Optical constants

Refractive index of K-PSK400 (SUMITA)

K-PSK400: 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: 1.59499
Extinction coefficient k: 3.12046e-08

Permittivity ε₁: 2.54401
Permittivity ε₂: 9.95422e-08

Absorption coefficient α: 0.00667338 cm⁻¹
Penetration depth δ = λ/(2πk): 2.99698e+09 nm

Abbe number V_d: 67.836
Chromatic dispersion dn/dλ: -0.0452981 µm⁻¹

Group index n_g: 1.62161
Group velocity dispersion: 80.0006 fs²/mm

Dispersion parameter D: -436.445 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-PSK400 (SUMITA): K-PSK400
sumita_k_psk400 = ls.fetch_refractiveindex("specs", "SUMITA-optical", "K-PSK400", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(sumita_k_psk400.range_nm)  # (360, 1550) nm
eps = sumita_k_psk400.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_5c0ee6b252ed/lightsmith"
sumita_k_psk400 = ls.Tabulated.model_validate(json.load(urllib.request.urlopen(url)))
print(sumita_k_psk400.source)  # citation and provenance travel with the data

Any dataset here, as the library's Tabulated material (sumita-k-psk400/sumita).

# ... load sumita_k_psk400 as above, then:
sim = ls.Simulation(
    particles=[ls.Particle(shape=ls.Sphere(radius_nm=50), material=sumita_k_psk400)],
    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} = 2.5082353 - 0.0073346094 λ^{2.0} + 0.012618342 λ^{- 2.0} + 0.00023225231 λ^{- 4.0} - 9.8397157 \times 10^{-6} λ^{- 6.0} + 6.9870981 \times 10^{-7} λ^{- 8.0}

Valid from 0.36 to 1.55 µm.

Coefficients as stored

C_i	Value
C1	2.5082353
C2	-0.0073346094
C3	2.0
C4	0.012618342
C5	-2.0
C6	0.00023225231
C7	-4.0
C8	-9.8397157e-06
C9	-6.0
C10	6.9870981e-07
C11	-8.0

Comments and conditions

Conditions

temperature: 293 K

Properties

thermal dispersion: type: formula A, coefficients: -1.29e-05 6.41e-09 -4.23e-11 4.04e-07 7.68e-10 0.173
nd: 1.59500
Vd: 67.8
glass code: 595678
density: value: 4050
thermal expansion: value: 1.01e-05, temperature range: 243 343; value: 1.29e-05, temperature range: 293 573
dPgF: 0.0129
resistance: acid: 1.0; climatic: 1.0

Thermo-optic coefficient

Schott thermal-dispersion model (reference temperature 293.0 K): dn/dT = -5.70e-06 K⁻¹ at 633 nm, dn/dT = -6.01e-06 K⁻¹ at 1310 nm, dn/dT = -6.03e-06 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-PSK400 (SUMITA), K-PSK400: n and k versus wavelength
λ (µm)	n	k
0.36	1.617539	5.908700e-07
0.36132	1.617264	5.510122e-07
0.362644	1.616991	5.110082e-07
0.363973	1.61672	4.708576e-07
0.365308	1.616452	4.305599e-07
0.366647	1.616186	3.901144e-07
0.367991	1.615922	3.495207e-07
0.36934	1.615661	3.087781e-07
0.37	1.615534	2.888300e-07
0.370693	1.615402	2.793656e-07
0.372052	1.615145	2.608191e-07
0.373416	1.61489	2.422046e-07
0.374785	1.614638	2.235219e-07
0.376159	1.614387	2.047706e-07
0.377537	1.614139	1.859507e-07
0.378921	1.613893	1.670617e-07
0.38	1.613703	1.523400e-07
0.38031	1.613649	1.501907e-07
0.381704	1.613407	1.405372e-07
0.383104	1.613167	1.308482e-07
0.384508	1.612929	1.211238e-07
0.385917	1.612694	1.113637e-07
0.387332	1.61246	1.015679e-07
0.388752	1.612228	9.173613e-08
0.39	1.612026	8.309300e-08
0.390177	1.611998	8.256406e-08
0.391607	1.61177	7.828651e-08
0.393043	1.611544	7.399327e-08
0.394483	1.61132	6.968430e-08
0.395929	1.611097	6.535953e-08
0.397381	1.610877	6.101891e-08
0.398837	1.610658	5.666238e-08
0.4	1.610485	5.318500e-08
0.400299	1.610441	5.272288e-08
0.401767	1.610226	5.045723e-08
0.403239	1.610013	4.818327e-08
0.404717	1.609801	4.590098e-08
0.406201	1.609591	4.361032e-08
0.40769	1.609383	4.131127e-08
0.409184	1.609176	3.900379e-08
0.410684	1.608972	3.668785e-08
0.41219	1.608769	3.436342e-08
0.413701	1.608567	3.203047e-08
0.415217	1.608367	2.968897e-08
0.416739	1.608169	2.733888e-08
0.418267	1.607972	2.498018e-08
0.4198	1.607777	2.261284e-08
0.42	1.607752	2.230400e-08
0.421339	1.607584	2.237509e-08
0.422883	1.607392	2.245710e-08
0.424433	1.607202	2.253941e-08
0.425989	1.607013	2.262203e-08
0.427551	1.606825	2.270494e-08
0.429118	1.60664	2.278816e-08
0.430691	1.606455	2.287169e-08
0.43227	1.606272	2.295552e-08
0.433854	1.606091	2.303966e-08
0.435445	1.605911	2.312411e-08
0.437041	1.605732	2.320886e-08
0.438643	1.605555	2.329393e-08
0.44	1.605407	2.336600e-08
0.440251	1.605379	2.337931e-08
0.441864	1.605205	2.346500e-08
0.443484	1.605032	2.355101e-08
0.44511	1.60486	2.363733e-08
0.446741	1.60469	2.372397e-08
0.448379	1.604521	2.381092e-08
0.450023	1.604353	2.389820e-08
0.451672	1.604187	2.398579e-08
0.453328	1.604022	2.407371e-08
0.45499	1.603858	2.416194e-08
0.456657	1.603696	2.425051e-08
0.458331	1.603535	2.433939e-08
0.46	1.603376	2.442800e-08
0.460011	1.603375	2.442860e-08
0.461698	1.603216	2.451814e-08
0.46339	1.603058	2.460801e-08
0.465089	1.602902	2.469820e-08
0.466793	1.602747	2.478873e-08
0.468505	1.602593	2.487959e-08
0.470222	1.60244	2.497078e-08
0.471946	1.602289	2.506231e-08
0.473675	1.602138	2.515417e-08
0.475412	1.601989	2.524637e-08
0.477154	1.601841	2.533890e-08
0.478904	1.601694	2.543178e-08
0.48	1.601603	2.549000e-08
0.480659	1.601548	2.552499e-08
0.482421	1.601403	2.561855e-08
0.484189	1.60126	2.571245e-08
0.485964	1.601117	2.580670e-08
0.487746	1.600976	2.590129e-08
0.489533	1.600835	2.599622e-08
0.491328	1.600696	2.609151e-08
0.493129	1.600558	2.618714e-08
0.494936	1.60042	2.628313e-08
0.496751	1.600284	2.637946e-08
0.498572	1.600149	2.647615e-08
0.5	1.600044	2.655200e-08
0.500399	1.600015	2.657321e-08
0.502233	1.599881	2.667064e-08
0.504074	1.599749	2.676844e-08
0.505922	1.599618	2.686659e-08
0.507777	1.599488	2.696510e-08
0.509638	1.599358	2.706397e-08
0.511506	1.59923	2.716321e-08
0.513381	1.599103	2.726281e-08
0.515263	1.598976	2.736277e-08
0.517152	1.598851	2.746310e-08
0.519047	1.598726	2.756380e-08
0.52095	1.598603	2.766487e-08
0.52286	1.59848	2.776631e-08
0.524776	1.598358	2.786812e-08
0.5267	1.598237	2.797030e-08
0.528631	1.598117	2.807286e-08
0.530568	1.597998	2.817579e-08
0.532513	1.597879	2.827910e-08
0.534465	1.597762	2.838279e-08
0.536424	1.597645	2.848686e-08
0.538391	1.597529	2.859131e-08
0.540364	1.597414	2.869615e-08
0.542345	1.5973	2.880136e-08
0.544333	1.597187	2.890697e-08
0.546328	1.597075	2.901296e-08
0.548331	1.596963	2.911934e-08
0.55	1.596871	2.920800e-08
0.550341	1.596852	2.922610e-08
0.552358	1.596742	2.933322e-08
0.554383	1.596633	2.944074e-08
0.556415	1.596524	2.954864e-08
0.558455	1.596416	2.965695e-08
0.560502	1.596309	2.976565e-08
0.562556	1.596203	2.987474e-08
0.564619	1.596098	2.998424e-08
0.566688	1.595993	3.009414e-08
0.568765	1.595889	3.020445e-08
0.57085	1.595786	3.031515e-08
0.572943	1.595683	3.042626e-08
0.575043	1.595581	3.053778e-08
0.577151	1.59548	3.064971e-08
0.579267	1.59538	3.076205e-08
0.58139	1.59528	3.087480e-08
0.583521	1.595181	3.098797e-08
0.58566	1.595083	3.110155e-08
0.587807	1.594985	3.121554e-08
0.589961	1.594888	3.132995e-08
0.592124	1.594792	3.144479e-08
0.594295	1.594696	3.156004e-08
0.596473	1.594601	3.167572e-08
0.598659	1.594507	3.179182e-08
0.6	1.594449	3.186300e-08
0.600854	1.594413	3.190834e-08
0.603056	1.59432	3.202529e-08
0.605267	1.594227	3.214268e-08
0.607486	1.594136	3.226049e-08
0.609712	1.594044	3.237873e-08
0.611947	1.593954	3.249741e-08
0.614191	1.593864	3.261652e-08
0.616442	1.593774	3.273607e-08
0.618702	1.593686	3.285606e-08
0.62097	1.593597	3.297648e-08
0.623246	1.59351	3.309735e-08
0.62553	1.593423	3.321866e-08
0.627823	1.593336	3.334042e-08
0.630125	1.59325	3.346262e-08
0.632434	1.593165	3.358527e-08
0.634753	1.59308	3.370837e-08
0.637079	1.592996	3.383192e-08
0.639415	1.592912	3.395592e-08
0.641759	1.592829	3.408038e-08
0.644111	1.592747	3.420530e-08
0.646472	1.592665	3.433067e-08
0.648842	1.592583	3.445650e-08
0.65	1.592544	3.451800e-08
0.65122	1.592502	3.458279e-08
0.653607	1.592422	3.470955e-08
0.656003	1.592342	3.483677e-08
0.658408	1.592262	3.496446e-08
0.660821	1.592183	3.509261e-08
0.663244	1.592105	3.522124e-08
0.665675	1.592027	3.535034e-08
0.668115	1.591949	3.547991e-08
0.670564	1.591872	3.560995e-08
0.673022	1.591796	3.574047e-08
0.675489	1.59172	3.587147e-08
0.677965	1.591644	3.600295e-08
0.68045	1.591569	3.613491e-08
0.682945	1.591494	3.626736e-08
0.685448	1.59142	3.640029e-08
0.687961	1.591346	3.653371e-08
0.690482	1.591273	3.666762e-08
0.693013	1.5912	3.680201e-08
0.695554	1.591128	3.693691e-08
0.698103	1.591056	3.707229e-08
0.7	1.591002	3.717300e-08
0.700662	1.590984	3.720818e-08
0.703231	1.590913	3.734458e-08
0.705809	1.590842	3.748149e-08
0.708396	1.590772	3.761890e-08
0.710992	1.590702	3.775681e-08
0.713599	1.590632	3.789523e-08
0.716214	1.590563	3.803415e-08
0.71884	1.590495	3.817358e-08
0.721475	1.590426	3.831353e-08
0.724119	1.590358	3.845398e-08
0.726774	1.590291	3.859496e-08
0.729438	1.590224	3.873644e-08
0.732112	1.590157	3.887845e-08
0.734795	1.590091	3.902098e-08
0.737489	1.590025	3.916403e-08
0.740192	1.589959	3.930761e-08
0.742905	1.589894	3.945171e-08
0.745629	1.589829	3.959634e-08
0.748362	1.589764	3.974150e-08
0.751105	1.5897	3.988719e-08
0.753858	1.589636	4.003341e-08
0.756622	1.589573	4.018018e-08
0.759395	1.589509	4.032748e-08
0.762179	1.589446	4.047531e-08
0.764973	1.589384	4.062370e-08
0.767777	1.589322	4.077262e-08
0.770591	1.58926	4.092209e-08
0.773416	1.589198	4.107211e-08
0.776251	1.589137	4.122268e-08
0.779096	1.589076	4.137380e-08
0.781952	1.589016	4.152548e-08
0.784818	1.588955	4.167771e-08
0.787695	1.588895	4.183050e-08
0.790583	1.588836	4.198385e-08
0.793481	1.588776	4.213776e-08
0.796389	1.588717	4.229223e-08
0.799309	1.588658	4.244728e-08
0.8	1.588644	4.248400e-08
0.802238	1.5886	4.260287e-08
0.805179	1.588541	4.275903e-08
0.808131	1.588483	4.291577e-08
0.811093	1.588426	4.307308e-08
0.814066	1.588368	4.323096e-08
0.81705	1.588311	4.338943e-08
0.820045	1.588254	4.354847e-08
0.823051	1.588198	4.370810e-08
0.826068	1.588141	4.386832e-08
0.829096	1.588085	4.402912e-08
0.832135	1.588029	4.419051e-08
0.835186	1.587974	4.435249e-08
0.838247	1.587918	4.451507e-08
0.84132	1.587863	4.467824e-08
0.844404	1.587808	4.484201e-08
0.847499	1.587754	4.500638e-08
0.850606	1.587699	4.517135e-08
0.853724	1.587645	4.533693e-08
0.856853	1.587591	4.550311e-08
0.859994	1.587537	4.566991e-08
0.863146	1.587484	4.583731e-08
0.86631	1.58743	4.600533e-08
0.869486	1.587377	4.617396e-08
0.872673	1.587324	4.634322e-08
0.875872	1.587272	4.651309e-08
0.879082	1.587219	4.668358e-08
0.882305	1.587167	4.685470e-08
0.885539	1.587115	4.702645e-08
0.888785	1.587063	4.719883e-08
0.892043	1.587011	4.737184e-08
0.895313	1.58696	4.754548e-08
0.898595	1.586909	4.771976e-08
0.901889	1.586857	4.789468e-08
0.905195	1.586807	4.807024e-08
0.908513	1.586756	4.824645e-08
0.911843	1.586705	4.842330e-08
0.915186	1.586655	4.860079e-08
0.91854	1.586605	4.877894e-08
0.921907	1.586554	4.895774e-08
0.925287	1.586505	4.913720e-08
0.928678	1.586455	4.931731e-08
0.932083	1.586405	4.949809e-08
0.935499	1.586356	4.967953e-08
0.938928	1.586306	4.986163e-08
0.94237	1.586257	5.004440e-08
0.945824	1.586208	5.022784e-08
0.949291	1.586159	5.041195e-08
0.952771	1.586111	5.059674e-08
0.956264	1.586062	5.078220e-08
0.959769	1.586014	5.096835e-08
0.963287	1.585965	5.115518e-08
0.966818	1.585917	5.134269e-08
0.970362	1.585869	5.153089e-08
0.973919	1.585821	5.171978e-08
0.977489	1.585773	5.190936e-08
0.981072	1.585726	5.209963e-08
0.984668	1.585678	5.229061e-08
0.988278	1.585631	5.248228e-08
0.991901	1.585583	5.267466e-08
0.995536	1.585536	5.286774e-08
0.999186	1.585489	5.306153e-08
1.00285	1.585442	5.325603e-08
1.00652	1.585395	5.345124e-08
1.01021	1.585348	5.364717e-08
1.01392	1.585301	5.384382e-08
1.01763	1.585255	5.404118e-08
1.02136	1.585208	5.423927e-08
1.02511	1.585162	5.443809e-08
1.02887	1.585115	5.463764e-08
1.03264	1.585069	5.483791e-08
1.03642	1.585023	5.503892e-08
1.04022	1.584977	5.524067e-08
1.04403	1.584931	5.544316e-08
1.04786	1.584885	5.564639e-08
1.0517	1.584839	5.585037e-08
1.05556	1.584793	5.605509e-08
1.05943	1.584747	5.626056e-08
1.06	1.58474	5.629100e-08
1.06331	1.584701	5.646679e-08
1.06721	1.584656	5.667377e-08
1.07112	1.58461	5.688152e-08
1.07505	1.584564	5.709002e-08
1.07899	1.584519	5.729929e-08
1.08294	1.584473	5.750933e-08
1.08691	1.584428	5.772013e-08
1.0909	1.584383	5.793171e-08
1.09489	1.584337	5.814407e-08
1.09891	1.584292	5.835720e-08
1.10294	1.584247	5.857112e-08
1.10698	1.584201	5.878581e-08
1.11104	1.584156	5.900130e-08
1.11511	1.584111	5.921758e-08
1.1192	1.584066	5.943464e-08
1.1233	1.584021	5.965251e-08
1.12742	1.583976	5.987117e-08
1.13155	1.583931	6.009063e-08
1.1357	1.583886	6.031090e-08
1.13986	1.58384	6.053198e-08
1.14404	1.583795	6.075386e-08
1.14823	1.58375	6.097656e-08
1.15244	1.583705	6.120008e-08
1.15667	1.58366	6.142442e-08
1.16091	1.583615	6.164957e-08
1.16516	1.58357	6.187556e-08
1.16943	1.583525	6.210237e-08
1.17372	1.58348	6.233001e-08
1.17802	1.583435	6.255849e-08
1.18234	1.58339	6.278780e-08
1.18667	1.583345	6.301796e-08
1.19102	1.5833	6.324896e-08
1.19539	1.583255	6.348080e-08
1.19977	1.58321	6.371350e-08
1.20417	1.583164	6.394705e-08
1.20858	1.583119	6.418145e-08
1.21301	1.583074	6.441671e-08
1.21746	1.583029	6.465284e-08
1.22192	1.582983	6.488983e-08
1.2264	1.582938	6.512769e-08
1.2309	1.582893	6.536642e-08
1.23541	1.582847	6.560603e-08
1.23994	1.582802	6.584652e-08
1.24448	1.582756	6.608788e-08
1.24904	1.582711	6.633014e-08
1.25362	1.582665	6.657328e-08
1.25822	1.58262	6.681731e-08
1.26283	1.582574	6.706223e-08
1.26746	1.582528	6.730806e-08
1.27211	1.582482	6.755478e-08
1.27677	1.582436	6.780241e-08
1.28145	1.58239	6.805095e-08
1.28615	1.582344	6.830040e-08
1.29086	1.582298	6.855076e-08
1.29559	1.582252	6.880204e-08
1.30034	1.582206	6.905424e-08
1.30511	1.582159	6.930737e-08
1.30989	1.582113	6.956142e-08
1.31469	1.582067	6.981640e-08
1.31951	1.58202	7.007232e-08
1.32435	1.581973	7.032918e-08
1.3292	1.581926	7.058698e-08
1.33408	1.58188	7.084572e-08
1.33897	1.581833	7.110542e-08
1.34388	1.581786	7.136606e-08
1.3488	1.581738	7.162766e-08
1.35375	1.581691	7.189022e-08
1.35871	1.581644	7.215374e-08
1.36369	1.581596	7.241823e-08
1.36869	1.581549	7.268368e-08
1.3737	1.581501	7.295011e-08
1.37874	1.581453	7.321752e-08
1.38379	1.581405	7.348591e-08
1.38887	1.581357	7.375528e-08
1.39396	1.581309	7.402563e-08
1.39907	1.58126	7.429698e-08
1.4042	1.581212	7.456933e-08
1.40934	1.581163	7.484267e-08
1.41451	1.581115	7.511701e-08
1.41969	1.581066	7.539236e-08
1.4249	1.581017	7.566872e-08
1.43012	1.580967	7.594609e-08
1.43536	1.580918	7.622448e-08
1.44062	1.580869	7.650389e-08
1.44591	1.580819	7.678432e-08
1.45121	1.580769	7.706578e-08
1.45652	1.580719	7.734828e-08
1.46186	1.580669	7.763180e-08
1.46722	1.580619	7.791637e-08
1.4726	1.580569	7.820198e-08
1.478	1.580518	7.848864e-08
1.48342	1.580467	7.877635e-08
1.48885	1.580416	7.906511e-08
1.49431	1.580365	7.935493e-08
1.49979	1.580314	7.964582e-08
1.5	1.580312	7.965700e-08
1.50529	1.580262	7.993778e-08
1.5108	1.580211	8.023080e-08
1.51634	1.580159	8.052491e-08
1.5219	1.580107	8.082009e-08
1.52748	1.580055	8.111635e-08
1.53308	1.580002	8.141370e-08
1.5387	1.579949	8.171214e-08
1.54434	1.579897	8.201167e-08
1.55	1.579844	8.231230e-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-PSK400 (SUMITA): all datasets

PSK (Dense phosphate crown)

K-PSK400 n,k 0.36–1.55 µm default

About K-PSK400 (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-PSK400 (SUMITA) →

Provenance

Version: 1 (snapshot c5c2f18)
Source page: refractiveindex.info
Original file: database/data/specs/sumita/optical/K-PSK400.yml
ID: ds_5c0ee6b252ed
API: /v1/datasets/ds_5c0ee6b252ed

Plot