Optical constants

Refractive index of Phosphate Buffered Saline (PBS)

Janeiro et al. 2019: 10x solution; n 1.50–1.62 µm, k 1.15–1.80 µm

Data
formula 5 + tabulated k
Range
1.5–1.62 µm
Licence
CC0-1.0

Plot

Click the plot to set the calculator wavelength.

At one wavelength

Range 1.5–1.62 µm
Refractive index n
1.33658
Extinction coefficient k
0.000106
Permittivity ε1
1.78643
Permittivity ε2
0.000283354
Absorption coefficient α
8.53869 cm⁻¹
Penetration depth δ = λ/(2πk)
2.34228e+06 nm
Abbe number Vd
—
Chromatic dispersion dn/dλ
-0.0232412 µm⁻¹
Group index ng
1.37283
Group velocity dispersion
-60166.6 fs²/mm
Dispersion parameter D
46570.1 ps/(nm·km)
Photon energy
0.794771 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

# Phosphate Buffered Saline (PBS): Janeiro et al. 2019: 10x solution; n 1.50–1.62 µm, k 1.15–1.80 µm
pbs = ls.fetch_refractiveindex("other", "PBS", "Janeiro", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(pbs.range_nm)  # (1500, 1620) nm
eps = pbs.eps([1560])  # 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

Cauchy (formula 5), λ in µm
n=23.15255−16.98818⁢λ−1.0−7.00392⁢λ

Valid from 1.5 to 1.62 µm.

Coefficients as stored
CiValue
C123.15255
C2-16.98818
C3-1.0
C4-7.00392
C51.0

Comments and conditions

10x water solution (P32060, RPI). Composition: 1.37 M sodium chloride, 27 mM potassium chloride, 101.4 mM sodium phosphate dibasic and 17.6 mM potassium phosphate monobasic (total: 1.516 M), where M stands for molar, a concentration unit defined as mol/L.

References

R. Janeiro, R. Flores, J. Viegas. Refractive index of phosphate-buffered saline in the telecom infrared C + L bands. OSA Continuum 4, 3039–3051 (2021)
  • doi:10.1364/osac.434864 Refractive index of phosphate-buffered saline in the telecom infrared C + L bands, OSA Continuum (2021)

Cite

Ricardo Janeiro, Raquel Flores and Jaime Viegas. Refractive index of phosphate-buffered saline in the telecom infrared C + L bands. OSA Continuum, 4, 3039 (2021), doi:10.1364/osac.434864; Data from the refractiveindex.info database (M. N. Polyanskiy, Sci. Data 11, 94 (2024), doi:10.1038/s41597-023-02898-2)

Data

Computed on 411 wavelengths, the same grid as the API and the library
Phosphate Buffered Saline (PBS), Janeiro et al. 2019: 10x solution; n 1.50–1.62 µm, k 1.15–1.80 µm: n and k versus wavelength
λ (µm)nk
1.51.3212170.000223
1.500291.3213740.0002221609
1.500581.3215310.0002213216
1.500871.3216870.0002204821
1.501161.3218430.0002196425
1.501451.3219970.0002188027
1.501741.3221510.0002179628
1.502031.3223030.0002171227
1.502321.3224550.0002162824
1.502611.3226070.000215442
1.50291.3227570.0002146014
1.503191.3229060.0002137607
1.503481.3230550.0002129198
1.503771.3232030.0002120787
1.504061.323350.0002112374
1.504351.3234970.000210396
1.504641.3236420.0002095545
1.504931.3237870.0002087128
1.505221.3239310.0002078709
1.505511.3240740.0002070288
1.50581.3242160.0002061866
1.506091.3243570.0002053442
1.506381.3244980.0002045017
1.506671.3246380.000203659
1.506961.3247770.0002028161
1.507251.3249150.0002019731
1.507541.3250520.0002011299
1.507831.3251890.0002002866
1.508121.3253250.0001994431
1.508411.325460.0001985994
1.50871.3255940.0001977556
1.5091.3257270.0001969116
1.509291.325860.0001960674
1.509581.3259910.0001952231
1.509871.3261220.0001943786
1.511.326180.000194
1.510161.3262520.0001936143
1.510451.3263810.0001929151
1.510741.326510.0001922158
1.511031.3266370.0001915164
1.511331.3267640.0001908169
1.511621.326890.0001901172
1.511911.3270150.0001894173
1.51221.327140.0001887174
1.512491.3272630.0001880173
1.512781.3273860.000187317
1.513081.3275080.0001866167
1.513371.3276290.0001859161
1.513661.327750.0001852155
1.513951.3278690.0001845147
1.514241.3279880.0001838138
1.514541.3281060.0001831128
1.514831.3282230.0001824116
1.515121.3283390.0001817103
1.515411.3284540.0001810088
1.515711.3285690.0001803072
1.5161.3286830.0001796055
1.516291.3287960.0001789037
1.516581.3289080.0001782017
1.516881.329020.0001774995
1.517171.329130.0001767973
1.517461.329240.0001760949
1.517751.3293490.0001753923
1.518051.3294570.0001746897
1.518341.3295640.0001739868
1.518631.3296710.0001732839
1.518921.3297760.0001725808
1.519221.3298810.0001718776
1.519511.3299850.0001711743
1.51981.3300890.0001704708
1.521.3301570.00017
1.52011.3301910.000169806
1.520391.3302930.0001692195
1.520681.3303940.0001686329
1.520981.3304940.0001680462
1.521271.3305930.0001674594
1.521561.3306910.0001668725
1.521861.3307890.0001662855
1.522151.3308860.0001656983
1.522441.3309820.0001651111
1.522741.3310770.0001645237
1.523031.3311710.0001639362
1.523331.3312650.0001633486
1.523621.3313570.0001627609
1.523911.3314490.0001621731
1.524211.331540.0001615852
1.52451.3316310.0001609971
1.52481.331720.000160409
1.525091.3318090.0001598207
1.525381.3318970.0001592323
1.525681.3319840.0001586438
1.525971.332070.0001580552
1.526271.3321550.0001574664
1.526561.332240.0001568776
1.526861.3323240.0001562886
1.527151.3324070.0001556996
1.527441.3324890.0001551104
1.527741.332570.0001545211
1.528031.3326510.0001539317
1.528331.332730.0001533421
1.528621.3328090.0001527525
1.528921.3328870.0001521627
1.529211.3329650.0001515729
1.529511.3330410.0001509829
1.52981.3331170.0001503928
1.531.3331670.00015
1.53011.3331920.0001498322
1.530391.3332660.0001493304
1.530691.3333390.0001488286
1.530981.3334110.0001483266
1.531281.3334830.0001478245
1.531581.3335540.0001473224
1.531871.3336240.0001468201
1.532171.3336930.0001463178
1.532461.3337610.0001458153
1.532761.3338290.0001453128
1.533051.3338960.0001448101
1.533351.3339620.0001443074
1.533641.3340270.0001438045
1.533941.3340910.0001433016
1.534241.3341540.0001427986
1.534531.3342170.0001422954
1.534831.3342790.0001417922
1.535121.334340.0001412889
1.535421.33440.0001407854
1.535721.334460.0001402819
1.536011.3345180.0001397783
1.536311.3345760.0001392746
1.536611.3346330.0001387708
1.53691.3346890.0001382669
1.53721.3347450.0001377629
1.537491.3347990.0001372588
1.537791.3348530.0001367546
1.538091.3349060.0001362503
1.538381.3349580.0001357459
1.538681.3350090.0001352414
1.538981.335060.0001347368
1.539281.335110.0001342321
1.539571.3351580.0001337273
1.539871.3352070.0001332225
1.541.3352270.000133
1.540171.3352540.0001327673
1.540461.33530.0001323514
1.540761.3353460.0001319354
1.541061.3353910.0001315193
1.541351.3354350.0001311031
1.541651.3354780.0001306868
1.541951.335520.0001302705
1.542251.3355620.000129854
1.542541.3356030.0001294375
1.542841.3356430.0001290209
1.543141.3356820.0001286043
1.543441.335720.0001281875
1.543741.3357580.0001277707
1.544031.3357940.0001273538
1.544331.335830.0001269368
1.544631.3358650.0001265197
1.544931.33590.0001261026
1.545221.3359330.0001256853
1.545521.3359660.000125268
1.545821.3359970.0001248506
1.546121.3360280.0001244332
1.546421.3360590.0001240156
1.546721.3360880.000123598
1.547011.3361170.0001231803
1.547311.3361440.0001227625
1.547611.3361710.0001223446
1.547911.3361980.0001219267
1.548211.3362230.0001215086
1.548511.3362470.0001210905
1.548811.3362710.0001206723
1.54911.3362940.000120254
1.54941.3363160.0001198357
1.54971.3363370.0001194172
1.551.3363580.000119
1.551.3363580.0001189988
1.55031.3363780.0001186101
1.55061.3363960.0001182213
1.55091.3364140.0001178325
1.55121.3364320.0001174435
1.55151.3364480.0001170545
1.55181.3364640.0001166655
1.55211.3364790.0001162763
1.552391.3364920.0001158871
1.552691.3365060.0001154978
1.552991.3365180.0001151084
1.553291.336530.000114719
1.553591.336540.0001143294
1.553891.336550.0001139398
1.554191.3365590.0001135502
1.554491.3365680.0001131604
1.554791.3365750.0001127706
1.555091.3365820.0001123807
1.555391.3365880.0001119907
1.555691.3365930.0001116007
1.555991.3365970.0001112105
1.556291.33660.0001108203
1.556591.3366030.00011043
1.556891.3366050.0001100397
1.557191.3366060.0001096493
1.557491.3366060.0001092588
1.557791.3366050.0001088682
1.558091.3366040.0001084775
1.558391.3366020.0001080868
1.55871.3365990.000107696
1.5591.3365950.0001073051
1.55931.336590.0001069141
1.55961.3365840.0001065231
1.55991.3365780.000106132
1.561.3365760.000106
1.56021.3365710.0001058186
1.56051.3365630.0001055447
1.56081.3365540.0001052708
1.56111.3365450.0001049968
1.56141.3365340.0001047227
1.56171.3365230.0001044486
1.562011.3365110.0001041745
1.562311.3364980.0001039003
1.562611.3364850.0001036261
1.562911.336470.0001033517
1.563211.3364550.0001030774
1.563511.3364390.000102803
1.563811.3364220.0001025285
1.564121.3364050.000102254
1.564421.3363860.0001019794
1.564721.3363670.0001017048
1.565021.3363470.0001014301
1.565321.3363260.0001011554
1.565631.3363040.0001008806
1.565931.3362810.0001006058
1.566231.3362580.0001003309
1.566531.3362340.000100056
1.566831.3362099.978098e-05
1.567141.3361839.950594e-05
1.567441.3361579.923084e-05
1.567741.3361299.895569e-05
1.568041.3361019.868048e-05
1.568351.3360729.840523e-05
1.568651.3360429.812992e-05
1.568951.3360119.785455e-05
1.569251.335989.757913e-05
1.569561.3359489.730366e-05
1.569861.3359149.702814e-05
1.571.3358999.690000e-05
1.570161.3358819.676067e-05
1.570461.3358469.650018e-05
1.570771.335819.623965e-05
1.571071.3357749.597906e-05
1.571371.3357379.571842e-05
1.571681.3356999.545774e-05
1.571981.335669.519700e-05
1.572281.335629.493621e-05
1.572591.335589.467538e-05
1.572891.3355399.441449e-05
1.573191.3354979.415355e-05
1.57351.3354549.389256e-05
1.57381.335419.363153e-05
1.57411.3353669.337044e-05
1.574411.3353219.310930e-05
1.574711.3352749.284811e-05
1.575021.3352289.258687e-05
1.575321.335189.232558e-05
1.575621.3351319.206424e-05
1.575931.3350829.180285e-05
1.576231.3350329.154141e-05
1.576531.3349819.127991e-05
1.576841.3349299.101837e-05
1.577141.3348779.075678e-05
1.577451.3348239.049514e-05
1.577751.3347699.023344e-05
1.578061.3347148.997170e-05
1.578361.3346588.970990e-05
1.578671.3346028.944806e-05
1.578971.3345448.918616e-05
1.579271.3344868.892422e-05
1.579581.3344278.866222e-05
1.579881.3343678.840017e-05
1.581.3343448.830000e-05
1.580191.3343068.817008e-05
1.580491.3342458.795975e-05
1.58081.3341828.774939e-05
1.58111.3341198.753898e-05
1.581411.3340558.732853e-05
1.581711.333998.711804e-05
1.582021.3339258.690750e-05
1.582321.3338598.669693e-05
1.582631.3337918.648632e-05
1.582931.3337238.627567e-05
1.583241.3336558.606497e-05
1.583541.3335858.585424e-05
1.583851.3335148.564346e-05
1.584161.3334438.543265e-05
1.584461.3333718.522179e-05
1.584771.3332988.501089e-05
1.585071.3332258.479996e-05
1.585381.333158.458898e-05
1.585681.3330758.437796e-05
1.585991.3329998.416690e-05
1.58631.3329228.395580e-05
1.58661.3328448.374466e-05
1.586911.3327658.353347e-05
1.587211.3326868.332225e-05
1.587521.3326068.311099e-05
1.587831.3325258.289968e-05
1.588131.3324438.268834e-05
1.588441.3323618.247695e-05
1.588751.3322778.226553e-05
1.589051.3321938.205406e-05
1.589361.3321088.184255e-05
1.589671.3320228.163100e-05
1.589971.3319358.141941e-05
1.591.3319278.140000e-05
1.590281.3318488.124400e-05
1.590591.3317598.107221e-05
1.590891.331678.090038e-05
1.59121.331588.072852e-05
1.591511.331498.055663e-05
1.591811.3313988.038471e-05
1.592121.3313068.021275e-05
1.592431.3312138.004076e-05
1.592731.3311197.986874e-05
1.593041.3310247.969668e-05
1.593351.3309287.952459e-05
1.593661.3308327.935247e-05
1.593961.3307357.918031e-05
1.594271.3306377.900812e-05
1.594581.3305387.883590e-05
1.594891.3304387.866364e-05
1.595191.3303387.849136e-05
1.59551.3302367.831903e-05
1.595811.3301347.814668e-05
1.596121.3300317.797429e-05
1.596431.3299287.780187e-05
1.596731.3298237.762941e-05
1.597041.3297187.745692e-05
1.597351.3296127.728440e-05
1.597661.3295057.711185e-05
1.597971.3293977.693926e-05
1.598271.3292887.676664e-05
1.598581.3291797.659398e-05
1.598891.3290697.642129e-05
1.59921.3289587.624857e-05
1.599511.3288467.607582e-05
1.599821.3287337.590303e-05
1.61.3286667.580000e-05
1.600121.328627.574765e-05
1.600431.3285057.561801e-05
1.600741.328397.548835e-05
1.601051.3282747.535866e-05
1.601361.3281587.522894e-05
1.601671.328047.509920e-05
1.601981.3279227.496943e-05
1.602291.3278037.483964e-05
1.60261.3276837.470982e-05
1.60291.3275627.457998e-05
1.603211.327447.445012e-05
1.603521.3273187.432023e-05
1.603831.3271957.419031e-05
1.604141.3270717.406037e-05
1.604451.3269467.393040e-05
1.604761.326827.380041e-05
1.605071.3266947.367039e-05
1.605381.3265667.354035e-05
1.605691.3264387.341028e-05
1.6061.3263097.328019e-05
1.606311.326187.315007e-05
1.606621.3260497.301993e-05
1.606931.3259187.288976e-05
1.607241.3257867.275957e-05
1.607551.3256537.262935e-05
1.607861.3255197.249911e-05
1.608171.3253847.236884e-05
1.608481.3252497.223855e-05
1.608791.3251137.210823e-05
1.60911.3249767.197789e-05
1.609411.3248387.184752e-05
1.609721.3246997.171713e-05
1.611.3245747.160000e-05
1.610031.324567.158956e-05
1.610341.324427.148706e-05
1.610651.3242797.138455e-05
1.610961.3241377.128202e-05
1.611271.3239947.117947e-05
1.611591.3238517.107690e-05
1.61191.3237067.097431e-05
1.612211.3235617.087170e-05
1.612521.3234157.076907e-05
1.612831.3232687.066642e-05
1.613141.3231217.056375e-05
1.613451.3229727.046106e-05
1.613761.3228237.035835e-05
1.614071.3226737.025562e-05
1.614391.3225227.015287e-05
1.61471.3223717.005010e-05
1.615011.3222186.994732e-05
1.615321.3220656.984451e-05
1.615631.3219116.974168e-05
1.615941.3217566.963883e-05
1.616251.32166.953596e-05
1.616571.3214446.943308e-05
1.616881.3212876.933017e-05
1.617191.3211286.922724e-05
1.61751.320976.912429e-05
1.617811.320816.902133e-05
1.618131.3206496.891834e-05
1.618441.3204886.881533e-05
1.618751.3203266.871231e-05
1.619061.3201636.860926e-05
1.619381.3199996.850619e-05
1.619691.3198346.840311e-05
1.621.3196696.830000e-05

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
—