Optical constants

Refractive index of K-LaFK50 (SUMITA)

K-LaFK50: n,k 0.36–1.55 µm

Data: formula 3 + tabulated k
Range: 0.36–1.55 µm
Temperature: 293 K
Licence: CC0-1.0

Axis Log x Log y

Click the plot to set the calculator wavelength.

At one wavelength

Refractive index n: 1.77199
Extinction coefficient k: 1.29605e-08

Permittivity ε₁: 3.13996
Permittivity ε₂: 4.59318e-08

Absorption coefficient α: 0.00277172 cm⁻¹
Penetration depth δ = λ/(2πk): 7.21573e+09 nm

Abbe number V_d: 49.983
Chromatic dispersion dn/dλ: -0.0793181 µm⁻¹

Group index n_g: 1.8186
Group velocity dispersion: 144.875 fs²/mm

Dispersion parameter D: -790.372 ps/(nm·km)
Photon energy: 2.11001 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

# K-LaFK50 (SUMITA): K-LaFK50
sumita_k_lafk50 = ls.fetch_refractiveindex("specs", "SUMITA-optical", "K-LaFK50", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(sumita_k_lafk50.range_nm)  # (360, 1550) nm
eps = sumita_k_lafk50.eps([633])  # 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_0a4ccb33e863/lightsmith"
sumita_k_lafk50 = ls.Tabulated.model_validate(json.load(urllib.request.urlopen(url)))
print(sumita_k_lafk50.source)  # citation and provenance travel with the data

Any dataset here, as the library's Tabulated material (sumita-k-lafk50/sumita).

# ... load sumita_k_lafk50 as above, then:
sim = ls.Simulation(
    particles=[ls.Particle(shape=ls.Sphere(radius_nm=50), material=sumita_k_lafk50)],
    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 wavelength

Same spec runs with DDA, FDTD, BEM or T-matrix: ls.compare(sim, ["mie", "dda"]).

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

Polynomial (formula 3), λ in µm

n^{2} = 3.070131 - 0.012037535 λ^{2.0} + 0.023978866 λ^{- 2.0} + 0.00056153238 λ^{- 4.0} - 1.0529871 \times 10^{-5} λ^{- 6.0} + 1.1710915 \times 10^{-6} λ^{- 8.0}

Valid from 0.36 to 1.55 µm.

Coefficients as stored

C_i	Value
C1	3.070131
C2	-0.012037535
C3	2.0
C4	0.023978866
C5	-2.0
C6	0.00056153238
C7	-4.0
C8	-1.0529871e-05
C9	-6.0
C10	1.1710915e-06
C11	-8.0

Comments and conditions

Conditions

temperature: 293 K

Properties

thermal dispersion: type: formula A, coefficients: -3.11e-07 1.35e-08 -2.34e-10 5.76e-07 8.89e-10 0.201
nd: 1.77200
Vd: 50.0
glass code: 772500
density: value: 5200
thermal expansion: value: 7.3e-06, temperature range: 243 343; value: 9e-06, temperature range: 293 573
dPgF: -0.0051
resistance: acid: 3.0; climatic: 1.0

Thermo-optic coefficient

Schott thermal-dispersion model (reference temperature 293.0 K): dn/dT = 7.75e-07 K⁻¹ at 633 nm, dn/dT = 1.93e-08 K⁻¹ at 1310 nm, dn/dT = -3.94e-08 K⁻¹ at 1550 nm

References

SUMITA Zemax catalog 2017-02-02 (obtained from http://www.sumita-opt.co.jp)
See also SUMITA optical glass data book

Cite

SUMITA Zemax catalog 2017-02-02 (obtained from http://www.sumita-opt.co.jp); See also SUMITA optical glass data book; Data from the refractiveindex.info database (M. N. Polyanskiy, Sci. Data 11, 94 (2024), doi:10.1038/s41597-023-02898-2)

Data

Computed on 416 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

K-LaFK50 (SUMITA), K-LaFK50: n and k versus wavelength
λ (µm)	n	k
0.36	1.812826	2.451100e-07
0.36132	1.812313	2.318768e-07
0.362644	1.811804	2.185952e-07
0.363973	1.811301	2.052648e-07
0.365308	1.810802	1.918856e-07
0.366647	1.810307	1.784573e-07
0.367991	1.809817	1.649798e-07
0.36934	1.809332	1.514530e-07
0.37	1.809097	1.448300e-07
0.370693	1.808851	1.413904e-07
0.372052	1.808375	1.346501e-07
0.373416	1.807903	1.278851e-07
0.374785	1.807435	1.210953e-07
0.376159	1.806972	1.142807e-07
0.377537	1.806513	1.074410e-07
0.378921	1.806058	1.005763e-07
0.38	1.805707	9.522600e-08
0.38031	1.805607	9.362845e-08
0.381704	1.80516	8.645316e-08
0.383104	1.804717	7.925158e-08
0.384508	1.804279	7.202359e-08
0.385917	1.803844	6.476911e-08
0.387332	1.803413	5.748804e-08
0.388752	1.802986	5.018028e-08
0.39	1.802615	4.375600e-08
0.390177	1.802563	4.371879e-08
0.391607	1.802143	4.341787e-08
0.393043	1.801727	4.311584e-08
0.394483	1.801315	4.281271e-08
0.395929	1.800907	4.250847e-08
0.397381	1.800502	4.220311e-08
0.398837	1.800101	4.189663e-08
0.4	1.799784	4.165200e-08
0.400299	1.799703	4.132969e-08
0.401767	1.799309	3.974951e-08
0.403239	1.798919	3.816354e-08
0.404717	1.798531	3.657175e-08
0.406201	1.798147	3.497413e-08
0.40769	1.797767	3.337065e-08
0.409184	1.797389	3.176129e-08
0.410684	1.797015	3.014603e-08
0.41219	1.796645	2.852486e-08
0.413701	1.796277	2.689774e-08
0.415217	1.795913	2.526465e-08
0.416739	1.795551	2.362559e-08
0.418267	1.795193	2.198051e-08
0.4198	1.794838	2.032940e-08
0.42	1.794792	2.011400e-08
0.421339	1.794486	2.041403e-08
0.422883	1.794137	2.076014e-08
0.424433	1.793791	2.110753e-08
0.425989	1.793448	2.145618e-08
0.427551	1.793108	2.180612e-08
0.429118	1.792771	2.215733e-08
0.430691	1.792436	2.250984e-08
0.43227	1.792104	2.286364e-08
0.433854	1.791776	2.321873e-08
0.435445	1.79145	2.357513e-08
0.437041	1.791126	2.393283e-08
0.438643	1.790806	2.429184e-08
0.44	1.790537	2.459600e-08
0.440251	1.790488	2.451771e-08
0.441864	1.790172	2.401364e-08
0.443484	1.78986	2.350773e-08
0.44511	1.78955	2.299996e-08
0.446741	1.789242	2.249033e-08
0.448379	1.788937	2.197883e-08
0.450023	1.788635	2.146545e-08
0.451672	1.788335	2.095020e-08
0.453328	1.788038	2.043305e-08
0.45499	1.787743	1.991401e-08
0.456657	1.78745	1.939307e-08
0.458331	1.78716	1.887022e-08
0.46	1.786874	1.834900e-08
0.460011	1.786872	1.834510e-08
0.461698	1.786587	1.776563e-08
0.46339	1.786304	1.718403e-08
0.465089	1.786023	1.660030e-08
0.466793	1.785745	1.601444e-08
0.468505	1.785468	1.542642e-08
0.470222	1.785195	1.483625e-08
0.471946	1.784923	1.424392e-08
0.473675	1.784653	1.364941e-08
0.475412	1.784386	1.305273e-08
0.477154	1.784121	1.245386e-08
0.478904	1.783858	1.185279e-08
0.48	1.783694	1.147600e-08
0.480659	1.783597	1.136033e-08
0.482421	1.783338	1.105109e-08
0.484189	1.783081	1.074071e-08
0.485964	1.782826	1.042920e-08
0.487746	1.782574	1.011655e-08
0.489533	1.782323	9.802745e-09
0.491328	1.782074	9.487793e-09
0.493129	1.781828	9.171688e-09
0.494936	1.781583	8.854423e-09
0.496751	1.78134	8.535996e-09
0.498572	1.781099	8.216401e-09
0.5	1.780912	7.965700e-09
0.500399	1.78086	7.972060e-09
0.502233	1.780623	8.001284e-09
0.504074	1.780388	8.030614e-09
0.505922	1.780154	8.060053e-09
0.507777	1.779923	8.089599e-09
0.509638	1.779693	8.119253e-09
0.511506	1.779465	8.149016e-09
0.513381	1.779239	8.178889e-09
0.515263	1.779014	8.208870e-09
0.517152	1.778792	8.238962e-09
0.519047	1.778571	8.269164e-09
0.52095	1.778351	8.299477e-09
0.52286	1.778134	8.329900e-09
0.524776	1.777918	8.360436e-09
0.5267	1.777704	8.391083e-09
0.528631	1.777491	8.421843e-09
0.530568	1.77728	8.452715e-09
0.532513	1.777071	8.483700e-09
0.534465	1.776863	8.514799e-09
0.536424	1.776657	8.546013e-09
0.538391	1.776452	8.577340e-09
0.540364	1.776249	8.608782e-09
0.542345	1.776048	8.640340e-09
0.544333	1.775848	8.672013e-09
0.546328	1.775649	8.703803e-09
0.548331	1.775452	8.735708e-09
0.55	1.77529	8.762300e-09
0.550341	1.775257	8.800363e-09
0.552358	1.775063	9.025607e-09
0.554383	1.77487	9.251676e-09
0.556415	1.774679	9.478575e-09
0.558455	1.77449	9.706304e-09
0.560502	1.774301	9.934869e-09
0.562556	1.774115	1.016427e-08
0.564619	1.773929	1.039451e-08
0.566688	1.773745	1.062560e-08
0.568765	1.773562	1.085754e-08
0.57085	1.773381	1.109032e-08
0.572943	1.773201	1.132396e-08
0.575043	1.773022	1.155845e-08
0.577151	1.772845	1.179381e-08
0.579267	1.772669	1.203002e-08
0.58139	1.772494	1.226711e-08
0.583521	1.77232	1.250506e-08
0.58566	1.772148	1.274388e-08
0.587807	1.771977	1.298358e-08
0.589961	1.771807	1.322416e-08
0.592124	1.771639	1.346562e-08
0.594295	1.771471	1.370796e-08
0.596473	1.771305	1.395120e-08
0.598659	1.77114	1.419532e-08
0.6	1.77104	1.434500e-08
0.600854	1.770976	1.427686e-08
0.603056	1.770814	1.410110e-08
0.605267	1.770652	1.392470e-08
0.607486	1.770492	1.374765e-08
0.609712	1.770333	1.356995e-08
0.611947	1.770175	1.339160e-08
0.614191	1.770018	1.321259e-08
0.616442	1.769862	1.303293e-08
0.618702	1.769707	1.285261e-08
0.62097	1.769554	1.267163e-08
0.623246	1.769401	1.248999e-08
0.62553	1.76925	1.230768e-08
0.627823	1.769099	1.212470e-08
0.630125	1.76895	1.194105e-08
0.632434	1.768801	1.175673e-08
0.634753	1.768654	1.157173e-08
0.637079	1.768508	1.138606e-08
0.639415	1.768362	1.119970e-08
0.641759	1.768218	1.101266e-08
0.644111	1.768075	1.082494e-08
0.646472	1.767932	1.063653e-08
0.648842	1.767791	1.044742e-08
0.65	1.767722	1.035500e-08
0.65122	1.767651	1.037445e-08
0.653607	1.767511	1.041250e-08
0.656003	1.767373	1.045069e-08
0.658408	1.767235	1.048902e-08
0.660821	1.767098	1.052749e-08
0.663244	1.766962	1.056610e-08
0.665675	1.766827	1.060486e-08
0.668115	1.766693	1.064375e-08
0.670564	1.76656	1.068279e-08
0.673022	1.766428	1.072197e-08
0.675489	1.766297	1.076130e-08
0.677965	1.766166	1.080077e-08
0.68045	1.766037	1.084038e-08
0.682945	1.765908	1.088014e-08
0.685448	1.76578	1.092004e-08
0.687961	1.765653	1.096009e-08
0.690482	1.765526	1.100029e-08
0.693013	1.765401	1.104063e-08
0.695554	1.765276	1.108113e-08
0.698103	1.765152	1.112177e-08
0.7	1.765061	1.115200e-08
0.700662	1.765029	1.124714e-08
0.703231	1.764906	1.161606e-08
0.705809	1.764785	1.198633e-08
0.708396	1.764664	1.235796e-08
0.710992	1.764544	1.273095e-08
0.713599	1.764424	1.310531e-08
0.716214	1.764306	1.348104e-08
0.71884	1.764188	1.385815e-08
0.721475	1.764071	1.423664e-08
0.724119	1.763954	1.461652e-08
0.726774	1.763839	1.499779e-08
0.729438	1.763723	1.538045e-08
0.732112	1.763609	1.576452e-08
0.734795	1.763495	1.615000e-08
0.737489	1.763382	1.653689e-08
0.740192	1.76327	1.692520e-08
0.742905	1.763159	1.731494e-08
0.745629	1.763048	1.770610e-08
0.748362	1.762937	1.809869e-08
0.751105	1.762828	1.849273e-08
0.753858	1.762718	1.888820e-08
0.756622	1.76261	1.928513e-08
0.759395	1.762502	1.968352e-08
0.762179	1.762395	2.008336e-08
0.764973	1.762289	2.048467e-08
0.767777	1.762183	2.088745e-08
0.770591	1.762077	2.129171e-08
0.773416	1.761972	2.169744e-08
0.776251	1.761868	2.210467e-08
0.779096	1.761765	2.251339e-08
0.781952	1.761662	2.292360e-08
0.784818	1.761559	2.333533e-08
0.787695	1.761457	2.374855e-08
0.790583	1.761356	2.416330e-08
0.793481	1.761255	2.457956e-08
0.796389	1.761155	2.499735e-08
0.799309	1.761055	2.541668e-08
0.8	1.761031	2.551600e-08
0.802238	1.760956	2.544171e-08
0.805179	1.760857	2.534411e-08
0.808131	1.760759	2.524616e-08
0.811093	1.760661	2.514784e-08
0.814066	1.760564	2.504917e-08
0.81705	1.760467	2.495013e-08
0.820045	1.760371	2.485073e-08
0.823051	1.760275	2.475097e-08
0.826068	1.76018	2.465084e-08
0.829096	1.760086	2.455034e-08
0.832135	1.759991	2.444948e-08
0.835186	1.759897	2.434824e-08
0.838247	1.759804	2.424664e-08
0.84132	1.759711	2.414466e-08
0.844404	1.759619	2.404231e-08
0.847499	1.759527	2.393958e-08
0.850606	1.759435	2.383648e-08
0.853724	1.759344	2.373300e-08
0.856853	1.759253	2.362914e-08
0.859994	1.759163	2.352490e-08
0.863146	1.759073	2.342027e-08
0.86631	1.758984	2.331527e-08
0.869486	1.758895	2.320987e-08
0.872673	1.758806	2.310410e-08
0.875872	1.758718	2.299793e-08
0.879082	1.75863	2.289137e-08
0.882305	1.758542	2.278443e-08
0.885539	1.758455	2.267709e-08
0.888785	1.758368	2.256936e-08
0.892043	1.758282	2.246123e-08
0.895313	1.758196	2.235271e-08
0.898595	1.75811	2.224379e-08
0.901889	1.758025	2.213447e-08
0.905195	1.75794	2.202475e-08
0.908513	1.757855	2.191463e-08
0.911843	1.757771	2.180410e-08
0.915186	1.757687	2.169317e-08
0.91854	1.757603	2.158183e-08
0.921907	1.75752	2.147009e-08
0.925287	1.757437	2.135793e-08
0.928678	1.757354	2.124536e-08
0.932083	1.757272	2.113238e-08
0.935499	1.75719	2.101899e-08
0.938928	1.757108	2.090518e-08
0.94237	1.757026	2.079096e-08
0.945824	1.756945	2.067631e-08
0.949291	1.756864	2.056125e-08
0.952771	1.756783	2.044576e-08
0.956264	1.756703	2.032985e-08
0.959769	1.756623	2.021351e-08
0.963287	1.756543	2.009675e-08
0.966818	1.756463	1.997956e-08
0.970362	1.756384	1.986194e-08
0.973919	1.756305	1.974389e-08
0.977489	1.756226	1.962541e-08
0.981072	1.756147	1.950649e-08
0.984668	1.756069	1.938714e-08
0.988278	1.755991	1.926735e-08
0.991901	1.755913	1.914712e-08
0.995536	1.755835	1.902644e-08
0.999186	1.755758	1.890533e-08
1.00285	1.75568	1.878377e-08
1.00652	1.755603	1.866177e-08
1.01021	1.755526	1.853932e-08
1.01392	1.75545	1.841642e-08
1.01763	1.755373	1.829307e-08
1.02136	1.755297	1.816927e-08
1.02511	1.755221	1.804502e-08
1.02887	1.755145	1.792031e-08
1.03264	1.755069	1.779514e-08
1.03642	1.754994	1.766951e-08
1.04022	1.754918	1.754343e-08
1.04403	1.754843	1.741688e-08
1.04786	1.754768	1.728986e-08
1.0517	1.754693	1.716238e-08
1.05556	1.754618	1.703444e-08
1.05943	1.754544	1.690602e-08
1.06	1.754533	1.688700e-08
1.06331	1.754469	1.702977e-08
1.06721	1.754395	1.719788e-08
1.07112	1.754321	1.736660e-08
1.07505	1.754247	1.753594e-08
1.07899	1.754173	1.770590e-08
1.08294	1.754099	1.787648e-08
1.08691	1.754025	1.804769e-08
1.0909	1.753952	1.821953e-08
1.09489	1.753878	1.839199e-08
1.09891	1.753805	1.856509e-08
1.10294	1.753731	1.873883e-08
1.10698	1.753658	1.891320e-08
1.11104	1.753585	1.908821e-08
1.11511	1.753512	1.926386e-08
1.1192	1.753439	1.944015e-08
1.1233	1.753366	1.961709e-08
1.12742	1.753294	1.979468e-08
1.13155	1.753221	1.997292e-08
1.1357	1.753148	2.015182e-08
1.13986	1.753076	2.033137e-08
1.14404	1.753003	2.051157e-08
1.14823	1.752931	2.069244e-08
1.15244	1.752858	2.087397e-08
1.15667	1.752786	2.105617e-08
1.16091	1.752714	2.123903e-08
1.16516	1.752642	2.142257e-08
1.16943	1.752569	2.160678e-08
1.17372	1.752497	2.179166e-08
1.17802	1.752425	2.197722e-08
1.18234	1.752353	2.216346e-08
1.18667	1.752281	2.235039e-08
1.19102	1.752209	2.253799e-08
1.19539	1.752136	2.272629e-08
1.19977	1.752064	2.291528e-08
1.20417	1.751992	2.310496e-08
1.20858	1.75192	2.329533e-08
1.21301	1.751848	2.348640e-08
1.21746	1.751776	2.367818e-08
1.22192	1.751704	2.387065e-08
1.2264	1.751632	2.406383e-08
1.2309	1.75156	2.425772e-08
1.23541	1.751487	2.445232e-08
1.23994	1.751415	2.464764e-08
1.24448	1.751343	2.484367e-08
1.24904	1.751271	2.504042e-08
1.25362	1.751198	2.523788e-08
1.25822	1.751126	2.543608e-08
1.26283	1.751054	2.563500e-08
1.26746	1.750981	2.583465e-08
1.27211	1.750909	2.603503e-08
1.27677	1.750836	2.623614e-08
1.28145	1.750763	2.643799e-08
1.28615	1.750691	2.664059e-08
1.29086	1.750618	2.684392e-08
1.29559	1.750545	2.704800e-08
1.30034	1.750472	2.725283e-08
1.30511	1.750399	2.745841e-08
1.30989	1.750326	2.766474e-08
1.31469	1.750253	2.787183e-08
1.31951	1.750179	2.807968e-08
1.32435	1.750106	2.828829e-08
1.3292	1.750032	2.849767e-08
1.33408	1.749959	2.870781e-08
1.33897	1.749885	2.891872e-08
1.34388	1.749811	2.913041e-08
1.3488	1.749737	2.934287e-08
1.35375	1.749663	2.955611e-08
1.35871	1.749589	2.977013e-08
1.36369	1.749514	2.998494e-08
1.36869	1.74944	3.020053e-08
1.3737	1.749365	3.041692e-08
1.37874	1.74929	3.063409e-08
1.38379	1.749215	3.085207e-08
1.38887	1.74914	3.107084e-08
1.39396	1.749065	3.129041e-08
1.39907	1.74899	3.151079e-08
1.4042	1.748914	3.173198e-08
1.40934	1.748838	3.195398e-08
1.41451	1.748762	3.217679e-08
1.41969	1.748686	3.240042e-08
1.4249	1.74861	3.262487e-08
1.43012	1.748533	3.285014e-08
1.43536	1.748457	3.307623e-08
1.44062	1.74838	3.330316e-08
1.44591	1.748303	3.353092e-08
1.45121	1.748225	3.375951e-08
1.45652	1.748148	3.398894e-08
1.46186	1.74807	3.421921e-08
1.46722	1.747992	3.445033e-08
1.4726	1.747914	3.468229e-08
1.478	1.747835	3.491510e-08
1.48342	1.747757	3.514877e-08
1.48885	1.747678	3.538329e-08
1.49431	1.747599	3.561867e-08
1.49979	1.74752	3.585492e-08
1.5	1.747516	3.586400e-08
1.50529	1.74744	4.061080e-08
1.5108	1.74736	4.556475e-08
1.51634	1.74728	5.053686e-08
1.5219	1.7472	5.552719e-08
1.52748	1.747119	6.053582e-08
1.53308	1.747038	6.556281e-08
1.5387	1.746957	7.060822e-08
1.54434	1.746875	7.567213e-08
1.55	1.746794	8.075460e-08

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: —

K-LaFK50 (SUMITA): all datasets

LaFK

K-LaFK50 n,k 0.36–1.55 µm default

About K-LaFK50 (SUMITA)

SUMITA Optical Glass, Inc. is a Japanese corporation known for its specialization in the production and development of optical glass, optical fiber, and various other photonic products. Founded in 1953, the company has established itself as a leading provider of high-quality optical materials that are used in a wide range of applications—from industrial and scientific optics to consumer electronics and medical devices. SUMITA's portfolio includes a variety of specialized optical glasses, including high-refractive-index, low-dispersion, and infrared-transmitting materials. These are often utilized in lenses, prisms, and other optical components requiring precision and high performance. With a strong commitment to research and development, SUMITA continually innovates to meet the evolving demands of the optics industry. Their rigorous quality control processes ensure that products meet the highest standards for optical clarity, consistency, and reliability. SUMITA Optical Glass, Inc. has garnered a reputation for excellence and innovation, making it a preferred supplier for organizations in need of advanced optical solutions.

SUMITA Optical Glass

More about K-LaFK50 (SUMITA) →

Provenance

Version: 1 (snapshot c5c2f18)
Source page: refractiveindex.info
Original file: database/data/specs/sumita/optical/K-LaFK50.yml
ID: ds_0a4ccb33e863
API: /v1/datasets/ds_0a4ccb33e863

Plot