersion formula based on data from Ref. 1
- doi:10.1063/1.1709079 Refractive Indices of HgS (Cinnabar) between 0.62 and 11 μ, Journal of Applied Physics (1967)
- doi:10.1364/ao.15.0305_1 Refractive index interpolation in phase-matching, Applied Optics (1976)
Cite
W. L. Bond, G. D. Boyd and H. L. Carter. Refractive Indices of HgS (Cinnabar) between 0.62 and 11 μ. Journal of Applied Physics, 38, 4090-4091 (1967), doi:10.1063/1.1709079; Gopal C. Bhar. Refractive index interpolation in phase-matching. Applied Optics, 15, 305_1 (1976), doi:10.1364/ao.15.0305_1; 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 |
|---|---|
| 0.62 | 2.900343 |
| 0.624485 | 2.894828 |
| 0.629002 | 2.889461 |
| 0.633553 | 2.884238 |
| 0.638136 | 2.879154 |
| 0.642752 | 2.874203 |
| 0.647401 | 2.869381 |
| 0.652085 | 2.864683 |
| 0.656802 | 2.860106 |
| 0.661553 | 2.855644 |
| 0.666339 | 2.851294 |
| 0.671159 | 2.847052 |
| 0.676014 | 2.842915 |
| 0.680904 | 2.838879 |
| 0.68583 | 2.834942 |
| 0.690791 | 2.831098 |
| 0.695788 | 2.827347 |
| 0.700821 | 2.823685 |
| 0.705891 | 2.820109 |
| 0.710997 | 2.816616 |
| 0.716141 | 2.813204 |
| 0.721321 | 2.809871 |
| 0.726539 | 2.806613 |
| 0.731795 | 2.80343 |
| 0.737088 | 2.800318 |
| 0.74242 | 2.797276 |
| 0.747791 | 2.794301 |
| 0.7532 | 2.791392 |
| 0.758649 | 2.788547 |
| 0.764137 | 2.785764 |
| 0.769665 | 2.783041 |
| 0.775232 | 2.780377 |
| 0.78084 | 2.777769 |
| 0.786489 | 2.775217 |
| 0.792178 | 2.772719 |
| 0.797909 | 2.770274 |
| 0.803681 | 2.767879 |
| 0.809494 | 2.765534 |
| 0.81535 | 2.763238 |
| 0.821248 | 2.760988 |
| 0.827189 | 2.758785 |
| 0.833173 | 2.756626 |
| 0.8392 | 2.754511 |
| 0.845271 | 2.752439 |
| 0.851385 | 2.750408 |
| 0.857544 | 2.748417 |
| 0.863747 | 2.746466 |
| 0.869996 | 2.744553 |
| 0.876289 | 2.742678 |
| 0.882628 | 2.740839 |
| 0.889013 | 2.739036 |
| 0.895444 | 2.737268 |
| 0.901922 | 2.735534 |
| 0.908446 | 2.733833 |
| 0.915018 | 2.732165 |
| 0.921637 | 2.730528 |
| 0.928304 | 2.728922 |
| 0.935019 | 2.727347 |
| 0.941783 | 2.725801 |
| 0.948595 | 2.724284 |
| 0.955458 | 2.722795 |
| 0.962369 | 2.721333 |
| 0.969331 | 2.719899 |
| 0.976343 | 2.718491 |
| 0.983406 | 2.717109 |
| 0.990519 | 2.715752 |
| 0.997685 | 2.714419 |
| 1.0049 | 2.713111 |
| 1.01217 | 2.711826 |
| 1.01949 | 2.710564 |
| 1.02687 | 2.709325 |
| 1.0343 | 2.708108 |
| 1.04178 | 2.706913 |
| 1.04931 | 2.705739 |
| 1.05691 | 2.704585 |
| 1.06455 | 2.703452 |
| 1.07225 | 2.702339 |
| 1.08001 | 2.701245 |
| 1.08782 | 2.70017 |
| 1.09569 | 2.699114 |
| 1.10362 | 2.698076 |
| 1.1116 | 2.697056 |
| 1.11964 | 2.696054 |
| 1.12774 | 2.695068 |
| 1.1359 | 2.6941 |
| 1.14411 | 2.693148 |
| 1.15239 | 2.692212 |
| 1.16073 | 2.691292 |
| 1.16912 | 2.690388 |
| 1.17758 | 2.689499 |
| 1.1861 | 2.688624 |
| 1.19468 | 2.687765 |
| 1.20332 | 2.68692 |
| 1.21203 | 2.686088 |
| 1.22079 | 2.685271 |
| 1.22963 | 2.684467 |
| 1.23852 | 2.683676 |
| 1.24748 | 2.682899 |
| 1.2565 | 2.682134 |
| 1.26559 | 2.681381 |
| 1.27475 | 2.680641 |
| 1.28397 | 2.679913 |
| 1.29326 | 2.679197 |
| 1.30261 | 2.678492 |
| 1.31204 | 2.677799 |
| 1.32153 | 2.677117 |
| 1.33109 | 2.676446 |
| 1.34072 | 2.675785 |
| 1.35041 | 2.675135 |
| 1.36018 | 2.674496 |
| 1.37002 | 2.673866 |
| 1.37993 | 2.673247 |
| 1.38992 | 2.672637 |
| 1.39997 | 2.672037 |
| 1.4101 | 2.671447 |
| 1.4203 | 2.670866 |
| 1.43057 | 2.670293 |
| 1.44092 | 2.66973 |
| 1.45134 | 2.669175 |
| 1.46184 | 2.668629 |
| 1.47242 | 2.668092 |
| 1.48307 | 2.667563 |
| 1.4938 | 2.667042 |
| 1.5046 | 2.666529 |
| 1.51549 | 2.666023 |
| 1.52645 | 2.665526 |
| 1.53749 | 2.665036 |
| 1.54861 | 2.664553 |
| 1.55982 | 2.664078 |
| 1.5711 | 2.66361 |
| 1.58247 | 2.663149 |
| 1.59391 | 2.662695 |
| 1.60544 | 2.662248 |
| 1.61706 | 2.661807 |
| 1.62875 | 2.661373 |
| 1.64054 | 2.660946 |
| 1.6524 | 2.660524 |
| 1.66436 | 2.660109 |
| 1.6764 | 2.6597 |
| 1.68852 | 2.659297 |
| 1.70074 | 2.6589 |
| 1.71304 | 2.658509 |
| 1.72543 | 2.658123 |
| 1.73792 | 2.657743 |
| 1.75049 | 2.657369 |
| 1.76315 | 2.657 |
| 1.7759 | 2.656636 |
| 1.78875 | 2.656277 |
| 1.80169 | 2.655923 |
| 1.81472 | 2.655575 |
| 1.82785 | 2.655231 |
| 1.84107 | 2.654892 |
| 1.85439 | 2.654558 |
| 1.86781 | 2.654229 |
| 1.88132 | 2.653904 |
| 1.89493 | 2.653584 |
| 1.90864 | 2.653268 |
| 1.92244 | 2.652957 |
| 1.93635 | 2.652649 |
| 1.95036 | 2.652346 |
| 1.96446 | 2.652047 |
| 1.97868 | 2.651752 |
| 1.99299 | 2.651461 |
| 2.00741 | 2.651174 |
| 2.02193 | 2.650891 |
| 2.03655 | 2.650611 |
| 2.05129 | 2.650336 |
| 2.06612 | 2.650063 |
| 2.08107 | 2.649795 |
| 2.09612 | 2.64953 |
| 2.11129 | 2.649268 |
| 2.12656 | 2.64901 |
| 2.14194 | 2.648755 |
| 2.15744 | 2.648503 |
| 2.17305 | 2.648254 |
| 2.18877 | 2.648008 |
| 2.2046 | 2.647766 |
| 2.22055 | 2.647527 |
| 2.23661 | 2.64729 |
| 2.25279 | 2.647056 |
| 2.26909 | 2.646826 |
| 2.2855 | 2.646598 |
| 2.30203 | 2.646372 |
| 2.31869 | 2.64615 |
| 2.33546 | 2.64593 |
| 2.35235 | 2.645712 |
| 2.36937 | 2.645497 |
| 2.38651 | 2.645285 |
| 2.40377 | 2.645075 |
| 2.42116 | 2.644867 |
| 2.43868 | 2.644662 |
| 2.45632 | 2.644458 |
| 2.47409 | 2.644258 |
| 2.49198 | 2.644059 |
| 2.51001 | 2.643862 |
| 2.52817 | 2.643668 |
| 2.54646 | 2.643475 |
| 2.56488 | 2.643285 |
| 2.58343 | 2.643097 |
| 2.60212 | 2.64291 |
| 2.62094 | 2.642725 |
| 2.6399 | 2.642542 |
| 2.659 | 2.642361 |
| 2.67823 | 2.642182 |
| 2.69761 | 2.642004 |
| 2.71712 | 2.641828 |
| 2.73678 | 2.641654 |
| 2.75657 | 2.641481 |
| 2.77651 | 2.64131 |
| 2.7966 | 2.64114 |
| 2.81683 | 2.640972 |
| 2.83721 | 2.640805 |
| 2.85773 | 2.64064 |
| 2.8784 | 2.640476 |
| 2.89923 | 2.640313 |
| 2.9202 | 2.640151 |
| 2.94132 | 2.639991 |
| 2.9626 | 2.639832 |
| 2.98403 | 2.639674 |
| 3.00562 | 2.639517 |
| 3.02736 | 2.639362 |
| 3.04926 | 2.639207 |
| 3.07132 | 2.639053 |
| 3.09353 | 2.638901 |
| 3.11591 | 2.638749 |
| 3.13845 | 2.638599 |
| 3.16116 | 2.638449 |
| 3.18402 | 2.6383 |
| 3.20706 | 2.638152 |
| 3.23026 | 2.638004 |
| 3.25362 | 2.637858 |
| 3.27716 | 2.637712 |
| 3.30087 | 2.637567 |
| 3.32474 | 2.637422 |
| 3.34879 | 2.637279 |
| 3.37302 | 2.637135 |
| 3.39742 | 2.636993 |
| 3.422 | 2.636851 |
| 3.44675 | 2.636709 |
| 3.47168 | 2.636568 |
| 3.4968 | 2.636427 |
| 3.52209 | 2.636287 |
| 3.54757 | 2.636147 |
| 3.57323 | 2.636007 |
| 3.59908 | 2.635868 |
| 3.62512 | 2.635729 |
| 3.65134 | 2.63559 |
| 3.67775 | 2.635451 |
| 3.70436 | 2.635313 |
| 3.73116 | 2.635175 |
| 3.75815 | 2.635037 |
| 3.78533 | 2.634899 |
| 3.81272 | 2.634761 |
| 3.8403 | 2.634623 |
| 3.86808 | 2.634485 |
| 3.89606 | 2.634347 |
| 3.92424 | 2.634209 |
| 3.95263 | 2.634071 |
| 3.98122 | 2.633933 |
| 4.01002 | 2.633794 |
| 4.03903 | 2.633656 |
| 4.06825 | 2.633517 |
| 4.09768 | 2.633378 |
| 4.12732 | 2.633238 |
| 4.15718 | 2.633099 |
| 4.18725 | 2.632959 |
| 4.21754 | 2.632818 |
| 4.24805 | 2.632678 |
| 4.27878 | 2.632536 |
| 4.30973 | 2.632395 |
| 4.34091 | 2.632252 |
| 4.37231 | 2.63211 |
| 4.40394 | 2.631966 |
| 4.43579 | 2.631822 |
| 4.46788 | 2.631678 |
| 4.5002 | 2.631532 |
| 4.53276 | 2.631386 |
| 4.56555 | 2.63124 |
| 4.59857 | 2.631092 |
| 4.63184 | 2.630944 |
| 4.66534 | 2.630794 |
| 4.69909 | 2.630644 |
| 4.73308 | 2.630493 |
| 4.76732 | 2.630341 |
| 4.80181 | 2.630188 |
| 4.83655 | 2.630034 |
| 4.87153 | 2.629879 |
| 4.90677 | 2.629723 |
| 4.94227 | 2.629565 |
| 4.97802 | 2.629407 |
| 5.01403 | 2.629247 |
| 5.0503 | 2.629086 |
| 5.08683 | 2.628923 |
| 5.12363 | 2.62876 |
| 5.1607 | 2.628595 |
| 5.19803 | 2.628428 |
| 5.23563 | 2.62826 |
| 5.2735 | 2.62809 |
| 5.31165 | 2.627919 |
| 5.35007 | 2.627747 |
| 5.38878 | 2.627572 |
| 5.42776 | 2.627396 |
| 5.46702 | 2.627219 |
| 5.50657 | 2.627039 |
| 5.5464 | 2.626858 |
| 5.58653 | 2.626675 |
| 5.62694 | 2.626489 |
| 5.66764 | 2.626302 |
| 5.70864 | 2.626113 |
| 5.74994 | 2.625922 |
| 5.79153 | 2.625729 |
| 5.83343 | 2.625533 |
| 5.87563 | 2.625336 |
| 5.91813 | 2.625136 |
| 5.96094 | 2.624933 |
| 6.00406 | 2.624729 |
| 6.04749 | 2.624522 |
| 6.09124 | 2.624312 |
| 6.1353 | 2.6241 |
| 6.17969 | 2.623885 |
| 6.22439 | 2.623668 |
| 6.26942 | 2.623447 |
| 6.31477 | 2.623224 |
| 6.36045 | 2.622999 |
| 6.40646 | 2.62277 |
| 6.4528 | 2.622538 |
| 6.49948 | 2.622303 |
| 6.5465 | 2.622066 |
| 6.59385 | 2.621825 |
| 6.64155 | 2.62158 |
| 6.6896 | 2.621333 |
| 6.73799 | 2.621082 |
| 6.78673 | 2.620827 |
| 6.83583 | 2.620569 |
| 6.88528 | 2.620307 |
| 6.93508 | 2.620042 |
| 6.98525 | 2.619773 |
| 7.03578 | 2.6195 |
| 7.08668 | 2.619223 |
| 7.13794 | 2.618942 |
| 7.18958 | 2.618657 |
| 7.24159 | 2.618367 |
| 7.29397 | 2.618074 |
| 7.34673 | 2.617776 |
| 7.39988 | 2.617473 |
| 7.45341 | 2.617166 |
| 7.50733 | 2.616854 |
| 7.56163 | 2.616538 |
| 7.61633 | 2.616216 |
| 7.67143 | 2.61589 |
| 7.72692 | 2.615558 |
| 7.78282 | 2.615221 |
| 7.83912 | 2.614879 |
| 7.89583 | 2.614532 |
| 7.95294 | 2.614179 |
| 8.01047 | 2.61382 |
| 8.06842 | 2.613456 |
| 8.12679 | 2.613085 |
| 8.18558 | 2.612709 |
| 8.24479 | 2.612326 |
| 8.30443 | 2.611937 |
| 8.3645 | 2.611541 |
| 8.42501 | 2.611139 |
| 8.48596 | 2.61073 |
| 8.54734 | 2.610315 |
| 8.60917 | 2.609892 |
| 8.67145 | 2.609462 |
| 8.73418 | 2.609024 |
| 8.79736 | 2.608579 |
| 8.861 | 2.608127 |
| 8.9251 | 2.607666 |
| 8.98966 | 2.607198 |
| 9.05469 | 2.606721 |
| 9.1202 | 2.606235 |
| 9.18617 | 2.605742 |
| 9.25262 | 2.605239 |
| 9.31955 | 2.604727 |
| 9.38697 | 2.604206 |
| 9.45487 | 2.603675 |
| 9.52327 | 2.603135 |
| 9.59216 | 2.602585 |
| 9.66155 | 2.602025 |
| 9.73144 | 2.601454 |
| 9.80184 | 2.600873 |
| 9.87274 | 2.600281 |
| 9.94416 | 2.599677 |
| 10.0161 | 2.599062 |
| 10.0885 | 2.598436 |
| 10.1615 | 2.597797 |
| 10.235 | 2.597146 |
| 10.3091 | 2.596483 |
| 10.3837 | 2.595807 |
| 10.4588 | 2.595117 |
| 10.5344 | 2.594414 |
| 10.6106 | 2.593696 |
| 10.6874 | 2.592965 |
| 10.7647 | 2.592219 |
| 10.8426 | 2.591458 |
| 10.921 | 2.590681 |
| 11 | 2.589888 |
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
- —
Ordinary ray (o).