Optical Materials 29 (2007) 1481–1490
`
`www.elsevier.com/locate/optmat
`
`Analysis of the dispersion of optical plastic materials q
`
`Stefka Nikolova Kasarova a,*, Nina Georgieva Sultanova a,
`Christo Dimitrov Ivanov b, Ivan Dechev Nikolov b
`
`a University of Burgas, Department of Physics, 1 Prof. Yakimov Str., Burgas, Bulgaria
`b Sofia University, Faculty of Physics, Department of Optics and Spectroscopy, 5 J. Bourchier Blvd. Sofia, Bulgaria
`
`Received 9 May 2006; received in revised form 17 July 2006; accepted 17 July 2006
`Available online 7 September 2006
`
`1. Introduction
`
`At present plastic materials find wide application in con-
`sumer and high quality optics. Optical plastics (OPs) are
`used mainly in the visible (VIS) and near-infrared (NIR)
`spectral regions from 400 nm to 1100 nm. Success in appli-
`cation of OPs depends on knowledge of their optical refrac-
`tion, transmission, birefringence, haze and homogeneity
`[1]. The optical properties of polymers are in details consid-
`ered in [2]. Chromatic dispersion is an important character-
`istic in the design of optical systems and devices. However,
`measurements of refractive indices are usually realized at
`several selected wavelengths. Determination of more exten-
`sive refractometric data is possible using dispersion formu-
`lae [3,4].
`The measuring methods for determination of OPs’
`refractometric characteristic are quite different. The refrac-
`tive indices of transparent polymers can be obtained using
`the Federal Test Method Standard [5] in which the Abbe
`refractometer is applied. It operates with a white light
`source and Amici prisms as colour compensators. The
`refractive index value for the sodium D-line can be read
`directly from the instrument. However, the measuring
`accuracy is not acceptable for modern optical design pro-
`jects. Furthermore, determination of refractive indices val-
`ues can not be realized at different wavelengths. Utilization
`of Zeiss Pulfrich refractometer (PR2) is possible too [6,7].
`We have measured the refractive indices in the VIS light
`using the PR2 instrument with its V-type prism [8] and
`additional goniometric set-up was applied for the entire
`
`q This work is supported, in part, by the Burgas University ‘‘Assen
`Zlatarov’’ under Research Project NIH77.
`* Corresponding author.
`E-mail address: kasarova_st@yahoo.com (S.N. Kasarova).
`
`0925-3467/$ - see front matter Ó 2006 Elsevier B.V. All rights reserved.
`doi:10.1016/j.optmat.2006.07.010
`
`1
`
`VIS and NIR regions. The obtained refractive values were
`compared with the data from Glass catalogues of OSLO
`[9], ZEMAX [10] and Code V [11]. Laser refractometric
`measurements of a number of OP specimens have been also
`accomplished using a He–Ne laser source with 632.8 nm
`emission wavelength [12].
`Most widely used OPs are thermoplastics as polymethyl
`methacrylate (PMMA), polystyrene (PS), polycarbonate
`(PC), methyl methacrylate styrene copolymer (NAS), sty-
`rene acrylonitrile (SAN) and methylpentene (TPX) [1,13].
`The only thermosetting plastic for optical applications is
`allyl diglycol carbonate (CR-39) [1]. The available cata-
`logue data for refractive indices and dispersion characteris-
`tics of OPs is yet scanty. Useful data of commonly used
`transparent polymers is presented in Refs.
`[1,13]. The
`refractive indices of the principal OPs are included in many
`patents [14–17] and available online web-pages [18,19].
`Companies producing trade-marks of optical polymers
`provide information on their refractometric and dispersive
`characteristics [20]. In comparison with glass, OPs have a
`restricted range of refractive indices and dispersion. The
`magnitude of the refractive index nD at the sodium D-line
`(589.3 nm) usually varies from 1.47 to 1.59 [1,21]. The
`Abbe number of OPs is in the range from about 100 to a
`little less than 20 [1,21]. However, there are some differ-
`ences in the reported refractometric data. For example,
`the refractive indices values of such a popular material as
`PMMA are different in references [15,16].
`Recently it has been noticed considerable interest in the
`development of OP materials. Plastics replace glasses in
`products as objectives, lens arrays, aspheric and ophthal-
`mic lenses, displays and lighting fixtures, windows, inter-
`nally illuminated outdoor signs and skylights [21,22]. The
`improvement of manufacturing processes makes possible
`the utilization of OPs in medicine, military optics, sensors
`
`APPLE 1045
`Apple v. Masimo
`IPR2021-00208
`
`

`

`1482
`
`S.N. Kasarova et al. / Optical Materials 29 (2007) 1481–1490
`
`and communications [21–24]. Chemical companies produce
`Ò
`, CTE-
`various trade-marks of OPs as NAS-21 Novacor
`Ò
`Ò
`Ò
`Ò
`, Zeonex
`, Optorez
`, Bayer
`, etc. but some
`Richardson
`of them have close dispersion data. Our previous refracto-
`metric measurements [7] show for example that Optorez
`Ò
`Ò
`and S – low Styrene
`have similar dispersive proper-
`1330
`Ò
`Ò
`Ò
`ties, Zeonex E48R
`and COC
`are equal, and Bayer
`is a
`PC-type plastic material. Using some new optical materials
`the designers can improve the performance and balance the
`production expenses [13]. It seems that OPs can be both a
`low-cost alternative to glass and an option that provides
`more degrees of freedom for product and optical design.
`In this paper we consider the refractometric and disper-
`sion properties of OP materials in the region of normal dis-
`persion. We have examined various types of OPs including
`the principal, selected trade marks and some control sam-
`ples of polymers.
`
`2. Theoretical analysis of dispersion
`
`of 43 functional groups, using an extensive regression anal-
`ysis [2]. With his group contributions the refractive index
`can be predicted with an average standard deviation of
`about 0.4%.
`Variation of the refractive index with respect to the
`wavelength depends also on the structure of the substance.
`In the spectral region of transmission the refractive index
`of the materials reduces towards longer wavelengths. Close
`to the absorption bands the refractive index enhances with
`the increase of the wavelength. The major OPs absorb in
`the blue portion of the visible spectrum and have some
`energy absorption at wavelengths of 900 nm, 1150 nm
`and 1350 nm in the NIR region [21]. At longer wavelengths
`high transmission is possible only in very thin sections of
`the material (0.022 mm) [1]. OPs become totally opaque
`at about 2100 nm [21]. The transmission characteristics
`depend strongly on quenching the material from tempera-
`ture of about 213 °C to 147 °C in 60 s or less to prevent
`crystallization [1]. At wavelengths within the absorption
`bands intramolecular oscillations appear and the bond
`lengths and valence angles of molecules are altered. The
`more complex chemical structures of polymers increase
`the number of absorption bands and therefore influence
`the dependence of the refractive index on the wavelength.
`There are several formulae in literature approximating
`the dispersion of optical materials. Most popular among
`them are the Hezberger’s experimental formula [3], Cau-
`chy’s and Sellmeier’s equations [4]. Only the last one, how-
`ever, has physical ground. Dispersion can be explained by
`applying the classical electromagnetic theory to the molec-
`ular structure of the medium. Sellmeier has considered the
`substance as a system of elastically bounded particles with
`natural angular frequency x0i (i = 1 . . . k – consecutive
`number of a single oscillator). The amplitude of the oscilla-
`tions of bound charges forced by the electromagnetic wave
`increases at resonance frequency. According to Sellmeier’s
`theory the well-known dependence of the refractive index
`on the wavelength is obtained:
`Xk
`i¼0
`
`n2ðkÞ ¼ 1 þ
`
`Aik2
`k2 k2
`0i
`
`;
`
`ð2:4Þ
`
`where Ai are constants proportional to the number of oscil-
`lators with natural wavelengths k0i per unit volume.
`An important characteristic of the dispersion properties
`of optical materials is their Abbe numbers, which usually
`decrease as the refractive indices increase. The USA stan-
`dard Abbe number md is defined by the following ratio:
`md ¼ nd 1
`ð2:5Þ
`nF nC
`The difference (nF nC), named a principal dispersion,
`involves refractive indices nF and nC at the blue hydrogen
`F-line (486.13 nm) and red hydrogen C-line (656.27 nm).
`The Abbe number m804 which is a measure of partial disper-
`sion in the NIR range is given by the equation
`
`:
`
`The interaction between the electromagnetic wave and
`the medium (the refractive index n, respectively) depends
`on its density and individual properties of the molecules
`on one hand, and the radiation wavelength on the other
`hand. A characteristic of the materials is the ratio, named
`a specific refraction r = f(n)/q, where q is the density of
`the substance and f(n) is a function of the refractive index.
`The product of the specific refraction and molar mass is the
`molar refraction R often used in practice. Considering the
`effective electric field acting on a molecule in a polarizable
`medium, Lorentz and Lorenz have formulated theoretically
`[2] the molar refraction RLL as
`RLL ¼ n2 1
`¼ 1
`n2 þ 2
`3
`where M is the molar mass, a is the molecular polarisability
`and NA is the Avogadro’s number. The molar refraction is
`a material characteristic of the refraction properties which
`is independent on the density, temperature and physical
`state. This equation is valid for isotropic materials in cases
`of ulrta-violet and visible illumination, where the electron
`polarisability is essential. For organic liquids Gladstone
`and Dale have obtained that at standard wavelengths the
`ratio (n 1)/q is a material characteristic constant and
`the molar refraction is:
`ðn 1Þ:
`
`N Aa;
`
`M q
`
`RGD ¼ M
`q
`
`ð2:1Þ
`
`ð2:2Þ
`
`Another correlation between the chemical structure of
`electrically insulating materials and the refractive index
`has been proposed by Vogel [2]:
`RV ¼ nM:
`ð2:3Þ
`It is known that the refraction is an additive value.
`Therefore, the refractive index can be estimated using
`Eqs. (2.1), (2.2) and (2.3), if the structure of the compounds
`is known. Goedhart estimated the molar refraction values
`
`2
`
`

`

`S.N. Kasarova et al. / Optical Materials 29 (2007) 1481–1490
`
`1483
`
`;
`
`ð2:6Þ
`
`m804 ¼ n804 1
`n703 n1052
`where n703, n804 and n1052 are the refractive indices at wave-
`lengths 703 nm, 804 nm and 1052 nm, respectively. In Eur-
`ope and Japan the Abbe number is defined according to the
`green mercury e-line (546.07 nm) as:
`
`;
`
`ð2:7Þ
`
`me ¼ ne 1
`nF 0 nC0
`where nF 0 and nC0 – refractive indices at the cadmium blue
`0
`0
`-line and red C
`-line. Materials with low refractive indi-
`F
`ces usually have low dispersion behaviour and therefore a
`high Abbe number.
`
`3. Measurement of the indices of refraction
`
`In this study we apply the measuring method described in
`details in our paper [7]. The OPs’ indices of refraction were
`measured with the aid of the Carl Zeiss Jena Pulfrich-
`Refractometer PR2 [8] in the visible spectral region at six
`standard spectral lines: green e-line 546.07 nm, blue g-line
`435.83 nm, yellow d-line 587.56 nm, red r-line 706.52 nm,
`blue F-line 486.13 nm and red C-line 656.27 nm. We have
`chosen the V-type SF3 glass prism (VoF3 prism) which usu-
`ally used for measuring liquids since the standard total
`internal reflection prism requires thick cubic of OP samples
`with satisfactory polished surfaces to observe a contrast
`image of the dividing border between the light and dark
`field in the eyepiece of the instrument. Furthermore, the
`standard prism does not avoid evaporating of the water
`contacting solutions and the precision of monitoring
`decreases at the end of the measuring series.
`The examined OP specimens were prepared as injection
`moulded plates with thickness varying from 2.54 mm to
`5.1 mm, except for the control samples which were cubic.
`Two mutually perpendicular surfaces of the samples were
`well polished to obtain a good refractometric data. Measur-
`ing temperature of 20 °C is maintained by a thermostat and
`temperature regulation is possible with stability of 0.2 °C. A
`saturated aqueous solution of zinc chloride (ne = 1.51) and
`
`silicon oil (nD = 1.56) for low refractive OP samples as
`PMMA, and a saturated water solution of potassium–mer-
`curic–iodide (KHgI) with ne = 1.73 for higher refractive PS,
`PC, etc. have been chosen to ensure the optical contact dur-
`ing the measurements. Initial estimation of the indices of
`refraction of the OP samples and the choice of immersion
`emulsions have been accomplished by means of an ellipso-
`metric laser system LEF-3 M-1 made by Carl Zeiss Jena
`which measuring accuracy of Dn = ±0.002 is completely
`insufficient to obtain precise OPs’ refractometric data.
`Refractive indices of OPs in VIS and NIR region are
`measured with the experimental
`set-up illustrated in
`Fig. 1. A G5-LOMO goniometer with an accuracy of one
`arc second was used with the VoF3 prism-measuring block
`positioned on the G5 test table. The lighting module oper-
`ates with a 250 W halogen lamp applied over the entire
`VIS and NIR regions with interference filters (IF) made
`by Carl Zeiss (Jena). A new photo detector device was
`assembled with the aid of a plane silicon diode, operating
`amplifier and indicating module. The collimator forms a
`white light beam that falls on the fixed filter. The prism
`block with the OP sample is illuminated monochromati-
`cally. We found some differences in the spectral bandwidths
`and maxima of the filters. Therefore, the amplitude trans-
`mittances of the interference filters have been measured
`with the aid of Varian Carry 5 VIS-NIR spectrophotometer
`and all deviations were considered in presentation of the
`refractometric results.
`The right-hand collimator with the attached photo
`detector determines the measuring angle a (see Fig. 1).
`The angle of deviation c is formed by the OP sample
`located into the V-shaped prism. The refractive index nk
`ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
`q
`of the examined OP is calculated as follows:
`ð3:1Þ
`
`k ¼ N 2k cos c
`k cos2 c
`c ¼ 90
` a;
`N 2
`n2
`;
`where Nk is the refractive index of the VoF3 prism, c is the
`calculated angle of the deviated beam, and a is the mea-
`sured angle on the G5 set-up. The index Nk of the SF3 glass
`is determined by the data published in [8] at standard spec-
`tral wavelengths. A new OptiColor program involving
`
`slit
`
`filter
`
`OP sample
`
`lighting
`module
`
`collimator
`
`α
`
`γ
`
`VoF3 prism
`
`G5
`test table
`
`indicator
`
`amplifier
`
`collimator
`
`photo
`detector
`
`slit
`
`Fig. 1. Experimental set-up for measurement of the OP’s refractive indices.
`
`3
`
`

`

`1484
`
`S.N. Kasarova et al. / Optical Materials 29 (2007) 1481–1490
`
`Table 1
`Measured refractive indices of sixteen OP materials
`
`Material
`
`WLs (nm)
`
`435.8
`
`1.502
`1.617
`1.612
`1.588
`1.602
`1.593
`1.532
`1.522
`1.543
`1.612
`1.480
`1.507
`1.534
`1.597
`1.615
`1.502
`
`486.1
`
`1.497
`1.606
`1.599
`1.578
`1.593
`1.584
`1.526
`1.516
`1.538
`1.600
`1.477
`1.500
`1.527
`1.587
`1.604
`1.498
`
`587.6
`
`1.491
`1.592
`1.585
`1.567
`1.580
`1.571
`1.518
`1.509
`1.531
`1.586
`1.471
`1.494
`1.519
`1.572
`1.592
`1.492
`
`703
`
`1.486
`1.582
`1.575
`1.558
`1.571
`1.564
`1.512
`1.505
`1.526
`1.577
`1.466
`1.491
`1.513
`1.565
`1.582
`1.488
`
`833
`
`1.484
`1.577
`1.570
`1.554
`1.566
`1.558
`1.509
`1.503
`1.523
`1.571
`1.463
`1.489
`1.510
`1.560
`1.576
`1.485
`
`1052
`
`1.481
`1.572
`1.565
`1.550
`1.562
`1.554
`1.506
`1.498
`1.520
`1.566
`1.461
`1.486
`1.507
`1.555
`1.572
`1.483
`
`PMMA
`PS
`PC
`SAN
`Ò
`CTE Richardson
`Ò
`NAS-21
`Ò
`S (low styrene)
`Ò
`Optorez 1330
`Ò
`Zeonex E48R
`Ò
`Bayer
`Cellulosea
`Polyacrylatea
`Styrenea
`Polycarbonatea
`Polystyrenea
`Acrylica
`a Control samples.
`
`Caushy’s dispersion formula was made to determine the
`dispersive coefficients of SF3 glass prism and then random
`refractive indices Nk in VIS or NIR region are calculated.
`The obtained measured data of the refractive indices of
`OPs at six wavelengths are presented in Table 1. The last
`six materials from Cellulose to Acrylic refer to laboratory
`specimens and are used as control samples. The presented
`values of measured refractive indices in Table 1 were
`obtained by averaging over all measured data of each series
`of at least five samples at given wavelength.
`
`4. Computer modelling of dispersion
`
`In spectral regions where materials are transparent and
`normal dispersion occurs (k  k0i) Eq. (2.4) is reduced to
`Cauchy’s equation. In our previous works [7,12,25] we
`have applied a modified Cauchy’s approximation in the
`form:
`
`ð4:1Þ
`
`þ ;
`
`þ A4
`k ¼ A1 þ A2k2 þ A3
`n2
`k4
`k2
`where A1, A2, A3, A4, . . . are the calculated dispersion coef-
`ficients and k is the wavelength expressed in microns.
`We have studied the precision of this approximation in
`respect to the number of the involved dispersion coeffi-
`cients. They were computed with the aid of linear systems
`consisting of four, five, six, seven and eight equations.
`The available optical catalogues do not provide sufficient
`data for refractive indices of OPs. Because of that, we have
`studied the accuracy of approximation (4.1) using the
`extensive refractometric information on optical glasses
`published in Glass Catalogues. Our calculations were made
`on the examples of catalogue data of SF3 [8] and SF6 glass
`[26]. The refractive indices are given with precision of
`5. Table 2 presents the results of our calculations
`1 · 10
`for the SF6 type glass.
`In column 2 the catalogue refractive indices at standard
`spectral lines are included. Columns 3, 4, 5, 6 and 7 present
`the deviation DNk between calculated and catalogue data.
`Blank places in these columns indicate the refractive indices
`used in the corresponding linear equation system involving
`4, 5, 6, 7 or 8 dispersion coefficients in Eq. (4.1), respec-
`tively. A maximal error DNk of 0.00064 and 0.00026 in
`the blue area of the spectrum are obtained applying four
`and five dispersion coefficients. We found that the accuracy
`to the fifth decimal place, as in SCHOTT catalogue apply-
`ing the Sellmeier’s approximation, is not achievable. Using
`six dispersion coefficients a maximal deviation up to
`0.00007 is obtained (column 5). One can see that utilization
`of more than six terms in the approximating row does not
`change significantly this result (columns 6 and 7). There-
`fore, we found that the usage of six dispersion coefficients
`in Cauchy’s approximation is sufficient to provide the accu-
`racy of ±0.001 of calculated refractive indices. Better pre-
`cision is achievable using Sellmeier’s approximation,
`which should be applied in case of experimental data pre-
`sented to the fourth decimal point.
`
`Table 2
`Deviation of computed indices in respect to the catalogue data of SF6 glass
`Calculated error DNk
`
`SF6 (SCHOTT)
`
`WLs (nm)
`
`404.7 (h)
`435.8 (g)
`0
`)
`480 (F
`486.1 (F)
`546.1 (e)
`587.6 (d)
`589.3 (D)
`632.8 (laser)
`0
`)
`643.9 (C
`656.3 (C )
`706.5 (r )
`852.1 (s)
`1014 (t)
`1064 (laser)
`
`1.86436
`1.84707
`1.82970
`1.82775
`1.81265
`1.80518
`1.80491
`1.79884
`1.79750
`1.79609
`1.79117
`1.78157
`1.77517
`1.77380
`
`4 coeff.
`
`0.00064
`0.00013
`0.00014
`0.00004
`
`0
`0.00002
`0
`0.00001
`0.00004
`
`5 coeff.
`
`0.00026
`0.00003
`0.00004
`0.00001
`
`0
`0
`0.00001
`
`0
`
`6 coeff.
`0.00005
`
`7 coeff.
`0.00023
`
`8 coeff.
`0.00020
`
`0.00001
`
`0.00001
`
`0.00001
`
`0
`
`0
`
`0
`0
`0.00001
`
`0
`0
`0.00001
`
`0
`0
`0.00001
`
`0.00001
`
`0.00010
`
`0.00006
`
`0.00007
`
`0.00006
`
`0.00006
`
`4
`
`

`

`S.N. Kasarova et al. / Optical Materials 29 (2007) 1481–1490
`
`1485
`
`According to the analysis of the approximation preci-
`sion best results are obtained using six dispersion coeffi-
`cients in Cauchy’s formula (4.1). We have realized the
`program OptiColor that allows us to compute the disper-
`sion coefficients of any optical material in the region of
`normal dispersion. The input data consists of six refractive
`indices at selected measuring wavelengths (see Table 1).
`The dispersion coefficients from A1 to A6 can be calculated
`using the linear system consisting of six equations [7].
`The obtained results are presented in Table 3. The com-
`puted dispersion coefficients vary in respect to the selected
`
`wavelengths, but analysis shows that A1 always corresponds
`to n2 with accuracy to the first decimal place and A2 . . . A6
`introduce additional corrections of higher accuracy.
`Substituting the obtained dispersion coefficients in Cau-
`chy’s dispersion formula (4.1), random refractive indices
`can be computed and compared with their measured val-
`ues. We have calculated OPs’ refractive indices at selected
`laser wavelengths in our earlier works [7,12,27]. In this
`paper we present results at some additional laser emission
`wavelengths. The calculated refractive data of various
`OPs, SF3 and SF6 glasses are given in Table 4. The Abbe
`
`Table 3
`Computed dispersion coefficients of the examined OP materials
`
`Material
`
`Dispersion coefficients
`
`PMMA
`PS
`PC
`SAN
`Ò
`CTE Rich.
`Ò
`NAS-21
`Ò
`S (low styrene)
`Ò
`Optorez 1330
`Ò
`Zeonex E48R
`Ò
`Bayer
`Cellulosea
`Polyacrylatea
`Styrenea
`Polycarbonatea
`Polystyrenea
`Acrylica
`a Control samples.
`
`A1
`
`2.399964
`2.610025
`2.633127
`2.595568
`2.663794
`2.054612
`2.360004
`2.291142
`2.482396
`2.542676
`2.139790
`2.364830
`2.274658
`2.496875
`2.721609
`1.866120
`
`A2
`8.308636E-2
`6.143673E-2
`7.937823E-2
`6.848245E-2
`1.059116E-1
`1.374019E-1
`4.014429E-2
`3.311944E-2
`6.959910E-2
`4.366727E-2
`6.317682E-3
`6.955268E-2
`5.700326E-3
`5.014035E-2
`9.982812E-2
`2.085454E-1
`
`A3
`1.919569E-1
`1.312267E-1
`1.734506E-1
`1.459074E-1
`2.492271E-1
`3.200690E-1
`8.371568E-2
`1.630099E-2
`1.597726E-1
`8.196872E-2
`5.920813E-3
`1.356107E-1
`7.262838E-3
`4.188992E-2
`2.518650E-1
`4.806770E-1
`
`A4
`
`8.720608E-2
`6.865432E-2
`8.609268E-2
`7.329172E-2
`1.165541E-1
`1.152867E-1
`4.160019E-2
`7.265983E-3
`7.383333E-2
`4.718432E-2
`9.613514E-3
`6.053900E-2
`1.233343E-2
`1.732175E-2
`1.269202E-1
`1.840693E-1
`
`A5
`1.666411E-2
`1.295968E-2
`1.617892E-2
`1.372433E-2
`2.211611E-2
`2.077225E-2
`7.586052E-3
`6.806145E-4
`1.398485E-2
`8.892747E-3
`1.967293E-3
`1.166640E-2
`2.481307E-3
`1.240544E-3
`2.549211E-2
`3.424849E-2
`
`A6
`
`1.169519E-3
`9.055861E-4
`1.128933E-3
`9.426682E-4
`1.545711E-3
`1.383569E-3
`5.071533E-4
`1.960732E-5
`9.728455E-4
`6.324010E-4
`1.363793E-4
`8.542615E-4
`1.784805E-4
`1.977750E-5
`1.867696E-3
`2.340796E-3
`
`Table 4
`Abbe numbers and refractive indices of two glasses and sixteen OP materials calculated for ten laser wavelengths
`
`Optical material Abbe
`numbers
`
`md
`28.14
`SF3
`25.44
`SF6
`59.2
`PMMA
`30.5
`PS
`29.1
`PC
`35.4
`SAN
`Ò
`32.8
`CTE Rich.
`Ò
`35.5
`NAS-21
`Ò
`44.9
`S (low Styrene)
`Ò
`52.0
`Optorez 1330
`Ò
`56.5
`Zeonex E48R
`Ò
`30.0
`Bayer
`Cellulosea
`54.1
`Polyacrylatea
`63.3
`Styrenea
`42.9
`Polycarbonatea
`28.9
`Polystyrenea
`32.0
`Acrylica
`57.8
`a Control samples.
`
`m804
`48.48
`44.81
`96.9
`56.6
`54.8
`66.8
`58.5
`56.3
`79.6
`71.9
`100.7
`54.5
`84.3
`97.8
`77.3
`56.7
`55.5
`97.2
`
`Lasing medium
`
`GaN
`
`Ar
`
`Cu
`
`Nd:YAG He–Ne
`
`Ruby
`
`Krypton Ti:Sapphire Nd:YAG Nd:YAG
`
`405 nm 488 nm 510.6 nm 532 nm
`
`632.8 nm 694.3 nm 799.3 nm 860 nm
`
`946 nm
`
`1064 nm
`
`1.7879
`1.8641
`1.516
`1.634
`1.631
`1.608
`1.612
`1.588
`1.542
`1.531
`1.555
`1.623
`1.484
`1.521
`1.540
`1.602
`1.640
`1.506
`
`1.7582
`1.8272
`1.497
`1.605
`1.599
`1.578
`1.592
`1.583
`1.526
`1.516
`1.537
`1.599
`1.476
`1.499
`1.527
`1.586
`1.604
`1.498
`
`1.7530
`1.8209
`1.496
`1.602
`1.595
`1.575
`1.589
`1.580
`1.524
`1.514
`1.536
`1.596
`1.475
`1.498
`1.525
`1.582
`1.601
`1.495
`
`1.7488
`1.8158
`1.495
`1.599
`1.592
`1.573
`1.587
`1.577
`1.522
`1.513
`1.535
`1.593
`1.474
`1.497
`1.523
`1.579
`1.598
`1.495
`
`1.7347
`1.7988
`1.489
`1.587
`1.580
`1.563
`1.576
`1.568
`1.515
`1.507
`1.528
`1.582
`1.469
`1.492
`1.516
`1.568
`1.587
`1.490
`
`1.7292
`1.7923
`1.487
`1.583
`1.575
`1.558
`1.571
`1.564
`1.512
`1.505
`1.526
`1.578
`1.467
`1.491
`1.514
`1.565
`1.582
`1.488
`
`1.7226
`1.7845
`1.484
`1.578
`1.571
`1.554
`1.567
`1.559
`1.510
`1.503
`1.524
`1.572
`1.464
`1.490
`1.510
`1.561
`1.577
`1.486
`
`1.7189
`1.7801
`1.484
`1.576
`1.569
`1.553
`1.566
`1.557
`1.509
`1.502
`1.523
`1.570
`1.463
`1.488
`1.509
`1.559
`1.576
`1.485
`
`1.7166
`1.7775
`1.483
`1.574
`1.567
`1.552
`1.564
`1.555
`1.508
`1.501
`1.522
`1.568
`1.462
`1.487
`1.508
`1.557
`1.574
`1.484
`
`1.7133
`1.7737
`1.481
`1.572
`1.564
`1.549
`1.562
`1.554
`1.506
`1.498
`1.520
`1.566
`1.461
`1.485
`1.507
`1.554
`1.571
`1.483
`
`5
`
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`

`1486
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`
`Fig. 2. Comparision of computed dispersion curves on the base of different input data for: (a) PMMA; (b) PS and (c) PC.
`
`6
`
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`S.N. Kasarova et al. / Optical Materials 29 (2007) 1481–1490
`
`1487
`
`numbers md and m804 estimating the principal and partial
`dispersion, respectively, are presented in the same table.
`Another option of the OptiColor program is calculation
`and illustration of dispersion curves of the examined mate-
`rial in a defined spectral area of normal dispersion. Plots of
`refractive indices versus wavelength for each optical poly-
`mer can be drawn. Fig. 2 presents calculated dispersion
`charts of the principal OPs plotted in our program on the
`base of our results [7] and published data of OSLO [9],
`ZEMAX [10] and Code V [11] program packages. A com-
`parative analysis between the obtained dispersion curves is
`possible. According to approximation (4.1) the dispersion
`diagrams should be smooth and monotonously decreasing
`in the range of normal dispersion as it can be seen for dis-
`persion curves computed on the base of our measurements.
`Fig. 2(a)
`illustrates significant differences among the
`obtained results in respect to the measuring method and
`involved approximation. Curve PMMA refers to our mea-
`
`suring data and it is calculated by means of Eq. (4.1). It is
`obviously identical with curve PMMA (OSLO) in the visi-
`ble part of the spectrum, but there is an intersection point
`between both curves in the NIR-region. This means that
`dn/dk in both cases are different. However, our curve coin-
`cides with the PMMA – curve of ZEMAX in the NIR-
`spectrum. It is also obvious that curves’ behaviour of mea-
`sured PMMA and PMMA (CODE V) are very similar in
`respect to the variation of dn/dk.
`As it can be seen in Fig. 2(b) and (c) all calculated curves
`of PS and PC are strictly identical in the whole VIS region
`from 400 nm and further up to 800 nm. There are slight dif-
`ferences of PS and PC curves in the NIR (800–1100 nm)
`and largest deviation occurs
`for PC (CODE V) at
`1050 nm. In general, the presented dispersion diagrams
`show good coincidence of the obtained results. The devia-
`tions in the NIR are probably due to the measuring accu-
`racy of the various methods. In this spectral area the
`
`Fig. 3. Dispersion charts of selected trade-marks of OPs: (a) n > 1.54 and (b) n < 1.54.
`
`7
`
`

`

`1488
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`S.N. Kasarova et al. / Optical Materials 29 (2007) 1481–1490
`
`Fig. 4. Dispersion curves of control samples with: (a) higher refractive and (b) lower refractive polymers.
`
`Fig. 5. The influence of birefringence and internal stresses on the refractive index values.
`
`8
`
`

`

`S.N. Kasarova et al. / Optical Materials 29 (2007) 1481–1490
`
`1489
`
`refractive index shows lower dependence on the wavelength
`and the accuracy falls down. In case of PMMA, the distinc-
`tion of curves could be interpreted in a similar way. Since
`the refractive index is lower, stronger dependence of the
`measuring accuracy on the applied refractometric instru-
`ments is encountered. Obviously, birefringence and inter-
`nal stresses in the samples play an additional role, too.
`Computed dispersion curves on the base of measured
`data (Table 1) are illustrated in Figs. 3 and 4. Presentation
`of several dispersion curves in one diagram makes possible
`the comparison between the values of refractive indices and
`dispersion behaviour of the optical polymers. Dispersion
`charts of selected trade-marks (Fig. 3) and control samples
`(Fig. 4) are grouped into two categories: OPs with higher
`refractive indices (Fig. 3(a) and Fig. 4(a)) and lower refrac-
`tive OP materials (Fig. 3(b) and Fig. 4(b)). The dissimilar-
`ity of the computed curves’ slopes in the NIR region (see,
`for example, SAN, NAS-21 and Optorez 1330) is also con-
`nected with the higher measuring errors.
`Internal stresses develop when a plastic part is injection
`moulded as a result of a temperature cycle involved [1,21].
`These stresses create two indices of refraction, one in the
`direction of the flow and the other across the flow of the
`hot material. In this way birefringence arises. Bulk plastics
`retain residual stresses even after annealing. For example,
`the difference of refractive indices for PS could be as high
`3 [1,21]. The moulding process may introduce
`as 8 · 10
`inhomogeneity too. The influence of these effects on the
`refractometric properties of OPs is presented for two con-
`trol samples (CS-1 and CS-2) of Polyacrylate in Fig. 5.
`Birefringence was established in advance with the aid of a
`polariscope. The measuring accuracy of our refractive
`index measuring method and the flexibility of the new Opti-
`Color program as well, allowed us to detect and illustrate
`small differences in refractive indices values.
`
`5. Summary and discussions
`
`In this paper some new measuring results for refractive
`and dispersion properties of OPs are presented and dis-
`cussed. Refractometric measurements of sixteen American,
`Japanese and German OP materials were accomplished
`with the aid of the V-type prism on the Zeiss Pulfrich
`PR2 instrument at standard spectral
`lines. Additional
`goniometric set-up with the same V-type SF3 glass prism,
`white lighting module with interference filters, and a new
`sensitive photodetector device was also applied in the entire
`VIS and NIR spectral regions from 546 nm to 1052 nm (see
`Fig. 1). Our measuring results are presented with an uncer-
`tainty to the third decimal place (Table 1).
`Computing accuracy of the Cauchy’s approximation
`formula (Eq. (4.1)) is analysed on the base of glass cata-
`logue data. Our examination shows that the usage of six
`dispersion coefficients ensures calculation accuracy of ran-
`dom refractive indices to the fourth decimal place in the
`region of normal dispersion (Table 2).
`
`A new OptiColor program for computing of the disper-
`sive properties of any optical material in the region of nor-
`mal dispersion is realized. Our program calculates the
`dispersion coefficients (Table 3), random refractive indices
`and dispersion charts of the examined materials (Figs. 2–5).
`The Abbe numbers md for the principal and m804 for the par-
`tial dispersion are estimated. Refractive indices of the six-
`teen examined OPs at ten laser wavelengths in the VIS
`and NIR spectral areas are also calculated (Table 4).
`Generation of various dispersion curves is another
`option of the program (Figs. 2(a)–(c)). In this way, com-
`parative analysis of distinct input data is possible. The
`OptiColor program gives us the opportunity to distinguish
`similar dispersion curves of different samples worked out of
`one and the same type of material, if the input data of
`refractive indices differs in the third or fourth decimal
`place. Such variation of measured data is possible in case
`of inhomogeneity or birefringence of the moulded polymer
`samples (Fig. 5). These results demonstrate the sensitivity
`of the OptiColor program and prove its precision in calcu-
`lations and plotting the dispersion charts.
`In conclusion, the newly reported refractometric and
`dispersion data give detailed information about the optical
`properties of the examined sixteen types of OP materials.
`Our results could be very useful for experts from the field
`of physics, chemistry, optical design and photonics
`technology.
`
`Acknowledgement
`
`The authors wish to thank Dr. Wesley R. Hale from
`Eastman Chemical Company for helpful discussions and
`providing the OP materials for producing the control
`samples.
`
`References
`
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