Optical constants
Refractive index of Zr (Zirconium)
Querry 1987: n,k 0.220–55.6 µm
- Data
- tabulated nk
- Range
- 0.22–55.56 µm
- Points
- 306
- Licence
- CC0-1.0
Plot
Click the plot to set the calculator wavelength.
At one wavelength
- Refractive index n
- 2.77888
- Extinction coefficient k
- 3.48006
- Permittivity ε1
- -4.38864
- Permittivity ε2
- 19.3413
- Absorption coefficient α
- 744243 cm⁻¹
- Penetration depth δ = λ/(2πk)
- 26.8729 nm
- Abbe number Vd
- —
- Chromatic dispersion dn/dλ
- 6.3 µm⁻¹
- Group index ng
- -0.923
- Group velocity dispersion
- — fs²/mm
- Dispersion parameter D
- — 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
# Zr (Zirconium): Querry 1987: n,k 0.220–55.6 µm
zr = ls.fetch_refractiveindex("main", "Zr", "Querry", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(zr.range_nm) # (220, 55555.6) nm
eps = zr.eps([633]) # 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_31860b534919/lightsmith"
zr = ls.Tabulated.model_validate(json.load(urllib.request.urlopen(url)))
print(zr.source) # citation and provenance travel with the dataAny dataset here, as the library's Tabulated material (zr/querry-1987).
# ... load zr as above, then:
sim = ls.Simulation(
particles=[ls.Particle(shape=ls.Sphere(radius_nm=50), material=zr)],
medium_index=1.0,
wavelengths=ls.WavelengthRange(start_nm=400, stop_nm=1000, 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.
References
M. R. Querry. Optical constants of minerals and other materials from the millimeter to the ultraviolet, Contractor Report CRDEC-CR-88009 (1987)
Cite
M. R. Querry. Optical constants of minerals and other materials from the millimeter to the ultraviolet, Contractor Report CRDEC-CR-88009 (1987); Data from the refractiveindex.info database (M. N. Polyanskiy, Sci. Data 11, 94 (2024), doi:10.1038/s41597-023-02898-2)
Data
306 rows as published
CSV comma separated
TXT tab separated
YAML n, k
Full database record original YAML
All quantities CSV
JSON metadata
| λ (µm) | n | k |
|---|---|---|
| 0.22 | 1.007 | 0.697 |
| 0.24 | 0.995 | 1.145 |
| 0.26 | 1.091 | 1.433 |
| 0.28 | 1.178 | 1.651 |
| 0.3 | 1.271 | 1.845 |
| 0.32 | 1.36 | 2.009 |
| 0.34 | 1.452 | 2.174 |
| 0.36 | 1.55 | 2.308 |
| 0.38 | 1.636 | 2.452 |
| 0.4 | 1.734 | 2.579 |
| 0.42 | 1.836 | 2.708 |
| 0.44 | 1.935 | 2.817 |
| 0.46 | 2.034 | 2.926 |
| 0.48 | 2.134 | 3.033 |
| 0.5 | 2.245 | 3.138 |
| 0.52 | 2.356 | 3.228 |
| 0.54 | 2.47 | 3.319 |
| 0.56 | 2.593 | 3.401 |
| 0.58 | 2.731 | 3.466 |
| 0.6 | 2.857 | 3.503 |
| 0.62 | 2.968 | 3.537 |
| 0.64 | 3.078 | 3.566 |
| 0.66 | 3.179 | 3.586 |
| 0.68 | 3.274 | 3.603 |
| 0.7 | 3.364 | 3.616 |
| 0.72 | 3.448 | 3.623 |
| 0.74 | 3.526 | 3.628 |
| 0.76 | 3.595 | 3.63 |
| 0.78 | 3.66 | 3.631 |
| 0.8 | 3.724 | 3.627 |
| 0.82 | 3.76 | 3.619 |
| 0.84 | 3.801 | 3.627 |
| 0.86 | 3.83 | 3.63 |
| 0.88 | 3.856 | 3.653 |
| 0.9 | 3.888 | 3.685 |
| 0.92 | 3.931 | 3.714 |
| 0.94 | 3.97 | 3.736 |
| 0.96 | 4.016 | 3.761 |
| 0.98 | 4.061 | 3.79 |
| 1.0 | 4.098 | 3.804 |
| 1.02 | 4.138 | 3.831 |
| 1.04 | 4.179 | 3.852 |
| 1.06 | 4.226 | 3.88 |
| 1.08 | 4.275 | 3.9 |
| 1.1 | 4.319 | 3.911 |
| 1.12 | 4.365 | 3.921 |
| 1.14 | 4.402 | 3.931 |
| 1.16 | 4.443 | 3.934 |
| 1.18 | 4.475 | 3.94 |
| 1.2 | 4.51 | 3.936 |
| 1.22 | 4.515 | 3.942 |
| 1.24 | 4.539 | 3.959 |
| 1.26 | 4.558 | 3.98 |
| 1.28 | 4.581 | 4.0 |
| 1.3 | 4.603 | 4.009 |
| 1.32 | 4.627 | 4.023 |
| 1.34 | 4.649 | 4.049 |
| 1.36 | 4.68 | 4.065 |
| 1.38 | 4.697 | 4.074 |
| 1.4 | 4.704 | 4.091 |
| 1.42 | 4.734 | 4.113 |
| 1.44 | 4.754 | 4.128 |
| 1.46 | 4.777 | 4.15 |
| 1.48 | 4.8 | 4.166 |
| 1.5 | 4.819 | 4.182 |
| 1.52 | 4.846 | 4.192 |
| 1.54 | 4.846 | 4.203 |
| 1.56 | 4.878 | 4.229 |
| 1.58 | 4.896 | 4.238 |
| 1.6 | 4.914 | 4.253 |
| 1.62 | 4.933 | 4.278 |
| 1.64 | 4.95 | 4.282 |
| 1.66 | 4.958 | 4.292 |
| 1.68 | 4.97 | 4.311 |
| 1.7 | 4.983 | 4.328 |
| 1.72 | 4.997 | 4.332 |
| 1.74 | 5.003 | 4.357 |
| 1.76 | 5.016 | 4.371 |
| 1.78 | 5.027 | 4.387 |
| 1.8 | 5.03 | 4.393 |
| 1.82 | 5.025 | 4.433 |
| 1.84 | 5.047 | 4.462 |
| 1.86 | 5.055 | 4.466 |
| 1.88 | 5.05 | 4.521 |
| 1.9 | 5.097 | 4.559 |
| 1.92 | 5.126 | 4.572 |
| 1.94 | 5.162 | 4.565 |
| 1.96 | 5.174 | 4.573 |
| 1.98 | 5.194 | 4.573 |
| 2.0 | 5.183 | 4.586 |
| 2.02 | 5.209 | 4.584 |
| 2.04 | 5.207 | 4.597 |
| 2.06 | 5.212 | 4.606 |
| 2.08 | 5.21 | 4.618 |
| 2.1 | 5.217 | 4.637 |
| 2.12 | 5.223 | 4.655 |
| 2.14 | 5.241 | 4.667 |
| 2.16 | 5.24 | 4.666 |
| 2.18 | 5.236 | 4.679 |
| 2.2 | 5.241 | 4.693 |
| 2.22 | 5.239 | 4.702 |
| 2.24 | 5.239 | 4.707 |
| 2.26 | 5.231 | 4.724 |
| 2.28 | 5.224 | 4.739 |
| 2.3 | 5.221 | 4.762 |
| 2.32 | 5.212 | 4.778 |
| 2.34 | 5.205 | 4.796 |
| 2.36 | 5.212 | 4.82 |
| 2.38 | 5.204 | 4.83 |
| 2.4 | 5.2 | 4.853 |
| 2.42 | 5.196 | 4.88 |
| 2.44 | 5.203 | 4.896 |
| 2.46 | 5.195 | 4.912 |
| 2.48 | 5.209 | 4.937 |
| 2.5 | 5.207 | 4.915 |
| 2.5126 | 5.189 | 4.924 |
| 2.5253 | 5.176 | 4.936 |
| 2.5381 | 5.165 | 4.948 |
| 2.551 | 5.153 | 4.962 |
| 2.5641 | 5.142 | 4.977 |
| 2.5773 | 5.131 | 4.992 |
| 2.5907 | 5.12 | 5.009 |
| 2.6042 | 5.11 | 5.028 |
| 2.6178 | 5.101 | 5.047 |
| 2.6316 | 5.092 | 5.069 |
| 2.6455 | 5.087 | 5.089 |
| 2.6596 | 5.08 | 5.109 |
| 2.6738 | 5.075 | 5.129 |
| 2.6882 | 5.07 | 5.149 |
| 2.7027 | 5.064 | 5.168 |
| 2.7322 | 5.052 | 5.206 |
| 2.7174 | 5.058 | 5.188 |
| 2.7473 | 5.045 | 5.227 |
| 2.7624 | 5.038 | 5.246 |
| 2.7778 | 5.03 | 5.264 |
| 2.7933 | 5.022 | 5.286 |
| 2.809 | 5.013 | 5.308 |
| 2.8249 | 5.002 | 5.328 |
| 2.8409 | 4.993 | 5.353 |
| 2.8571 | 4.983 | 5.377 |
| 2.8736 | 4.974 | 5.4 |
| 2.8902 | 4.964 | 5.427 |
| 2.907 | 4.954 | 5.451 |
| 2.924 | 4.943 | 5.478 |
| 2.9412 | 4.93 | 5.506 |
| 2.9586 | 4.921 | 5.534 |
| 2.9762 | 4.909 | 5.564 |
| 2.994 | 4.898 | 5.596 |
| 3.012 | 4.888 | 5.628 |
| 3.0303 | 4.88 | 5.659 |
| 3.0488 | 4.869 | 5.693 |
| 3.0675 | 4.86 | 5.726 |
| 3.0864 | 4.85 | 5.759 |
| 3.1056 | 4.839 | 5.795 |
| 3.125 | 4.831 | 5.832 |
| 3.1447 | 4.821 | 5.867 |
| 3.1646 | 4.811 | 5.907 |
| 3.1847 | 4.802 | 5.945 |
| 3.2051 | 4.793 | 5.983 |
| 3.2258 | 4.784 | 6.022 |
| 3.2468 | 4.774 | 6.064 |
| 3.268 | 4.766 | 6.108 |
| 3.2895 | 4.758 | 6.15 |
| 3.3113 | 4.749 | 6.194 |
| 3.3333 | 4.744 | 6.242 |
| 3.3557 | 4.739 | 6.286 |
| 3.3764 | 4.733 | 6.332 |
| 3.4014 | 4.728 | 6.377 |
| 3.4247 | 4.72 | 6.423 |
| 3.4483 | 4.715 | 6.473 |
| 3.4722 | 4.71 | 6.518 |
| 3.4965 | 4.701 | 6.568 |
| 3.5211 | 4.697 | 6.619 |
| 3.5461 | 4.693 | 6.67 |
| 3.5714 | 4.686 | 6.721 |
| 3.5971 | 4.68 | 6.774 |
| 3.6232 | 4.674 | 6.827 |
| 3.6496 | 4.669 | 6.883 |
| 3.6765 | 4.664 | 6.938 |
| 3.7037 | 4.657 | 6.996 |
| 3.7313 | 4.654 | 7.056 |
| 3.7594 | 4.651 | 7.115 |
| 3.7879 | 4.647 | 7.174 |
| 3.8168 | 4.639 | 7.236 |
| 3.8462 | 4.636 | 7.301 |
| 3.876 | 4.633 | 7.366 |
| 3.9063 | 4.63 | 7.433 |
| 3.937 | 4.628 | 7.502 |
| 3.9683 | 4.628 | 7.573 |
| 4.0 | 4.63 | 7.642 |
| 4.0323 | 4.63 | 7.711 |
| 4.065 | 4.627 | 7.784 |
| 4.0984 | 4.629 | 7.86 |
| 4.1322 | 4.634 | 7.936 |
| 4.1667 | 4.634 | 8.012 |
| 4.2017 | 4.642 | 8.09 |
| 4.2373 | 4.646 | 8.166 |
| 4.2735 | 4.654 | 8.245 |
| 4.3103 | 4.656 | 8.324 |
| 4.3478 | 4.663 | 8.408 |
| 4.386 | 4.67 | 8.491 |
| 4.4248 | 4.677 | 8.573 |
| 4.4643 | 4.684 | 8.66 |
| 4.5045 | 4.697 | 8.744 |
| 4.5455 | 4.705 | 8.826 |
| 4.5872 | 4.711 | 8.912 |
| 4.6296 | 4.718 | 9.0 |
| 4.6729 | 4.723 | 9.093 |
| 4.717 | 4.726 | 9.187 |
| 4.7619 | 4.733 | 9.285 |
| 4.8077 | 4.74 | 9.386 |
| 4.8544 | 4.748 | 9.49 |
| 4.902 | 4.758 | 9.599 |
| 4.9505 | 4.772 | 9.708 |
| 5.0 | 4.788 | 9.819 |
| 5.0505 | 4.804 | 9.932 |
| 5.102 | 4.825 | 10.039 |
| 5.1546 | 4.837 | 10.152 |
| 5.2083 | 4.856 | 10.277 |
| 5.2632 | 4.873 | 10.388 |
| 5.3191 | 4.889 | 10.514 |
| 5.3763 | 4.91 | 10.641 |
| 5.4348 | 4.929 | 10.779 |
| 5.4945 | 4.961 | 10.917 |
| 5.5556 | 5.001 | 11.042 |
| 5.618 | 5.024 | 11.177 |
| 5.6818 | 5.051 | 11.32 |
| 5.7471 | 5.089 | 11.453 |
| 5.814 | 5.115 | 11.595 |
| 5.8824 | 5.151 | 11.746 |
| 5.9524 | 5.183 | 11.902 |
| 6.0241 | 5.23 | 12.057 |
| 6.0976 | 5.271 | 12.212 |
| 6.1728 | 5.31 | 12.376 |
| 6.25 | 5.36 | 12.543 |
| 6.3291 | 5.41 | 12.714 |
| 6.4103 | 5.47 | 12.889 |
| 6.4935 | 5.532 | 13.06 |
| 6.5789 | 5.595 | 13.237 |
| 6.6667 | 5.661 | 13.416 |
| 6.7568 | 5.732 | 13.596 |
| 6.8493 | 5.802 | 13.787 |
| 6.9444 | 5.887 | 13.963 |
| 7.0423 | 5.952 | 14.15 |
| 7.1429 | 6.035 | 14.344 |
| 7.2464 | 6.127 | 14.539 |
| 7.3529 | 6.213 | 14.727 |
| 7.4627 | 6.309 | 14.911 |
| 7.5758 | 6.383 | 15.092 |
| 7.6923 | 6.456 | 15.31 |
| 7.8125 | 6.55 | 15.527 |
| 7.9365 | 6.632 | 15.735 |
| 8.0645 | 6.72 | 15.97 |
| 8.1967 | 6.819 | 16.197 |
| 8.3333 | 6.924 | 16.439 |
| 8.4746 | 7.018 | 16.674 |
| 8.6207 | 7.115 | 16.929 |
| 8.7719 | 7.218 | 17.195 |
| 8.9286 | 7.317 | 17.476 |
| 9.0909 | 7.455 | 17.774 |
| 9.2593 | 7.584 | 18.059 |
| 9.434 | 7.721 | 18.366 |
| 9.6154 | 7.864 | 18.676 |
| 9.8039 | 8.025 | 18.992 |
| 10.0 | 8.201 | 19.327 |
| 10.2041 | 8.37 | 19.66 |
| 10.4167 | 8.546 | 19.986 |
| 10.6383 | 8.732 | 20.344 |
| 10.8696 | 8.937 | 20.716 |
| 11.1111 | 9.136 | 21.086 |
| 11.3636 | 9.369 | 21.473 |
| 11.6279 | 9.595 | 21.856 |
| 11.9048 | 9.831 | 22.265 |
| 12.1951 | 10.079 | 22.688 |
| 12.5 | 10.335 | 23.123 |
| 12.8205 | 10.619 | 23.577 |
| 13.1579 | 10.911 | 24.042 |
| 13.5135 | 11.205 | 24.5 |
| 13.8889 | 11.515 | 25.016 |
| 14.2857 | 11.814 | 25.545 |
| 14.7059 | 12.166 | 26.097 |
| 15.1515 | 12.516 | 26.686 |
| 15.625 | 12.929 | 27.32 |
| 16.129 | 13.352 | 27.954 |
| 16.6667 | 13.803 | 28.636 |
| 17.2414 | 14.266 | 29.301 |
| 17.8571 | 14.769 | 30.059 |
| 18.5185 | 15.347 | 30.829 |
| 19.2308 | 15.92 | 31.621 |
| 20.0 | 16.515 | 32.549 |
| 20.8333 | 17.198 | 33.469 |
| 21.7391 | 18.038 | 34.513 |
| 22.7273 | 18.944 | 35.431 |
| 23.8095 | 20.031 | 36.348 |
| 25.0 | 20.688 | 37.284 |
| 26.3158 | 21.445 | 38.482 |
| 27.7778 | 22.327 | 39.897 |
| 29.4118 | 23.283 | 41.521 |
| 31.25 | 24.459 | 43.439 |
| 33.3333 | 25.82 | 45.534 |
| 35.7143 | 27.455 | 47.998 |
| 38.4615 | 29.442 | 50.816 |
| 41.6667 | 31.972 | 54.228 |
| 45.4545 | 35.375 | 58.2 |
| 50.0 | 39.98 | 62.499 |
| 55.5556 | 46.731 | 67.736 |
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
- —