Optical constants
Refractive index of Te (Tellurium)
Caldwell and Fan 1959: n(e) 4.0–14 µm
- Data
- formula 2
- Range
- 4–14 µm
- Optical axis
- e
- State
- crystalline
- Licence
- CC0-1.0
Uniaxial crystal, axes: oe
Plot
Click the plot to set the calculator wavelength.
At one wavelength
- Refractive index n
- 6.26418
- Extinction coefficient k
- 0
- Permittivity ε1
- 39.2399
- Permittivity ε2
- 0
- Absorption coefficient α
- 0 cm⁻¹
- Penetration depth δ = λ/(2πk)
- — nm
- Abbe number Vd
- —
- Chromatic dispersion dn/dλ
- -0.0108738 µm⁻¹
- Group index ng
- 6.34551
- Group velocity dispersion
- 3083.15 fs²/mm
- Dispersion parameter D
- -103.799 ps/(nm·km)
- Photon energy
- 0.165754 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
# Te (Tellurium): Caldwell and Fan 1959: n(e) 4.0–14 µm
te = ls.fetch_refractiveindex("main", "Te", "Caldwell-e", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(te.range_nm) # (4000, 14000) nm
eps = te.eps([7480]) # 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_d6ca7c79e494/lightsmith"
te = ls.Tabulated.model_validate(json.load(urllib.request.urlopen(url)))
print(te.source) # citation and provenance travel with the data
Any dataset here, as the library's Tabulated material (te/caldwell-fan-1959-e).
# ... load te as above, then:
sim = ls.Simulation(
particles=[ls.Particle(shape=ls.Sphere(radius_nm=50), material=te)],
medium_index=1.0,
wavelengths=ls.WavelengthRange(start_nm=4000, stop_nm=14000, 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_d6ca7c79e494/lightsmith?model=drude_lorentz"
te_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 4.0 to 14.0 µm.
Coefficients as stored
| Ci | Value |
|---|---|
| C1 | 28.5222 |
| C2 | 9.3068 |
| C3 | 2.5766 |
| C4 | 9.235 |
| C5 | 13521.0 |
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:10.1103/physrev.114.664 Optical Properties of Tellurium and Selenium, Physical Review (1959)
- doi:10.1364/ao.15.0305_1 Refractive index interpolation in phase-matching, Applied Optics (1976)
Cite
Robert S. Caldwell and H. Y. Fan. Optical Properties of Tellurium and Selenium. Physical Review, 114, 664-675 (1959), doi:10.1103/physrev.114.664; 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 |
|---|---|
| 4 | 6.372165 |
| 4.01258 | 6.371115 |
| 4.0252 | 6.370073 |
| 4.03786 | 6.369041 |
| 4.05055 | 6.368017 |
| 4.06329 | 6.367001 |
| 4.07607 | 6.365994 |
| 4.08889 | 6.364996 |
| 4.10174 | 6.364005 |
| 4.11464 | 6.363023 |
| 4.12758 | 6.362049 |
| 4.14056 | 6.361083 |
| 4.15358 | 6.360125 |
| 4.16665 | 6.359175 |
| 4.17975 | 6.358233 |
| 4.19289 | 6.357298 |
| 4.20608 | 6.356371 |
| 4.2193 | 6.355451 |
| 4.23257 | 6.354539 |
| 4.24588 | 6.353635 |
| 4.25923 | 6.352738 |
| 4.27263 | 6.351847 |
| 4.28606 | 6.350965 |
| 4.29954 | 6.350089 |
| 4.31306 | 6.34922 |
| 4.32663 | 6.348358 |
| 4.34023 | 6.347504 |
| 4.35388 | 6.346656 |
| 4.36757 | 6.345814 |
| 4.38131 | 6.34498 |
| 4.39509 | 6.344152 |
| 4.40891 | 6.343331 |
| 4.42277 | 6.342516 |
| 4.43668 | 6.341707 |
| 4.45063 | 6.340905 |
| 4.46463 | 6.34011 |
| 4.47867 | 6.33932 |
| 4.49275 | 6.338537 |
| 4.50688 | 6.33776 |
| 4.52105 | 6.336989 |
| 4.53527 | 6.336224 |
| 4.54953 | 6.335465 |
| 4.56384 | 6.334712 |
| 4.57819 | 6.333964 |
| 4.59259 | 6.333223 |
| 4.60703 | 6.332487 |
| 4.62152 | 6.331757 |
| 4.63605 | 6.331033 |
| 4.65063 | 6.330314 |
| 4.66525 | 6.329601 |
| 4.67993 | 6.328893 |
| 4.69464 | 6.32819 |
| 4.70941 | 6.327493 |
| 4.72422 | 6.326802 |
| 4.73907 | 6.326115 |
| 4.75397 | 6.325434 |
| 4.76892 | 6.324758 |
| 4.78392 | 6.324087 |
| 4.79896 | 6.323421 |
| 4.81406 | 6.32276 |
| 4.82919 | 6.322105 |
| 4.84438 | 6.321454 |
| 4.85962 | 6.320808 |
| 4.8749 | 6.320167 |
| 4.89023 | 6.31953 |
| 4.90561 | 6.318899 |
| 4.92103 | 6.318272 |
| 4.93651 | 6.31765 |
| 4.95203 | 6.317032 |
| 4.9676 | 6.316419 |
| 4.98323 | 6.315811 |
| 4.9989 | 6.315207 |
| 5.01462 | 6.314608 |
| 5.03039 | 6.314013 |
| 5.0462 | 6.313422 |
| 5.06207 | 6.312836 |
| 5.07799 | 6.312254 |
| 5.09396 | 6.311676 |
| 5.10998 | 6.311103 |
| 5.12605 | 6.310534 |
| 5.14217 | 6.309969 |
| 5.15834 | 6.309408 |
| 5.17456 | 6.308851 |
| 5.19083 | 6.308298 |
| 5.20716 | 6.30775 |
| 5.22353 | 6.307205 |
| 5.23996 | 6.306664 |
| 5.25644 | 6.306127 |
| 5.27297 | 6.305594 |
| 5.28955 | 6.305065 |
| 5.30618 | 6.304539 |
| 5.32287 | 6.304018 |
| 5.33961 | 6.3035 |
| 5.3564 | 6.302985 |
| 5.37324 | 6.302475 |
| 5.39014 | 6.301968 |
| 5.40709 | 6.301465 |
| 5.42409 | 6.300965 |
| 5.44115 | 6.300469 |
| 5.45826 | 6.299976 |
| 5.47543 | 6.299487 |
| 5.49264 | 6.299001 |
| 5.50992 | 6.298519 |
| 5.52724 | 6.29804 |
| 5.54463 | 6.297565 |
| 5.56206 | 6.297093 |
| 5.57955 | 6.296624 |
| 5.5971 | 6.296158 |
| 5.6147 | 6.295696 |
| 5.63236 | 6.295237 |
| 5.65007 | 6.294781 |
| 5.66784 | 6.294328 |
| 5.68566 | 6.293879 |
| 5.70354 | 6.293432 |
| 5.72147 | 6.292989 |
| 5.73947 | 6.292549 |
| 5.75752 | 6.292112 |
| 5.77562 | 6.291677 |
| 5.79378 | 6.291246 |
| 5.812 | 6.290818 |
| 5.83028 | 6.290392 |
| 5.84862 | 6.28997 |
| 5.86701 | 6.28955 |
| 5.88546 | 6.289134 |
| 5.90397 | 6.28872 |
| 5.92253 | 6.288309 |
| 5.94116 | 6.287901 |
| 5.95984 | 6.287495 |
| 5.97858 | 6.287092 |
| 5.99738 | 6.286692 |
| 6.01624 | 6.286295 |
| 6.03516 | 6.2859 |
| 6.05414 | 6.285508 |
| 6.07318 | 6.285119 |
| 6.09228 | 6.284732 |
| 6.11143 | 6.284348 |
| 6.13065 | 6.283966 |
| 6.14993 | 6.283587 |
| 6.16927 | 6.283211 |
| 6.18867 | 6.282837 |
| 6.20813 | 6.282465 |
| 6.22766 | 6.282096 |
| 6.24724 | 6.28173 |
| 6.26689 | 6.281365 |
| 6.28659 | 6.281003 |
| 6.30636 | 6.280644 |
| 6.32619 | 6.280287 |
| 6.34609 | 6.279932 |
| 6.36604 | 6.27958 |
| 6.38606 | 6.279229 |
| 6.40615 | 6.278882 |
| 6.42629 | 6.278536 |
| 6.4465 | 6.278192 |
| 6.46677 | 6.277851 |
| 6.48711 | 6.277512 |
| 6.50751 | 6.277176 |
| 6.52797 | 6.276841 |
| 6.5485 | 6.276509 |
| 6.56909 | 6.276178 |
| 6.58975 | 6.27585 |
| 6.61047 | 6.275524 |
| 6.63126 | 6.2752 |
| 6.65212 | 6.274878 |
| 6.67303 | 6.274558 |
| 6.69402 | 6.27424 |
| 6.71507 | 6.273924 |
| 6.73619 | 6.27361 |
| 6.75737 | 6.273298 |
| 6.77862 | 6.272988 |
| 6.79994 | 6.27268 |
| 6.82132 | 6.272374 |
| 6.84277 | 6.27207 |
| 6.86429 | 6.271768 |
| 6.88588 | 6.271468 |
| 6.90753 | 6.271169 |
| 6.92925 | 6.270872 |
| 6.95104 | 6.270577 |
| 6.9729 | 6.270284 |
| 6.99483 | 6.269993 |
| 7.01682 | 6.269704 |
| 7.03889 | 6.269416 |
| 7.06103 | 6.26913 |
| 7.08323 | 6.268846 |
| 7.10551 | 6.268564 |
| 7.12785 | 6.268283 |
| 7.15026 | 6.268004 |
| 7.17275 | 6.267727 |
| 7.19531 | 6.267451 |
| 7.21793 | 6.267177 |
| 7.24063 | 6.266905 |
| 7.2634 | 6.266634 |
| 7.28624 | 6.266365 |
| 7.30915 | 6.266097 |
| 7.33214 | 6.265831 |
| 7.3552 | 6.265567 |
| 7.37833 | 6.265304 |
| 7.40153 | 6.265043 |
| 7.42481 | 6.264783 |
| 7.44815 | 6.264525 |
| 7.47158 | 6.264268 |
| 7.49507 | 6.264013 |
| 7.51864 | 6.26376 |
| 7.54229 | 6.263507 |
| 7.566 | 6.263257 |
| 7.5898 | 6.263007 |
| 7.61366 | 6.262759 |
| 7.63761 | 6.262513 |
| 7.66162 | 6.262268 |
| 7.68572 | 6.262024 |
| 7.70989 | 6.261782 |
| 7.73413 | 6.261541 |
| 7.75845 | 6.261302 |
| 7.78285 | 6.261063 |
| 7.80733 | 6.260827 |
| 7.83188 | 6.260591 |
| 7.85651 | 6.260357 |
| 7.88121 | 6.260124 |
| 7.906 | 6.259893 |
| 7.93086 | 6.259662 |
| 7.9558 | 6.259433 |
| 7.98082 | 6.259205 |
| 8.00591 | 6.258979 |
| 8.03109 | 6.258754 |
| 8.05635 | 6.25853 |
| 8.08168 | 6.258307 |
| 8.1071 | 6.258085 |
| 8.13259 | 6.257865 |
| 8.15816 | 6.257645 |
| 8.18382 | 6.257427 |
| 8.20955 | 6.25721 |
| 8.23537 | 6.256995 |
| 8.26127 | 6.25678 |
| 8.28725 | 6.256566 |
| 8.31331 | 6.256354 |
| 8.33945 | 6.256143 |
| 8.36568 | 6.255933 |
| 8.39198 | 6.255724 |
| 8.41837 | 6.255516 |
| 8.44485 | 6.255309 |
| 8.4714 | 6.255103 |
| 8.49804 | 6.254898 |
| 8.52477 | 6.254694 |
| 8.55158 | 6.254492 |
| 8.57847 | 6.25429 |
| 8.60544 | 6.254089 |
| 8.63251 | 6.25389 |
| 8.65965 | 6.253691 |
| 8.68688 | 6.253493 |
| 8.7142 | 6.253297 |
| 8.7416 | 6.253101 |
| 8.76909 | 6.252906 |
| 8.79667 | 6.252712 |
| 8.82433 | 6.252519 |
| 8.85208 | 6.252327 |
| 8.87992 | 6.252136 |
| 8.90784 | 6.251946 |
| 8.93586 | 6.251757 |
| 8.96396 | 6.251569 |
| 8.99215 | 6.251381 |
| 9.02042 | 6.251195 |
| 9.04879 | 6.251009 |
| 9.07725 | 6.250824 |
| 9.10579 | 6.25064 |
| 9.13443 | 6.250457 |
| 9.16315 | 6.250275 |
| 9.19197 | 6.250093 |
| 9.22087 | 6.249913 |
| 9.24987 | 6.249733 |
| 9.27896 | 6.249554 |
| 9.30814 | 6.249376 |
| 9.33741 | 6.249198 |
| 9.36677 | 6.249022 |
| 9.39623 | 6.248846 |
| 9.42578 | 6.248671 |
| 9.45542 | 6.248496 |
| 9.48515 | 6.248323 |
| 9.51498 | 6.24815 |
| 9.5449 | 6.247978 |
| 9.57492 | 6.247806 |
| 9.60503 | 6.247635 |
| 9.63523 | 6.247465 |
| 9.66553 | 6.247296 |
| 9.69593 | 6.247128 |
| 9.72642 | 6.24696 |
| 9.757 | 6.246792 |
| 9.78769 | 6.246626 |
| 9.81847 | 6.24646 |
| 9.84934 | 6.246295 |
| 9.88031 | 6.24613 |
| 9.91138 | 6.245966 |
| 9.94255 | 6.245803 |
| 9.97382 | 6.24564 |
| 10.0052 | 6.245478 |
| 10.0366 | 6.245317 |
| 10.0682 | 6.245156 |
| 10.0999 | 6.244996 |
| 10.1316 | 6.244836 |
| 10.1635 | 6.244677 |
| 10.1955 | 6.244518 |
| 10.2275 | 6.24436 |
| 10.2597 | 6.244203 |
| 10.2919 | 6.244046 |
| 10.3243 | 6.24389 |
| 10.3568 | 6.243734 |
| 10.3893 | 6.243579 |
| 10.422 | 6.243424 |
| 10.4548 | 6.24327 |
| 10.4877 | 6.243117 |
| 10.5206 | 6.242963 |
| 10.5537 | 6.242811 |
| 10.5869 | 6.242659 |
| 10.6202 | 6.242507 |
| 10.6536 | 6.242356 |
| 10.6871 | 6.242205 |
| 10.7207 | 6.242055 |
| 10.7544 | 6.241905 |
| 10.7882 | 6.241756 |
| 10.8222 | 6.241607 |
| 10.8562 | 6.241459 |
| 10.8903 | 6.241311 |
| 10.9246 | 6.241163 |
| 10.9589 | 6.241016 |
| 10.9934 | 6.240869 |
| 11.028 | 6.240723 |
| 11.0627 | 6.240577 |
| 11.0974 | 6.240432 |
| 11.1323 | 6.240287 |
| 11.1674 | 6.240142 |
| 11.2025 | 6.239998 |
| 11.2377 | 6.239854 |
| 11.273 | 6.23971 |
| 11.3085 | 6.239567 |
| 11.3441 | 6.239424 |
| 11.3797 | 6.239281 |
| 11.4155 | 6.239139 |
| 11.4514 | 6.238997 |
| 11.4874 | 6.238856 |
| 11.5235 | 6.238714 |
| 11.5598 | 6.238573 |
| 11.5961 | 6.238433 |
| 11.6326 | 6.238293 |
| 11.6692 | 6.238153 |
| 11.7059 | 6.238013 |
| 11.7427 | 6.237873 |
| 11.7796 | 6.237734 |
| 11.8167 | 6.237595 |
| 11.8538 | 6.237457 |
| 11.8911 | 6.237318 |
| 11.9285 | 6.23718 |
| 11.966 | 6.237043 |
| 12.0036 | 6.236905 |
| 12.0414 | 6.236768 |
| 12.0792 | 6.23663 |
| 12.1172 | 6.236494 |
| 12.1553 | 6.236357 |
| 12.1936 | 6.23622 |
| 12.2319 | 6.236084 |
| 12.2704 | 6.235948 |
| 12.309 | 6.235812 |
| 12.3477 | 6.235677 |
| 12.3865 | 6.235541 |
| 12.4254 | 6.235406 |
| 12.4645 | 6.235271 |
| 12.5037 | 6.235136 |
| 12.543 | 6.235001 |
| 12.5825 | 6.234866 |
| 12.6221 | 6.234732 |
| 12.6617 | 6.234597 |
| 12.7016 | 6.234463 |
| 12.7415 | 6.234329 |
| 12.7816 | 6.234195 |
| 12.8218 | 6.234061 |
| 12.8621 | 6.233928 |
| 12.9025 | 6.233794 |
| 12.9431 | 6.23366 |
| 12.9838 | 6.233527 |
| 13.0246 | 6.233394 |
| 13.0656 | 6.233261 |
| 13.1067 | 6.233127 |
| 13.1479 | 6.232994 |
| 13.1892 | 6.232861 |
| 13.2307 | 6.232728 |
| 13.2723 | 6.232595 |
| 13.3141 | 6.232463 |
| 13.3559 | 6.23233 |
| 13.3979 | 6.232197 |
| 13.4401 | 6.232064 |
| 13.4823 | 6.231932 |
| 13.5247 | 6.231799 |
| 13.5673 | 6.231667 |
| 13.6099 | 6.231534 |
| 13.6527 | 6.231401 |
| 13.6957 | 6.231269 |
| 13.7387 | 6.231136 |
| 13.7819 | 6.231003 |
| 13.8253 | 6.230871 |
| 13.8687 | 6.230738 |
| 13.9124 | 6.230605 |
| 13.9561 | 6.230473 |
| 14 | 6.23034 |
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).