Optical constants

Refractive index of Er (Erbium)

Larruquert et al. 2011: n,k 0.000784–0.383 µm

Data
tabulated nk
Range
0.0007836–0.3827 µm
Points
1329
Licence
CC0-1.0

Plot

Click the plot to set the calculator wavelength.

At one wavelength

Range 0.0007836–0.3827 µm
Refractive index n
0.958034
Extinction coefficient k
0.0351297
Permittivity ε1
0.916595
Permittivity ε2
0.0673109
Absorption coefficient α
255175 cm⁻¹
Penetration depth δ = λ/(2πk)
78.3776 nm
Abbe number Vd
—
Chromatic dispersion dn/dλ
-5.15576 µm⁻¹
Group index ng
1.04723
Group velocity dispersion
— fs²/mm
Dispersion parameter D
— ps/(nm·km)
Photon energy
71.6672 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

# Er (Erbium): Larruquert et al. 2011: n,k 0.000784–0.383 µm
er = ls.fetch_refractiveindex("main", "Er", "Larruquert", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(er.range_nm)  # (0.783614, 382.667) nm
eps = er.eps([17.3])  # 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

Density: 9.066 g/cm3. Film deposited at room temperature.

References

J. I. Larruquert, F. Frassetto, S. García-Cortés, M. Vidal-Dasilva, M. Fernández-Perea, J. A. Aznárez, J. A. Méndez, L. Poletto, A. M. Malvezzi, A. Giglia, S. Nannarone. Transmittance and optical constants of erbium films in the 3.25−1580 eV spectral range. Appl. Opt. 50, 2211-2219 (2011) (Numerical data kindly provided by Juan Larruquert)
  • doi:10.1364/ao.50.002211 Transmittance and optical constants of erbium films in the 325−1580 eV spectral range, Applied Optics (2011)

Cite

Juan I. Larruquert et al.. Transmittance and optical constants of erbium films in the 325−1580 eV spectral range. Applied Optics, 50, 2211 (2011), doi:10.1364/ao.50.002211; Data from the refractiveindex.info database (M. N. Polyanskiy, Sci. Data 11, 94 (2024), doi:10.1038/s41597-023-02898-2)

Data

1329 rows as published
Er (Erbium), Larruquert et al. 2011: n,k 0.000784–0.383 µm: n and k versus wavelength
λ (µm)nk
0.0007836140.999663570.000309323
0.0007860530.999665140.000312807
0.0007885130.999667010.000316338
0.0007909880.999669220.000319882
0.0007934780.999671810.000323407
0.000795980.9996750.000326863
0.0007985020.999678440.000330214
0.000801040.999682340.000333392
0.0008035890.999686730.00033632
0.000806160.999691650.000338928
0.0008087470.999697080.000341115
0.0008113460.999703010.000342771
0.0008139660.999709450.000343783
0.0008166040.999716350.000344012
0.0008192590.999723630.000343309
0.0008219260.99973120.000341513
0.0008246150.999738920.000338437
0.0008273220.999746560.000333883
0.0008300420.999753650.00032765
0.0008327850.999760740.000320503
0.0008355460.999767340.000309479
0.000838320.999769270.000293481
0.0008411180.999763070.0002775
0.0008439350.999751150.0002684
0.0008468110.999737690.0002655
0.0008469110.999736990.000264975
0.0008470320.999736070.000265167
0.0008471410.999735490.000265001
0.0008472530.999734170.000264409
0.0008474890.999734530.000264654
0.0008474950.999734460.000266866
0.0008476080.999732330.0002668
0.0008477290.999732110.000265372
0.0008478370.999730740.000265611
0.0008479510.999729880.000266344
0.0008480710.999729760.000267115
0.0008481910.999729580.000266525
0.0008483080.999728910.000266274
0.0008484220.999727380.000265343
0.0008485310.999726060.000266781
0.0008486490.999725440.000266979
0.0008487780.999724580.000267668
0.0008488990.999724470.000268379
0.0008490150.99972380.000267252
0.000849120.999722070.000267352
0.000849230.999721070.000268868
0.0008493510.99972090.00026927
0.0008494730.999719720.000268642
0.0008495910.999718560.000269991
0.0008497130.999718330.000270191
0.0008498220.999716680.000268828
0.0008499320.999714240.000270264
0.0008500430.999713480.00027237
0.0008501660.999712910.000272488
0.0008502880.999711260.000272986
0.000850410.999710070.000274666
0.0008505190.999708980.000274789
0.0008506240.99970720.000275701
0.000850750.999705330.000277599
0.0008508720.999704040.00027961
0.0008509950.999702630.000281172
0.0008512160.999701430.000285352
0.0008512280.999701440.000286098
0.000851330.999700760.000287102
0.0008514470.99970.000287925
0.000851570.999698140.000288956
0.0008516920.999696230.000291354
0.0008518130.999694540.000293161
0.0008519180.999691910.000294486
0.0008520230.999689960.000298598
0.0008521390.999687280.000299808
0.0008522710.999682730.000305535
0.0008523890.999679460.00031162
0.0008525050.999676910.000319173
0.0008526150.999675230.000327127
0.0008527250.999675260.000337062
0.0008528460.999676680.000346815
0.0008529640.999679290.000358654
0.0008530870.999685370.0003715
0.0008532070.999694630.000383097
0.0008533120.999704230.000391091
0.0008534220.999715920.000399181
0.0008535330.999728760.0004042
0.0008536610.999744410.000410063
0.0008537790.999761420.000413231
0.00085390.99978080.00041281
0.0008540040.99979820.000408109
0.0008541140.999814050.000398251
0.000854230.999827790.000386955
0.0008543560.999841110.000372453
0.0008544850.999850710.000352696
0.0008545940.999853020.000334712
0.0008546980.999850220.000319858
0.0008548160.999845760.00030895
0.0008549410.999841740.000298741
0.0008550580.999836950.000289568
0.0008551780.999829920.000282022
0.0008554050.999828650.000272225
0.0008554170.999828380.000279509
0.0008555140.999818490.000270246
0.0008556470.999811940.000267332
0.0008556590.999811430.000268252
0.0008568040.999792250.000255796
0.0008579440.999781970.000249607
0.0008590750.999775760.000242437
0.0008602080.999770430.000235583
0.0008613540.999764820.000227266
0.0008625090.999757640.000218802
0.0008636670.999749330.000210889
0.000864830.999739480.000202159
0.0008659940.999726470.000193019
0.0008671470.99971050.000186016
0.0008683020.999692240.000180377
0.0008694720.99967010.000174966
0.0008706460.999642710.000171771
0.0008706630.999642260.00017156
0.0008707590.999639980.000171433
0.0008708850.999636550.000170743
0.0008710040.999632610.000170216
0.0008711280.999628870.000171106
0.0008712440.999626250.000171215
0.0008713540.999623120.000170062
0.0008714750.999618710.000169845
0.0008716050.999614480.000170513
0.0008717340.999610350.00017032
0.0008718550.999606460.000170802
0.0008719720.999602590.000170397
0.0008720950.99959770.000170247
0.0008722070.999593730.000171476
0.0008723260.999589890.000171182
0.000872450.999584710.000170596
0.0008725810.999578980.000171405
0.0008726940.999574150.00017169
0.0008728120.999568930.000172388
0.0008729430.9995630.00017292
0.0008730670.999556560.000173383
0.0008731820.999551140.000175672
0.0008733030.999545760.000176054
0.0008734210.999539440.000176862
0.0008735480.999532940.000178778
0.0008736650.999526360.0001789
0.0008737880.999519210.000181577
0.000873910.999512010.000182058
0.0008740350.999504040.000184841
0.0008741520.999496690.000186098
0.0008742680.999488510.000188192
0.0008743840.999480020.000190515
0.000874510.999471170.000194112
0.0008746310.999462210.000195864
0.0008747570.999451130.000198559
0.0008748740.999440330.000202228
0.0008750040.999428060.000207062
0.0008751250.999415810.000211354
0.0008752470.99940270.000217246
0.0008753680.999388580.000223321
0.0008754980.999373260.000232959
0.0008756340.999355650.000241338
0.0008757550.999338450.000254433
0.0008758850.999321430.000270306
0.0008760160.999305570.000288944
0.0008761370.999291890.000307169
0.0008762590.999281190.000329224
0.0008763840.999273210.000348471
0.0008765150.999263660.000365851
0.0008766410.999251260.000381895
0.0008767670.999234010.000399631
0.0008768980.999211640.000424607
0.0008770190.999189960.000458349
0.0008771490.999171110.000505395
0.0008772660.999164880.000561147
0.0008773910.999182940.00062638
0.0008775180.999223130.000671264
0.0008776490.999269950.000689276
0.0008777790.999301920.000677211
0.0008779050.999303230.000654378
0.0008780260.999279020.000645103
0.0008781520.999237960.000653399
0.0008782780.999187520.000686394
0.0008783990.99914010.00074695
0.0008785250.999104620.000836196
0.0008786560.999089270.000951295
0.0008787820.999106360.001086696
0.0008789120.999177330.001236188
0.0008790430.999293270.001351306
0.0008791650.999436070.001441329
0.0008792950.999611910.001472421
0.0008794120.999763160.001453033
0.0008795420.999909540.001392119
0.0008796661.00001210.001292842
0.0008797941.00006570.001182998
0.0008799121.00007070.001090975
0.0008800431.00004460.001028925
0.0008801721.00000370.001004778
0.0008802960.999967910.001030729
0.0008804170.999963550.001096573
0.0008805441.0000160.001186583
0.0008806721.00013070.001255464
0.0008807981.00028370.001268547
0.0008809221.00044160.001215823
0.0008810561.00057440.001091669
0.0008811821.00065210.000956097
0.00088131.0006760.000815094
0.0008814231.00067550.000713806
0.0008815491.00066380.000599714
0.0008816831.00063040.000503459
0.0008818121.00058830.00042232
0.0008819281.0005420.000365211
0.000882061.00049070.00031987
0.0008821781.00044830.000288045
0.0008823091.00040550.000262582
0.0008824331.00037020.00024466
0.0008825681.00033690.000227943
0.0008826991.00030770.000214022
0.0008828161.00028270.000202687
0.0008829391.00025870.000194596
0.0008830691.00023620.000187229
0.0008831891.0002170.000180368
0.0008833231.00019720.000175165
0.0008834511.00018030.000170131
0.0008835771.00016460.000165679
0.0008836981.000150.000161499
0.0008838241.00013610.000159132
0.000883951.00012380.000156023
0.0008840811.00011120.00015274
0.0008842111.00009960.000150761
0.0008843321.00008920.000147502
0.0008844631.00007840.000146435
0.0008845841.00006980.000144638
0.000884711.00006020.000141665
0.0008848361.0000510.000141639
0.0008849621.00004360.000140465
0.0008850931.00003550.000138196
0.0008852281.00002750.000137898
0.000885351.00002110.000136283
0.000885471.00001460.000135289
0.0008855961.00000840.000134271
0.0008857221.00000180.000132331
0.0008858440.999995590.000132304
0.000885970.999989910.00013125
0.00088610.999983950.0001306
0.0008862410.999978650.000130258
0.0008862460.999978450.000129717
0.000887510.999933170.000124367
0.0008887840.999899790.000122561
0.0008900530.999874490.000120721
0.0008913220.999853530.000119022
0.0008926150.999835760.000118308
0.0008942690.99981570.000116
0.0008955420.999801950.000116859
0.0008968180.999790450.000117081
0.0008980910.999779280.000117165
0.0008993750.999770370.000120409
0.0009006620.99976440.0001209
0.0009019460.999758370.000119267
0.000903240.999750650.000116602
0.0009045380.999741370.000115747
0.000905840.999734110.000118565
0.0009071390.999729050.000118506
0.0009084490.999722170.000117079
0.0009097620.999716550.000120056
0.0009110720.999712290.000118467
0.0009123930.999705370.000117136
0.0009137180.999698410.000119397
0.0009150460.999694750.000123002
0.0009163720.999693880.000123337
0.0009177080.999690080.00011791
0.0009190480.999681320.000115529
0.0009203850.999673120.000119024
0.0009217330.999669420.000124126
0.0009230850.999669130.00012575
0.0009244410.999667250.000121967
0.0009257940.999661320.000118333
0.0009278380.99964650.000116037
0.0009311970.999637860.000138802
0.000934650.99963490.000131245
0.000938130.999629580.000141875
0.0009416350.999624440.000132807
0.000945160.999615730.000138737
0.0009487180.999609280.00013503
0.0009523030.999595960.000134594
0.0009559080.999590650.000148658
0.0009595480.999589310.000143766
0.0009632160.999583280.000144964
0.0009669040.999574010.000140254
0.0009706280.999565420.00014819
0.0009743810.999562610.000149346
0.0009781640.99955720.00014652
0.0009819670.999547410.000144218
0.0009858090.999536590.000147301
0.000989680.99952940.000153667
0.0009935740.999525690.000156611
0.0009975070.999518780.000154482
0.0010014720.999511990.000159744
0.0010054590.999504520.000157391
0.0010094870.999496450.000163969
0.0010135470.999491170.000165642
0.001017640.999483910.000167758
0.0010217580.999477950.000172899
0.0010259180.999474660.000175821
0.0010301110.99946830.000173653
0.0010343310.999460050.000178039
0.0010385940.999455120.000182781
0.0010428920.999452870.000185691
0.0010472170.999447910.000182079
0.0010515870.999440180.000183565
0.0010559930.999432430.00018362
0.0010604370.999424280.000186367
0.0010649090.999417110.000188819
0.0010694280.999409450.000190918
0.0010739860.99940280.000195173
0.0010785740.9993960.000196259
0.001083210.999390310.000201175
0.0010878860.999383770.000199098
0.0010925930.999373370.000201256
0.0010973510.999364560.000206896
0.001102150.999357420.000211442
0.0011069920.999352330.000217424
0.0011118660.999347270.000218327
0.0011167940.999340850.000221228
0.0011217650.99933390.000221991
0.001126770.999326170.000225564
0.0011318310.999318390.000227135
0.0011369380.999309370.000230152
0.001142080.99929970.000233851
0.0011472790.999291560.000241022
0.0011525260.999284540.000245418
0.0011578220.999278780.000252528
0.0011631550.999273270.000254758
0.0011685490.999265850.000259337
0.0011739930.999261220.000266023
0.0011794760.999256890.000266772
0.0011850230.999249390.000268642
0.0011906220.999243290.000273684
0.0011962620.999238080.000274323
0.0012019680.999229840.000274066
0.0012077280.999219120.000275785
0.0012135440.999209430.000281497
0.0012194050.999201560.000285591
0.0012253340.999193170.00028907
0.0012313210.999183760.000292955
0.0012373550.999175640.000299631
0.001243460.999168830.000303741
0.0012496260.999162740.000308325
0.0012558410.99915450.000308032
0.0012621310.999143670.000312418
0.0012684840.999134450.000318242
0.0012740890.999128450.000323647
0.0012805640.999122110.00032631
0.0012871040.999114760.000328016
0.0012937260.999103150.000326179
0.0013004020.999090380.000332411
0.0013071610.999077820.000335135
0.0013139760.9990670.000345243
0.0013208640.999057310.000348169
0.0013278380.999046780.000356646
0.0013348710.999039830.00036302
0.0013419940.999029870.000363515
0.0013491790.999018710.000370937
0.0013564420.999008770.000374252
0.0013637970.998996870.000378969
0.0013712180.998984880.000384845
0.0013785980.998973940.000391341
0.0013861810.998961370.000396491
0.0013938640.998950560.000407519
0.0014016160.998943550.000414159
0.0014094560.99893540.000416931
0.00141740.99892270.000417402
0.0014254170.99890750.000423122
0.0014335420.998894220.000430594
0.0014417440.998880020.000435377
0.001450040.998866210.000445522
0.0014584490.998853950.000452286
0.0014669390.998838770.000459534
0.0014693730.99883560.000465772
0.0014780260.998826790.000471411
0.0014867640.998813990.000476426
0.0014956230.998798630.000482115
0.0015045890.998782860.000491864
0.0015136640.998770.000502761
0.0015228290.998758140.000510218
0.0015321250.998743750.000516456
0.0015415360.998729260.000526188
0.0015510630.998714850.000533109
0.0015606880.998699130.000541936
0.0015704540.998684250.000551387
0.0015803420.99866720.000558655
0.0015903560.998651590.000572782
0.0016004770.998636690.000579875
0.0016107490.99861990.000591733
0.0016211530.998603510.000602112
0.0016316930.998588510.000616132
0.0016423490.998574970.000625987
0.0016531670.998560310.00063585
0.0016641280.998544970.000644277
0.0016752360.99852570.000650705
0.001686470.998504840.000663827
0.0016978790.998486760.000677923
0.0017094430.998469630.000691117
0.0017211660.998452950.000704427
0.0017330270.99843880.000717394
0.0017450760.998415480.000718815
0.0017572950.998395250.0007475
0.0017696860.998385320.000756582
0.0017822270.998370650.000763327
0.0017907730.998350490.000759039
0.0018035110.998327520.000788936
0.0018164320.998309480.000788808
0.0018295390.998284310.000807143
0.0018428360.998260570.000816685
0.0018563290.99823670.000836463
0.0018699920.99821410.000848071
0.0018838860.998187980.000864378
0.0018979880.99816360.000882844
0.0019123030.998138170.000898621
0.0019268360.998114110.000920994
0.0019415910.998092890.000938189
0.0019565740.998069650.000953251
0.001971790.998040930.000965987
0.0019872450.998010020.000987776
0.0020029430.997984040.00101149
0.0020188590.997957440.001028698
0.0020350630.997927480.001050222
0.002051530.997901210.001075162
0.0020682650.997869950.001088898
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0.2484653051.27390811.2602486
0.3107373121.28707341.49879
0.3826672451.28504471.8

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
—