Optical constants
Refractive index of Ge (Germanium)
Icenogle et al. 1976: n 2.5–12 µm; 293 K
- Data
- formula 2
- Range
- 2.5–12 µm
- Licence
- CC0-1.0
Plot
Click the plot to set the calculator wavelength.
At one wavelength
- Refractive index n
- 4.0136
- Extinction coefficient k
- 0
- Permittivity ε1
- 16.109
- Permittivity ε2
- 0
- Absorption coefficient α
- 0 cm⁻¹
- Penetration depth δ = λ/(2πk)
- — nm
- Abbe number Vd
- —
- Chromatic dispersion dn/dλ
- -0.00470443 µm⁻¹
- Group index ng
- 4.03938
- Group velocity dispersion
- 747.23 fs²/mm
- Dispersion parameter D
- -46.8698 ps/(nm·km)
- Photon energy
- 0.226249 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
# Ge (Germanium): Icenogle et al. 1976: n 2.5–12 µm; 293 K
ge = ls.fetch_refractiveindex("main", "Ge", "Icenogle", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(ge.range_nm) # (2500, 12000) nm
eps = ge.eps([5480]) # 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_a1690c5aeb6a/lightsmith"
ge = ls.Tabulated.model_validate(json.load(urllib.request.urlopen(url)))
print(ge.source) # citation and provenance travel with the dataAny dataset here, as the library's Tabulated material (ge/icenogle-1976).
# ... load ge as above, then:
sim = ls.Simulation(
particles=[ls.Particle(shape=ls.Sphere(radius_nm=50), material=ge)],
medium_index=1.0,
wavelengths=ls.WavelengthRange(start_nm=2500, stop_nm=12000, 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"]).
import json, urllib.request
import lightsmith as ls
url = "https://materials.lightsmith.dev/v1/datasets/ds_a1690c5aeb6a/lightsmith?model=drude_lorentz"
ge_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 2.5 to 12.0 µm.
Coefficients as stored
| Ci | Value |
|---|---|
| C1 | 8.28156 |
| C2 | 6.7288 |
| C3 | 0.44105 |
| C4 | 0.21307 |
| C5 | 3870.1 |
Comments and conditions
References
1) Icenogle, B. C. Platt, W. L. Wolfe
Refractive indexes and temperature coefficients of germanium and silicon,
Appl. Opt. 15 2348-2351 (1976)
2) N. P. Barnes and M. S. Piltch. Temperature-dependent Sellmeier coefficients and nonlinear optics average power limit for germanium. J. Opt. Soc. Am. 69 178-180 (1979)
* Ref. 2 provides temperature-dependent Sellmeier equations based on data from Ref. 1.
2) N. P. Barnes and M. S. Piltch. Temperature-dependent Sellmeier coefficients and nonlinear optics average power limit for germanium. J. Opt. Soc. Am. 69 178-180 (1979)
* Ref. 2 provides temperature-dependent Sellmeier equations based on data from Ref. 1.
- doi:10.1364/ao.15.002348 Refractive indexes and temperature coefficients of germanium and silicon, Applied Optics (1976)
- doi:10.1364/josa.69.000178 Temperature-dependent Sellmeier coefficients and nonlinear optics average power limit for germanium, Journal of the Optical Society of America (1979)
Cite
H. W. Icenogle, Ben C. Platt and William L. Wolfe. Refractive indexes and temperature coefficients of germanium and silicon. Applied Optics, 15, 2348 (1976), doi:10.1364/ao.15.002348; Norman P. Barnes and Martin S. Piltch. Temperature-dependent Sellmeier coefficients and nonlinear optics average power limit for germanium. Journal of the Optical Society of America, 69, 178 (1979), doi:10.1364/josa.69.000178; 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
CSV comma separated
TXT tab separated
YAML n, k
Full database record original YAML
All quantities CSV
JSON metadata
| λ (µm) | n |
|---|---|
| 2.5 | 4.064592 |
| 2.50985 | 4.064062 |
| 2.51973 | 4.063537 |
| 2.52966 | 4.063017 |
| 2.53962 | 4.062501 |
| 2.54963 | 4.06199 |
| 2.55967 | 4.061483 |
| 2.56975 | 4.060981 |
| 2.57988 | 4.060484 |
| 2.59004 | 4.05999 |
| 2.60024 | 4.059501 |
| 2.61048 | 4.059017 |
| 2.62077 | 4.058536 |
| 2.63109 | 4.05806 |
| 2.64145 | 4.057588 |
| 2.65186 | 4.05712 |
| 2.66231 | 4.056656 |
| 2.67279 | 4.056196 |
| 2.68332 | 4.055741 |
| 2.69389 | 4.055289 |
| 2.7045 | 4.054841 |
| 2.71516 | 4.054397 |
| 2.72585 | 4.053957 |
| 2.73659 | 4.053521 |
| 2.74737 | 4.053088 |
| 2.75819 | 4.052659 |
| 2.76906 | 4.052235 |
| 2.77996 | 4.051813 |
| 2.79091 | 4.051396 |
| 2.80191 | 4.050981 |
| 2.81294 | 4.050571 |
| 2.82402 | 4.050164 |
| 2.83515 | 4.049761 |
| 2.84632 | 4.049361 |
| 2.85753 | 4.048964 |
| 2.86879 | 4.048571 |
| 2.88009 | 4.048181 |
| 2.89143 | 4.047795 |
| 2.90282 | 4.047412 |
| 2.91425 | 4.047032 |
| 2.92573 | 4.046656 |
| 2.93726 | 4.046283 |
| 2.94883 | 4.045912 |
| 2.96044 | 4.045546 |
| 2.97211 | 4.045182 |
| 2.98381 | 4.044821 |
| 2.99557 | 4.044464 |
| 3.00737 | 4.044109 |
| 3.01921 | 4.043758 |
| 3.03111 | 4.043409 |
| 3.04305 | 4.043063 |
| 3.05503 | 4.042721 |
| 3.06707 | 4.042381 |
| 3.07915 | 4.042044 |
| 3.09128 | 4.04171 |
| 3.10345 | 4.041379 |
| 3.11568 | 4.041051 |
| 3.12795 | 4.040725 |
| 3.14027 | 4.040403 |
| 3.15264 | 4.040083 |
| 3.16506 | 4.039765 |
| 3.17753 | 4.03945 |
| 3.19005 | 4.039138 |
| 3.20261 | 4.038829 |
| 3.21523 | 4.038522 |
| 3.22789 | 4.038218 |
| 3.24061 | 4.037916 |
| 3.25337 | 4.037617 |
| 3.26619 | 4.037321 |
| 3.27905 | 4.037027 |
| 3.29197 | 4.036735 |
| 3.30494 | 4.036446 |
| 3.31796 | 4.036159 |
| 3.33103 | 4.035875 |
| 3.34415 | 4.035593 |
| 3.35732 | 4.035313 |
| 3.37055 | 4.035036 |
| 3.38382 | 4.034761 |
| 3.39715 | 4.034488 |
| 3.41053 | 4.034218 |
| 3.42397 | 4.03395 |
| 3.43746 | 4.033684 |
| 3.451 | 4.03342 |
| 3.46459 | 4.033159 |
| 3.47824 | 4.0329 |
| 3.49194 | 4.032642 |
| 3.50569 | 4.032387 |
| 3.5195 | 4.032134 |
| 3.53337 | 4.031884 |
| 3.54728 | 4.031635 |
| 3.56126 | 4.031388 |
| 3.57529 | 4.031144 |
| 3.58937 | 4.030901 |
| 3.60351 | 4.030661 |
| 3.6177 | 4.030422 |
| 3.63195 | 4.030185 |
| 3.64626 | 4.029951 |
| 3.66062 | 4.029718 |
| 3.67504 | 4.029487 |
| 3.68952 | 4.029258 |
| 3.70405 | 4.029031 |
| 3.71864 | 4.028806 |
| 3.73329 | 4.028583 |
| 3.748 | 4.028362 |
| 3.76276 | 4.028142 |
| 3.77758 | 4.027924 |
| 3.79246 | 4.027708 |
| 3.8074 | 4.027494 |
| 3.8224 | 4.027281 |
| 3.83746 | 4.027071 |
| 3.85257 | 4.026862 |
| 3.86775 | 4.026654 |
| 3.88298 | 4.026449 |
| 3.89828 | 4.026245 |
| 3.91364 | 4.026043 |
| 3.92905 | 4.025842 |
| 3.94453 | 4.025643 |
| 3.96007 | 4.025446 |
| 3.97567 | 4.02525 |
| 3.99133 | 4.025056 |
| 4.00705 | 4.024863 |
| 4.02283 | 4.024672 |
| 4.03868 | 4.024483 |
| 4.05459 | 4.024295 |
| 4.07056 | 4.024109 |
| 4.08659 | 4.023924 |
| 4.10269 | 4.023741 |
| 4.11885 | 4.023559 |
| 4.13508 | 4.023378 |
| 4.15137 | 4.023199 |
| 4.16772 | 4.023022 |
| 4.18413 | 4.022846 |
| 4.20062 | 4.022671 |
| 4.21716 | 4.022498 |
| 4.23378 | 4.022327 |
| 4.25045 | 4.022156 |
| 4.2672 | 4.021987 |
| 4.284 | 4.02182 |
| 4.30088 | 4.021653 |
| 4.31782 | 4.021488 |
| 4.33483 | 4.021325 |
| 4.3519 | 4.021162 |
| 4.36905 | 4.021001 |
| 4.38626 | 4.020842 |
| 4.40354 | 4.020683 |
| 4.42088 | 4.020526 |
| 4.4383 | 4.02037 |
| 4.45578 | 4.020216 |
| 4.47333 | 4.020063 |
| 4.49095 | 4.01991 |
| 4.50864 | 4.019759 |
| 4.5264 | 4.01961 |
| 4.54423 | 4.019461 |
| 4.56213 | 4.019314 |
| 4.5801 | 4.019168 |
| 4.59814 | 4.019023 |
| 4.61626 | 4.018879 |
| 4.63444 | 4.018737 |
| 4.6527 | 4.018595 |
| 4.67102 | 4.018455 |
| 4.68942 | 4.018315 |
| 4.7079 | 4.018177 |
| 4.72644 | 4.01804 |
| 4.74506 | 4.017904 |
| 4.76375 | 4.017769 |
| 4.78251 | 4.017636 |
| 4.80135 | 4.017503 |
| 4.82027 | 4.017371 |
| 4.83925 | 4.017241 |
| 4.85832 | 4.017111 |
| 4.87745 | 4.016982 |
| 4.89667 | 4.016855 |
| 4.91596 | 4.016728 |
| 4.93532 | 4.016603 |
| 4.95476 | 4.016478 |
| 4.97428 | 4.016355 |
| 4.99387 | 4.016232 |
| 5.01354 | 4.016111 |
| 5.03329 | 4.01599 |
| 5.05312 | 4.01587 |
| 5.07302 | 4.015752 |
| 5.09301 | 4.015634 |
| 5.11307 | 4.015517 |
| 5.13321 | 4.015401 |
| 5.15343 | 4.015286 |
| 5.17373 | 4.015172 |
| 5.19411 | 4.015059 |
| 5.21457 | 4.014946 |
| 5.23511 | 4.014835 |
| 5.25573 | 4.014724 |
| 5.27644 | 4.014614 |
| 5.29722 | 4.014506 |
| 5.31809 | 4.014398 |
| 5.33903 | 4.01429 |
| 5.36007 | 4.014184 |
| 5.38118 | 4.014079 |
| 5.40238 | 4.013974 |
| 5.42366 | 4.01387 |
| 5.44502 | 4.013767 |
| 5.46647 | 4.013665 |
| 5.488 | 4.013563 |
| 5.50962 | 4.013463 |
| 5.53132 | 4.013363 |
| 5.55311 | 4.013264 |
| 5.57499 | 4.013165 |
| 5.59695 | 4.013068 |
| 5.61899 | 4.012971 |
| 5.64113 | 4.012875 |
| 5.66335 | 4.012779 |
| 5.68566 | 4.012685 |
| 5.70805 | 4.012591 |
| 5.73054 | 4.012498 |
| 5.75311 | 4.012405 |
| 5.77577 | 4.012314 |
| 5.79852 | 4.012223 |
| 5.82137 | 4.012132 |
| 5.8443 | 4.012043 |
| 5.86732 | 4.011954 |
| 5.89043 | 4.011866 |
| 5.91363 | 4.011778 |
| 5.93693 | 4.011691 |
| 5.96031 | 4.011605 |
| 5.98379 | 4.011519 |
| 6.00736 | 4.011435 |
| 6.03103 | 4.01135 |
| 6.05478 | 4.011267 |
| 6.07863 | 4.011184 |
| 6.10258 | 4.011101 |
| 6.12662 | 4.01102 |
| 6.15075 | 4.010938 |
| 6.17498 | 4.010858 |
| 6.1993 | 4.010778 |
| 6.22372 | 4.010699 |
| 6.24824 | 4.01062 |
| 6.27285 | 4.010542 |
| 6.29756 | 4.010465 |
| 6.32237 | 4.010388 |
| 6.34727 | 4.010311 |
| 6.37227 | 4.010236 |
| 6.39737 | 4.01016 |
| 6.42257 | 4.010086 |
| 6.44787 | 4.010012 |
| 6.47327 | 4.009938 |
| 6.49877 | 4.009865 |
| 6.52437 | 4.009793 |
| 6.55007 | 4.009721 |
| 6.57587 | 4.00965 |
| 6.60178 | 4.009579 |
| 6.62778 | 4.009509 |
| 6.65389 | 4.009439 |
| 6.6801 | 4.00937 |
| 6.70641 | 4.009301 |
| 6.73283 | 4.009233 |
| 6.75935 | 4.009165 |
| 6.78598 | 4.009098 |
| 6.81271 | 4.009031 |
| 6.83954 | 4.008965 |
| 6.86649 | 4.008899 |
| 6.89353 | 4.008834 |
| 6.92069 | 4.008769 |
| 6.94795 | 4.008705 |
| 6.97532 | 4.008641 |
| 7.00279 | 4.008577 |
| 7.03038 | 4.008514 |
| 7.05807 | 4.008452 |
| 7.08587 | 4.00839 |
| 7.11379 | 4.008328 |
| 7.14181 | 4.008267 |
| 7.16994 | 4.008207 |
| 7.19818 | 4.008146 |
| 7.22654 | 4.008087 |
| 7.255 | 4.008027 |
| 7.28358 | 4.007968 |
| 7.31227 | 4.00791 |
| 7.34108 | 4.007852 |
| 7.36999 | 4.007794 |
| 7.39903 | 4.007737 |
| 7.42817 | 4.00768 |
| 7.45743 | 4.007623 |
| 7.48681 | 4.007567 |
| 7.5163 | 4.007511 |
| 7.54591 | 4.007456 |
| 7.57563 | 4.007401 |
| 7.60547 | 4.007347 |
| 7.63543 | 4.007293 |
| 7.66551 | 4.007239 |
| 7.6957 | 4.007185 |
| 7.72602 | 4.007132 |
| 7.75645 | 4.00708 |
| 7.787 | 4.007027 |
| 7.81768 | 4.006976 |
| 7.84847 | 4.006924 |
| 7.87939 | 4.006873 |
| 7.91043 | 4.006822 |
| 7.94159 | 4.006771 |
| 7.97287 | 4.006721 |
| 8.00427 | 4.006671 |
| 8.0358 | 4.006622 |
| 8.06746 | 4.006573 |
| 8.09924 | 4.006524 |
| 8.13114 | 4.006475 |
| 8.16317 | 4.006427 |
| 8.19533 | 4.006379 |
| 8.22761 | 4.006332 |
| 8.26002 | 4.006285 |
| 8.29255 | 4.006238 |
| 8.32522 | 4.006191 |
| 8.35801 | 4.006145 |
| 8.39094 | 4.006099 |
| 8.42399 | 4.006053 |
| 8.45717 | 4.006008 |
| 8.49049 | 4.005963 |
| 8.52393 | 4.005918 |
| 8.55751 | 4.005873 |
| 8.59122 | 4.005829 |
| 8.62506 | 4.005785 |
| 8.65903 | 4.005742 |
| 8.69314 | 4.005698 |
| 8.72739 | 4.005655 |
| 8.76176 | 4.005612 |
| 8.79628 | 4.00557 |
| 8.83093 | 4.005527 |
| 8.86571 | 4.005485 |
| 8.90064 | 4.005444 |
| 8.9357 | 4.005402 |
| 8.97089 | 4.005361 |
| 9.00623 | 4.00532 |
| 9.04171 | 4.005279 |
| 9.07732 | 4.005239 |
| 9.11308 | 4.005198 |
| 9.14898 | 4.005158 |
| 9.18502 | 4.005118 |
| 9.2212 | 4.005079 |
| 9.25752 | 4.00504 |
| 9.29399 | 4.005001 |
| 9.3306 | 4.004962 |
| 9.36735 | 4.004923 |
| 9.40425 | 4.004885 |
| 9.4413 | 4.004847 |
| 9.47849 | 4.004809 |
| 9.51582 | 4.004771 |
| 9.55331 | 4.004733 |
| 9.59094 | 4.004696 |
| 9.62872 | 4.004659 |
| 9.66665 | 4.004622 |
| 9.70472 | 4.004585 |
| 9.74295 | 4.004549 |
| 9.78133 | 4.004513 |
| 9.81986 | 4.004477 |
| 9.85854 | 4.004441 |
| 9.89738 | 4.004405 |
| 9.93636 | 4.00437 |
| 9.9755 | 4.004334 |
| 10.0148 | 4.004299 |
| 10.0542 | 4.004264 |
| 10.0939 | 4.004229 |
| 10.1336 | 4.004195 |
| 10.1735 | 4.004161 |
| 10.2136 | 4.004126 |
| 10.2538 | 4.004092 |
| 10.2942 | 4.004058 |
| 10.3348 | 4.004025 |
| 10.3755 | 4.003991 |
| 10.4164 | 4.003958 |
| 10.4574 | 4.003925 |
| 10.4986 | 4.003892 |
| 10.5399 | 4.003859 |
| 10.5815 | 4.003826 |
| 10.6231 | 4.003793 |
| 10.665 | 4.003761 |
| 10.707 | 4.003729 |
| 10.7492 | 4.003697 |
| 10.7915 | 4.003665 |
| 10.834 | 4.003633 |
| 10.8767 | 4.003601 |
| 10.9195 | 4.003569 |
| 10.9626 | 4.003538 |
| 11.0057 | 4.003507 |
| 11.0491 | 4.003476 |
| 11.0926 | 4.003445 |
| 11.1363 | 4.003414 |
| 11.1802 | 4.003383 |
| 11.2242 | 4.003352 |
| 11.2684 | 4.003322 |
| 11.3128 | 4.003291 |
| 11.3574 | 4.003261 |
| 11.4021 | 4.003231 |
| 11.447 | 4.003201 |
| 11.4921 | 4.003171 |
| 11.5374 | 4.003141 |
| 11.5828 | 4.003112 |
| 11.6285 | 4.003082 |
| 11.6743 | 4.003052 |
| 11.7203 | 4.003023 |
| 11.7664 | 4.002994 |
| 11.8128 | 4.002965 |
| 11.8593 | 4.002935 |
| 11.906 | 4.002906 |
| 11.9529 | 4.002878 |
| 12 | 4.002849 |
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
- —
293 K (20 °C)