Optical constants

Refractive index of BaF2 (Barium fluoride)

Bosomworth 1967: n,k 56.5–1000 µm; 80 K

Data
formula 4 + tabulated k
Range
56–1000 µm
Temperature
80 K
Licence
CC0-1.0

Plot

Click the plot to set the calculator wavelength. Note: k data cover 56497-1e+06 nm only; k = 0 elsewhere in the n range 56000-1e+06 nm.

At one wavelength

Range 56–1000 µm
Refractive index n
2.60595
Extinction coefficient k
0.00414375
Permittivity ε1
6.79094
Permittivity ε2
0.0215968
Absorption coefficient α
2.19713 cm⁻¹
Penetration depth δ = λ/(2πk)
9.10279e+06 nm
Abbe number Vd
—
Chromatic dispersion dn/dλ
-0.000393567 µm⁻¹
Group index ng
2.69922
Group velocity dispersion
124252 fs²/mm
Dispersion parameter D
-4.16685 ps/(nm·km)
Photon energy
0.0052314 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

# BaF2 (Barium fluoride): Bosomworth 1967: n,k 56.5–1000 µm; 80 K
baf2 = ls.fetch_refractiveindex("main", "BaF2", "Bosomworth-80K", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(baf2.range_nm)  # (56000, 1e+06) nm
eps = baf2.eps([237000])  # 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.

Dispersion formula

RefractiveIndex.INFO (formula 4), λ in µm
n2=0.0+6.56λ2.0λ2−52.912.0−6038.5λ0.0λ2−52.912.0

Valid from 56.0 to 1000.0 µm.

Coefficients as stored
CiValue
C10.0
C26.56
C32.0
C452.91
C52.0
C6-6038.5
C70.0
C852.91
C92.0

Comments and conditions

80 K

Conditions

temperature
80 K
Notes on the source data (kept exactly as published):
  • k data cover 56497-1e+06 nm only; k = 0 elsewhere in the n range 56000-1e+06 nm

References

D. R. Bosomworth. Far-infrared optical properties of CaF2, SrF2, BaF2, and CdF2. Phys. Rev., 157, 709 (1967)
  • doi:10.1103/physrev.157.709 Far-Infrared Optical Properties of Ca<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">F</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>, Sr<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">F</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>, Ba<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">F</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>, and Cd<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">F</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>, Physical Review (1967)

Cite

D. R. Bosomworth. Far-Infrared Optical Properties of Ca<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">F</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>, Sr<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">F</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>, Ba<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">F</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>, and Cd<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">F</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>. Physical Review, 157, 709-715 (1967), doi:10.1103/physrev.157.709; Data from the refractiveindex.info database (M. N. Polyanskiy, Sci. Data 11, 94 (2024), doi:10.1038/s41597-023-02898-2)

Data

Computed on 567 wavelengths, the same grid as the API and the library
BaF2 (Barium fluoride), Bosomworth 1967: n,k 56.5–1000 µm; 80 K: n and k versus wavelength
λ (µm)nk
566.5716490
56.4066.2299820
56.4976.1618520.0596
56.8155.9436790.05246799
56.8185.9417350.0524
57.1435.7462110.0496
57.22695.6995610.04913963
57.4715.5716420.0478
57.64185.4884420.04743988
57.8035.4141970.0471
58.05975.3037010.04664294
58.145.2709370.0465
58.485.140670.046
58.48075.140430.04599885
58.8245.0212860.0454
58.90474.9949030.0449828
59.1724.9114140.0436
59.33174.8642360.04223866
59.5244.8099140.0406
59.76194.7461560.03866206
59.884.7158280.0377
60.19524.6388460.03499342
60.2414.6281080.0346
60.6064.5463320.0314
60.63164.5408320.03120616
60.9764.4696970.0286
61.07124.4509080.02793813
61.354.3979110.026
61.5144.368070.02500219
61.7284.3305160.0237
61.964.2914830.02255219
62.1124.2667940.0218
62.40924.2204390.02042123
62.54.2067570.02
62.86174.1543370.0185275
62.8934.1499490.0184
63.2914.0961170.0169
63.31744.0926640.0168147
63.6944.0450370.0156
63.77654.0349750.01543861
64.1033.996390.0148
64.23893.9808850.01456965
64.5163.950230.0141
64.70473.9300610.01387488
64.9353.9061670.0136
65.17383.8822080.01331843
65.3593.8641650.0131
65.64633.8370680.01283275
65.7893.8239950.0127
66.12223.7944120.01239427
66.2253.7855480.0123
66.60163.7540380.01204436
66.6673.7487230.012
67.08453.7157640.01181319
67.1143.7135010.0118
67.5683.679640.0118
67.57093.679430.01179937
68.0273.647210.0117
68.06083.6448890.01167823
68.4933.6159940.0114
68.55433.6120110.01136114
68.9663.5859350.0111
69.05133.5806790.01104646
69.4443.5570960.0108
69.55193.5507860.01073337
69.933.529240.0105
70.05623.5222340.0104232
70.4233.5023810.0102
70.56413.4949360.01012647
70.9223.4765230.00994
71.07573.4688110.009876324
71.4293.4515220.00973
71.5913.4437860.009666823
71.9423.4274360.00953
72.11013.4197930.009468814
72.4643.4040880.00934
72.63293.3967710.009279331
72.9933.381540.00915
73.15953.3746610.009094079
73.5293.3597560.00897
73.68993.3534130.008922751
74.0743.3386290.00881
74.22423.3329770.008766539
74.6273.3181730.00865
74.76243.3133090.008616222
75.1883.2983640.00851
75.30443.2943670.008481411
75.7583.2791460.00837
75.85043.2761130.008349225
76.3363.260530.00824
76.40033.2585110.008225759
76.9233.2424660.00811
76.95423.2415280.008103714
77.51223.2251320.007991378
77.5193.2249350.00799
78.07413.2092940.007898393
78.1253.2078930.00789
78.64023.1939890.007806229
78.743.1913540.00779
79.21043.1791890.007722269
79.3653.1752770.0077
79.78463.1648730.007633914
803.159650.0076
80.36313.1510160.007543705
80.6453.1444590.0075
80.94583.1375990.007458738
81.3013.1296720.00741
81.53263.1246030.007375221
81.9673.11530.00731
82.12383.1120070.007289191
82.6453.1012920.00722
82.71923.0997960.007210297
83.31893.0879520.007131844
83.3333.0876790.00713
83.9233.0764610.007062669
84.0343.0743950.00705
84.53143.0653070.006994107
84.7463.0614710.00697
85.14433.0544780.006931488
85.473.0488810.0069
85.76163.0439590.006868343
86.2073.0366020.00682
86.38343.033740.006798829
86.9573.0246290.00673
87.00973.0238070.006724464
87.64063.0141490.006658234
87.7193.0129720.00665
88.2763.0047580.006585485
88.4963.0015810.00656
88.9162.9956210.006517468
89.2862.9904810.00648
89.56072.9867310.006449254
90.092.9796540.00639
90.212.9780770.006378279
90.8642.9696520.006314392
90.9092.9690830.00631
91.52282.9614470.00625112
91.7432.9587650.00623
92.18642.9534540.00618827
92.5932.9486850.00615
92.85482.9456660.006122765
93.4582.9388530.00606
93.5282.9380760.006053653
94.20612.9306770.005992147
94.342.9292440.00598
94.88912.9234630.005931083
95.2382.9198660.0059
95.57712.9164270.005870388
96.1542.9106970.00582
96.272.9095630.005811296
96.9682.9028670.005758929
97.0872.9017460.00575
97.6712.8963320.005694787
98.0392.8929930.00566
98.37922.8899540.005610954
99.012.8844370.00552
99.09242.8837270.005506676
99.81092.8776470.005390564
1002.8760770.00536
100.5352.8717090.005307076
101.012.8679050.00526
101.2632.8659080.005250158
101.9982.8602410.005221646
102.042.8599190.00522
102.7372.8547040.005193443
103.092.852120.00518
103.4822.8492930.005165482
104.172.8444360.00514
104.2322.8440030.005137144
104.9882.8388320.005102479
105.262.8370080.00509
105.7492.8337760.005063796
106.382.8296970.00503
106.5162.8288310.005020549
107.2882.8239950.004966827
107.532.8225090.00495
108.0662.8192650.004913352
108.72.8155090.00487
108.8492.8146370.004858694
109.6392.8101080.004799008
109.892.8086930.00478
110.4342.8056770.0047399
111.112.8020040.00469
111.2342.8013390.004687018
112.0412.7970940.004667663
112.362.7954460.00466
112.8532.7929370.004667704
113.642.7890210.00468
113.6712.7888680.004680481
114.4952.7848830.00469316
114.942.7827790.0047
115.3262.780980.004702877
116.1622.7771570.004709117
116.282.7766250.00471
117.0042.7734130.00471
117.652.770610.00471
117.8522.7697450.004707112
118.7072.7661510.004694906
119.052.7647340.00469
119.5672.7626290.004675532
120.4342.7591780.004651283
120.482.7589980.00465
121.3072.7557950.004616232
121.952.7533640.00459
122.1872.752480.004574317
123.0732.749230.004515649
123.462.7478370.00449
123.9652.7460440.004450649
124.8642.742920.004380615
1252.7424540.00437
125.7692.7398570.004306722
126.582.7371810.00424
126.6812.7368530.004231332
127.5992.7339070.004152445
128.212.7319910.0041
128.5252.7310180.004073475
129.4562.7281830.003994887
129.872.7269490.00396
130.3952.7254030.003917023
131.342.7226760.003839623
131.582.7219960.00382
132.2932.720.003767066
133.2522.7173740.003695815
133.332.7171630.00369
134.2182.7147970.003626233
135.142.71240.00356
135.1912.7122690.003556696
136.1712.7097870.003493118
136.992.7077630.00344
137.1582.7073520.003432024
138.1532.7049610.00338492
138.892.7032280.00335
139.1542.7026140.003337857
140.1632.700310.00329153
140.852.6987750.00326
141.182.6980480.003246883
142.2032.6958280.003206144
142.862.6944320.00318
143.2342.6936470.003169155
144.2732.6915060.003139054
144.932.6901780.00312
145.3192.6894030.003110877
146.3722.6873380.003086145
147.062.6860180.00307
147.4332.685310.003066589
148.5022.6833180.003056828
149.252.6819540.00305
149.5792.6813620.003047101
150.6642.679440.003037546
151.522.6779550.00303
151.7562.6775520.003028988
152.8562.6756970.003024265
153.852.674060.00302
153.9642.6738740.003020953
155.0812.6720840.003030256
156.2052.6703250.003039625
156.252.6702550.00304
157.3382.6685960.003061927
158.4782.6668970.003084925
158.732.6665280.00309
159.6272.6652280.003114536
160.7852.6635880.003146181
161.292.6628840.00316
161.952.6619750.003182512
163.1252.6603910.003222541
163.932.6593260.00325
164.3072.6588330.003267897
165.4982.6573020.003324417
166.672.6558330.00338
166.6982.6557970.003382618
167.9072.6543180.003494049
169.1242.6528640.003606288
169.492.6524340.00364
170.3512.6514340.003749042
171.5862.6500280.003905541
172.412.6491090.00401
172.832.6486460.004069556
174.0832.6472880.004247382
175.3452.6459520.004426497
175.442.6458520.00444
176.6162.6446380.004590306
177.8972.6433460.004753949
178.572.6426790.00484
179.1862.6420760.004896902
180.4862.6408260.005016823
181.7942.6395980.005137613
181.822.6395740.00514
183.1122.6383890.005193682
184.442.6372010.005248834
185.192.6365420.00528
185.7772.6360320.005285046
187.1242.6348830.005296624
188.4812.6337520.005308286
188.682.6335880.00531
189.8472.632640.005300354
191.2242.6315450.005288978
192.312.63070.00528
192.612.6304690.005275225
194.0062.629410.005253
195.4132.6283690.005230614
196.082.6278830.00522
196.832.6273440.005204697
198.2572.6263360.005175573
199.6942.6253440.005146238
2002.6251360.00514
201.1422.6243680.005114805
202.62.6234080.005082636
204.0692.6224630.005050234
204.082.6224570.00505
205.5492.6215340.005018893
207.0392.6206190.004987334
208.332.6198440.00496
208.542.6197190.004955264
210.0522.6188330.00492121
211.5752.6179620.00488691
212.772.6172920.00486
213.1092.6171040.004851925
214.6542.616260.004815137
216.2112.6154290.004778083
217.392.6148130.00475
217.7782.6146120.004739554
219.3572.6138070.004697057
220.9472.6130160.004654251
222.222.6123950.00462
222.5492.6122360.004609565
224.1632.6114690.004558443
225.7882.6107140.004506951
227.272.6100410.00446
227.4252.6099710.004454721
229.0742.609240.004398616
230.7352.608520.004342103
232.4082.6078110.004285181
232.562.6077470.00428
234.0932.6071130.004232966
235.792.6064260.004180885
237.52.605750.004128427
238.12.6055170.00411
239.2212.6050850.004080998
240.9562.604430.004036142
242.7032.6037850.003990962
243.92.6033510.00396
244.4622.603150.003948935
246.2352.6025250.003914068
248.022.6019090.003878948
249.8182.6013030.003843574
2502.6012430.00384
251.632.6007070.003812035
253.4542.6001190.003780728
255.2922.5995410.003749193
256.412.5991950.00373
257.1422.5989720.003719149
259.0072.5984110.003691529
260.8852.5978590.003663709
262.7762.5973160.003635687
263.162.5972070.00363
264.6812.596780.003608603
266.62.5962530.003581613
268.5332.5957340.003554427
270.272.5952780.00353
270.482.5952230.003527481
272.4412.594720.00350398
274.4162.5942250.003480309
276.4062.5937370.003456465
277.782.5934060.00344
278.412.5932560.003432849
280.4292.5927830.00340994
282.4622.5923170.003386865
284.512.5918580.003363623
285.712.5915940.00335
286.5722.5914060.003341796
288.652.5909610.003322032
290.7432.5905230.003302124
292.8512.5900910.003282073
294.122.5898360.00327
294.9742.5896660.003261373
297.1132.5892480.00323977
299.2672.5888350.003218011
301.4372.5884290.003196095
303.032.5881370.00318
303.6222.5880290.003174373
305.8232.5876350.003153452
308.0412.5872470.00313238
310.2742.5868650.003111154
312.52.5864920.00309
312.5242.5864890.003089812
314.792.5861180.003071829
317.0722.5857530.003053716
319.3712.5853930.003035471
321.6862.5850390.003017094
322.582.5849040.00301
324.0182.584690.002999295
326.3682.5843460.002981813
328.7342.5840070.002964203
331.1172.5836740.002946467
333.332.5833710.00293
333.5182.5833450.002928856
335.9362.5830220.002914137
338.3722.5827030.002899312
340.8252.5823890.002884379
343.2962.5820790.002869337
344.832.5818910.00286
345.7852.5817750.002853794
348.2922.5814740.002837501
350.8172.5811790.002821091
353.3612.5808870.002804561
355.9232.58060.002787911
357.142.5804660.00278
358.5032.5803180.002773818
361.1022.5800390.00276203
363.722.5797650.002750157
366.3582.5794950.002738197
369.0142.5792280.002726151
370.372.5790950.00272
371.6892.5789660.002715372
374.3842.5787080.002705916
377.0982.5784530.002696392
379.8322.5782020.002686799
382.5862.5779550.002677136
384.622.5777760.00267
385.362.5777120.002667594
388.1542.5774720.002658511
390.9682.5772350.002649362
393.8032.5770030.002640147
396.6582.5767730.002630865
399.5342.5765470.002621515
4002.5765110.00262
402.4312.5763250.002614168
405.3482.5761050.002607167
408.2872.5758890.002600115
411.2472.5756760.002593012
414.2292.5754660.002585857
416.672.5752980.00258
417.2322.575260.002578758
420.2572.5750560.002572077
423.3042.5748550.002565347
426.3732.5746580.002558568
429.4652.5744630.00255174
432.5782.5742710.002544863
434.782.5741380.00254
435.7152.5740820.002538109
438.8742.5738960.002531718
442.0562.5737120.00252528
445.2612.5735310.002518795
448.4892.5733530.002512264
451.742.5731770.002505685
454.552.5730290.0025
455.0162.5730040.002499355
458.3152.5728340.002494781
461.6372.5726660.002490174
464.9842.57250.002485535
468.3562.5723370.002480861
471.7512.5721760.002476153
475.1722.5720180.002471412
476.192.5719710.00247
478.6172.5718620.002464904
482.0872.5717080.002457617
485.5822.5715570.002450277
489.1032.5714070.002442884
492.6492.571260.002435437
496.2212.5711150.002427937
499.8182.5709720.002420382
5002.5709650.00242
503.4422.5708320.002413461
507.0922.5706930.002406527
510.7692.5705560.002399543
514.4722.5704220.002392508
518.2022.5702890.002385422
521.9592.5701580.002378285
525.7432.5700290.002371096
526.322.570010.00237
529.5552.5699020.002364468
533.3942.5697770.002357903
537.2622.5696540.00235129
541.1572.5695320.002344629
545.082.5694120.00233792
549.0322.5692940.002331162
553.0132.5691780.002324355
555.562.5691050.00232
557.0232.5690640.002317762
561.0612.5689510.002311583
565.1292.5688390.00230536
569.2262.568730.002299091
573.3532.5686220.002292777
577.512.5685150.002286417
581.6972.568410.00228001
585.9152.5683070.002273558
588.242.5682510.00227
590.1632.5682050.002267385
594.4412.5681050.002261565
598.7512.5680060.002255703
603.0922.5679080.002249798
607.4652.5678120.002243851
611.8692.5677170.00223786
616.3052.5676240.002231826
620.7742.5675320.002225748
6252.5674470.00222
625.2752.5674410.002219736
629.8082.5673520.002215385
634.3742.5672640.002211002
638.9742.5671770.002206587
643.6062.5670920.002202139
648.2722.5670070.00219766
652.9732.5669240.002193148
657.7072.5668420.002188604
662.4752.5667620.002184027
666.672.5666920.00218
667.2782.5666820.002179744
672.1162.5666040.002177713
676.9892.5665270.002175666
681.8982.5664510.002173605
686.8422.5663760.002171528
691.8212.5663020.002169437
696.8372.5662290.00216733
701.8892.5661570.002165208
706.9782.5660860.002163071
712.1042.5660170.002160918
714.292.5659880.00216
717.2672.5659480.00216
722.4672.565880.00216
727.7052.5658140.00216
732.9812.5657480.00216
738.2962.5656830.00216
743.6482.5656190.00216
749.042.5655560.00216
754.4712.5654940.00216
759.9412.5654330.00216
765.4512.5653730.00216
769.232.5653320.00216
7712.5653140.002160552
776.592.5652550.002162296
782.2212.5651970.002164053
787.8922.5651410.002165823
793.6042.5650840.002167605
799.3582.5650290.0021694
805.1542.5649750.002171209
810.9912.5649210.00217303
816.8712.5648680.002174865
822.7942.5648160.002176713
828.7592.5647650.002178574
833.332.5647260.00218
834.7682.5647140.002180569
840.822.5646650.002182966
846.9162.5646150.00218538
853.0562.5645670.002187811
859.2412.5645190.002190261
865.4712.5644720.002192727
871.7462.5644260.002195212
878.0662.564380.002197715
884.4322.5643350.002200236
890.8452.5642910.002202775
897.3042.5642470.002205333
903.8092.5642040.002207909
909.092.5641690.00221
910.3622.5641610.0022107
916.9622.5641190.00221433
923.6112.5640780.002217986
930.3072.5640370.002221669
937.0522.5639970.002225379
943.8462.5639580.002229115
950.6892.5639190.002232879
957.5822.5638810.00223667
964.5242.5638430.002240489
971.5172.5638050.002244335
978.5612.5637690.002248209
985.6562.5637320.002252111
992.8022.5636970.002256041
10002.5636620.00226

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
—