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Abstract
A novel white compound material with spectral band pass filtering was proposed and demonstrated in the UV region for wavelengths smaller than 310 nm. This compound material can be obtained by dispersing CaF2 in polydimethylsiloxane (PDMS). Refractive index matching (RIM) of the compound material resulted in transmittance of up to 80% at RIM wavelength. In no-RIM wavelength region, refractive index difference about 0.005 could result in transmittance of down to 30% due to intense Rayleigh isotropic scattering. A good reproducibility of the transparent wavelength can be obtained with the specific CaF2 particle and PDMS matrix in this study. Meanwhile, simple calculation based on Rayleigh-Gans-Debye approximation [J. Am. Ceram. Soc. 86(3), 480 (2003)] in the soft diffusion model can explain the CaF2: PDMS compound film transmittance spectrum in the UV region, and the bandwidth narrowing condition.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
In recent biological research, ultraviolet (UV) light-emitting diodes (LEDs) in the wavelength range of 250-300 nm were established as compact, low-heating light sources for the evaluation of DNA/protein samples based on their absorption peaks [1–3]. As most organic materials such as polymers are not transparent, SiO2 and some types of fluoropolymers must be used to fabricate sample containers and liquid tubes [4]. Similarly, special materials such as CaF2 or MgF2 with interference structures are predominantly used to fabricate spectroscopic components for UV applications, such as wavelength filters of the pass-through type [5]. Optical filters are the principal and fundamental components in spectroscopic applications such as absorptiometers or fluorescence microscopes [6]. Conventionally, an optical component for filtering light by wavelength requires an optical-grade surface that is prepared via polishing, etching, or imprinting. In addition, versatile and simpler integration of the filtering structures for the UV region have been reported in studies on silver and silica layers [7] and nano-imprint lithography [8]. However, the optical surface also needs to be an interference interface. Therefore, owing to its high transmittance in the UV and visible regions, printability, and ability to provide an optical surface without polishing, polydimethylsiloxane (PDMS) is used as the potting or embedding material to fabricate some optical components, such as the optical lens [9–12] for microfluidic channels and smartphone microscopes, waveguide systems using soft-lithography techniques [13,14], and optical filters using dye-doped PDMS [15]. In a previous study, we designed and fabricated a compact optical system [16] with a single matrix and soft mold using the highly transparent PDMS. As its optical path is filled with solid PDMS, each optical component can be easily embedded and integrated with very little stray light. The present study is aimed at demonstrating and investigating a novel scheme of UV-band-pass function in a compound material for potting, coating, and embedding. The material does not require polishing, lithography, or layer coating. The scheme of the spectroscopic band-pass compound is based on optical scattering due to trace differences in the refractive index and refractive index matching (RIM) that can make a colloid transparent [17], and is useful for reducing the scattered light from the measurement [18]. Potting or embedding UV band-pass filtering materials are the key step toward the development of compact DNA/protein measurement devices for point-of-care diagnostics.
2. Principle and sample preparation
The wavelength-dependent RIM in this study is based on the trace difference in the slopes of normal dispersion exhibited by organic and inorganic materials (Fig. 1). Inorganic UV-transparent materials such as MgF2, CaF2, and SiO2 exhibit slightly higher refractive indices compared with PDMS, owing to their higher density, and smaller dispersion in the range 250-300 nm due to their shorter cut-off wavelength. On the other hand, organic materials such as PDMS exhibit a lower refractive index due to their lower density, and a larger dispersion due to their longer cut off wavelength. From Ref [19–21], the refractive indices of PDMS (no information about the detail of product, tagged PDMSR) may match that of SiO2 [20] at the wavelength λcp1 is ~315 nm, and that of CaF2 [21] at wavelength λcp2 is ~355 nm. It was expected that, incident light with wavelength at the cross point would pass through the compound medium of an organic matrix and inorganic particle, and light with other wavelengths would get scattered.
Fig. 1 Refractive index dispersion of PDMSR (Ref [19].), SiO2 (Ref [20].), and CaF2 (Ref [21].) from literature; PDMS with matrix- A, B, C (A: SIM-360, B: KE-103 from Shinetsu Chemical, C: SYLGARD 184 from Dow Corning) measured by spectroscopic ellipsometer (SEMILAB, SE-2000). λcp1 is the cross-point wavelength of SiO2 and PDMSR; λcp2 is the cross-point wavelength of CaF2 and PDMS.
Figure 1 also shows preliminary measured refractive indices of several products of PDMS (A: SIM-360, B: KE-103 from Shinetsu Chemical, C: SYLGARD 184 from Dow Corning, measured by SE-2000 (SEMILAB Inc.)) as the matrix candidates. The dispersion curves are quite different from those in Ref. 19, and no RIM is expected for SiO2 and CaF2 at a wavelength λcp2 of 287 nm (less than 300 nm) in the case of matrix B. It indicates that the order of λcp is A > B > C; however, this does not agree with the experimental results (B < A <C) described in section 3.2. Spectroscopic ellipsometry cannot provide absolute accuracy within 0.001 in refractive indices, due to the complicated and reverse fitting procedures of n and k estimation. Hence, the error of λcp was 4 nm, even if the relative index dispersion in Fig. 1 was correct. Therefore, the prediction and design of wavelength-transparent materials is difficult using only spectroscopic ellipsometry measurements.
Figure 2(a) shows the calculated absorption spectra of the PDMS matrices (A, B, C, D: RTV thinner from Shinetsu Chemical), they are calculated by the measured transmittance spectra of 1.0 mm thick PDMS matrices (A, B, C in solid and D in the liquid state) as shown in Fig. 2(b) to observe the cut-off wavelengths. The difference among the cut-off wavelengths originates from the contained cross-linker molecules in each PDMS product. The shortest cut-off wavelength was observed for matrix-D, because it is incurable pure PDMS, and the longest cut-off wavelength was observed for matrix-C. Hence, the order of the cut-off wavelength was determined as D < B < A < C, which agrees with the experimental results described in section 3.2.
Fig. 2 (a) Calculated absorption spectra of PDMS matrices A, B, C and D. (b) The measured transmittance spectra of 1.0 mm thick matrices A, B, C in solid state and D in liquid state.
From the preliminary estimations above, the most effective experimental approach for the mixed compounds was identified. Figure 3 shows the fabrication process of the samples. SiO2 powder (Shinetsu, X-24-9163A) or CaF2 powder (grinded by CaF2 window from OKEN) was mixed with PDMS matrices (A, B, C, and D) using a planetary centrifugal mixer (Kurabo, KK-50S). De-bubbling was performed four times by using centrifugal mixer, each at 1440/1108 rpm (revolution/autorotation) for 200 s. In order to remove heat by friction, the sample was cooled down after de-bubbling. Subsequently, a curing agent was added to the mixture, and quick mixing was applied for short duration time (90 s) to avoid curing quickly. Finally, the mixture was poured into a 1 mm-thick mold, and cured at 50 °C for 10 h after vacuum de-bubbling and covering with an acrylic plate. The transmittance of the samples (1.0 mm, 1.3 mm and 1.5 mm thick films of matrix-A and its mixtures, 1.0 mm thick films of matrix-B and its mixtures, 1.0 mm thick films of C and its mixture, 1.0 mm thick liquid state of D and its mixtures, and for each sample, error in thickness measurement is less than ± 0.1 mm) were measured with a spectrophotometer (JASCO, V-630), and microscopic observations were performed by an optical microscope (Nikon, ECLIPSE TE2000-U).
3. Experimental results
3.1 Fabrication and evaluation of SiO2: PDMS films
Figure 4(a) shows the transmittance spectra of the fabricated SiO2: PDMS films using matrix-A with varying concentrations (16 wt.%, 20 wt.%, 24 wt.%) of SiO2, and Fig. 4(b) shows the neat transmittance spectra obtained by normalizing with the calibrated transmittance of matrix-A. Matrix-A shows a cut-off wavelength of approximately 220 nm, and the films are also partially transparent over the visible range of wavelengths, because of small Mie scattering from SiO2 particles of size 100 nm. Even though the estimation from Fig. 1 provided no RIM, the experimental λcp1 can be confirmed as a small peak at about 233 nm. This does not agree with the estimations in Fig. 1. In addition, the ability of the mixture to block visible light is weak owing to the smaller size of the particles. This limitation can be overcome by using particles of larger size. As shown in Fig. 4(b), the peak transmittance is 7-80%, despite being a part of normalized spectra. This 2-30% loss comes from larger scattering (discussed in section 3.3). These results confirmed whether or not the transparency of the film to light was effected by RIM. However, the cross-point wavelength was considerably shorter in comparison with previously reported predicted values. Further, the obtained transmittance spectra were strongly affected by the absorption of PDMS; hence, it is necessary to shift the cross-point wavelength λcp to a longer wavelength. Though it was expected that a larger particle size would decrease the transmittance in the visible region, SiO2 should be replaced by another material, because the obtained RIM wavelength at λcp cannot be modified by the concentration of SiO2 particles.
Fig. 4 (a) Transmittance spectra of 1.3 mm thick films dispersing SiO2 particles (16 wt.%, 20 wt.%, 24 wt.%) in matrix-A. (b) Transmittance spectra normalized by PDMS (only matrix-A) film spectrum.
3.2 Evaluation of CaF2-mixed PDMS sample
Owing to the smaller index difference in comparison with SiO2, longer RIM wavelengths could be expected by using CaF2 particle. Four kinds of commercial CaF2 powders (I: ground excimer laser window from OKEN, II-IV synthesized and obtained from Fujifilm-Wako Pure Chemical Co., Purity Chemicals, and Hakushin Chemical Laboratory Co., Ltd., respectively) were evaluated by combining with four kinds of PDMS A-D, as shown in Table 1. The transmittance of the samples was measured using a cured solid film of 1.0 mm thickness, but the compound with matrix-D and CaF2 was measured using a 1.0 mm quartz cell. In addition, the relationship among the transmittance values in the visible region for the compounds with different mixing concentrations are plotted in Fig. 5. The result of Powder I shows a transmittance peak in the UV region as expected. The synthesized powders II, III, and IV contain trace impurities, caused the higher refractive index dispersion curve unlike in Ref [21]. It can be confirmed by the experimental results: Samples from powders II-IV showed lower transmittance due to the slightly greater refractive index difference in the 500 nm region. Thus, the slight difference in refractive index can cause a large shift in the wavelength, or the transparency condition may disappear as shown in Fig. 1. Therefore, the results of powders II, III, and IV did not show the transmittance peak in the UV region. Increasing the concentration and using a larger particle size (comparing to that used in the SiO2: PDMS films) are effective ways to improve the spectroscopic performance, because these factors can increase the spatial density and scattering cross section of CaF2 to decrease the transmittance in the visible region. Meanwhile, peak wavelengths of 251, 259, 278, and 304 nm were obtained for samples with matrices D, B, A, and C, respectively; this order agrees with the cut-off wavelength shown in Fig. 2.
Table 1. Evaluation of compound of commercial CaF2 powders dispersed in different PDMSs
Fig. 5 Evaluated results for different commercial CaF2 materials. Combination I: powder I dispersed in PDMS (matrix-A) film with 15, 20, 25, 30, and 35 wt.% concentrations; Combination II: powder II dispersed in PDMS (matrix-A) film with 5 and 10 wt.% concentrations; Combination III: powder III dispersed in PDMS (matrix-A) film with 30 wt.% concentration; Combination IV: powder IV dispersed in PDMS (matrix-A) film with 10 and 30 wt.% concentrations.
The images of the CaF2: PDMS film samples fabricated by powder I and PDMS with matrices-A and B, shown in Figs. 6(b) and 6(d), confirm that a concentration of 30 wt.% and thickness of 1 mm are suitable for scattering in the visible region. This may be due to the larger particle size of CaF2.
Fig. 6 Transparency of 1.0 mm-thick film of the samples. (a) only matrix-A (b) 30 wt.% CaF2 in matrix-A (c) only matrix-B, and (d) 30 wt.% CaF2 in matrix-B.
Figure 7 shows the transmittance spectra of the CaF2: PDMS films fabricated with matrix-A and varying CaF2 concentrations of 15, 20, 25, 30, and 35 wt.%. Figure 7(a) is the raw spectra, it also shows the measured error at 220 nm is within 0.54%. Figure 7(b) shows the spectra normalized with the PDMS (only matrix-A) film. A constant peak wavelength of approximately 275 nm was obtained from Fig. 7(b), whereas the peak wavelength of the raw spectra slightly varied to 278 nm due to the effect of PDMS absorption.
Fig. 7 (a) Transmittance spectra of CaF2: PDMS films (1.0 mm thickness) with matrix-A and varying concentrations of 15, 20, 25, 30, 35 and 60 wt.% CaF2 (b) Normalized spectra by PDMS (only matrix-A) film transmittance.
As shown in Fig. 7(b), transmittances of 90-95% and lower than 20% were obtained for the peak wavelength and in the visible region, respectively. The bandwidth decreased with increasing CaF2 concentration. The full width at half maximum (FWHM) bandwidth was 40 nm for a concentration of 35 wt.%. This implies that about 45% of the light with a wavelength of 255 nm can pass through the film; hence, the spectroscopic performance is considered insufficient. However, the spectroscopic performance can be improved by increasing the concentration, because the spatial density of the CaF2 particles will be affected by the concentration (35 wt.% corresponds to 14.7 vol.%). Note, however, that a high-concentration sample is difficult to fabricate owing to the higher viscosity. Despite this, we used existing process to make a CaF2: PDMS (matrix-A) film with a concentration of 60 wt.%. The result is shown in Fig. 7. 28 nm bandwidth and visible transmittance of 1.5% were obtained from normalized spectrum. However, there is about 50% loss at peak wavelength (278 nm) due to scattering (discussed in section 3.3). Therefore, increasing the concentration should be supplemented by an improved fabrication process.
Subsequently, the condition for transparency was investigated by changing the matrix form. Figure 8 shows the raw transmittance spectra of the matrix-B films (a; CaF2 concentration: 20, 30 wt.%), the matrix-C film (b; CaF2 concentration: 10 wt.%), and the matrix-D in liquid mixtures (b; CaF2 concentration: 10 wt.%). Peak wavelengths of 251, 259, and 304 nm were obtained for the samples with matrices D, B, and C, respectively. In addition, the FWHM bandwidth change from 38 nm (20 wt.%) to 28 nm (30 wt.%) was estimated after the spectra from Fig. 8 (a) was normalized.
Fig. 8 (a) Transmittance spectra of CaF2: PDMS films (1.0 mm thickness) with matrix-B. The CaF2 particle concentrations were 20 and 30 wt.%. (b)Transmittance spectra of CaF2: PDMS with matrices C (1.0 mm thick film) and D (liquid state in 1.0 mm quartz cell). The CaF2 particle concentrations are 10 wt.%
Thus, the target wavelengths of 260 and 280 nm for DNA/protein measurement were attained by changing the PDMS matrix, and the obtained wavelengths were 259 and 278 nm, respectively.
3.3 Discussion of transmittance loss
Although we show that four combinations of CaF2 and PDMS can show transparency at specific wavelengths, the transmittance at the peak of the normalized transmittance spectra is not 100%. This could be due to the scattering by (i) residual micro-bubbles in curing process of PDMS, (ii) internal micro-sized cracks and grooves of ground particles, (iii) inhomogeneous distribution of refractive index due to the PDMS purity (mixed with low molecular weight siloxane), and (iv) refractive index difference in imaginary part between particles and matrices. As shown in Fig. 3 and Table 2, even though three de-bubbling steps were carried out during sample fabrication, the removing performance was limited by the viscosity and curing time. These four reasons could be explained as following in detail.
Table 2. Property of four kinds of PDMS matrices
(i): Fig. 9(a) shows optical microscopic image of CaF2: PDMS film, and residual bubbles can be confirmed. (ii): Fig. 9(b) shows scanning electron microscope (SEM) image of ground CaF2 powder, and many sub-micron sized grooves and cracks can be observed. These grooves seemed too difficult to be completely filled with viscous matrix. (iii): It seemed due to the purity of PDMS. The matrix-A was purified by removing low molecular weight siloxane, the scattering due to (iii) could be minimized by using matrix-A, and relatively increased by using matrix-C. (iv): The scattering was increased if the peak wavelength becomes closer to the cut-off wavelength of the matrix, so the scattering is larger in the cases of CaF2&matrix-C and SiO2&matrix-A combinations. Figure 9(c) is maximum transmittance as peak wavelength from normalized transmittance measurement of 15~35 wt.% CaF2 and matrix A samples. The large scattering of maximum transmittance shows the scattering caused by (i) could be dominant, and it can be improved by optimization of the fabrication process. Furthermore, the upper limit of the maximum transmittance must be improved by reducing (ii)-(iv). The surface smoothing treatment of ground CaF2 by acid can improve (ii), and scattering due to (iii), (iv) seemed less than 10% in the transmittance loss. In addition, the peak wavelength of 15-35 wt.% in the Fig. 9(c) shows the error of peak wavelength less than ± 0.5 nm.
Fig. 9 (a) The microscopic image of 30 wt.% CaF2: PDMS with matrix-A film was measured by optical microscope (Nikon, ECLIPSE TE2000-U). (b) Scanning electron microscope image of powder I measured by scanning electron microscope (Hitachi, SU3500). (c) The maximum transmittance as peak wavelength from normalized transmittance measurement of 15~35 wt.% CaF2 and matrix A samples
3.4 Evaluation of particle size distribution of powder I
The transparent wavelength was determined by the kind of PDMS matrix in the preceding sections, whereas the spectroscopic performance of the scattering films is considered insufficient, even if the narrowest bandwidth is 28 nm (CaF2 30 wt.% dispersed in matrix-B). Therefore, two other factors affecting the bandwidth, except the concentration, should be considered: They are the particle size and the distribution of the CaF2 powder. Figure 10(a) shows the microscopic image of the CaF2 powder I (1 wt.%) dispersed in the H2O sample, and the distribution of the particle size shown in Fig. 10(b) was observed and measured using 16 images with different shooting conditions. The dominant particle size ranged from 0.1 to 10 μm, and the distribution of particle size can be fitted with log-normal distribution, as shown in Eq. (1):
where the μ and σ are fitted by −1.05 and 1.53, respectively. Hence, the lower transmittance of CaF2 samples in the visible region can be attributed to the stronger scattering caused by the larger particle size.Fig. 10 (a) Microscope image of CaF2 particle in H2O (concentration of CaF2: 1 wt.%), measured by optical microscope (Nikon, ECLIPSE TE2000-U). (b) Distribution of CaF2 particle size counted using 16 microscope images with different shooting conditions; it can be fitted with log-normal distribution (μ = −1.05, σ = 1.53).
3.5 Diffusing property of scattering film
The particle size and distribution of the CaF2 powder I were considered to be the two other factors affecting the bandwidth. Since the control of the particle size and distribution obtained by grinding is challenging in the current fabrication process, we tried to calculate a scattering model to guide the next research steps.
In order to identify the scattering model in our samples, the properties of the transmitted light in the visible region were first measured using the set up shown in Fig. 11(a). The light source is a DPSS laser, and a CaF2: PDMS film with matrix-A (1.5 mm thick) was set to be close to the DPSS laser. The transmitted and diffused light were detected using an oscilloscope (Tektronix, TDS680B). The angular profile of the diffused light at a wavelength of 532 nm is shown in Fig. 11(b). The incident light was scattered clearly in the visible region, and it can be considered to be the Mie scattering in this region, because the distribution can be fitted with cos6.2 θ.
Fig. 11 (a) Set-up of diffusing profile measurement in the visible region. (b) Diffusing profile in the visible region (CaF2: PDMS film with matrix-A (CaF2 concentration: 30 wt.%), incident light wavelength: 532 nm).
On the other hand, the properties of the transmitted light in the UV region were measured too, and the set-up is shown in Fig. 12(a). A UV LED was used as the light source, and the CaF2: PDMS film with matrix-A (1.0 mm thick) was fixed using 1-mm-diameter pinhole. The transmitted and diffused light were measured using a fiber-coupled spectrometer (Ocean optics, HR-4000). Figure 12(b) shows the angular profile of the diffused light at a wavelength of 300 nm. Evidently, the incident light was virtually not scattered in the UV region because of the small difference in the refractive index between CaF2 and PDMS in this region. Not Mie scattering but a soft scattering, i.e., the Rayleigh-Gans-Debye scattering (RGD model) [22] should be considered in this region.
Fig. 12 (a) Set-up of diffusing profile measurement in the UV field. (b) Diffusing profile in UV field for the CaF2: PDMS film with matrix-A (CaF2 concentration: 30 wt.%), incident light wavelength: 300 nm).
4. Simulation
4.1 Calculation theory of scattering models in UV & visible regions
The basic transmission theory of the scattering medium, Beer-lambert theory, as shown in Eq. (2) was considered to calculate the transmittance spectra in our scattering model. Since we are mainly concerned with the area affected by trace difference refractive index, multiple scattering is not discussed in this study.
Where T is the transmittance, σ is the scattering cross section, N is the spatial density, and L is the thickness of scattering medium.The spatial density of our samples can be calculated using Eq. (3).
ϒ describes the volume fraction that was affected by the concentration of CaF2 in our sample. D is the diameter of the CaF2 particles. Therefore, the spatial density N is affected by the CaF2 concentration and particle size.
Thus, there are different methods for calculating the scattering cross section σ owing to the different scattering theories, and by considering the scattering profile measurement results in UV region and the trace difference in the refractive index between the materials, the scattering cross section can be approximated using Eq. (4) based on the RGD scattering theory [22].
where σRGD is the scattering cross section in the RGD model, k is the wavenumber, Δn is the RI difference between CaF2 and PDMS, and n is the refractive index of the medium. This approximation is valid whenwhere m is the relative refractive index and k is the wavenumber. This means that the RGD theory can be used only when the two materials have a very small RI difference and phase shift.On the other hand, in the visible region, Eq. (5) is not valid, so the scattering cross section was calculated using the Hulst approximation [23] as shown in Eq. (6), owing to the Mie scattering in this area.
where σHulst is the scattering cross section in the Hulst model and p is the size parameter.Hence, a combined scattering model consisting of Rayleigh scattering (RGD model) in the UV region, and Mie scattering (Hulst model) in the visible region has been constructed, and the calculation model can be switched from the RGD model to the Hulst model using the size parameter p (when p « 1, the RGD model will be used).
4.2 Simulation results with combined scattering model
Based on the combined scattering model, we simulated the transmittance spectra of the light passing through a 1 mm-thick sample film (CaF2: PDMS film with matrix-A), and fitted with experimental data as shown in Fig. 13(a). When the difference in the refractive index is less than 0.005, the experimental data are in excellent agreement with the simulation curve in the area from 240 nm to 310 nm, whereas the transmittance of the experiment is slightly higher than the simulated results in the other area, owing to the multiple scattering light rays entering the detector. However, it is sufficient for analyzing the bandwidth and improving the spectroscopic performance. Thus, the calculated values of the bandwidth can also be fitted with our experimental data, as shown in Fig. 13(b). These results also agreed with each other very well. Hence, it can be inferred that the UV light with a wavelength of 310 nm branched into 70% and 30% isotropic scattering and non-diffused light, respectively, due to the Rayleigh (RGD) scattering.
Fig. 13 Fitting results: (a) simulation conditions: CaF2: PDMS film with matrix-A, particle diameter and distribution of CaF2 powder I in Fig. 9(b) (μ = −1.05, σ = 1.53), concentration: 30 wt.%, thickness: 1 mm; experimental data: the spectra of CaF2: PDMS film with matrix-A, concentration: 30 wt.%, thickness: 1 mm; (b) simulation conditions: CaF2:PDMS film with matrix-A, particle diameter and distribution of CaF2 powder I in Fig. 9(b) (μ = −1.05, σ = 1.53), concentration: 10–60 wt.%, thickness: 1 mm; experimental data: bandwidth (FWHM) calculated from the spectra of CaF2:PDMS films with matrix-A, concentration: 15, 20, 25, 30, 35, 60 wt.%, thickness: 1 mm.
Next, the CaF2 particle size and distribution have to be discussed using our scattering model. Because the particle size and distribution measured in Fig. 10(b) can be fitted using the log-normal distribution, we simulated some different particle size and distribution based on the log-normal distribution and used it in the calculation with the combined scattering model. Figure 14 shows the simulation results: (a) shows the effect of the different particle size distributions with the same average particle size (1 μm) on the bandwidth. Obviously, the bandwidth can be narrowed using monodisperse samples. On the other hand, (b) shows the bandwidth changing with different average particle sizes in the same distribution, and it indicates that increasing the particle size is very effective way to narrow the bandwidth.
Fig. 14 Simulation results based on simulated or experimental particles size and distribution of log-normal distribution; simulation conditions: CaF2: PDMS film with matrix-A, 1 mm thickness, concentration: 10–60 wt.%, (a) mean CaF2 particle size: 1 μm, standard deviation of polydisperse particles (simulation) is 9.0 μm (μ = −2, σ = 2.05); standard deviation of polydisperse particles (experiment) is 3.4 μm (μ = −1.05, σ = 1.53); standard deviation of monodisperse particles (simulation) is 0 μm (μ = σ = 0); (b) standard deviation of distribution is 3.4 μm, the average particle sizes are 0.5 μm (μ = −2.63, σ = 1.97), 1 μm (μ = −1.05, σ = 1.53), 5 μm (μ = 1.41, σ = 0.62), and 10 μm (μ = 2.25, σ = 0.34).
Hence, the simulation curves of Fig. 14 clearly establish that in addition to its concentration, the particle size and distribution of CaF2 are critical for the control of the bandwidth.
The larger particle size and narrower distribution of CaF2 powder are needed for improving the spectroscopic performance of the scattering filters. Also, with the same particle size distribution as in the experiment, when the CaF2 concentration is increased to 50 wt.% and the average particle size is 10 µm, a filter with a bandwidth of 10 nm can be expected. However, as the existing fabrication process is not equipped with a measure to control the particle size and distribution, there is ample scope for further process improvements specially to control the size and distribution of the CaF2 particles, and to build a comprehensive scattering model by adding the calculation of the multiple scattering using the Monte-Carlo theory.
5. Conclusions
In this study, we proposed and demonstrated a novel scheme for preparing a simple white compound with UV transparency by combining the PDMS matrix and CaF2 particles. Though the refractive index matching (RIM) design required the refractive index accuracy about 0.001, our optimized combination with careful selection of materials showed good reproducibility of transparent condition up to T = 80% (95% excluding absorption) at a wavelength of 278 nm. It was also discovered that the UV filtering property can be explained by only the Rayleigh-Gans-Debye (RGD) model, and it showed intense isotropic scattering up to 70% in the RIM condition. The simple RGD calculation predicted the bandwidth performance will be improved down to 10 nm by optimizing ground CaF2 particle diameter and distribution. In future, this material must be useful for not only filter coating but also as potting or embedding material in UV optical modules or integrated microstructures, e.g., in microflow-cytometry and micro-TAS.
Acknowledgment
Cong Chen (Kyushu university) and Harunobu Takeda (Kyushu university) are thanked for the experimental support. Japan SEMILAB Inc. is thanked for the support in the spectroscopic ellipsometry measurement.
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