Optical properties of perfluorocyclobutyl polymers - OSA Publishing

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J. Opt. Soc. Am. B / Vol. 20, No. 9 / September 2003

Ballato et al.

Optical properties of perfluorocyclobutyl polymers John Ballato* and Stephen Foulger Center for Optical Materials Science and Engineering Technologies, School of Materials Science and Engineering, Clemson University, Clemson, South Carolina 29634

Dennis W. Smith, Jr. Department of Chemistry, Clemson University, Clemson, South Carolina 29634 Received November 19, 2002; revised manuscript received April 16, 2003 As the interest in utilizing fluoropolymers in a greater number of value-added photonic applications continues to grow, so does the necessity for accurate and broadband characterization of their optical properties. This paper provides the canonical optical properties of the refractive index and the extinction coefficient for two perfluorocyclobutyl-based polymers over the spectral range from approximately 0.13 ␮m to 33 ␮m, including their respective Sellmeier coefficients. In addition, the data are used to compare Sellmeier versus Cauchy fits to dispersion data in order to elucidate the potential pitfalls in computing system-level design criterion, such as bandwidth. © 2003 Optical Society of America OCIS codes: 160.0160, 130.3130, 160.4670, 160.4760, 160.4890, 160.5470, 160.6840.

1. INTRODUCTION Polymers, both in fiber and thin-film form, continue to receive global attention as enabling materials in photonic components that aim to maintain information in the optical domain progressively closer to the home and office (i.e., the ‘‘last mile’’). Of particular interest are fluorocarbon-based polymers since, with respect to hydrocarbon analogs, the C—F bond allows lower intrinsic absorption, not only in the commercially important near-infrared wavelengths of interest to telecommunications but also in the mid and far infrared, where defense communications, countermeasures, and sensing applications lie. There exist several commercially available fluoropolymers for use in research, development, and component manufacturing. These include DuPont’s Teflon AF,1 Asahi’s Cytop,2 Corning’s fluoroacrylates,3 Dow Chemical’s trifluorovinyl ether-based perfluorocyclobutyl (PFCB),4 and new PFCB-containing polymers under development at Tetramer Technologies.5 In this paper, the focus is on the latter, as PFCB materials have enjoyed considerable recent interest as materials for thermo-optic and electrooptic switches,6,7 large-core optical interconnects,8 and thin-film gratings,9 including several review papers.10,11 PFCB chemistry is based on the thermally induced cyclopolymerization of bi- or tri-functional aryl trifluorovinyl ethers to form perfluorocyclobutyl-containing polymers. The general scheme is given in Fig. 1, which also includes the two aryl constituents treated here. PFCB chemistry is particularly useful since (1) it is thermally initiated and controllably progresses without catalysts or condensates, (2) the stereochemistry is unbiased to cis- or trans-configured PFCB linkages leading, typically, to fully amorphous compounds (although optically interesting liquid-crystalline versions are known),12 (3) the ‘‘standard’’ monomers and prenetwork oligomers have been found to be very soluble in commercial microelectronicsgrade solvents so that films with thickness in excess of 20 0740-3224/2003/091838-06$15.00

␮m can be realized from a single casting (important for planar waveguide applications), and (4) there is a very wide range of copolymers that can be prepared by substituting the aryl groups derived from low-cost phenolics (see Fig. 1). Recently, our efforts have shown that PFCB copolymers can permit highly tailored thermal, mechanical, and optical properties, including refractive indices in the range from 1.44 to above 1.51 (at 1550 nm) and glass transition temperatures, T g , in the range from 120 to 350 °C. In addition, spin-cast films exhibit very low refractive-index birefringence (⬍0.003).11 These latter two points are important for integrated optics applications, where the high T g can mitigate creep or other thermomechanical distortions and the low birefringence can obviate certain dispersion-related bandwidth limitations that plague more rigid polymeric systems such as the polyimides. The purpose of this paper is to provide the refractive index and extinction coefficients for PFCB polymers over a very broad spectral range (0.2 to 33 ␮m). From this information, application areas for consideration are discussed. This paper also uses the aforementioned data to provide a cautionary note on the liberal use of dispersionfitting functions.

2. EXPERIMENT The PFCB polymers utilized in this study consist of the biphenyl derivative (BP) and the hexafluoropropyl derivative (6F) as defined in Fig. 1. Their respective syntheses were performed equivalently to that reported previously.11 Solutions containing 20 vol.% monomer in mesitylene were spin cast at a rate of 2000 rpm (revolutions per minute) onto Si wafers yielding films 3 to 6 ␮m in thickness. Following this deposition, the films were cured in an oven under nitrogen gas for 2 h at 200 °C. © 2003 Optical Society of America

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Fig. 1. Polymerization of selected trifluorovinyl ether monomers into perfluorocyclobutyl polymers. Aryl constituents used are a biphenyl (BP) and hexafluoroisopropylidene (6F).

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ation should longer-length planar or fiber waveguides be made from these materials. The extinction coefficient, k, is related to the absorption coefficient, ␣, through k ⫽ 4 ␲ ␣ /␭, where ␭ is the wavelength of light. The absorption coefficient is ␣ ⫽ ln(I0 /I), where I 0 is the incident intensity and I is the intensity of light after transmission through the material. This often is divided through by the propagation distance to give attenuation. See Ref. 16 for greater detail.

3. RESULTS AND DISCUSSIONS Measurement of the refractive index and extinction coefficient were performed by Woolam, Inc., using their vacuum-ultraviolet (VUV) variable-angle spectroscopic ellipsometry technique,13 from which measurements were taken over the range from 138 nm to 1700 nm, approximately every 1.9 nm, at multiple angles of incidence (60, 67.5, and 75°). Infrared measurements (IR variableangle spectroscopic ellipsometry) were taken from 2 ␮m to 33 ␮m, approximately every 11 nm, at angles of 60 and 67.5°. The beam diameters were fixed at 5 and 6 mm for VUV and IR variable-angle spectroscopic ellipsometry measurements, respectively. All data were acquired at room temperature and analyzed using WVASE™ version 3.403. The PFCB films were analyzed as single, homogeneous layers on silicon. The silicon was modeled using optical constants from previous studies.14 Infrared absorption peaks were modeled using a Gaussian line shape. The VUV–visible electronic absorptions (PFCB 6F only) were modeled using an ensemble of Tauc-Lorentz and Gaussian line shapes. Wavelength-by-wavelength (point-bypoint) fits also were performed. For the PFCB 6F film, which was approximately 3 ␮m thick and possessed good thickness uniformity, the optical constants were calculable over the full spectral range evaluated (0.138 to 33 ␮m). For the BP film, the optical constants were calculated over the range from 1.45 to 33 ␮m. This slightly more limited range of measurements arose from the sample being thicker (approximately 6 ␮m, still single cast) and less spatially uniform, which led to a depolarization of the probe beam, thus preventing the accurate determination of the optical constants. Specifically, these optical constants are the real and imaginary parts, n and k, respectively, of the complex refractive index, ˜n , which is defined as ˜n ⫽ n ⫹ ik, where i ⫽ 冑⫺1. In regards to measurement precision, the refractive index and extinction coefficient of a single film on a known substrate can be measured with a precision of ⫾0.001, assuming that the ellipsometric measurement is accurate to within 0.1° in ⌿ and ⌬, and that the angle of incidence is correct in the model to within 0.01°. Sample quality can further diminish the precision of the measured optical constant. Quality issues affecting precision include accuracy of the substrate’s optical constants, thickness nonuniformity, surface or interface roughness, index grading, and lateral index uniformity of the film.15 Lastly, for this paper, since the samples were thin films and the path length was negligibly small for a meaningful computation of loss (in dB/km units, for example), we use the extinction coefficient as a predictor of spectral attenu-

A. Refractive Indices and Extinction Coefficients of PFCB The refractive indices for the BP and 6F PFCB polymers (Fig. 1) are given in Figs. 2(a) and 2(b), respectively, over the full spectral ranges measured. The extinction coefficients for the BP and 6F PFCB polymers, which again are proportional to the intrinsic absorption, are shown in Figs. 3(a) and 3(b), respectively, over the full spectral range. The inset in Fig. 3(b) gives the extinction coefficient, rescaled logarithmically, for the 6F PFCB polymer in the ultraviolet, visible, and near-IR low-absorption region (138 nm to 3 ␮m). As can be seen from the data in Figs. 2 and 3, the optical properties of PFCB provide some interesting possibilities for numerous photonic applications. In the visible and near-infrared portion of the spectrum, the PFCB polymers exhibit ‘‘normal’’ dispersion. In this regime

Fig. 2. Refractive index as a function of wavelength for (a) BP and (b) 6F PFCB polymers.

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Fig. 3. Extinction coefficient as a function of wavelength for (a) BP and (b) 6F PFCB polymers. Inset to (b) shows magnified view of 6F extinction coefficient in the low-loss ultraviolet, visible, and near-IR wavelengths.

away from resonances, the spectral dependence of the refractive index is often given in its Sellmeier form: n共 ␭ 兲 ⫺ 1 ⫽ 2

兺␭ i

A i ␭ i2 2

⫺ ␭ i2

.

(1)

For the PFCB polymers treated here the Sellmeier constants, A i and ␭ i , are given in Table 1. Figure 2(b) further marks the region of anomalous dispersion in the 6F PFCB where there exists a fairly strong n ⬍ 1 range centered approximately at 9.3 ␮m. Although the exceedingly high loss that would accompany this n ⬍ 1 behavior, per the Kramers–Kro¨nig relations, would negate the use of PFCB for light transmission in the more common sense, it does indicate promise for their use in hollow-waveguide technologies, including applications in biomedical and infrared power delivery.17,18 In the case of n ⬍ 1 hollow waveguides based on the anomalous dispersion of alumina (Al2 O3 ), the extinction coefficient is 0.05 at the commercially interesting wavelength of 10.6 ␮m, whereas for 6F PFCB, it is ⬃0.62 at 9.32 ␮m, where the refractive index is 0.74. In addition to the lower refractive index, which implies lower waveguide and bend losses, PFCB is likely more flexible19 and more easily fabricated11 than are alumina films or hollow glass fibers.20,18 The data of Fig. 2(b) also show that the PFCB materials, operating within the anomalous dispersion region, can exhibit refractive indices in excess of 2.0 and, in

the case of the 6F, can approach 2.4 values (at approximately 9.78 ␮m). It should be noted that, in the case of pure 6F PFCB, the n ⬍ 1 region does not coincide with a particular wavelength of commercial interest such as 10.6 ␮m, where CO2 lasers for defense and laser welding and machining applications lie. However, although not directly substantiated here, the copolymerization range of the PFCB family of polymers that enables the broad tailorability in refractive indices should also provide some resultant control over the spectral location of features such as n ⬍ 1 anomalous dispersion wavelengths. PFCB materials, as noted in greater detail below, are amenable to direct transfer as well as injection molding,9 and so may be candidate materials for mid-infrared air/ polymer photonic crystal structures that possess fairly large contrast ratios and are lightweight and flexible. Conceivably, indices may be further increased by synthesizing hybrids with TiO2 or semiconducting nanoparticles. Figure 3(a) corroborates the common suggestions in the present literature10,11 that PFCB polymers are quite low loss in the visible and possess extended transparency out past the terrestrial telecommunication wavelengths of 1300 and 1550 nm. Although higher-harmonic absorptions of the C—F and aromatic and aliphatic C—H bonds are too weak to be measured using the spectroscopic ellipsometry of thin films, their diminution in intensity with increasing harmonic implies that PFCB polymers would possess sufficiently low loss to be of commercial interest despite their nonfully perfluorinated nature. Although more difficult to confirm, whereas a fully perfluorinated system is intrinsically preferred from the optical performance perspective, such materials tend to suffer from anisotropy, stress birefringence, poor processability, and lower thermal and mechanical properties than do many hydrocarbon-based polymers. It is suggested that some hydrocarbon nature to a mainly fluorocarbon material promotes sufficient robustness for greater applicability, while not, necessarily, reducing the optical properties to a point that removes them from commercial marketability. Both Figs. 3(a) and 3(b) show that PFCB polymers possess low extinction coefficients in the 3–5-␮m atmospheric transmission window as well as in the mid infrared for wavelengths between 12 and 33 ␮m (limit of measurement), though the biphenyl derivative form, BP, does possess some additional extinctions centered at approximately 17 and 20 ␮m. The BP and, to a lesser extent, the 6F absorptions at 6.2 ␮m, correspond to the known vibrations of the phenyl ring (1605 cm⫺1).21 The longer-wavelength, lower-energy vibrational absorptions are due to breathing modes of the PFCB ring (960 cm⫺1) and disubstituted phenyl wagging and bending modes (680–900 cm⫺1). PFCB polymers might be useful for selective wavelengths in the 6–12-␮m range, provided sample thickness were kept small, particularly if the operating wavelength were coincident with one of the several strong molecular resonance absorptions (or those of combination bands) in this range. Given the known resistance of PFCB polymers to atomic oxygen and ozone, applications exemplifying this potential include space durable coatings and structures for low-Earth-orbit satellites.22

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Figure 3(b) (inset), to the best of the authors’ knowledge, represents the first evaluation of the ultraviolet optical properties of these fluoropolymers. As is observed, PFCB polymers, particularly the 6F, exhibit reasonably low extinction coefficients below approximately 150 nm. However, it is expected that the scattering component will be quite large in this region,23 especially for samples processed to higher molecular weights. As is computed in Ref. 23, the loss in PFCB polymers due to Rayleigh scattering is intermediate to that for Teflon and for pure SiO2 glass indicating that, although nontrivial, the scattering may be acceptable for some applications. Still, given prior successes in micromold submicrometer features directly into PFCB polymers (for linear gratings) without the need for intermediate steps usually associated with soft lithographic processes,9 this result suggests possible utility of the fluoropolymers for deep-UV gratings and related value-added microstructured reflective optical elements. B. Dispersion Curves and Sellmeier Coefficients Based on the Fig. 2 data, the Sellmeier constants for these materials are given in Table 1 over the range of normal dispersion. Figure 4(a) shows graphically the resultant dispersion curves for the BP, 6F, and SiO2 glass containing 4 wt.% GeO2 . 24 This germanosilicate glass is considered, since it represents an approximate composition for the core of a standard telecommunications-grade optical fiber. Accordingly, it is the material against which comparisons are to be made. As is observed, PFCB polymers (at least the 6F form) possess a lower degree of dispersion than does the inorganic SiO2 glass. Figure 4(a) yields two important observations. First, the dispersion of the BP and the 6F are spectrally very similar and differ mainly in magnitude of the index (i.e., the slopes are similar, but the instantaneous index at any wavelength is offset from one another by ⬃0.1 index unit). Given the complete copolymerization between these PFCB forms, this equivalent dispersion suggests that copolymers should also possess a similar dispersion and simply have an intermediate index as determined by the appropriate rule of mixing.11 Second, it is observed that the PFCB 6F, certainly a copolymer with a small BP content, has a reasonably good index match to silica optical fibers. This is an important consideration for limiting Fresnel reflections, without the need for antireflection measures, which lead to higher insertion losses in optical components. For completeness, Fig. 4(b) presents the material dispersion for the BP and 6F PFCB as well as for the aforeTable 1. Sellmeier Coefficients for BP and 6F PFCB Polymers Term (i)

Ai

␭i

Spectral Range (␮m)

BP

1 2

1.352 0.15579

0.16346 7.8362

1.45 ⭐ ␭ ⭐ 3.5

6F

1 2 3

1.0177 0.052081 0.11618

0.11491 0.2411 7.2807

0.335 ⭐ ␭ ⭐ 3.85

Material

Fig. 4. (a) Dispersion curves, with selected measured data points, for the BP and 6F PFCB polymers and a germania-doped SiO2 glass (4 wt.% GeO2 and 96 wt.% SiO2 , computed using known Sellmeier coefficients for SiO2 and GeO2 ); (b) material dispersion as a function of wavelength for BP and 6F PFCB polymers and a germania-doped SiO2 glass. For comparison, stars mark dispersion exhibited by commercially available dispersionshifted fiber (DSF) and nonzero-dispersion-shifted fiber (NZDSF).

mentioned germania-doped SiO2 . Chromatic dispersion, originating from a nonconstant refractive index as a function of wavelength, which is the case in all materials, serves as a principal source of bandwidth limitation in optical information systems. This effect can be mitigated by finding the zero in a material’s dispersion, M(␭), using M共 ␭ 兲 ⫽

冏冏

␭ d2 n c d␭ 2

,

(2)

where c is the speed of light and the argument of the absolute value is the second derivative of the refractive index with respect to wavelength. Applying Eq. (2) to the Sellmeier equations generated from the Table 1 data (and Ref. 21) yields the Fig. 4(b) dispersion curves. For the BP and 6F PFCB, the zero dispersion points are approximately 2.32 and 1.99 ␮m, respectively, whereas for silica, this value is the well known value 1.3 ␮m. Figure 4(b) also shows the dispersion values, at 1.55 ␮m, for dispersion-shifted fiber (DSF) and nonzero-dispersionshifted fiber (NZ-DSF). These specialty fibers are experiencing increased commercial installation and usage since they permit the fiber dispersion to be moved to

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coincide with the amplification band of erbium-doped amplifiers, thus permitting loss and bandwidth optimization at the same 1550-nm wavelength. C. Aside on Fitting Dispersion Relations In order to provide both an ‘‘analytical’’ expression for a material’s optical dispersion function as well as to minimize interpolative and extrapolative errors, the values of refractive index measured at discrete wavelengths are typically curve fit. The two most common fitting functions for such data are the Sellmeier form (as done in this paper) and a Cauchy form. It is the purpose of this subsection to use the data given above to show the potential problems that can arise by representing the optical properties using a Cauchy fit. The Sellmeier form describing the refractive index of a material as a function of wavelength was given as Eq. (1). In contrast to this, the Cauchy form is

n共 ␭ 兲 ⫽ C0 ⫹ C1

冉冊冉冊 1

␭

2

⫹ C2

1

␭4

.

(3)

As with any mathematical fit to discrete data, both are valid over a certain spectral range. With respect to optical dispersion, this range typically is the region between refractive-index resonances where the dispersion is ‘‘normal.’’ Figure 5(a) displays the Sellmeier and Cauchy fits to the data of Fig. 2(b) (i.e., for the BP form of PFCB). Both fits provide reasonable equivalency in calculated refractive index over the commonly measured spectral range in the visible from approximately 500 to 650 nm. As can be seen, there is an increasing divergence between

the two fits as the wavelength goes beyond the measured, though still normally dispersive, range. A problem truly is realized when one uses these analyticized expressions to compute related properties such as the zero-dispersion wavelength, as is done in this paper. This particular property is noted since it is a performance-critical one and further exemplifies the concerns motivating this subsection. Since the Cauchy function is a monotonically decreasing function with wavelength, it can only asymptotically approach a zero in its second derivative of index with wavelength, as is the criterion for zero group-velocity dispersion [see Eq. (3) and related text]. This problem arises because the Cauchy function, although faithfully reproducing the refractive index over a small spectral range, has no relationship to the true physical refractive-index dispersion function (i.e., it is a nonphysical representation but one that is fairly straightforward to compute). The Sellmeier form is derived from the microscopic refractive-index function and therefore still contains the appropriate physics; i.e., the Sellmeier A i coefficients determine the magnitude of the refractive index at the Sellmeier ␭ i coefficient resonance points. This comparison is made in Fig. 5(b). It is of further importance to note that, as with all curve fits, the resultant equation (using the computed coefficients) becomes progressively more accurate with both increasing number of data points and, especially in the case of optical dispersion, the broader the spectral range measured becomes. In order to calculate the magnitude and resonant wavelength coefficients, data must be taken broadly covering all ranges. Although a few measurements can yield a Sellmeier or Cauchy fit to the data, interpolations and extrapolations of the data, or functions derived from the data, can be in profound error.

4. CONCLUSIONS The refractive index and extinction coefficient for the biphenyl derivative (BP) and hexafluoroisopropylidene (6F) forms of PFCB polymers has been measured using spectroscopic ellipsometry over the wavelength range from approximately 0.13 ␮m to 33 ␮m. These materials are known to possess intrinsic solution and melt processability, thermal stability, low birefringence, and tailorable optical, thermal, and mechanical properties through copolymerization. Coupled synergistically with these physical and chemical attributes, the data given here provide a more complete characterization of the optical properties and further marks PFCB fluoropolymers as materials to receive special attention for a myriad of applications ranging from deep-UV reflective optics, to visible and near-IR photonic devices, to mid-IR photonic crystal materials, to premise-scale telecommunication components.

ACKNOWLEDGMENTS

Fig. 5. (a) Dispersion curves for BP PFCB polymer using Sellmeier and Cauchy curve fits to the data of Fig. 2; (b) curvature of refractive index as a function of wavelength as computed from the dispersion fits of (a).

The authors wish to acknowledge the expertise of Tom Tiwald of J. A. Woollam Company, Inc., and of Shengrong Chen of Clemson University for measurements and sample preparation. The authors also acknowledge the financial support of the 3M Corporation (Nontenured faculty grants), the Defense Advanced Research Project

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Agency through grant N66001-01-1-8938 (Laboratory for Advanced Photonic Composites), and the U.S. Department of Commerce through grant 99-27-07400 (National Textile Center). The authors also wish to thank Bob Norwood (Photon-X, Inc., Malvern, Pa.) Earl Wagener (Tetramer Technologies, LLC, Clemson, S.C.), and Matt Dejneka (Corning Incorporated, Corning, N.Y.) for their insights.

Shah, and S. Foulger, ‘‘Perfluorocyclobutyl copolymers for microphotonics,’’ Adv. Mater. 14, 1585–1589 (2002). R. Traiphol, H. Shah, D. Smith, and D. Perahia, ‘‘Bulk and interfacial studies of a new and versatile semifluorinated lyotropic liquid crystalline polymer,’’ Macromolecules 34, 3954–3961 (2001). J. A. Woollam Co., Inc., 645 M St., Suite 102, Lincoln, Neb. 68508; (http://www.jawoollam.com). C. M. Herzinger, B. Johs, W. A. McGahan, J. A. Woollam, and W. Paulson, ‘‘Ellipsometric determination of optical constants for silicon and thermally grown silicon dioxide via multi-sample, multi-wavelength, multi-angle investigation,’’ J. Appl. Phys. 83, 3323–3336 (1998). T. Tiwald, J. A. Woollam Company, 645 M St., Suite 102, Lincoln, Neb. 68508 (personal communication, 2003). G. H. Sigel, ‘‘Optical absorption in glasses,’’ Glass I: Interaction with Electromagnetic Radiation, Vol. 13 of Treatise on Materials Science and Engineering (Academic, New York, 1978), pp. 5–89. R. Nubling and J. Harrington, ‘‘Hollow waveguide delivery systems for high-power, industrial CO2 lasers,’’ Appl. Opt. 34, 372–380 (1996). J. Harrington, ‘‘A review of IR transmitting, hollow waveguides,’’ Fiber Integr. Opt. 19, 211–228 (2000). D. Smith, D. Babb, H. Shah, A. Hoeglund, R. Traiphol, D. Perahia, H. Boone, C. Langhoff, and M. Radler, ‘‘Perfluorocyclobutane (PFCB) polyaryl ethers: versatile coatings materials,’’ J. Fluorine Chem. 104, 109–117 (2000). R. Nubling and J. Harrington, ‘‘Optical properties of singlecrystal sapphire fibers,’’ Appl. Opt. 36, 5934–5940 (1997). C. Cheatham, S.-N. Lee, J. Laane, D. Babb, and D. Smith, ‘‘Kinetics of the trifluorovinyl ether cyclopolymerization via Raman spectroscopy,’’ Polym. Int. 46, 320–324 (1998). J. Jin, S. Kumar, S. Foulger, D. Smith, H. Liu, B. Mojazza, P. Go, and A. Shep, Polym. Prepr. Am. Chem. Soc. Div. Polym. Chem. 43, 609–610 (2002). J. Ballato, D. Smith, S. Foulger, and E. Wagener, eds., Design and Fabrication of Planar Optical Waveguide Devices and Materials, Proc. SPIE 4805, 1–8 (2003). W. Tropf, M. Thomas, and T. Harris, ‘‘Properties of crystals and glasses,’’ in Handbook of Optics, M. Bass, ed. (McGrawHill, New York, 1995), Chap. 33, pp. 33.3–33.101. For the GeO2 -doped SiO2 glass, the dispersion curve was computed using Eq. (2), where the n(␭) function, whose second derivative is taken with respect to ␭, was a combination of the SiO2 and GeO2 refractive indices following the rule of mixing. In other words, n(␭) ⫽ 0.96 n silica(␭) ⫹ 0.04 n germania(␭), where the Sellmeier forms of n silica and n germania were used (per the above reference).

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should

be

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addressed: 15. 16.

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17. 18. 19.

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