Optical constants
Refractive index of HgS (Mercury sulfide)
Bond et al. 1967: α-HgS; n(e) 0.62–11 µm
- Data
- formula 2
- Range
- 0.62–11 µm
- Optical axis
- e
- Licence
- CC0-1.0
Uniaxial crystal, axes: oe
Plot
Click the plot to set the calculator wavelength.
At one wavelength
- Refractive index n
- 2.90732
- Extinction coefficient k
- 0
- Permittivity ε1
- 8.4525
- Permittivity ε2
- 0
- Absorption coefficient α
- 0 cm⁻¹
- Penetration depth δ = λ/(2πk)
- — nm
- Abbe number Vd
- —
- Chromatic dispersion dn/dλ
- -0.0133114 µm⁻¹
- Group index ng
- 2.94206
- Group velocity dispersion
- 391.562 fs²/mm
- Dispersion parameter D
- -108.273 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(e) 0.62–11 µm
hgs = ls.fetch_refractiveindex("main", "HgS", "Bond-e", 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_e8fb226a8d55/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-e).
# ... 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_e8fb226a8d55/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 | 3.0101 |
| C2 | 4.3736 |
| C3 | 0.1284 |
| C4 | 1.5604 |
| C5 | 705.0 |
Comments and conditions
Conditions
- direction
- e
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 | 3.25215 |
| 0.624485 | 3.244944 |
| 0.629002 | 3.237926 |
| 0.633553 | 3.231088 |
| 0.638136 | 3.224425 |
| 0.642752 | 3.21793 |
| 0.647401 | 3.211599 |
| 0.652085 | 3.205425 |
| 0.656802 | 3.199403 |
| 0.661553 | 3.193529 |
| 0.666339 | 3.187797 |
| 0.671159 | 3.182203 |
| 0.676014 | 3.176743 |
| 0.680904 | 3.171411 |
| 0.68583 | 3.166205 |
| 0.690791 | 3.161121 |
| 0.695788 | 3.156154 |
| 0.700821 | 3.151302 |
| 0.705891 | 3.14656 |
| 0.710997 | 3.141925 |
| 0.716141 | 3.137395 |
| 0.721321 | 3.132966 |
| 0.726539 | 3.128635 |
| 0.731795 | 3.1244 |
| 0.737088 | 3.120257 |
| 0.74242 | 3.116205 |
| 0.747791 | 3.11224 |
| 0.7532 | 3.108361 |
| 0.758649 | 3.104564 |
| 0.764137 | 3.100848 |
| 0.769665 | 3.09721 |
| 0.775232 | 3.093649 |
| 0.78084 | 3.090162 |
| 0.786489 | 3.086747 |
| 0.792178 | 3.083403 |
| 0.797909 | 3.080127 |
| 0.803681 | 3.076918 |
| 0.809494 | 3.073774 |
| 0.81535 | 3.070694 |
| 0.821248 | 3.067675 |
| 0.827189 | 3.064717 |
| 0.833173 | 3.061818 |
| 0.8392 | 3.058975 |
| 0.845271 | 3.056189 |
| 0.851385 | 3.053458 |
| 0.857544 | 3.050779 |
| 0.863747 | 3.048153 |
| 0.869996 | 3.045577 |
| 0.876289 | 3.043051 |
| 0.882628 | 3.040574 |
| 0.889013 | 3.038143 |
| 0.895444 | 3.035759 |
| 0.901922 | 3.033419 |
| 0.908446 | 3.031124 |
| 0.915018 | 3.028872 |
| 0.921637 | 3.026661 |
| 0.928304 | 3.024492 |
| 0.935019 | 3.022363 |
| 0.941783 | 3.020273 |
| 0.948595 | 3.018222 |
| 0.955458 | 3.016208 |
| 0.962369 | 3.014231 |
| 0.969331 | 3.012289 |
| 0.976343 | 3.010383 |
| 0.983406 | 3.008511 |
| 0.990519 | 3.006673 |
| 0.997685 | 3.004868 |
| 1.0049 | 3.003094 |
| 1.01217 | 3.001353 |
| 1.01949 | 2.999642 |
| 1.02687 | 2.997961 |
| 1.0343 | 2.99631 |
| 1.04178 | 2.994688 |
| 1.04931 | 2.993094 |
| 1.05691 | 2.991528 |
| 1.06455 | 2.98999 |
| 1.07225 | 2.988477 |
| 1.08001 | 2.986991 |
| 1.08782 | 2.985531 |
| 1.09569 | 2.984095 |
| 1.10362 | 2.982684 |
| 1.1116 | 2.981297 |
| 1.11964 | 2.979934 |
| 1.12774 | 2.978594 |
| 1.1359 | 2.977276 |
| 1.14411 | 2.975981 |
| 1.15239 | 2.974707 |
| 1.16073 | 2.973455 |
| 1.16912 | 2.972224 |
| 1.17758 | 2.971013 |
| 1.1861 | 2.969822 |
| 1.19468 | 2.968651 |
| 1.20332 | 2.9675 |
| 1.21203 | 2.966367 |
| 1.22079 | 2.965253 |
| 1.22963 | 2.964157 |
| 1.23852 | 2.963079 |
| 1.24748 | 2.962019 |
| 1.2565 | 2.960976 |
| 1.26559 | 2.95995 |
| 1.27475 | 2.958941 |
| 1.28397 | 2.957947 |
| 1.29326 | 2.95697 |
| 1.30261 | 2.956009 |
| 1.31204 | 2.955063 |
| 1.32153 | 2.954132 |
| 1.33109 | 2.953216 |
| 1.34072 | 2.952314 |
| 1.35041 | 2.951427 |
| 1.36018 | 2.950554 |
| 1.37002 | 2.949694 |
| 1.37993 | 2.948848 |
| 1.38992 | 2.948016 |
| 1.39997 | 2.947196 |
| 1.4101 | 2.946389 |
| 1.4203 | 2.945595 |
| 1.43057 | 2.944813 |
| 1.44092 | 2.944044 |
| 1.45134 | 2.943286 |
| 1.46184 | 2.94254 |
| 1.47242 | 2.941805 |
| 1.48307 | 2.941082 |
| 1.4938 | 2.94037 |
| 1.5046 | 2.939668 |
| 1.51549 | 2.938978 |
| 1.52645 | 2.938298 |
| 1.53749 | 2.937628 |
| 1.54861 | 2.936968 |
| 1.55982 | 2.936319 |
| 1.5711 | 2.935679 |
| 1.58247 | 2.935048 |
| 1.59391 | 2.934427 |
| 1.60544 | 2.933816 |
| 1.61706 | 2.933213 |
| 1.62875 | 2.93262 |
| 1.64054 | 2.932035 |
| 1.6524 | 2.931459 |
| 1.66436 | 2.930891 |
| 1.6764 | 2.930332 |
| 1.68852 | 2.929781 |
| 1.70074 | 2.929238 |
| 1.71304 | 2.928703 |
| 1.72543 | 2.928176 |
| 1.73792 | 2.927656 |
| 1.75049 | 2.927144 |
| 1.76315 | 2.926639 |
| 1.7759 | 2.926142 |
| 1.78875 | 2.925651 |
| 1.80169 | 2.925168 |
| 1.81472 | 2.924691 |
| 1.82785 | 2.924221 |
| 1.84107 | 2.923758 |
| 1.85439 | 2.923301 |
| 1.86781 | 2.922851 |
| 1.88132 | 2.922407 |
| 1.89493 | 2.921969 |
| 1.90864 | 2.921538 |
| 1.92244 | 2.921112 |
| 1.93635 | 2.920692 |
| 1.95036 | 2.920278 |
| 1.96446 | 2.919869 |
| 1.97868 | 2.919466 |
| 1.99299 | 2.919069 |
| 2.00741 | 2.918677 |
| 2.02193 | 2.91829 |
| 2.03655 | 2.917908 |
| 2.05129 | 2.917532 |
| 2.06612 | 2.91716 |
| 2.08107 | 2.916793 |
| 2.09612 | 2.916432 |
| 2.11129 | 2.916074 |
| 2.12656 | 2.915722 |
| 2.14194 | 2.915374 |
| 2.15744 | 2.91503 |
| 2.17305 | 2.914691 |
| 2.18877 | 2.914356 |
| 2.2046 | 2.914026 |
| 2.22055 | 2.913699 |
| 2.23661 | 2.913377 |
| 2.25279 | 2.913059 |
| 2.26909 | 2.912744 |
| 2.2855 | 2.912434 |
| 2.30203 | 2.912127 |
| 2.31869 | 2.911824 |
| 2.33546 | 2.911524 |
| 2.35235 | 2.911228 |
| 2.36937 | 2.910936 |
| 2.38651 | 2.910647 |
| 2.40377 | 2.910361 |
| 2.42116 | 2.910079 |
| 2.43868 | 2.9098 |
| 2.45632 | 2.909524 |
| 2.47409 | 2.909251 |
| 2.49198 | 2.908981 |
| 2.51001 | 2.908715 |
| 2.52817 | 2.908451 |
| 2.54646 | 2.90819 |
| 2.56488 | 2.907931 |
| 2.58343 | 2.907676 |
| 2.60212 | 2.907423 |
| 2.62094 | 2.907173 |
| 2.6399 | 2.906925 |
| 2.659 | 2.90668 |
| 2.67823 | 2.906437 |
| 2.69761 | 2.906197 |
| 2.71712 | 2.905959 |
| 2.73678 | 2.905723 |
| 2.75657 | 2.90549 |
| 2.77651 | 2.905259 |
| 2.7966 | 2.90503 |
| 2.81683 | 2.904803 |
| 2.83721 | 2.904578 |
| 2.85773 | 2.904355 |
| 2.8784 | 2.904133 |
| 2.89923 | 2.903914 |
| 2.9202 | 2.903697 |
| 2.94132 | 2.903481 |
| 2.9626 | 2.903267 |
| 2.98403 | 2.903055 |
| 3.00562 | 2.902844 |
| 3.02736 | 2.902635 |
| 3.04926 | 2.902428 |
| 3.07132 | 2.902222 |
| 3.09353 | 2.902018 |
| 3.11591 | 2.901814 |
| 3.13845 | 2.901613 |
| 3.16116 | 2.901412 |
| 3.18402 | 2.901213 |
| 3.20706 | 2.901015 |
| 3.23026 | 2.900818 |
| 3.25362 | 2.900623 |
| 3.27716 | 2.900428 |
| 3.30087 | 2.900235 |
| 3.32474 | 2.900042 |
| 3.34879 | 2.899851 |
| 3.37302 | 2.89966 |
| 3.39742 | 2.89947 |
| 3.422 | 2.899281 |
| 3.44675 | 2.899093 |
| 3.47168 | 2.898906 |
| 3.4968 | 2.898719 |
| 3.52209 | 2.898533 |
| 3.54757 | 2.898348 |
| 3.57323 | 2.898163 |
| 3.59908 | 2.897979 |
| 3.62512 | 2.897795 |
| 3.65134 | 2.897612 |
| 3.67775 | 2.897429 |
| 3.70436 | 2.897246 |
| 3.73116 | 2.897064 |
| 3.75815 | 2.896882 |
| 3.78533 | 2.896701 |
| 3.81272 | 2.896519 |
| 3.8403 | 2.896338 |
| 3.86808 | 2.896157 |
| 3.89606 | 2.895976 |
| 3.92424 | 2.895795 |
| 3.95263 | 2.895614 |
| 3.98122 | 2.895433 |
| 4.01002 | 2.895252 |
| 4.03903 | 2.89507 |
| 4.06825 | 2.894889 |
| 4.09768 | 2.894708 |
| 4.12732 | 2.894526 |
| 4.15718 | 2.894344 |
| 4.18725 | 2.894161 |
| 4.21754 | 2.893978 |
| 4.24805 | 2.893795 |
| 4.27878 | 2.893612 |
| 4.30973 | 2.893428 |
| 4.34091 | 2.893243 |
| 4.37231 | 2.893058 |
| 4.40394 | 2.892872 |
| 4.43579 | 2.892685 |
| 4.46788 | 2.892498 |
| 4.5002 | 2.89231 |
| 4.53276 | 2.892121 |
| 4.56555 | 2.891931 |
| 4.59857 | 2.891741 |
| 4.63184 | 2.891549 |
| 4.66534 | 2.891357 |
| 4.69909 | 2.891164 |
| 4.73308 | 2.890969 |
| 4.76732 | 2.890773 |
| 4.80181 | 2.890577 |
| 4.83655 | 2.890378 |
| 4.87153 | 2.890179 |
| 4.90677 | 2.889979 |
| 4.94227 | 2.889777 |
| 4.97802 | 2.889573 |
| 5.01403 | 2.889368 |
| 5.0503 | 2.889162 |
| 5.08683 | 2.888954 |
| 5.12363 | 2.888745 |
| 5.1607 | 2.888534 |
| 5.19803 | 2.888321 |
| 5.23563 | 2.888106 |
| 5.2735 | 2.88789 |
| 5.31165 | 2.887671 |
| 5.35007 | 2.887451 |
| 5.38878 | 2.887229 |
| 5.42776 | 2.887005 |
| 5.46702 | 2.886778 |
| 5.50657 | 2.88655 |
| 5.5464 | 2.886319 |
| 5.58653 | 2.886086 |
| 5.62694 | 2.885851 |
| 5.66764 | 2.885613 |
| 5.70864 | 2.885373 |
| 5.74994 | 2.88513 |
| 5.79153 | 2.884885 |
| 5.83343 | 2.884637 |
| 5.87563 | 2.884386 |
| 5.91813 | 2.884132 |
| 5.96094 | 2.883876 |
| 6.00406 | 2.883617 |
| 6.04749 | 2.883355 |
| 6.09124 | 2.883089 |
| 6.1353 | 2.882821 |
| 6.17969 | 2.882549 |
| 6.22439 | 2.882274 |
| 6.26942 | 2.881996 |
| 6.31477 | 2.881714 |
| 6.36045 | 2.881429 |
| 6.40646 | 2.88114 |
| 6.4528 | 2.880848 |
| 6.49948 | 2.880551 |
| 6.5465 | 2.880251 |
| 6.59385 | 2.879947 |
| 6.64155 | 2.879639 |
| 6.6896 | 2.879327 |
| 6.73799 | 2.87901 |
| 6.78673 | 2.87869 |
| 6.83583 | 2.878365 |
| 6.88528 | 2.878035 |
| 6.93508 | 2.877701 |
| 6.98525 | 2.877362 |
| 7.03578 | 2.877018 |
| 7.08668 | 2.87667 |
| 7.13794 | 2.876316 |
| 7.18958 | 2.875958 |
| 7.24159 | 2.875594 |
| 7.29397 | 2.875224 |
| 7.34673 | 2.87485 |
| 7.39988 | 2.87447 |
| 7.45341 | 2.874084 |
| 7.50733 | 2.873692 |
| 7.56163 | 2.873294 |
| 7.61633 | 2.87289 |
| 7.67143 | 2.87248 |
| 7.72692 | 2.872064 |
| 7.78282 | 2.871641 |
| 7.83912 | 2.871212 |
| 7.89583 | 2.870775 |
| 7.95294 | 2.870332 |
| 8.01047 | 2.869882 |
| 8.06842 | 2.869425 |
| 8.12679 | 2.86896 |
| 8.18558 | 2.868488 |
| 8.24479 | 2.868008 |
| 8.30443 | 2.86752 |
| 8.3645 | 2.867024 |
| 8.42501 | 2.866519 |
| 8.48596 | 2.866007 |
| 8.54734 | 2.865485 |
| 8.60917 | 2.864955 |
| 8.67145 | 2.864416 |
| 8.73418 | 2.863868 |
| 8.79736 | 2.86331 |
| 8.861 | 2.862743 |
| 8.9251 | 2.862166 |
| 8.98966 | 2.861579 |
| 9.05469 | 2.860981 |
| 9.1202 | 2.860373 |
| 9.18617 | 2.859754 |
| 9.25262 | 2.859125 |
| 9.31955 | 2.858483 |
| 9.38697 | 2.857831 |
| 9.45487 | 2.857166 |
| 9.52327 | 2.85649 |
| 9.59216 | 2.855801 |
| 9.66155 | 2.855099 |
| 9.73144 | 2.854384 |
| 9.80184 | 2.853656 |
| 9.87274 | 2.852914 |
| 9.94416 | 2.852159 |
| 10.0161 | 2.851389 |
| 10.0885 | 2.850604 |
| 10.1615 | 2.849805 |
| 10.235 | 2.84899 |
| 10.3091 | 2.848159 |
| 10.3837 | 2.847312 |
| 10.4588 | 2.846449 |
| 10.5344 | 2.845568 |
| 10.6106 | 2.84467 |
| 10.6874 | 2.843754 |
| 10.7647 | 2.84282 |
| 10.8426 | 2.841867 |
| 10.921 | 2.840894 |
| 11 | 2.839902 |
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
- —
Extraordinary ray (e).