Optical constants

Refractive index of CaF2 (Calcium fluoride)

Bosomworth 1967: n,k 49.5–1000 µm; 80 K

Data
formula 4 + tabulated k
Range
49.5–999.9 µm
Temperature
80 K
Licence
CC0-1.0

Plot

Click the plot to set the calculator wavelength. Note: k data cover 49505-1e+06 nm only; k = 0 elsewhere in the n range 49500-999900 nm.

At one wavelength

Range 49.5–999.9 µm
Refractive index n
2.54514
Extinction coefficient k
0.00213137
Permittivity ε1
6.47775
Permittivity ε2
0.0108493
Absorption coefficient α
1.20647 cm⁻¹
Penetration depth δ = λ/(2πk)
1.65773e+07 nm
Abbe number Vd
—
Chromatic dispersion dn/dλ
-0.000177281 µm⁻¹
Group index ng
2.5845
Group velocity dispersion
47704.1 fs²/mm
Dispersion parameter D
-1.82327 ps/(nm·km)
Photon energy
0.00558487 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

# CaF2 (Calcium fluoride): Bosomworth 1967: n,k 49.5–1000 µm; 80 K
caf2 = ls.fetch_refractiveindex("main", "CaF2", "Bosomworth-80K", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(caf2.range_nm)  # (49500, 999900) nm
eps = caf2.eps([222000])  # 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+6.38λ2.0λ2−34.4532.0−2871.4λ0.0λ2−34.4532.0

Valid from 49.5 to 999.9 µm.

Coefficients as stored
CiValue
C10.0
C26.38
C32.0
C434.453
C52.0
C6-2871.4
C70.0
C834.453
C92.0

Comments and conditions

80 K

Conditions

temperature
80 K
Notes on the source data (kept exactly as published):
  • k data cover 49505-1e+06 nm only; k = 0 elsewhere in the n range 49500-999900 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 592 wavelengths, the same grid as the API and the library
CaF2 (Calcium fluoride), Bosomworth 1967: n,k 49.5–1000 µm; 80 K: n and k versus wavelength
λ (µm)nk
49.53.1783560
49.5053.1781270.00575
49.7513.1670130.00571
49.87433.1615650.005685242
503.1560930.00566
50.2513.1454070.00562
50.25143.145390.005619918
50.5053.1349080.00557
50.63143.1297980.005545314
50.7613.1246340.00552
51.01423.114760.005471112
51.023.1145380.00547
51.2823.1046210.00543
51.43.1002480.005407655
51.5463.0949140.00538
51.78863.0862350.005334561
51.8133.0853770.00533
52.0833.0760070.00529
52.18023.0726980.005275752
52.3563.0668030.00525
52.57483.0596150.005218289
52.6323.0577620.00521
52.913.0489130.00516
52.97233.0469620.005148906
53.1913.0402190.00511
53.37293.0347220.005084471
53.4763.031650.00507
53.7633.0232620.00502
53.77653.0228740.005018148
54.0543.0149950.00498
54.18313.0114020.004962435
54.3483.0068760.00494
54.59283.0002880.004907029
54.6452.9989030.0049
54.9452.9910730.00485
55.00562.9895180.004842025
55.2492.9833590.00481
55.42152.9790760.00478752
55.5562.9757840.00477
55.84062.9689490.004733277
55.8662.9683470.00473
56.182.9610220.00469
56.26282.9591230.004679547
56.4972.953830.00465
56.68832.9495860.004632124
56.8182.9467480.00462
57.11692.9403270.00458321
57.1432.9397750.00458
57.4712.9329310.00455
57.54882.9313350.004542969
57.8032.9261930.00452
57.9842.9225980.004498521
58.142.9195410.00448
58.42242.9141080.004455082
58.482.9130150.00445
58.8242.9065920.00442
58.86422.9058540.004416537
59.1722.9002720.00439
59.30932.8978270.004378301
59.5242.8940550.00436
59.75772.890020.004340303
59.882.8879380.00433
60.20962.8824240.00430261
60.2412.8819060.0043
60.6062.8759730.00427
60.66492.8750310.004266818
60.9762.8701230.00425
61.12362.8678340.004238162
61.352.8643720.00422
61.58582.8608270.004207526
61.7282.8587180.0042
62.05142.8540020.004174731
62.1122.8531310.00417
62.52.847640.00415
62.52062.8473520.004148949
62.8932.8422310.00413
62.99342.8408730.004122432
63.2912.8369030.0041
63.46972.8345580.00409113
63.6942.8316560.00408
63.94962.8284020.004073749
64.1032.8264770.00407
64.43322.8223990.00405401
64.5162.8213910.00405
64.92042.8165450.004040348
64.9352.8163730.00404
65.3592.8114340.00403
65.41132.8108340.004028784
65.7892.8065630.00402
65.90592.8052620.004017319
66.2252.8017610.00401
66.40432.7998250.00401
66.6672.7970270.00401
66.90642.7945180.00401
67.1142.7923720.00401
67.41232.7893370.00400343
67.5682.7877750.004
67.9222.7842790.004
68.0272.7832560.004
68.43562.7793380.004008769
68.4932.7787960.00401
68.95312.7745130.00401
68.9662.7743950.00401
69.4442.7700710.00402
69.47452.76980.00402
69.932.7657980.00402
69.99982.7651940.004021416
70.4232.7615850.00403
70.52912.7606930.004034253
70.9222.757440.00405
71.06242.7562950.004052769
71.4292.7533470.00406
71.59982.7519950.004063328
71.9422.7493230.00407
72.14122.7477910.00407763
72.4642.7453440.00409
72.68662.7436810.004094209
72.9932.7414260.0041
73.23632.7396610.004109077
73.5292.7375690.00412
73.792.735730.00412479
74.0742.7337590.00413
74.3482.7318840.004134955
74.6272.7300030.00414
74.91022.7281220.004145048
75.1882.7263030.00415
75.47662.7244410.004155063
75.7582.7226510.00416
76.04732.7208380.004165006
76.3362.7190560.00417
76.62242.7173130.004174878
76.9232.7155090.00418
77.20172.7138620.00418
77.5192.7120140.00418
77.78552.7104840.004184398
78.1252.7085630.00419
78.37372.7071760.00419
78.742.7051630.00419
78.96632.7039380.00419
79.3652.701810.00419
79.56342.7007670.00419
802.6985040.00419
80.1652.6976610.00419
80.6452.6952450.00419
80.77122.6946190.00419
81.3012.6920290.00419
81.38192.6916390.00419
81.9672.6888620.00419
81.99732.688720.00419
82.61732.685860.00419
82.6452.6857340.00419
83.2422.6830570.00419
83.3332.6826560.00419
83.87152.6803110.004182319
84.0342.6796140.00418
84.50572.677620.00418
84.7462.6766190.00418
85.14462.6749820.004174494
85.472.6736660.00417
85.78852.6723960.004165679
86.2072.6707530.00416
86.43722.6698620.004156931
86.9572.667880.00415
87.09072.6673770.004148245
87.7192.6650510.00414
87.74932.664940.004139221
88.41282.6625510.004122142
88.4962.6622560.00412
89.08132.6602080.004112591
89.2862.6595040.00411
89.75492.6579110.004098336
90.092.6567910.00409
90.43362.6556580.004081609
90.9092.6541150.00407
91.11742.6534470.004065002
91.7432.6514770.00405
91.80642.6512790.004048509
92.50062.6491530.004032175
92.5932.6488740.00403
93.22.6470660.004015965
93.4582.6463110.00401
93.90482.6450190.003994804
94.342.6437820.00398
94.61482.6430110.003970819
95.2382.6412910.00395
95.33022.641040.003946979
96.05112.6391060.003923371
96.1542.6388340.00392
96.77742.6372070.003899956
97.0872.6364130.00389
97.50912.6353450.003876697
98.0392.6340260.00386
98.24652.6335160.00385359
98.98932.6317210.003830638
99.012.6316720.00383
99.73792.629960.003807944
1002.6293530.0038
100.4922.628230.003785385
101.012.6270680.00377
101.2522.6265320.003762955
102.0182.6248650.003740655
102.042.6248170.00374
102.7892.6232280.003725735
103.092.6226010.00372
103.5662.6216210.003711182
104.172.6204010.0037
104.3492.6200430.003695066
105.1382.6184930.00367335
105.262.6182580.00367
105.9332.6169710.003651965
106.382.6161330.00364
106.7342.6154770.003633838
107.532.6140290.00362
107.5412.6140090.003619611
108.3552.6125670.00359181
108.72.6119650.00358
109.1742.611150.003568054
109.892.6099410.00355
109.9992.6097590.00354731
110.8312.6083920.003526857
111.112.6079420.00352
111.6692.607050.003506579
112.362.6059680.00349
112.5142.6057310.0034864
113.3642.6044350.003466461
113.642.6040220.00346
114.2222.6031620.00344658
114.942.6021190.00343
115.0852.601910.003427832
115.9552.6006810.003414844
116.282.6002310.00341
116.8322.5994730.003397907
117.652.5983730.00338
117.7162.5982860.003378124
118.6062.597120.003352692
119.052.5965480.00334
119.5032.5959730.003330505
120.4062.5948470.003311548
120.482.5947560.00331
121.3172.5937390.003292925
121.952.5929850.00328
122.2342.5926510.003274357
123.1582.5915810.003255994
123.462.5912380.00325
124.092.590530.003233648
1252.5895270.00321
125.0282.5894970.003209471
125.9732.5884810.003191521
126.582.5878420.00318
126.9262.5874820.003175757
127.8862.58650.003163981
128.212.5861730.00316
128.8532.5855350.003148388
129.8272.5845860.00313078
129.872.5845440.00313
130.8092.5836530.003113534
131.582.5829360.0031
131.7982.5827360.003096269
132.7942.5818340.003079185
133.332.5813580.00307
133.7982.5809470.003064825
134.812.5800750.003053646
135.142.5797950.00305
135.8292.5792180.00303882
136.8572.5783750.003022165
136.992.5782670.00302
137.8912.5775460.003005768
138.892.5767640.00299
138.9342.576730.002989551
139.9852.5759290.002978831
140.852.5752820.00297
141.0432.575140.002967119
142.112.5743650.002951201
142.862.573830.00294
143.1842.5736020.002935303
144.2672.5728520.002919612
144.932.5724010.00291
145.3582.5721140.002903977
146.4572.5713890.002888496
147.062.5709980.00288
147.5642.5706750.002873093
148.682.5699730.002857808
149.252.5696210.00285
149.8042.5692820.002842675
150.9372.5686030.002827705
151.522.568260.00282
152.0782.5679350.002810416
153.2282.5672780.002790674
153.852.5669290.00278
154.3872.5666310.002773289
155.5542.5659950.002758697
156.252.5656240.00275
156.732.565370.002744188
157.9162.5647540.002729852
158.732.564340.00272
159.112.5641490.002715551
160.3132.5635530.002701452
161.292.5630790.00269
161.5252.5629670.00268733
162.7462.562390.002673451
163.932.5618440.00266
163.9772.5618230.002659315
165.2172.5612650.002641214
166.4662.5607150.002622976
166.672.5606270.00262
167.7252.5601750.002608778
168.9932.5596430.002595286
169.492.5594380.00259
170.2712.559120.002579302
171.5582.5586050.002561665
172.412.5582710.00255
172.8562.5580990.002545587
174.1632.55760.002532646
175.442.5571240.00252
175.482.557110.002519493
176.8072.5566270.002502536
178.1432.5561520.002485451
178.572.5560030.00248
179.4912.5556840.002471503
180.8482.5552240.002458975
181.822.5549010.00245
182.2152.5547720.002445309
183.5932.5543260.002428955
184.9812.5538880.002412478
185.192.5538230.00241
186.382.5534560.002396361
187.7892.5530320.002380209
188.682.5527680.00237
189.2092.5526140.002365626
190.642.5522020.002353802
192.0812.5517970.002341889
192.312.5517340.00234
193.5342.5513990.002330261
194.9972.5510070.002318616
196.082.5507230.00231
196.4722.5506210.002307002
197.9572.5502410.002295632
199.4542.5498670.002284177
2002.5497330.00228
200.9622.5494990.002272923
202.4822.5491370.00226175
204.0132.548780.002250492
204.082.5487650.00225
205.5562.5484290.002239583
207.112.5480840.002228612
208.332.5478180.00222
208.6762.5477440.002217662
210.2542.5474090.002207
211.8442.5470790.002196258
212.772.5468910.00219
213.4462.5467550.002185613
215.062.5464360.002175132
216.6862.5461210.002164573
217.392.5459880.00216
218.3242.5458120.002154197
219.9752.5455070.002143943
221.6382.5452080.002133612
222.222.5451040.00213
223.3142.5449130.002121332
225.0032.5446220.002107957
226.7042.5443360.002094481
227.272.5442420.00209
228.4192.5440540.002083487
230.1462.5437770.002073692
231.8862.5435040.002063823
232.562.54340.00206
233.6392.5432350.002052207
235.4062.5429710.002039451
237.1862.5427110.002026599
238.12.5425790.00202
238.982.5424540.002013934
240.7872.5422020.002001472
242.6072.5419530.001988915
243.92.541780.00198
244.4422.5417090.001977336
246.292.5414680.001968246
248.1522.5412310.001959087
2502.5410010.00195
250.0292.5409970.00194982
251.9192.5407670.001938023
253.8242.5405410.001926136
255.7442.5403180.001914159
256.412.5402420.00191
257.6772.5400990.00190249
259.6262.5398820.001890944
261.5892.539670.00187931
263.162.5395030.00187
263.5672.539460.001867711
265.562.5392540.001856499
267.5682.5390510.001845202
269.5912.5388510.001833819
270.272.5387850.00183
271.632.5386540.001822758
273.6842.5384610.001811819
275.7532.538270.001800796
277.782.5380870.00179
277.8382.5380820.001789707
279.9392.5378970.00177911
282.0562.5377150.001768433
284.1882.5375350.001757675
285.712.537410.00175
286.3372.5373580.001747016
288.5032.5371850.001736718
290.6842.5370130.001726342
292.8822.5368450.001715888
294.122.5367510.00171
295.0972.5366790.001705615
297.3282.5365150.001695598
299.5762.5363540.001685505
301.8422.5361950.001675336
303.032.5361140.00167
304.1242.5360390.00166538
306.4242.5358850.001655666
308.7412.5357340.00164588
311.0752.5355850.001636019
312.52.5354960.00163
313.4272.5354380.00162632
315.7972.5352940.001616916
318.1852.5351510.00160744
320.5912.5350110.001597893
322.582.5348970.00159
323.0152.5348730.001588381
325.4582.5347370.001579292
327.9192.5346030.001570135
330.3982.5344710.001560909
332.8962.5343410.001551613
333.332.5343190.00155
335.4142.5342130.001542752
337.952.5340880.001533931
340.5052.5339640.001525042
343.082.5338410.001516087
344.832.533760.00151
345.6742.5337210.001507257
348.2882.5336030.001498764
350.9222.5334860.001490206
353.5752.5333710.001481584
356.2492.5332580.001472896
357.142.5332210.00147
358.9422.5331470.001463188
361.6572.5330370.001452931
364.3912.5329290.001442596
367.1472.5328230.001432182
369.9232.5327180.00142169
370.372.5327010.00142
372.722.5326150.001411755
375.5382.5325130.001401866
378.3782.5324130.001391902
381.2392.5323140.001381863
384.1222.5322170.001371749
384.622.5322010.00137
387.0262.5321220.001362178
389.9532.5320270.001352664
392.9012.5319350.001343078
395.8722.5318430.001333419
398.8662.5317530.001323688
4002.531720.00132
401.8822.5316650.001314356
404.922.5315780.001305242
407.9822.5314920.001296058
411.0672.5314070.001286805
414.1752.5313240.001277482
416.672.5312580.00127
417.3072.5312420.001268241
420.4632.5311610.001259529
423.6422.5310810.001250751
426.8452.5310030.001241907
430.0732.5309260.001232996
433.3252.5308490.001224017
434.782.5308160.00122
436.6022.5307750.001214472
439.9032.5307010.001204453
443.2292.5306280.001194357
446.5812.5305570.001184186
449.9572.5304860.001173938
453.362.5304170.001163612
454.552.5303930.00116
456.7882.5303480.001153795
460.2422.5302810.001144218
463.7222.5302150.001134569
467.2282.5301490.001124847
470.7612.5300850.001115052
474.3212.5300220.001105182
476.192.5299890.0011
477.9082.5299590.001095672
481.5212.5298980.001086565
485.1622.5298370.00107739
488.8312.5297780.001068146
492.5272.5297190.001058831
496.2512.5296610.001049446
5002.5296040.00104
500.0042.5296040.001039991
503.7852.5295480.001031373
507.5942.5294930.001022689
511.4322.5294380.001013939
515.2992.5293850.001005123
519.1962.5293320.0009962408
523.1222.529280.0009872912
526.322.5292380.00098
527.0772.5292290.0009783686
531.0632.5291780.0009697816
535.0782.5291280.0009611296
539.1242.5290790.0009524122
543.2012.5290310.0009436289
547.3082.5289840.0009347791
551.4472.5289370.0009258625
555.562.5288910.000917
555.6162.5288910.0009168894
559.8182.5288450.0009086617
564.0512.5288010.0009003718
568.3162.5287570.0008920191
572.6132.5287130.0008836034
576.9432.5286710.0008751239
581.3062.5286290.0008665804
585.7012.5285870.0008579722
588.242.5285640.000853
590.132.5285460.0008497098
594.5922.5285060.0008419409
599.0882.5284670.0008341133
603.6182.5284280.0008262264
608.1822.5283890.00081828
612.7812.5283510.0008102734
617.4152.5283140.0008022063
622.0832.5282770.0007940783
6252.5282550.000789
626.7872.5282410.0007861695
631.5262.5282060.0007786629
636.3022.5281710.0007710994
641.1132.5281360.0007634788
645.9612.5281020.0007558006
650.8452.5280690.0007480643
655.7672.5280360.0007402694
660.7252.5280030.0007324157
665.7212.5279710.0007245026
666.672.5279650.000723
670.7552.5279390.0007166518
675.8272.5279080.0007087702
680.9372.5278780.000700829
686.0862.5278480.0006928278
691.2742.5278180.0006847661
696.5012.5277890.0006766434
701.7682.527760.0006684593
707.0742.5277320.0006602133
712.4212.5277040.0006519049
714.292.5276940.000649
717.8082.5276760.0006430456
723.2352.5276490.0006338578
728.7042.5276220.0006246006
734.2142.5275960.0006152734
739.7662.527570.0006058756
745.362.5275440.0005964068
750.9962.5275190.0005868664
756.6742.5274950.0005772538
762.3962.527470.0005675686
768.1612.5274460.0005578101
769.232.5274420.000556
773.9692.5274230.0005474977
779.8212.5273990.0005369982
785.7182.5273760.0005264192
791.6592.5273540.0005157603
797.6452.5273310.0005050208
803.6772.5273090.0004942001
809.7542.5272880.0004832975
815.8772.5272660.0004723125
822.0462.5272460.0004612444
828.2622.5272250.0004500927
833.332.5272080.000441
834.5252.5272050.0004387765
840.8352.5271840.0004270323
847.1932.5271650.0004151992
853.5992.5271450.0004032767
860.0532.5271260.000391264
866.5572.5271070.0003791605
873.1092.5270890.0003669654
879.7112.527070.0003546782
886.3632.5270520.000342298
893.0652.5270350.0003298242
899.8182.5270170.0003172561
906.6222.5270.000304593
909.092.5269940.0003
913.4782.5269830.0002916988
920.3852.5269660.0002786305
927.3442.526950.0002654633
934.3562.5269330.0002521965
941.4212.5269180.0002388294
948.542.5269020.0002253613
955.7122.5268860.0002117913
962.9392.5268710.0001981187
970.222.5268560.0001843427
977.5572.5268410.0001704626
984.9482.5268270.0001564775
992.3962.5268120.0001423866
999.92.5267980.0001281892

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
—