Optical constants
Refractive index of Si (Silicon)
Edwards and Ochoa 1980: n 2.5–25 µm
- Data
- formula 7
- Range
- 2.437–25 µm
- State
- crystalline
- Licence
- CC0-1.0
Plot
Click the plot to set the calculator wavelength.
At one wavelength
- Refractive index n
- 3.42249
- Extinction coefficient k
- 0
- Permittivity ε1
- 11.7134
- Permittivity ε2
- 0
- Absorption coefficient α
- 0 cm⁻¹
- Penetration depth δ = λ/(2πk)
- — nm
- Abbe number Vd
- —
- Chromatic dispersion dn/dλ
- -0.000638884 µm⁻¹
- Group index ng
- 3.42748
- Group velocity dispersion
- 209.641 fs²/mm
- Dispersion parameter D
- -6.47404 ps/(nm·km)
- Photon energy
- 0.158751 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
# Si (Silicon): Edwards and Ochoa 1980: n 2.5–25 µm
si = ls.fetch_refractiveindex("main", "Si", "Edwards", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(si.range_nm) # (2437.3, 25000) nm
eps = si.eps([7810]) # 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_5b953cb25f72/lightsmith"
si = ls.Tabulated.model_validate(json.load(urllib.request.urlopen(url)))
print(si.source) # citation and provenance travel with the data
Any dataset here, as the library's Tabulated material (si/edwards-ochoa-1980).
# ... load si as above, then:
sim = ls.Simulation(
particles=[ls.Particle(shape=ls.Sphere(radius_nm=50), material=si)],
medium_index=1.0,
wavelengths=ls.WavelengthRange(start_nm=2438, stop_nm=25000, 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"]).
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
Herzberger (formula 7), λ in µmValid from 2.4373 to 25.0 µm.
Coefficients as stored
| Ci | Value |
|---|---|
| C1 | 3.41983 |
| C2 | 0.159906 |
| C3 | -0.123109 |
| C4 | 1.26878e-06 |
| C5 | -1.95104e-09 |
Comments and conditions
References
- doi:10.1364/ao.19.004130 Infrared refractive index of silicon, Applied Optics (1980)
Cite
David F. Edwards and Ellen Ochoa. Infrared refractive index of silicon. Applied Optics, 19, 4130 (1980), doi:10.1364/ao.19.004130; 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 |
|---|---|
| 2.4373 | 3.443361 |
| 2.45156 | 3.443128 |
| 2.46591 | 3.442896 |
| 2.48034 | 3.442666 |
| 2.49485 | 3.442438 |
| 2.50945 | 3.442212 |
| 2.52413 | 3.441987 |
| 2.5389 | 3.441764 |
| 2.55376 | 3.441544 |
| 2.5687 | 3.441324 |
| 2.58374 | 3.441107 |
| 2.59885 | 3.440891 |
| 2.61406 | 3.440678 |
| 2.62936 | 3.440466 |
| 2.64474 | 3.440255 |
| 2.66022 | 3.440047 |
| 2.67579 | 3.43984 |
| 2.69144 | 3.439635 |
| 2.70719 | 3.439432 |
| 2.72304 | 3.43923 |
| 2.73897 | 3.439031 |
| 2.755 | 3.438833 |
| 2.77112 | 3.438636 |
| 2.78733 | 3.438442 |
| 2.80364 | 3.438249 |
| 2.82005 | 3.438058 |
| 2.83655 | 3.437868 |
| 2.85315 | 3.437681 |
| 2.86985 | 3.437495 |
| 2.88664 | 3.43731 |
| 2.90353 | 3.437128 |
| 2.92052 | 3.436947 |
| 2.93761 | 3.436767 |
| 2.9548 | 3.436589 |
| 2.97209 | 3.436413 |
| 2.98948 | 3.436239 |
| 3.00698 | 3.436066 |
| 3.02457 | 3.435895 |
| 3.04227 | 3.435725 |
| 3.06007 | 3.435557 |
| 3.07798 | 3.435391 |
| 3.09599 | 3.435226 |
| 3.11411 | 3.435062 |
| 3.13233 | 3.434901 |
| 3.15066 | 3.43474 |
| 3.16909 | 3.434582 |
| 3.18764 | 3.434424 |
| 3.20629 | 3.434269 |
| 3.22505 | 3.434114 |
| 3.24392 | 3.433962 |
| 3.26291 | 3.433811 |
| 3.282 | 3.433661 |
| 3.3012 | 3.433513 |
| 3.32052 | 3.433366 |
| 3.33995 | 3.43322 |
| 3.3595 | 3.433076 |
| 3.37915 | 3.432934 |
| 3.39893 | 3.432793 |
| 3.41882 | 3.432653 |
| 3.43882 | 3.432514 |
| 3.45895 | 3.432377 |
| 3.47919 | 3.432242 |
| 3.49954 | 3.432108 |
| 3.52002 | 3.431975 |
| 3.54062 | 3.431843 |
| 3.56134 | 3.431713 |
| 3.58218 | 3.431584 |
| 3.60314 | 3.431456 |
| 3.62422 | 3.43133 |
| 3.64543 | 3.431205 |
| 3.66676 | 3.431081 |
| 3.68822 | 3.430958 |
| 3.7098 | 3.430837 |
| 3.73151 | 3.430717 |
| 3.75335 | 3.430598 |
| 3.77531 | 3.430481 |
| 3.7974 | 3.430364 |
| 3.81962 | 3.430249 |
| 3.84197 | 3.430135 |
| 3.86445 | 3.430022 |
| 3.88707 | 3.42991 |
| 3.90981 | 3.4298 |
| 3.93269 | 3.429691 |
| 3.9557 | 3.429582 |
| 3.97885 | 3.429475 |
| 4.00213 | 3.429369 |
| 4.02555 | 3.429264 |
| 4.04911 | 3.429161 |
| 4.0728 | 3.429058 |
| 4.09663 | 3.428956 |
| 4.12061 | 3.428856 |
| 4.14472 | 3.428756 |
| 4.16897 | 3.428658 |
| 4.19337 | 3.42856 |
| 4.2179 | 3.428464 |
| 4.24259 | 3.428369 |
| 4.26741 | 3.428274 |
| 4.29238 | 3.428181 |
| 4.3175 | 3.428089 |
| 4.34276 | 3.427997 |
| 4.36818 | 3.427907 |
| 4.39374 | 3.427818 |
| 4.41945 | 3.427729 |
| 4.44531 | 3.427642 |
| 4.47132 | 3.427555 |
| 4.49749 | 3.42747 |
| 4.5238 | 3.427385 |
| 4.55027 | 3.427301 |
| 4.5769 | 3.427218 |
| 4.60368 | 3.427136 |
| 4.63062 | 3.427055 |
| 4.65772 | 3.426975 |
| 4.68497 | 3.426895 |
| 4.71239 | 3.426817 |
| 4.73996 | 3.426739 |
| 4.7677 | 3.426662 |
| 4.7956 | 3.426586 |
| 4.82366 | 3.426511 |
| 4.85189 | 3.426437 |
| 4.88028 | 3.426363 |
| 4.90884 | 3.426291 |
| 4.93756 | 3.426219 |
| 4.96645 | 3.426148 |
| 4.99551 | 3.426077 |
| 5.02475 | 3.426008 |
| 5.05415 | 3.425939 |
| 5.08372 | 3.425871 |
| 5.11347 | 3.425803 |
| 5.14339 | 3.425737 |
| 5.17349 | 3.425671 |
| 5.20376 | 3.425606 |
| 5.23421 | 3.425542 |
| 5.26484 | 3.425478 |
| 5.29565 | 3.425415 |
| 5.32664 | 3.425353 |
| 5.35781 | 3.425291 |
| 5.38916 | 3.42523 |
| 5.4207 | 3.42517 |
| 5.45241 | 3.42511 |
| 5.48432 | 3.425051 |
| 5.51641 | 3.424993 |
| 5.54869 | 3.424936 |
| 5.58116 | 3.424879 |
| 5.61382 | 3.424822 |
| 5.64667 | 3.424767 |
| 5.67971 | 3.424712 |
| 5.71295 | 3.424657 |
| 5.74638 | 3.424603 |
| 5.78 | 3.42455 |
| 5.81382 | 3.424498 |
| 5.84784 | 3.424445 |
| 5.88206 | 3.424394 |
| 5.91648 | 3.424343 |
| 5.9511 | 3.424293 |
| 5.98593 | 3.424243 |
| 6.02096 | 3.424194 |
| 6.05619 | 3.424145 |
| 6.09163 | 3.424097 |
| 6.12727 | 3.42405 |
| 6.16313 | 3.424003 |
| 6.19919 | 3.423956 |
| 6.23547 | 3.42391 |
| 6.27195 | 3.423865 |
| 6.30865 | 3.42382 |
| 6.34557 | 3.423776 |
| 6.3827 | 3.423732 |
| 6.42005 | 3.423689 |
| 6.45762 | 3.423646 |
| 6.49541 | 3.423603 |
| 6.53341 | 3.423562 |
| 6.57164 | 3.42352 |
| 6.6101 | 3.423479 |
| 6.64878 | 3.423439 |
| 6.68769 | 3.423399 |
| 6.72682 | 3.423359 |
| 6.76618 | 3.42332 |
| 6.80577 | 3.423282 |
| 6.8456 | 3.423243 |
| 6.88566 | 3.423206 |
| 6.92595 | 3.423168 |
| 6.96648 | 3.423131 |
| 7.00724 | 3.423095 |
| 7.04825 | 3.423059 |
| 7.08949 | 3.423023 |
| 7.13097 | 3.422988 |
| 7.1727 | 3.422953 |
| 7.21467 | 3.422919 |
| 7.25689 | 3.422885 |
| 7.29936 | 3.422851 |
| 7.34207 | 3.422818 |
| 7.38503 | 3.422785 |
| 7.42825 | 3.422753 |
| 7.47171 | 3.422721 |
| 7.51543 | 3.422689 |
| 7.55941 | 3.422658 |
| 7.60365 | 3.422627 |
| 7.64814 | 3.422597 |
| 7.69289 | 3.422566 |
| 7.73791 | 3.422537 |
| 7.78319 | 3.422507 |
| 7.82873 | 3.422478 |
| 7.87454 | 3.422449 |
| 7.92062 | 3.422421 |
| 7.96697 | 3.422392 |
| 8.01359 | 3.422365 |
| 8.06048 | 3.422337 |
| 8.10765 | 3.42231 |
| 8.15509 | 3.422283 |
| 8.20281 | 3.422257 |
| 8.25081 | 3.422231 |
| 8.29909 | 3.422205 |
| 8.34765 | 3.422179 |
| 8.3965 | 3.422154 |
| 8.44564 | 3.422129 |
| 8.49506 | 3.422104 |
| 8.54477 | 3.42208 |
| 8.59477 | 3.422056 |
| 8.64506 | 3.422032 |
| 8.69565 | 3.422009 |
| 8.74653 | 3.421986 |
| 8.79771 | 3.421963 |
| 8.84919 | 3.42194 |
| 8.90097 | 3.421918 |
| 8.95306 | 3.421896 |
| 9.00545 | 3.421874 |
| 9.05814 | 3.421852 |
| 9.11115 | 3.421831 |
| 9.16446 | 3.42181 |
| 9.21809 | 3.421789 |
| 9.27203 | 3.421769 |
| 9.32629 | 3.421748 |
| 9.38086 | 3.421728 |
| 9.43575 | 3.421709 |
| 9.49097 | 3.421689 |
| 9.54651 | 3.42167 |
| 9.60237 | 3.421651 |
| 9.65856 | 3.421632 |
| 9.71508 | 3.421613 |
| 9.77192 | 3.421595 |
| 9.82911 | 3.421577 |
| 9.88662 | 3.421559 |
| 9.94448 | 3.421541 |
| 10.0027 | 3.421524 |
| 10.0612 | 3.421507 |
| 10.1201 | 3.42149 |
| 10.1793 | 3.421473 |
| 10.2389 | 3.421456 |
| 10.2988 | 3.42144 |
| 10.359 | 3.421424 |
| 10.4197 | 3.421408 |
| 10.4806 | 3.421392 |
| 10.542 | 3.421376 |
| 10.6036 | 3.421361 |
| 10.6657 | 3.421346 |
| 10.7281 | 3.421331 |
| 10.7909 | 3.421316 |
| 10.854 | 3.421301 |
| 10.9175 | 3.421287 |
| 10.9814 | 3.421272 |
| 11.0457 | 3.421258 |
| 11.1103 | 3.421245 |
| 11.1753 | 3.421231 |
| 11.2407 | 3.421217 |
| 11.3065 | 3.421204 |
| 11.3727 | 3.421191 |
| 11.4392 | 3.421178 |
| 11.5061 | 3.421165 |
| 11.5735 | 3.421152 |
| 11.6412 | 3.42114 |
| 11.7093 | 3.421127 |
| 11.7778 | 3.421115 |
| 11.8468 | 3.421103 |
| 11.9161 | 3.421091 |
| 11.9858 | 3.421079 |
| 12.0559 | 3.421068 |
| 12.1265 | 3.421056 |
| 12.1974 | 3.421045 |
| 12.2688 | 3.421034 |
| 12.3406 | 3.421023 |
| 12.4128 | 3.421012 |
| 12.4855 | 3.421001 |
| 12.5585 | 3.420991 |
| 12.632 | 3.42098 |
| 12.7059 | 3.42097 |
| 12.7803 | 3.42096 |
| 12.8551 | 3.42095 |
| 12.9303 | 3.42094 |
| 13.0059 | 3.42093 |
| 13.082 | 3.42092 |
| 13.1586 | 3.420911 |
| 13.2356 | 3.420901 |
| 13.313 | 3.420892 |
| 13.391 | 3.420883 |
| 13.4693 | 3.420874 |
| 13.5481 | 3.420865 |
| 13.6274 | 3.420856 |
| 13.7071 | 3.420847 |
| 13.7874 | 3.420839 |
| 13.868 | 3.42083 |
| 13.9492 | 3.420822 |
| 14.0308 | 3.420813 |
| 14.1129 | 3.420805 |
| 14.1955 | 3.420797 |
| 14.2786 | 3.420789 |
| 14.3621 | 3.420781 |
| 14.4462 | 3.420773 |
| 14.5307 | 3.420766 |
| 14.6157 | 3.420758 |
| 14.7012 | 3.42075 |
| 14.7873 | 3.420743 |
| 14.8738 | 3.420736 |
| 14.9608 | 3.420728 |
| 15.0484 | 3.420721 |
| 15.1364 | 3.420714 |
| 15.225 | 3.420707 |
| 15.3141 | 3.4207 |
| 15.4037 | 3.420693 |
| 15.4938 | 3.420686 |
| 15.5845 | 3.420679 |
| 15.6757 | 3.420673 |
| 15.7674 | 3.420666 |
| 15.8597 | 3.42066 |
| 15.9525 | 3.420653 |
| 16.0458 | 3.420647 |
| 16.1397 | 3.42064 |
| 16.2342 | 3.420634 |
| 16.3292 | 3.420628 |
| 16.4247 | 3.420621 |
| 16.5208 | 3.420615 |
| 16.6175 | 3.420609 |
| 16.7148 | 3.420603 |
| 16.8126 | 3.420597 |
| 16.9109 | 3.420591 |
| 17.0099 | 3.420585 |
| 17.1094 | 3.420579 |
| 17.2096 | 3.420573 |
| 17.3103 | 3.420567 |
| 17.4116 | 3.420562 |
| 17.5134 | 3.420556 |
| 17.6159 | 3.42055 |
| 17.719 | 3.420544 |
| 17.8227 | 3.420538 |
| 17.927 | 3.420533 |
| 18.0319 | 3.420527 |
| 18.1374 | 3.420521 |
| 18.2435 | 3.420516 |
| 18.3503 | 3.42051 |
| 18.4577 | 3.420504 |
| 18.5657 | 3.420498 |
| 18.6743 | 3.420493 |
| 18.7836 | 3.420487 |
| 18.8935 | 3.420481 |
| 19.004 | 3.420476 |
| 19.1153 | 3.42047 |
| 19.2271 | 3.420464 |
| 19.3396 | 3.420458 |
| 19.4528 | 3.420452 |
| 19.5666 | 3.420447 |
| 19.6811 | 3.420441 |
| 19.7963 | 3.420435 |
| 19.9121 | 3.420429 |
| 20.0286 | 3.420423 |
| 20.1458 | 3.420417 |
| 20.2637 | 3.420411 |
| 20.3823 | 3.420405 |
| 20.5016 | 3.420398 |
| 20.6215 | 3.420392 |
| 20.7422 | 3.420386 |
| 20.8636 | 3.420379 |
| 20.9857 | 3.420373 |
| 21.1085 | 3.420366 |
| 21.232 | 3.42036 |
| 21.3562 | 3.420353 |
| 21.4812 | 3.420346 |
| 21.6069 | 3.420339 |
| 21.7333 | 3.420332 |
| 21.8605 | 3.420325 |
| 21.9884 | 3.420318 |
| 22.1171 | 3.42031 |
| 22.2465 | 3.420303 |
| 22.3767 | 3.420295 |
| 22.5076 | 3.420287 |
| 22.6393 | 3.420279 |
| 22.7718 | 3.420271 |
| 22.9051 | 3.420263 |
| 23.0391 | 3.420255 |
| 23.1739 | 3.420246 |
| 23.3095 | 3.420237 |
| 23.4459 | 3.420228 |
| 23.5831 | 3.420219 |
| 23.7211 | 3.42021 |
| 23.8599 | 3.420201 |
| 23.9995 | 3.420191 |
| 24.14 | 3.420181 |
| 24.2812 | 3.420171 |
| 24.4233 | 3.42016 |
| 24.5662 | 3.42015 |
| 24.71 | 3.420139 |
| 24.8546 | 3.420128 |
| 25 | 3.420116 |
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
- —
26 °C, crystal orientation <111>; 3-4 Ω-cm, n-type (phosporous-dopped)