Optical constants

Refractive index of WS2 (Tungsten disulfide)

Hsu et al. 2019: 3-layer (3L) film; n,k 0.40–0.85 µm

Data
tabulated nk
Range
0.397–0.8502 µm
Points
1973
Licence
CC0-1.0

Plot

Click the plot to set the calculator wavelength.

At one wavelength

Range 0.397–0.8502 µm
Refractive index n
4.22633
Extinction coefficient k
0.55715
Permittivity ε1
17.5515
Permittivity ε2
4.7094
Absorption coefficient α
119152 cm⁻¹
Penetration depth δ = λ/(2πk)
167.853 nm
Abbe number Vd
—
Chromatic dispersion dn/dλ
-5.21739 µm⁻¹
Group index ng
7.29207
Group velocity dispersion
— fs²/mm
Dispersion parameter D
— ps/(nm·km)
Photon energy
2.11001 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

# WS2 (Tungsten disulfide): Hsu et al. 2019: 3-layer (3L) film; n,k 0.40–0.85 µm
ws2 = ls.fetch_refractiveindex("main", "WS2", "Hsu-3L", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(ws2.range_nm)  # (396.97, 850.23) nm
eps = ws2.eps([633])  # complex permittivity

Downloads the original record once (pinned to the imported snapshot) and caches it.

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.

Comments and conditions

3-layer (3L)

Conditions

film thickness
3L

References

C. Hsu, R. Frisenda, R. Schmidt, A. Arora, S. M. de Vasconcellos, R. Bratschitsch, H. S. J. van der Zant, A. Castellanos-Gomez. Thickness-dependent refractive index of 1L, 2L, and 3L MoS2, MoSe2, WS2, and WSe2. Adv. Optical Mater. 7, 1900239 (2019) (Numerical data kindly provided by Andres Castellanos-Gomez)
  • doi:10.1002/adom.201900239 Thickness‐Dependent Refractive Index of 1L, 2L, and 3L MoS <sub>2</sub> , MoSe <sub>2</sub> , WS <sub>2</sub> , and WSe <sub>2</sub>, Advanced Optical Materials (2019)

Cite

Chunwei Hsu et al.. Thickness‐Dependent Refractive Index of 1L, 2L, and 3L MoS <sub>2</sub> , MoSe <sub>2</sub> , WS <sub>2</sub> , and WSe <sub>2</sub>. Advanced Optical Materials, 7, 1900239 (2019), doi:10.1002/adom.201900239; Data from the refractiveindex.info database (M. N. Polyanskiy, Sci. Data 11, 94 (2024), doi:10.1038/s41597-023-02898-2)

Data

1973 rows as published
WS2 (Tungsten disulfide), Hsu et al. 2019: 3-layer (3L) film; n,k 0.40–0.85 µm: n and k versus wavelength
λ (µm)nk
0.396973.6192.563
0.397193.70112.3064
0.397413.66982.2297
0.397623.84472.3329
0.397843.95242.3476
0.398064.06012.4281
0.398274.15422.5018
0.398494.28462.5982
0.398714.37412.6628
0.398934.40252.6843
0.399144.4242.6991
0.399364.43422.7025
0.399584.44442.7104
0.39984.47512.7319
0.400014.5172.7603
0.400234.54992.7841
0.400454.57822.8056
0.400664.60882.8272
0.400884.64172.8533
0.40114.66552.8703
0.401324.67352.8782
0.401534.69052.8952
0.401754.7122.9122
0.401974.73362.9292
0.402194.75512.9462
0.40244.77442.961
0.402624.78462.9621
0.402844.79482.961
0.403064.78912.944
0.403274.76532.9111
0.403494.73472.8691
0.403714.71772.8431
0.403934.70072.817
0.404144.69052.8
0.404364.67572.7762
0.404584.66782.7592
0.40484.66442.7444
0.405014.67232.7433
0.405234.66892.7285
0.405454.66552.7115
0.405674.67122.7036
0.405894.68142.7025
0.40614.69612.7059
0.406324.72682.7297
0.406544.76422.7603
0.406764.80392.7932
0.406974.84352.8261
0.407194.87642.8544
0.407414.90932.8805
0.407634.93992.9043
0.407854.9662.9236
0.408064.98752.9383
0.408285.00452.9508
0.40855.02152.9632
0.408725.03852.978
0.408945.05562.995
0.409155.07713.0188
0.409375.09413.0335
0.409595.10663.0415
0.409815.11453.0403
0.410025.12243.0415
0.410245.12813.0358
0.410465.13613.0347
0.410685.13723.0245
0.41095.13833.0143
0.411115.13953.0063
0.411335.14513.0075
0.411555.15083.0063
0.411775.15873.0097
0.411995.16213.0041
0.412215.16783.0029
0.412425.17122.9995
0.412645.17232.9893
0.412865.17122.9768
0.413085.17692.9757
0.41335.1782.9678
0.413515.18142.9666
0.413735.18252.961
0.413955.18592.9598
0.414175.19162.9632
0.414395.19952.9689
0.414615.19842.961
0.414825.19952.9576
0.415045.20522.961
0.415265.21092.9621
0.415485.21662.9632
0.41575.21772.9598
0.415925.21882.9564
0.416135.22452.9598
0.416355.22792.9587
0.416575.22682.9462
0.416795.22792.9383
0.417015.2292.9326
0.417235.23242.9292
0.417455.23362.9213
0.417665.23242.9111
0.417885.23362.9054
0.41815.23472.8998
0.418325.23132.8895
0.418545.22792.8771
0.418765.22682.8691
0.418975.23022.868
0.419195.23132.8623
0.419415.23022.8544
0.419635.22682.8419
0.419855.22792.8385
0.420075.2292.8351
0.420295.23022.8295
0.420515.2292.8215
0.420725.23022.8181
0.420945.23362.8147
0.421165.2372.8113
0.421385.24042.8056
0.42165.24382.8
0.421825.24722.7943
0.422045.24832.7841
0.422265.25172.7762
0.422475.25512.7682
0.422695.2632.7716
0.422915.2712.775
0.423135.27662.7716
0.423355.28232.7728
0.423575.29022.7762
0.423795.29822.7796
0.424015.30612.7807
0.424235.31182.7773
0.424445.31752.7739
0.424665.32542.775
0.424885.33112.7694
0.42515.33672.766
0.425325.34012.758
0.425545.34352.7524
0.425765.34242.7376
0.425985.34132.7229
0.42625.34012.7104
0.426425.34132.7002
0.426635.34012.6855
0.426855.3392.6707
0.427075.33792.6583
0.427295.3392.6526
0.427515.34012.6446
0.427735.3392.6322
0.427955.33792.6242
0.428175.33672.6163
0.428395.33792.6129
0.428615.33452.6004
0.428835.33332.5902
0.429055.33222.5823
0.429275.33112.5744
0.429485.32772.5596
0.42975.32432.5471
0.429925.31862.5301
0.430145.31752.5245
0.430365.31182.512
0.430585.30612.4995
0.43085.30272.4916
0.431025.29932.4859
0.431245.29372.4757
0.431465.29022.47
0.431685.28232.4553
0.43195.27662.4451
0.432125.26872.4326
0.432345.25852.4156
0.432565.25062.4032
0.432785.24262.3907
0.4335.23242.3759
0.433215.22452.368
0.433435.21662.3578
0.433655.20632.3431
0.433875.19612.3306
0.434095.18142.3113
0.434315.17122.2988
0.434535.1612.2864
0.434755.15082.2716
0.434975.13832.2569
0.435195.13272.2535
0.435415.1272.2501
0.435635.12362.249
0.435855.12022.2501
0.436075.11682.2512
0.436295.11342.2524
0.436515.11452.2603
0.436735.11112.2614
0.436955.10772.2626
0.437175.10662.2682
0.437395.10542.2739
0.437615.10432.2796
0.437835.10322.2852
0.438055.10432.2932
0.438275.10542.3011
0.438495.10432.3068
0.438715.10092.3079
0.438935.09752.309
0.439155.09412.3102
0.439375.09072.3113
0.439595.08282.3056
0.439815.07482.3
0.440035.07142.2988
0.440255.0682.2977
0.440475.06462.2966
0.440695.06122.2932
0.440915.06012.2943
0.441135.05672.2932
0.441355.05332.292
0.441575.04762.2864
0.441795.04652.2875
0.442015.04312.2818
0.442235.03972.2807
0.442455.0342.2728
0.442675.03292.2716
0.442895.03172.2705
0.443115.03062.2694
0.443335.02492.2614
0.443555.02152.258
0.443775.01812.2524
0.443995.0172.2512
0.444215.01362.2456
0.444435.01252.2422
0.444655.01362.2433
0.444875.01472.2444
0.445095.01362.2433
0.445315.01252.2399
0.445535.00912.2342
0.445755.00792.2308
0.445975.00232.2206
0.446194.99662.2104
0.446414.99322.2025
0.446634.98982.1945
0.446854.98872.1911
0.447074.98532.1832
0.447294.98192.1753
0.447514.98072.1696
0.447744.97512.1571
0.447964.96492.1378
0.448184.95692.1208
0.44844.9492.1016
0.448624.9412.0823
0.448844.93312.063
0.449064.92522.0437
0.449284.92182.029
0.44954.91612.012
0.449724.90821.9905
0.449944.90251.9734
0.450164.89681.9564
0.450384.88891.9349
0.45064.87411.9066
0.450824.85941.8805
0.451044.85371.8635
0.451274.84581.8442
0.451494.84011.8272
0.451714.83221.8079
0.451934.82651.7909
0.452154.83221.7875
0.452374.83331.7773
0.452594.83221.7671
0.452814.83331.7592
0.453034.82991.7444
0.453254.83561.741
0.453474.8391.7354
0.453694.84011.7251
0.453914.84581.7195
0.454144.85371.7161
0.454364.86171.7127
0.454584.86961.7093
0.45484.87531.7013
0.455024.88321.6957
0.455244.89121.69
0.455464.89681.6843
0.455684.90021.6741
0.45594.90591.6662
0.456124.91161.6605
0.456354.91721.6549
0.456574.92291.6492
0.456794.92631.6412
0.457014.9321.6356
0.457234.93761.6299
0.457454.94331.6242
0.457674.94671.6163
0.457894.95011.6084
0.458114.95351.6027
0.458344.95691.597
0.458564.96031.5914
0.458784.96371.5857
0.4594.96491.58
0.459224.96831.5744
0.459444.97171.5687
0.459664.97511.563
0.459884.98071.5596
0.460114.98641.5539
0.460334.98981.5483
0.460554.99551.5426
0.460775.00111.5392
0.460995.00681.5358
0.461215.01021.5301
0.461435.01361.5245
0.461655.0171.5188
0.461885.02491.5154
0.46215.03061.512
0.462325.03631.5063
0.462545.0421.5007
0.462765.04991.4973
0.462985.05781.4939
0.46325.06351.4905
0.463435.06691.4848
0.463655.07261.4791
0.463875.07821.4757
0.464095.08391.4723
0.464315.08731.4666
0.464535.09071.461
0.464755.09641.4576
0.464985.1021.4542
0.46525.10541.4508
0.465425.11111.4474
0.465645.11451.444
0.465865.12021.4406
0.466085.12591.4394
0.466315.12931.436
0.466535.13271.4326
0.466755.13611.4292
0.466975.13721.4258
0.467195.14061.4224
0.467415.14171.419
0.467645.14511.4156
0.467865.14851.4122
0.468085.14971.4088
0.46835.15311.4077
0.468525.15651.4043
0.468755.15761.4009
0.468975.16331.3998
0.469195.16441.3963
0.469415.16551.3929
0.469635.17121.3918
0.469855.17461.3884
0.470085.17571.385
0.47035.18141.3839
0.470525.18251.3805
0.470745.18371.3771
0.470965.18931.3759
0.471195.19051.3725
0.471415.19161.3691
0.471635.19731.368
0.471855.19841.3646
0.472075.20181.3635
0.47235.20521.3623
0.472525.20631.3589
0.472745.20981.3578
0.472965.21321.3567
0.473185.21431.3555
0.473415.21541.3544
0.473635.21431.351
0.473855.21771.3499
0.474075.21881.3487
0.47435.221.3476
0.474525.22111.3465
0.474745.22221.3431
0.474965.22561.3419
0.475185.2291.3408
0.475415.22791.3374
0.475635.2291.3363
0.475855.23021.3329
0.476075.23361.3317
0.47635.23471.3306
0.476525.23581.3272
0.476745.23921.3261
0.476965.24261.3249
0.477185.2461.3238
0.477415.24721.3227
0.477635.2461.3193
0.477855.24941.3181
0.478075.25061.317
0.47835.25171.3159
0.478525.25281.3147
0.478745.2541.3136
0.478965.25511.3124
0.479195.25621.3113
0.479415.25511.3102
0.479635.25851.3113
0.479855.25961.3102
0.480085.26081.309
0.48035.26191.3079
0.480525.26531.3068
0.480745.2711.3079
0.480975.27441.3068
0.481195.27321.3034
0.481415.27441.3022
0.481635.27781.3011
0.481865.28121.3
0.482085.28231.2988
0.48235.28341.2977
0.482535.28461.2966
0.482755.28571.2954
0.482975.28681.2943
0.483195.2881.2932
0.483425.28911.292
0.483645.29021.2909
0.483865.29141.2898
0.484085.29251.2886
0.484315.29591.2898
0.484535.29711.2886
0.484755.29821.2898
0.484985.29711.2886
0.48525.29591.2875
0.485425.29481.2864
0.485645.29371.2852
0.485875.29251.2841
0.486095.29591.2852
0.486315.29711.2841
0.486545.29821.283
0.486765.30161.2841
0.486985.30271.283
0.48725.30611.2841
0.487435.30731.283
0.487655.30611.2818
0.487875.3051.2807
0.48815.30391.2796
0.488325.30271.2784
0.488545.30611.2796
0.488775.30731.2784
0.488995.31071.2796
0.489215.31181.2784
0.489435.31521.2796
0.489665.31861.2807
0.489885.3221.2818
0.49015.32091.2807
0.490335.31971.2796
0.490555.31861.2784
0.490775.31751.2773
0.4915.31631.2762
0.491225.31521.275
0.491445.31181.2716
0.491675.30841.2682
0.491895.3051.2648
0.492115.29931.2592
0.492345.29591.2558
0.492565.29021.2501
0.492785.28461.2444
0.493015.27891.2388
0.493235.27321.2331
0.493455.25851.2206
0.493685.2461.2104
0.49395.22451.1934
0.494125.20291.1764
0.494355.17691.1571
0.494575.15081.1378
0.494795.12021.1163
0.495025.09861.1016
0.495245.07031.0823
0.495465.0511.0698
0.495695.02721.0551
0.495915.00571.0426
0.496134.98411.0301
0.496364.96491.0199
0.496584.94561.0097
0.49684.92861.0018
0.497034.91160.99385
0.497254.89910.98819
0.497484.88660.98252
0.49774.87190.97685
0.497924.86170.97345
0.498154.84920.97005
0.498374.8390.96664
0.498594.82430.96097
0.498824.81180.95757
0.499044.79930.95417
0.499264.78680.95077
0.499494.77210.9451
0.499714.76190.9417
0.499944.74940.9383
0.500164.7370.9349
0.500384.720.92923
0.500614.70750.92583
0.500834.6950.92243
0.501054.68480.92129
0.501284.67010.91789
0.50154.65760.91449
0.501734.64740.91336
0.501954.63950.91222
0.502174.62930.91109
0.50244.62130.90995
0.502624.61110.90882
0.502854.60090.90769
0.503074.5930.90882
0.503294.58730.90995
0.503524.57940.91109
0.503744.57370.91222
0.503974.56580.91336
0.504194.56010.91449
0.504414.55440.91562
0.504644.54650.91676
0.504864.53630.91562
0.505094.52830.91676
0.505314.51590.91562
0.505534.50790.91676
0.505764.49550.91562
0.505984.48750.91676
0.506214.48190.91789
0.506434.47390.91902
0.506654.4660.92016
0.506884.46030.92129
0.50714.45240.92243
0.507334.4490.92583
0.507554.44330.92696
0.507784.43540.9281
0.5084.4320.9315
0.508224.42630.93263
0.508454.42290.93603
0.508674.41950.93717
0.50894.41380.9383
0.509124.41040.9417
0.509344.40480.94283
0.509574.39910.94397
0.509794.3980.94737
0.510024.39230.9485
0.510244.38890.9519
0.510474.38780.95531
0.510694.38210.95644
0.510924.3810.95984
0.511144.37760.96097
0.511364.37190.96211
0.511594.37070.96551
0.511814.36960.96891
0.512044.36390.97005
0.512264.36280.97345
0.512494.36170.97685
0.512714.36050.98025
0.512944.36170.98365
0.513164.36050.98478
0.513384.35710.98592
0.513614.35830.98932
0.513834.35710.99045
0.514064.3560.99159
0.514284.35710.99499
0.514514.3560.99612
0.514734.35710.99952
0.514964.36051.0029
0.515184.36391.0041
0.515414.36961.0075
0.515634.3731.0086
0.515864.37641.0097
0.516084.38211.0131
0.51634.38551.0143
0.516534.38891.0154
0.516754.39231.0188
0.516984.39571.0199
0.51724.40141.0233
0.517434.40481.0245
0.517654.40821.0256
0.517884.41381.029
0.51814.41951.0301
0.518334.42521.0313
0.518554.42861.0324
0.518784.4321.0335
0.5194.43761.0347
0.519234.44331.0358
0.519454.4491.0369
0.519684.45461.0381
0.51994.46031.0392
0.520134.4661.0403
0.520354.46941.0392
0.520584.47511.0403
0.52084.47851.0392
0.521034.48191.0381
0.521254.48531.0369
0.521484.48641.0335
0.52174.49211.0324
0.521934.49771.0313
0.522154.50111.0301
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0.828852.93760.0
0.829092.92970.0
0.829332.90820.0
0.829572.88660.0
0.829812.86280.0
0.830052.83670.0
0.830292.81070.0
0.830532.78910.0
0.830772.76980.0
0.831012.75510.0
0.831252.74260.0
0.831492.73020.0
0.831732.71320.0
0.831972.70070.0
0.832212.69050.0
0.832452.66890.0
0.832692.65420.0
0.832932.64170.0
0.833172.63610.0
0.833412.63040.0
0.833652.62240.0
0.833892.60540.0
0.834132.59750.0
0.834372.5850.0
0.834612.57030.0
0.834852.55330.0
0.835092.54540.0
0.835332.53970.0
0.835572.5340.0
0.835812.53510.0
0.836052.54990.0
0.836292.56460.0
0.836532.57940.0
0.836772.58730.0
0.837012.5930.0
0.837252.60090.0
0.837492.60660.0
0.837732.59410.0
0.837972.58390.0
0.838212.57370.0
0.838452.55670.0
0.838692.53290.0
0.838932.51130.0
0.839172.49210.0
0.839412.47730.0
0.839652.46710.0
0.839892.45010.0
0.840132.43990.0
0.840372.4320.0
0.840622.4240.0
0.840862.42060.0
0.84112.42180.0
0.841342.42290.0
0.841582.43310.0
0.841822.44330.0
0.842062.46030.0
0.84232.47730.0
0.842542.4830.0
0.842782.47960.0
0.843022.46260.0
0.843262.43880.0
0.84352.41720.0
0.843742.39340.0
0.843982.37410.0
0.844222.36390.0
0.844462.36050.0
0.84472.36620.0
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0.845182.36620.0
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0.84592.35830.0
0.846142.35490.0
0.846382.36050.0
0.846622.37530.0
0.846862.39910.0
0.847112.42290.0
0.847352.44440.0
0.847592.47050.0
0.847832.4830.0
0.848072.49550.0
0.848312.49890.0
0.848552.50910.0
0.848792.5170.0
0.849032.52720.0
0.849272.53510.0
0.849512.5590.0
0.849752.57140.0
0.849992.58840.0
0.850232.59640.0

Optical transmission calculator

Free-standing sample in vacuum, normal incidence
Method
Transmittance T
—
Reflectance R
—

Fresnel reflection calculator

Direction
Rp
—
Rs
—
R = (Rp+Rs)/2
—
Phase φp
—
Phase φs
—
Brewster angle θB
—
Critical angle θC
—