Axis Log x Log y

Click the plot to set the calculator wavelength.

At one wavelength

Refractive index n: 2.78504
Extinction coefficient k: 2.87274e-07

Permittivity ε₁: 7.75645
Permittivity ε₂: 1.60014e-06

Absorption coefficient α: 0.00999997 cm⁻¹
Penetration depth δ = λ/(2πk): 2.00001e+09 nm

Abbe number V_d: —
Chromatic dispersion dn/dλ: -0.00587734 µm⁻¹

Group index n_g: 2.80626
Group velocity dispersion: 367.461 fs²/mm

Dispersion parameter D: -53.1126 ps/(nm·km)
Photon energy: 0.343447 eV

ε = (n + ik)², α = 4πk/λ, n_g = 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

# AMTIR-2 (AMI): AMTIR-2
ami_amtir_2 = ls.fetch_refractiveindex("specs", "AMI-infrared", "AMTIR-2", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(ami_amtir_2.range_nm)  # (1000, 13000) nm
eps = ami_amtir_2.eps([3610])  # 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_62fdda917349/lightsmith"
ami_amtir_2 = ls.Tabulated.model_validate(json.load(urllib.request.urlopen(url)))
print(ami_amtir_2.source)  # citation and provenance travel with the data

Any dataset here, as the library's Tabulated material (ami-amtir-2/ami).

# ... load ami_amtir_2 as above, then:
sim = ls.Simulation(
    particles=[ls.Particle(shape=ls.Sphere(radius_nm=50), material=ami_amtir_2)],
    medium_index=1.0,
    wavelengths=ls.WavelengthRange(start_nm=1000, stop_nm=13000, 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_62fdda917349/lightsmith?model=drude_lorentz"
ami_amtir_2_dl = ls.DrudeLorentz.model_validate(json.load(urllib.request.urlopen(url)))

A dispersive Drude–Lorentz model for time-domain solvers.

Materials guide Open a sphere of it in Studio Quick start Ask the community

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 (formula 1), λ in µm

n^{2} - 1 = \frac{4.9948719 λ^{2}}{λ^{2} - {0.24164}^{2}} + \frac{0.1207152 λ^{2}}{λ^{2} - {19.0}^{2}} + \frac{1.7123685 λ^{2}}{λ^{2} - {0.48328}^{2}}

Valid from 1.0 to 13.0 µm.

Coefficients as stored

C_i	Value
C1	0.0
C2	4.9948719
C3	0.24164
C4	0.1207152
C5	19.0
C6	1.7123685
C7	0.48328

References

Amorphous Materials AMTIR-2 Information (2013) - downloaded 2014-01-11

Cite

Amorphous Materials AMTIR-2 Information (2013) - downloaded 2014-01-11; Data from the refractiveindex.info database (M. N. Polyanskiy, Sci. Data 11, 94 (2024), doi:10.1038/s41597-023-02898-2)

Data

Computed on 415 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

AMTIR-2 (AMI), AMTIR-2: n and k versus wavelength
λ (µm)	n	k
1	2.922064	4.456300e-07
1.00645	2.919861	4.348529e-07
1.01294	2.917697	4.240062e-07
1.01947	2.915572	4.130896e-07
1.02605	2.913483	4.021026e-07
1.03266	2.911431	3.910448e-07
1.03932	2.909414	3.799156e-07
1.04603	2.907432	3.687147e-07
1.05277	2.905484	3.574415e-07
1.05956	2.90357	3.460956e-07
1.064	2.902342	3.386800e-07
1.0664	2.901688	3.372646e-07
1.07327	2.899837	3.332014e-07
1.08019	2.898018	3.291120e-07
1.08716	2.89623	3.249963e-07
1.09417	2.894471	3.208540e-07
1.10123	2.892741	3.166850e-07
1.10833	2.891041	3.124891e-07
1.11548	2.889368	3.082661e-07
1.12267	2.887723	3.040159e-07
1.12991	2.886105	2.997383e-07
1.1372	2.884513	2.954331e-07
1.14453	2.882947	2.911002e-07
1.15192	2.881406	2.867392e-07
1.15934	2.879891	2.823502e-07
1.16682	2.8784	2.779329e-07
1.17435	2.876932	2.734871e-07
1.18192	2.875488	2.690126e-07
1.18954	2.874068	2.645092e-07
1.19721	2.872669	2.599768e-07
1.20493	2.871293	2.554152e-07
1.2127	2.869939	2.508242e-07
1.22053	2.868606	2.462035e-07
1.2284	2.867294	2.415531e-07
1.23632	2.866002	2.368726e-07
1.24429	2.86473	2.321620e-07
1.25	2.863837	2.287900e-07
1.25232	2.863479	2.284396e-07
1.26039	2.862246	2.272185e-07
1.26852	2.861033	2.259895e-07
1.2767	2.859838	2.247525e-07
1.28494	2.858662	2.235076e-07
1.29322	2.857504	2.222546e-07
1.30156	2.856364	2.209936e-07
1.30996	2.85524	2.197244e-07
1.31841	2.854134	2.184471e-07
1.32691	2.853045	2.171615e-07
1.33547	2.851972	2.158676e-07
1.34408	2.850916	2.145654e-07
1.35275	2.849875	2.132547e-07
1.36147	2.84885	2.119357e-07
1.37025	2.847841	2.106081e-07
1.37909	2.846846	2.092719e-07
1.38798	2.845866	2.079272e-07
1.39693	2.844901	2.065737e-07
1.40594	2.84395	2.052116e-07
1.41501	2.843013	2.038406e-07
1.42413	2.842091	2.024608e-07
1.43332	2.841181	2.010721e-07
1.44256	2.840285	1.996745e-07
1.45187	2.839403	1.982678e-07
1.46123	2.838533	1.968521e-07
1.47065	2.837676	1.954272e-07
1.48014	2.836831	1.939932e-07
1.48968	2.835999	1.925499e-07
1.49929	2.835179	1.910973e-07
1.5	2.835119	1.909900e-07
1.50896	2.83437	1.916315e-07
1.51869	2.833574	1.923283e-07
1.52849	2.832789	1.930296e-07
1.53834	2.832015	1.937353e-07
1.54826	2.831252	1.944457e-07
1.55825	2.830501	1.951606e-07
1.5683	2.82976	1.958802e-07
1.57841	2.82903	1.966043e-07
1.58859	2.82831	1.973332e-07
1.59884	2.8276	1.980667e-07
1.60915	2.826901	1.988050e-07
1.61953	2.826212	1.995480e-07
1.62997	2.825532	2.002959e-07
1.64048	2.824862	2.010485e-07
1.65106	2.824201	2.018060e-07
1.66171	2.82355	2.025684e-07
1.67243	2.822908	2.033357e-07
1.68321	2.822275	2.041080e-07
1.69407	2.821651	2.048852e-07
1.70499	2.821035	2.056675e-07
1.71599	2.820429	2.064548e-07
1.72706	2.819831	2.072472e-07
1.73819	2.819241	2.080446e-07
1.7494	2.818659	2.088473e-07
1.75	2.818628	2.088900e-07
1.76069	2.818085	2.101654e-07
1.77204	2.81752	2.115207e-07
1.78347	2.816962	2.128848e-07
1.79497	2.816412	2.142576e-07
1.80655	2.81587	2.156394e-07
1.8182	2.815335	2.170300e-07
1.82992	2.814807	2.184296e-07
1.84172	2.814287	2.198382e-07
1.8536	2.813774	2.212559e-07
1.86556	2.813268	2.226828e-07
1.87759	2.812769	2.241188e-07
1.8897	2.812277	2.255641e-07
1.90188	2.811791	2.270188e-07
1.91415	2.811313	2.284828e-07
1.92649	2.81084	2.299562e-07
1.93892	2.810374	2.314392e-07
1.95142	2.809915	2.329317e-07
1.96401	2.809462	2.344339e-07
1.97667	2.809014	2.359457e-07
1.98942	2.808573	2.374673e-07
2	2.808214	2.387300e-07
2.00225	2.808138	2.387300e-07
2.01516	2.807709	2.387300e-07
2.02816	2.807286	2.387300e-07
2.04124	2.806868	2.387300e-07
2.0544	2.806456	2.387300e-07
2.06765	2.806049	2.387300e-07
2.08099	2.805648	2.387300e-07
2.09441	2.805253	2.387300e-07
2.10792	2.804862	2.387300e-07
2.12151	2.804477	2.387300e-07
2.13519	2.804097	2.387300e-07
2.14896	2.803722	2.387300e-07
2.16282	2.803352	2.387300e-07
2.17677	2.802987	2.387300e-07
2.19081	2.802627	2.387300e-07
2.20494	2.802271	2.387300e-07
2.21916	2.801921	2.387300e-07
2.23347	2.801575	2.387300e-07
2.24787	2.801233	2.387300e-07
2.26237	2.800896	2.387300e-07
2.27696	2.800563	2.387300e-07
2.29164	2.800235	2.387300e-07
2.30642	2.799911	2.387300e-07
2.3213	2.799592	2.387300e-07
2.33627	2.799276	2.387300e-07
2.35133	2.798965	2.387300e-07
2.3665	2.798658	2.387300e-07
2.38176	2.798355	2.387300e-07
2.39712	2.798055	2.387300e-07
2.41258	2.79776	2.387300e-07
2.42814	2.797468	2.387300e-07
2.4438	2.797181	2.387300e-07
2.45956	2.796897	2.387300e-07
2.47542	2.796616	2.387300e-07
2.49139	2.79634	2.387300e-07
2.50745	2.796066	2.387300e-07
2.52362	2.795797	2.387300e-07
2.5399	2.795531	2.387300e-07
2.55628	2.795268	2.387300e-07
2.57277	2.795008	2.387300e-07
2.58936	2.794752	2.387300e-07
2.60606	2.794499	2.387300e-07
2.62286	2.79425	2.387300e-07
2.63978	2.794003	2.387300e-07
2.6568	2.79376	2.387300e-07
2.67394	2.79352	2.387300e-07
2.69118	2.793283	2.387300e-07
2.70854	2.793048	2.387300e-07
2.72601	2.792817	2.387300e-07
2.74359	2.792589	2.387300e-07
2.76128	2.792363	2.387300e-07
2.77909	2.792141	2.387300e-07
2.79701	2.791921	2.387300e-07
2.81505	2.791704	2.387300e-07
2.8332	2.791489	2.387300e-07
2.85148	2.791277	2.387300e-07
2.86986	2.791068	2.387300e-07
2.88837	2.790862	2.387300e-07
2.907	2.790658	2.387300e-07
2.92575	2.790456	2.387300e-07
2.94462	2.790257	2.387300e-07
2.96361	2.790061	2.387300e-07
2.98272	2.789867	2.387300e-07
3	2.789694	2.387300e-07
3.00196	2.789675	2.388856e-07
3.02132	2.789485	2.404263e-07
3.0408	2.789298	2.419769e-07
3.06041	2.789113	2.435375e-07
3.08015	2.78893	2.451082e-07
3.10001	2.78875	2.466890e-07
3.12001	2.788572	2.482800e-07
3.14013	2.788395	2.498813e-07
3.16038	2.788221	2.514929e-07
3.18076	2.788049	2.531148e-07
3.20127	2.787879	2.547473e-07
3.22192	2.787711	2.563903e-07
3.2427	2.787545	2.580438e-07
3.26361	2.787381	2.597080e-07
3.28466	2.787219	2.613830e-07
3.30584	2.787059	2.630688e-07
3.32716	2.7869	2.647654e-07
3.34862	2.786744	2.664730e-07
3.37021	2.786589	2.681916e-07
3.39195	2.786436	2.699212e-07
3.41382	2.786285	2.716621e-07
3.43584	2.786135	2.734141e-07
3.458	2.785988	2.751775e-07
3.4803	2.785841	2.769522e-07
3.50274	2.785697	2.787384e-07
3.52533	2.785554	2.805361e-07
3.54807	2.785413	2.823453e-07
3.57095	2.785273	2.841663e-07
3.59398	2.785135	2.859990e-07
3.61716	2.784998	2.878435e-07
3.64049	2.784863	2.896999e-07
3.66396	2.784729	2.915683e-07
3.68759	2.784597	2.934487e-07
3.71138	2.784466	2.953413e-07
3.73531	2.784337	2.972461e-07
3.7594	2.784209	2.991631e-07
3.78365	2.784082	3.010925e-07
3.80805	2.783956	3.030344e-07
3.83261	2.783832	3.049888e-07
3.85732	2.783709	3.069557e-07
3.8822	2.783588	3.089354e-07
3.90724	2.783468	3.109278e-07
3.93243	2.783348	3.129331e-07
3.9578	2.783231	3.149513e-07
3.98332	2.783114	3.169826e-07
4	2.783039	3.183100e-07
4.00901	2.782998	3.226113e-07
4.03486	2.782884	3.349559e-07
4.06088	2.78277	3.473801e-07
4.08707	2.782658	3.598844e-07
4.11343	2.782547	3.724694e-07
4.13996	2.782437	3.851355e-07
4.16666	2.782328	3.978833e-07
4.19353	2.78222	4.107134e-07
4.22058	2.782113	4.236261e-07
4.24779	2.782007	4.366222e-07
4.27519	2.781901	4.497020e-07
4.30276	2.781797	4.628663e-07
4.33051	2.781694	4.761154e-07
4.35844	2.781592	4.894499e-07
4.38655	2.78149	5.028705e-07
4.41484	2.78139	5.163776e-07
4.44331	2.78129	5.299718e-07
4.47196	2.781191	5.436537e-07
4.5008	2.781093	5.574238e-07
4.52983	2.780995	5.712827e-07
4.55904	2.780899	5.852310e-07
4.58845	2.780803	5.992693e-07
4.61804	2.780708	6.133981e-07
4.64782	2.780613	6.276180e-07
4.67779	2.78052	6.419296e-07
4.70796	2.780427	6.563336e-07
4.73832	2.780334	6.708304e-07
4.76888	2.780243	6.854207e-07
4.79964	2.780152	7.001051e-07
4.83059	2.780061	7.148842e-07
4.86174	2.779971	7.297586e-07
4.8931	2.779882	7.447289e-07
4.92466	2.779794	7.597958e-07
4.95641	2.779706	7.749599e-07
4.98838	2.779618	7.902217e-07
5	2.779586	7.957700e-07
5.02055	2.779531	7.892286e-07
5.05293	2.779444	7.789223e-07
5.08552	2.779358	7.685495e-07
5.11831	2.779273	7.581098e-07
5.15132	2.779188	7.476027e-07
5.18454	2.779103	7.370280e-07
5.21798	2.779019	7.263850e-07
5.25163	2.778935	7.156734e-07
5.2855	2.778851	7.048927e-07
5.31959	2.778768	6.940424e-07
5.35389	2.778685	6.831222e-07
5.38842	2.778603	6.721316e-07
5.42317	2.778521	6.610701e-07
5.45815	2.778439	6.499372e-07
5.49335	2.778357	6.387326e-07
5.52877	2.778276	6.274557e-07
5.56443	2.778195	6.161061e-07
5.60032	2.778114	6.046832e-07
5.63643	2.778034	5.931867e-07
5.67278	2.777953	5.816161e-07
5.70937	2.777873	5.699708e-07
5.74619	2.777793	5.582505e-07
5.78325	2.777713	5.464545e-07
5.82054	2.777634	5.345825e-07
5.85808	2.777554	5.226339e-07
5.89586	2.777475	5.106083e-07
5.93388	2.777395	4.985051e-07
5.97215	2.777316	4.863238e-07
6	2.777259	4.774600e-07
6.01067	2.777237	4.783090e-07
6.04943	2.777157	4.813938e-07
6.08845	2.777078	4.844985e-07
6.12771	2.776999	4.876233e-07
6.16723	2.77692	4.907682e-07
6.207	2.776841	4.939333e-07
6.24703	2.776761	4.971189e-07
6.28732	2.776682	5.003250e-07
6.32787	2.776602	5.035518e-07
6.36868	2.776523	5.067994e-07
6.40975	2.776443	5.100680e-07
6.45109	2.776363	5.133576e-07
6.49269	2.776283	5.166685e-07
6.53457	2.776203	5.200007e-07
6.57671	2.776123	5.233544e-07
6.61912	2.776042	5.267297e-07
6.66181	2.775961	5.301268e-07
6.70477	2.77588	5.335458e-07
6.74801	2.775798	5.369868e-07
6.79153	2.775717	5.404501e-07
6.83533	2.775635	5.439356e-07
6.87941	2.775552	5.474437e-07
6.92378	2.775469	5.509744e-07
6.96843	2.775386	5.545278e-07
7	2.775327	5.570400e-07
7.01337	2.775303	5.581042e-07
7.0586	2.775218	5.617036e-07
7.10412	2.775134	5.653263e-07
7.14994	2.775049	5.689723e-07
7.19605	2.774963	5.726418e-07
7.24246	2.774877	5.763350e-07
7.28917	2.774791	5.800520e-07
7.33618	2.774703	5.837929e-07
7.38349	2.774616	5.875580e-07
7.43111	2.774527	5.913474e-07
7.47903	2.774438	5.951612e-07
7.52726	2.774348	5.989996e-07
7.57581	2.774257	6.028628e-07
7.62467	2.774166	6.067509e-07
7.67384	2.774074	6.106640e-07
7.72333	2.773981	6.146024e-07
7.77314	2.773887	6.185662e-07
7.82327	2.773793	6.225556e-07
7.87372	2.773697	6.265707e-07
7.9245	2.773601	6.306116e-07
7.97561	2.773503	6.346787e-07
8	2.773456	6.366200e-07
8.02704	2.773405	6.387720e-07
8.07881	2.773305	6.428916e-07
8.13091	2.773205	6.470379e-07
8.18335	2.773103	6.512108e-07
8.23612	2.773	6.554107e-07
8.28924	2.772896	6.596377e-07
8.3427	2.77279	6.638919e-07
8.3965	2.772684	6.681736e-07
8.45065	2.772576	6.724829e-07
8.50515	2.772467	6.768199e-07
8.56	2.772356	6.811850e-07
8.61521	2.772244	6.855782e-07
8.67077	2.77213	6.899997e-07
8.72669	2.772015	6.944497e-07
8.78297	2.771898	6.989285e-07
8.83961	2.77178	7.034361e-07
8.89662	2.771659	7.079728e-07
8.95399	2.771538	7.125388e-07
9	2.771439	7.162000e-07
9.01174	2.771414	7.171340e-07
9.06986	2.771288	7.217585e-07
9.12835	2.771161	7.264128e-07
9.18722	2.771031	7.310971e-07
9.24647	2.770899	7.358116e-07
9.3061	2.770765	7.405565e-07
9.36612	2.770629	7.453320e-07
9.42652	2.770491	7.501383e-07
9.48731	2.770351	7.549756e-07
9.5485	2.770208	7.598441e-07
9.61008	2.770062	7.647440e-07
9.67206	2.769914	7.696755e-07
9.73443	2.769763	7.746388e-07
9.79721	2.769609	7.796341e-07
9.8604	2.769453	7.846616e-07
9.92399	2.769293	7.897216e-07
9.98799	2.769131	7.948142e-07
10	2.7691	7.957700e-07
10.0524	2.768965	8.274641e-07
10.1172	2.768796	8.666749e-07
10.1825	2.768624	9.061386e-07
10.2481	2.768448	9.458568e-07
10.3142	2.768269	9.858311e-07
10.3808	2.768086	1.026063e-06
10.4477	2.767899	1.066555e-06
10.5151	2.767708	1.107308e-06
10.5829	2.767513	1.148323e-06
10.6511	2.767314	1.189603e-06
10.7198	2.76711	1.231149e-06
10.789	2.766901	1.272964e-06
10.8586	2.766688	1.315048e-06
10.9286	2.76647	1.357403e-06
10.9991	2.766246	1.400031e-06
11	2.766243	1.400600e-06
11.07	2.766018	1.509770e-06
11.1414	2.765784	1.621121e-06
11.2132	2.765544	1.733189e-06
11.2856	2.765298	1.845980e-06
11.3583	2.765045	1.959498e-06
11.4316	2.764787	2.073749e-06
11.5053	2.764521	2.188736e-06
11.5795	2.764249	2.304465e-06
11.6542	2.76397	2.420941e-06
11.7293	2.763682	2.538167e-06
11.805	2.763387	2.656150e-06
11.8811	2.763084	2.774893e-06
11.9577	2.762772	2.894402e-06
12	2.762597	2.960300e-06
12.0349	2.762451	3.650622e-06
12.1125	2.762121	5.187292e-06
12.1906	2.761781	6.733872e-06
12.2692	2.761431	8.290426e-06
12.3483	2.76107	9.857018e-06
12.428	2.760698	1.143371e-05
12.5081	2.760314	1.302058e-05
12.5888	2.759918	1.461768e-05
12.67	2.759509	1.622507e-05
12.7517	2.759087	1.784284e-05
12.8339	2.75865	1.947104e-05
12.9167	2.758198	2.110973e-05
13	2.757731	2.275900e-05

Optical transmission calculator

Free-standing sample in vacuum, normal incidence

Transmittance T: —
Reflectance R: —

Fresnel reflection calculator

R_p: —
R_s: —
R = (R_p+R_s)/2: —
Phase φ_p: —
Phase φ_s: —
Brewster angle θ_B: —
Critical angle θ_C: —

Plot