High refractive index polyimide–nanocrystalline-titania hybrid optical
materials†
Hung-Wen Su
acand Wen-Chang Chen*
abReceived 5th November 2007, Accepted 4th January 2008
First published as an Advance Article on the web 30th January 2008 DOI: 10.1039/b717069f
In this study, a new synthetic route was developed to prepare polyimide–nanocrystalline-titania hybrid materials with a relatively high titania content (up to 90 wt%). A soluble polyimide with carboxylic acid end groups (6FDA–6FpDA–COOH) was first synthesized from 4,40-(hexafluoroisopropylidene)
diphthalic anhydride (6FDA), 4,40-(hexafluoroisopropylidene) dianiline (6FpDA), and
4-aminobenzoic acid (4ABA). Such end groups could undergo an esterification reaction with titanium butoxide and provide organic–inorganic bonding. A homogeneous hybrid solution was obtained through the mole ratio of titanium butoxide/carboxylic acid, water/acid content, and a mixed solvent system. HRTEM and XRD results indicated the formation of nanocrystalline-titania domains of around 3–4 nm in the hybrid films. The spin-coated hybrid films had relatively good surface planarity, high thermal stability, tunable refractive index (1.571 < n < 1.993), and optical transparency in the visible range. The achieved refractive index of 1.943 is the highest among the polymer–titania based hybrid materials as far as we know. A three-layer anti-reflection coating based on the prepared hybrid films was designed and possessed a reflectance of less than 0.5% in the visible range. Our study demonstrates a new route for preparing high refractive index polyimide–nanocrystalline-titania hybrid materials for potential optical applications.
Introduction
Organic–inorganic hybrid materials have been recognized as a new class of advanced materials because of their versatile synthetic approaches and molecular tailing properties.1–5 We
are particularly interested in the hybrid materials for optical applications, such as high refractive index materials, optical waveguides, anti-reflective films, etc.4 For such applications,
the inorganic domains must be well controlled, less than 40 nm, to avoid scattering loss and retain the optical transparency.1e
Polymer–titania hybrid materials have been extensively studied as high refractive index materials, including poly(methyl methacrylate) (PMMA),6–8 polyimide,9 polysilsesquioxanes,10
and others.11For controlling the titania domain size, a
combina-tion of in situ sol–gel processing with polymer molecular weight control, a coupling or chelating agent is commonly employed to prepare hybrid materials.6,7,9 Our laboratory has successfully
prepared trialkoxysilane-capped poly(methyl methacrylate) (PMMA)–titania hybrid optical films with their refractive index in the range 1.505–1.876.7a,bLater, such materials were treated by
a hydrothermal process to produce nanocrystalline-titania hybrids with an ultra-fast nonlinear optical response.6Although
the PMMA–titania hybrid optical materials were successfully prepared, the poor thermal stability of the PMMA moiety limited their device applications, which might be resolved using thermally stable polyimide as the organic moiety.
Several polyimide–titania hybrid materials have been explored in the literature.9The homogeneous hybrid materials prepared
by chelating poly(amic acid) (PAA) and titanium alkoxide monomer could control the titania size to around 1.5 nm but only up to 12 wt% titania.9a The highly electronegative OR
groups of titanium alkoxide are very susceptible to nucleophilic attack by PAA and result in uncontrolled gelation or a relatively large titania domain (100 nm–1 mm) in the hybrid materials. By using a chelating agent (such as acetylacetone) or a coupling agent (such as 3-aminopropyl trimethoxysilane), the titania content in the homogeneous films was further enhanced to be around 40–59 wt%.9However, additional coupling or chelating
agent remaining in the hybrid materials might affect important thermal/mechanical/optical properties. Also, the refractive indices of such hybrid materials are limited to be only around 1.80, which is only slightly higher than recently developed high refractive index organic polymers.12Hence, the development of
polyimide–titania hybrid optical materials with a higher titania content than 60 wt% is necessary.
In this study, a new synthetic route was developed to prepare polyimide–nanocrystalline-titania hybrid materials with a relatively high titania content (up to 90 wt%), which led to a refractive index of around 1.943. Instead of using poly(amic acid) to prepare the titania hybrid materials, a soluble polyimide with carboxylic acid end groups (6FDA–6FpDA–COOH) was synthesized from 4,40-(hexafluoroisopropylidene)diphthalic
anhydride (6FDA), 4,40-(hexafluoroisopropylidene)dianiline
aInstitute of Polymer Science and Engineering, National Taiwan
University, Taipei, Taiwan, 106. E-mail: [email protected]; Fax: +886-2-23623040; Tel: +886-2-23628398
bDepartment of Chemical Engineering, National Taiwan University,
Taipei, Taiwan, 106
cAGI Corporation, Taipei, Taiwan, 114
† Electronic supplementary information (ESI) available: DSC curves of the TP-series films and variation of the extinction coefficients of the polyimide–titania hybrid films. See DOI: 10.1039/b717069f
(6FpDA), and 4-aminobenzoic acid (4ABA), as shown in Scheme 1. The carboxylic acid end groups could have an esterifi-cation reaction with titanium butoxide [Ti(OBu)4] and provide organic–inorganic bonding. Thus, no additional coupling agents or chelating ligands were used in the preparation of the hybrid materials. By using a molar ratio where Ti/COOH is greater than 1, a stable sol with an isolated monodentate structure of carboxylate ligands with titanium tetraalkoxide was formed in the case of methacrylic acid.8In the present study, a mole ratio
of Ti/COOH higher than 3 was used to obtain the stable sol. In the following, an appropriate amount of water and acid were added drop-wise for the hydrolysis–condensation reaction of Ti(OBu)4 in the mixed solvent of n-butyl alcohol and N,N0 -dimethylacetamide to proceed. Highly homogeneous hybrid films with different titania contents were thus obtained using spin-coating and thermal curing. AFM, SEM, HRTEM, and XRD were used to characterize the morphologies of the prepared hybrid materials. The thermal properties, optical absorption, and refrac-tive index dispersion of the prepared hybrid films were studied.
Experimental
Materials
4,40-(Hexafluoroisopropylidene)diphthalic anhydride (6FDA, 99%) and 4,40-(hexafluoroisopropylidene)dianiline (6FpDA, 99%) were obtained from Chriskev (Lenexa, USA). 4-Aminoben-zoic acid (4ABA, 99%), aniline (99.5%), and titanium n-butoxide [Ti(OBu)4, 99%] were obtained from ACROS (Geel, Belgium).
All monomers were purchased and used without purification. 1-Methyl-2-pyrrolidinone (NMP, 99.9 %), 1,3-dichlorobenzene (DCB, 99.9 %), N,N0-dimethylacetamide (DMAc, 99.5 %), and n-butyl alcohol (BuOH, 99.9 %) were obtained from TEDIA (Fairfield, USA). The acid catalyst of titanium n-butoxide, 37.5 wt% HCl, was used as received from Scharlau Chemie (Barcelona, Spain). Synthesis of the PMSSQ precursor and its cured film was according to our previous report.13
Synthesis of organo-soluble polyimide with carboxylic acid end groups (6FDA–6FpDA–COOH)
A solution-imidization technique was employed to synthesize organo-soluble polyimide (6FDA–6FpDA–COOH) with carboxylic acid end groups, as show in Scheme 1. The molecular weight and end group functionality were controlled by the reactant stoichiometry. Firstly, 3.34 g (0.01 mol) of 4,40
-(hexa-fluoroisopropylidene)dianiline (6FpDA) was added into a 150 ml three-necked round bottom flask and 50 ml of NMP was used to dissolve the reactants. 8.88 g (0.02 mole) of 4,40
-(hexafluoro-isopropylidene)diphthalic anhydride (6FDA) was then slowly added into the above solution with vigorous stirring under nitrogen purging. The mixture solution was allowed to react for 8 h at room temperature. Secondly, 2.88 g (0.021 mole) of 4-aminobenzoic acid (4ABA) and 15 ml of 1,3-dichlorobenzene were added into the above solution. The 20 wt% of polyamic acid (PAA) solution was thus formed after constantly stirring the reactants for 16 h at room temperature. Then, the PAA
solution was thermally imidized in a 180C silicon oil bath for
another 12 h and cooled to room temperature. The homo-geneous 6FDA–6FpDA–COOH solution was precipitated with 500 ml of methanol and re-dissolved in 30 ml of THF twice. A white–gray precipitate was recovered and subsequently dried in a vacuum oven at 150 C for 24 h to obtain 4.62 g of 6FDA–
6FpDA–COOH (yield: 28.2 %). The acid value of 6FDA– 6FpDA–COOH was found to be 40 mg KOH g1using titration.
The average molecular weight estimated by the acid value was around 3000. The weight-average molecular weight estimated by GPC was 3670 with a polydispersity index of 1.20. The 6FDA–6FpDA–COOH film was prepared using the following procedure: 0.5 g of 6FDA–6FpDA–COOH was dissolved in 5 ml of DMAc while stirring. The solution was filtered with a 0.2 mm PTFE filter prior to use and spin-coated on to a silicon wafer at 1000 rpm for 20 s. Then, the film was then baked at 60
C on a hot plate for 10 min and at 150C for another 30 min to
evaporate the solvent. In order to be compared with the polyimide–titania hybrid films, the cured film of 6FDA– 6FpDA–COOH is named TP0. FTIR (cm1): 3434 (COOH),
1788 (CO), 1726 (CO), 1610 (C6H5), 1517 (C6H5), 1435 (C6H5), 1370 (CN).
Synthesis of organo-soluble polyimide without carboxylic acid end groups (6FDA–6FpDA–H)
The same procedure used to prepare 6FDA–6FpDA–COOH was followed to prepare 6FDA–6FpDA–H, except that 1.96 g (0.021 mole) of aniline was used in place of 2.88 g (0.021 mole) 4ABA. The yield of 6FDA–6FpDA–H was 24 % and the acid value was about 0 mg KOH g1 using titration. The
weight-average molecular weight estimated by GPC was 3440 with a polydispersity index of 1.26. FTIR (cm1): 1787 (CO), 1731
(CO), 1604 (C6H5), 1518 (C6H5), 1436 (C6H5), 1373 (CN). Synthesis of polyimide–titania precursors and their hybrid films The reaction scheme for polyimide–titania precursors is shown in Scheme 2. The compositions for preparing the hybrid thin films are listed in Table 1, which are named as TPX. TPX represents the theoretical amount (X wt%) of titania in the hybrid film. Using TP50 as an example, firstly, 1.06 g (3.1 103mole) of
Ti(OBu)4 and 2.5 ml of butanol were added to 25 ml round bottom flask. Butanol was used to avoid alcohol interchange reaction with titanium n-butoxide. 0.25 g (1.8 104 mole
COOH) of 6FDA–6FpDA–COOH dissolved in 2.5 ml of
Scheme 2 Synthesis of the polyimide–titania precursor and hybrid thin films, TP30–TP90: (i) esterification reaction, (ii) hydrolysis and condensation reaction under acid catalyzed conditions, (iii) spin-coating and thermal curing
Table 1 Reaction composition and properties of the studied films, TP0–TP100
Sample
Reactant composition Hybrid film
6FDA-6FpDA-COOH (wt%) Ti(OBu)4 (wt%) TiO2content a (wt%) TiO2content b (wt%) hc/nm R qd/nm lmax/nm ledge/nm ne, 633 nm TP0 100 0 0 0 972 6.45 280 346 1.571 TP30 35.4 64.6 30 21.0 582 5.12 286 358 1.625 TP50 19.0 81.0 50 46.8 345 1.60 287 361 1.752 TP70 9.2 90.8 70 69.1 318 0.36 292 364 1.834 TP90 2.5 97.5 90 88.6 201 0.21 296 363 1.943 TP100 0 100 100 100 130 0.30 297 365 1.993
aTheoretical titania content in the hybrid films.bExperimental titania content estimated from TGA curves.ch: Film thicknessdR
q: the root mean square roughness determined from AFM.en: Refractive index
DMAc were added drop-wise to the above solution with a syringe and the mixture was then stirred at room temperature for 30 min. In the following, 0.0625 g (37 wt%) of HCl aqueous solution, 0.073 g of H2O, and 1.25 ml of butanol were well-mixed and added very slowly to the above mixture and stirred at room temperature for 30 min to obtain the precursor solution of TP50. To prepare the TP50 hybrid thin film, the precursor solu-tion was filtered through a 0.2 mm PTFE filter and spin-coated on to a silicon wafer at 2000 rpm for 20 s. Then, the films were soft-baked at 60C on a hot plate for 10 min, at 150C for 30
min, and then at 350C in a furnace for 90 min under nitrogen.
In order to study the effect of the carboxylic acid end groups on the morphology of the hybrid materials, a comparable film (TA50) without the acid end group was prepared using a similar procedure to that for TP50 except that 0.25 g of 6FDA–6FpDA– H was used to replace the 0.25 g of 6FDA–6FpDA–COOH.
Preparation of titania films (TP100)
The titania parent film (TP100) was prepared by the following procedure: 6.8 g (0.02 moles) of Ti(OBu)4and 15 ml of butanol were added to a 50 ml round bottom flask. 0.25 g (37 wt%) of HCl aqueous solution, 0.56 g of H2O, and 5 ml of butanol were mixed very well to get a homogeneous solution. Then, the solution was added very slowly into the above Ti(OBu)4solution and stirred at room temperature for 1 h. To prepare the TP100 hybrid thin film, the precursor solution was filtered with a 0.2 mm PTFE filter prior to use and spin-coated on to a silicon wafer at 2000 rpm for 20 s. Then, the substrates coated with the films were soft-baked at 60C on a hot plate for 10 min, cured at
150C for 30 min, and then at 350C in a furnace for 90 min
under nitrogen.
Characterization
FTIR spectra of the prepared films on the doubly polished silicon wafers were obtained with a Perkin Elmer PARAGON 1000. Gel permeation chromatography (GPC) analysis was performed on a Waters GPC system consisting of Waters 2414 RI detector, Shodex columns (KF-802, 803, 805), Waters 717 plus auto-sampler, and Waters 515 HPLC pump. The system was calibrated using polystyrene standards. THF was used as the eluent, at a flow rate of 1.0 ml min1.
TGA and DSC thermal analyses were conducted on a Perkin Elmer pyris 1 TGA and a TA Q100 with a refrigerated cooling system, respectively. Both measurements were performed under continuous nitrogen flow, at a heating rate 10C min1. An atomic
force microscope (AFM, Nanoscope Inc., Model DI 5000) and field emission scanning electron microscopy (FE-SEM, JEOL, JSM-6700F) were used to examine the surface morphology of the coated films. The microstructure of the prepared films was examined using a high-resolution transmission electron micro-scope (HRTEM, JEOL, JEM-2100F). X-Ray diffraction was performed on a MicroMax 002 X-ray scattering instrument (XRD, Osmic, PSAXS-USH-WAXS-002) using Cu Ka radiation (1.5406 A˚ ) with comparable intensity to a focused beam from a rotating anode generator at room temperature.
UV-Vis-NIR optical absorption spectra of the prepared films on quartz were obtained using a Perkin Elmer Lambda 20 at
room temperature. An ellipsometer (SOPRA, GES-5E) was used to measure the refractive index (n) and the extinction coefficient (k) of the prepared films in the wavelength range of 300–800 nm. The thickness (h) of the prepared film was also determined simultaneously. Reflectance measurements were performed using a multi channel photo detector (Photal, MCPD-3000) from 380 nm to 780 nm at a 10angle of incidence. To eliminate back reflection from the glass, the other side of glass was covered with black tape.
Results and discussion
Fig. 1 shows the FTIR spectra of 6FDA–6FpDA–COOH (TP0), TP50, and TP100 films on double polished silicon wafers. In the spectrum of 6FDA–6FpDA–COOH, the characteristic imide groups are observed as below: 1788 cm1 (C]O asym., str.),
1726 cm1(C]O sym., str.), and 1370 cm1(C–N str.),
respec-tively. Besides, the characteristic peak of polyamic acid at 1690 cm1disappears, which suggests successful solution-imidization.
Also, the characteristic peak of the carboxylic acid end group is shown in the region of 3100–3600 cm1. The acid value of TP0
determined by titration was 40 mg KOH g1. The average
mole-cular weight estimated by the acid value was around 3000, which was in fair agreement with that estimated by GPC, 3670. These results reveal that the organo-soluble polyimide, 6FDA– 6FpDA–COOH, with carboxylic acid end groups is successfully synthesized. The low molecular weight of TP0 was designed to ensure good miscibility between the polyimide and titania for preparing homogeneous hybrid films. Higher molecular weight polyimides could be used to prepare the polyimide–titania hybrid materials, similar to our previous report of polyimide–silica hybrid films.4b
In the FTIR spectrum of the polyimide–titania thin film, TP50, the large reduction of the absorption peak at 3200–3600 cm1suggests an esterification reaction between carboxylic acid
Fig. 1 FTIR spectra of the studied films on double polished silicon wafers: (a) 6FDA–6FpDA–COOH (TP0), (b) TP50, and (c) TP100.
and titanium butoxide occurred. In addition, the inorganic Ti–O–Ti band is also observed at 600–850 cm1. The coordination
characteristic peak of the carboxylate groups with titanium could not be clearly observed in the 1630–1340 cm1 region
due to overlap with the absorption of the phenylene and imide groups. The FTIR spectrum of TP100 is similar to that in the literature6dor our previous report.7b
Fig. 2 shows the TGA curves of the studied materials at a heat-ing rate of 10C min1under nitrogen flow. It is clearly seen that
the all studied materials exhibit good thermal stability with thermal decomposition temperatures greater than 480 C. The
char yields of TP0 and TP100 at 800C are 51 and 99%, which
contain 0 and 100% titania. Based on the char yields of these two materials, the titania contents in the hybrid materials are estimated as 21.0–88.6 wt% by assuming a linear relationship. They are in fair agreement with the theoretical content of 30–90 wt%, as shown in Table 1. This indicates that the titania has been successfully incorporated into the polyimide. The DSC curve of pure polyimide, TP0, shows a glass transition temperature (Tg) of 248 C. However, no Tg is observed for any of the polyimide–titania hybrid materials (TP30–TP90), as shown in the ESI†. It is probably that the titania limits the mobility of the polyimide segment and thus no Tgis observed.
Fig. 3(a) and 3(b) show the height and phase AFM images of TP50 and TP70 thin films. The root mean square surface rough-ness (Rq) of the hybrid films analyzed by AFM is listed in Table 1. As shown in the table, the Rqvalues of the films TP30, TP50, TP70, TP90, and TP100, are 5.12, 1.61, 0.36, 0.21, and 0.31 nm, respectively. The low Rqand smooth images suggest that homogeneous hybrid films are prepared. On the contrary, a relatively rough surface (Rq ¼ 38.6 nm) is observed on the AFM image of TA50, as shown in Fig. 3(c). Note that the hybrid material TA50 was prepared from 6FDA–6FpDA–H (without carboxylic acid end groups) with Ti(OBu)4 for comparison with that of 6FDA–6FpDA–COOH. The aggregated domain of 1 mm shown in Fig. 3(c) is probably due to the titania, without the bonding with the polyimide moiety. Fig. 4(a–c) shows the cross-sectional SEM images of TP50, TP70, and TA50 obtained by tilting the specimen by 45. The images of
TP50 and TP70 show a uniform surface without apparent
microstructure or significant titania aggregates. However, the image of TA50 in Fig. 4(c) shows the severe phase separation with a large aggregated domain similar to that from the AFM image of Fig. 3(c). Both the AFM and SEM images suggest the importance of carboxylic acid end groups of polyimide for bonding with titania and the resultant morphologies of the hybrid materials.
The cross-sectional HRTEM images of the TP50 and TP70 films are shown in Fig. 5. As shown in the figure, titania nano-crystallites with an average size of 3–4 nm are shown in both hybrid materials. Fig. 6 shows the XRD patterns of the powder prepared from the TP0–TP100 films. In the XRD pattern of TP0, a very broad peak is observed in the range 2q¼ 10–20, which
originates from the amorphous characteristic of polyimide.
Fig. 2 TGA curves of the studied materials, TP0–TP100, at a heating rate of 10C min1under nitrogen flow.
Fig. 3 AFM images of the hybrid films coated on silicon wafers: (a) TP50, (b) TP70, and (c) TA50. (a1, b1, c1) and (a2, b2, c2) are height and phase images, respectively.
Fig. 4 SEM images of the hybrid films coated on silicon wafers: (a) TP50, (b) TP70, and (c) TA50.
With increasing titania content, the intensity of a titanina crystalline peak gradually increases in the range 2q ¼ 23–27,
but that of the amorphous polyimide peak decreases. It suggests that the titania clusters are well dispersed in polyimides through the esterification and hydrolysis–condensation reactions. The broad width of the peaks is probably due to X-ray scattering resulting from the small titania nanocrystalline grains. Much more enhanced titania crystallization is obviously shown in TP100, four peaks, 25.538.4, 48.3, and 54.8, corresponding
to the (101), (112), (200), and (211) crystalline planes of the anatase titania phase, which are similar to those reported in the literature.6
Fig. 7 shows UV-Vis-NIR absorption spectra of the studied thin films, TP0–TP100. All the samples show high optical trans-parency in the visible region of 400–700 nm. The absorption band around 280–297 nm in the UV region is contributed from the chromophores of polyimide. By increasing the titania content, the intensity of the absorption band is enhanced and the corresponding band edge (346–365 nm) is red-shifted. Such band shift is usually observed for titania sizes less than 10 nm.14It indicates that highly homogeneous
polyimide–nanocrys-talline-titania hybrid materials are obtained. Fig. 8 shows the refractive index dispersion of the studied films at wavelengths of 300–800 nm while the insert figure shows the variation in
refractive index with titania content. As shown in the figure, the refractive index at 633 nm increases linearly with titania content, 1.571 (TP0), 1.625 (TP30), 1.752 (TP50), 1.834 (TP70), and 1.943 (TP90), respectively. The refractive index of pure titania (TP100) is 1.993 at 633 nm, similar to our previous report.7bThe extinction coefficient of the prepared films shown in
the ESI† also suggests excellent optical transparency in the visible region. The refractive index of the hybrid film, TP90, is larger than for any other reported polymer–titania hybrid films6–11as far as we know. It indicates the successful approach
of using a soluble polyimide with carboxylic end groups for preparing titania hybrid materials. The T90 hybrid optical film could have a crack-free film thicker than T100 since the polyimide moiety could release the thermal stress of titania during thermal curing. Note that the thick T100 films may have a cracking defect and limit its optical applications.
The prepared hybrid films may have potential applications in optical devices, such as anti-reflective coatings. Fig. 9 shows the structure of a three-layer anti-reflective coating on the BK7 substrate and the reflectance spectra. The BK7 optical glass
Fig. 5 HRTEM images of the hybrid films: (a) TP50 and (b) TP70. The circles in the figure indicate the nanocrystalline–titania in the hybrid films.
Fig. 6 XRD patterns of the studied materials, TP0–TP100.
Fig. 7 UV-Vis-NIR absorption spectra of the hybrid films on quartz, TP0–TP100.
Fig. 8 Variation of the refractive index of the hybrid films, TP0–TP100, with wavelength. The insert figure shows the variation of refractive index with titania content.
has a refractive index (n¼ 1.518) higher than air (n ¼ 1.0) and leads to an average reflectance of about 5% in the visible range. The reflectance could be reduced significantly via a three-layer anti-reflection coating consisting of polymethyl silsesquioxane (PMSSQ), TP90, and TP30 as the first, second, and third layers, respectively. In order to reduce reflection through adjusting the phase of light, the optical thickness (physical thickness refractive index) is designed to be 0.25 l0, 0.5 l0, and 0.25 l0 (l0 ¼ 550 nm) for the three-layer structure. Thus, the film thickness and refractive indices of PMSSQ, TP90, and TP30 are 100 nm and 1.379; 140 nm and 1.943; 85 nm and 1.625, respectively. An average reflectance of less than 0.5% in the visible range (425 nm to 675 nm) is obtained, which is signifi-cantly smaller than that of BK7 with 5%. It suggests the potential application of the prepared polyimide–titania hybrid films in optical devices.
Conclusion
High refractive index polyimide–titania hybrid optical thin films were successfully synthesized from a soluble polyimide with carboxylic acid end groups with titanium butoxide by controlling the organic/inorganic mole ratio, water/acid content, and mixed solvent system. The titania content in the hybrid materials could be as high as 90 wt% and thus a relatively high refractive index of 1.943 was achieved. To the best of our knowledge, the refractive index is highest among the polymer–titania hybrid optical materials. The hybrid films also possessed excellent thermal properties, tunable high refractive index and optical transpa-rency in the visible region. Three-layer anti-reflective coating based on the hybrid films possessed reflectance of less than 0.5% in the visible range. It suggested potential optical applica-tions of the prepared polyimide–titania hybrid films.
Acknowledgements
We thank the National Science Council of Taiwan and Ministry of Economic Affairs of Taiwan for the financial support for this work (Grant number: 95-EC-17-A-08-S1-015).
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Fig. 9 Variation of the reflectance with wavelength: (a) BK7 optical glass and (b) the three-layer anti-reflection coating. The insert figure shows the structure of the three-layer anti-reflection coating.
