Polarization dependence in optical reflection and transmission of opal photonic crystals - Le Duc Tuyen

Journal of Science and Technology 54 (1A) (2016) 143-150 POLARIZATION DEPENDENCE IN OPTICAL REFLECTION AND TRANSMISSION OF OPAL PHOTONIC CRYSTALS Le Dac Tuyen 1, * , Do Danh Bich 2 , Du Thi Xuan Thao 1 , Le Quoc Minh 3 , Chia Chen Hsu 4 1 Department of Physics, Hanoi University of Mining and Geology, 18 Pho Vien Street, Hanoi, Vietnam 2 Department of Physics, Hanoi National University of Education, 136 Xuan Thuy Street, Hanoi, Vietnam 3 Institute of Materials Science, VAST, 18 Hoang Quoc Viet Road, Hanoi, Vietnam 4 Department of Physics, National Chung Cheng University, 168 University Road, Chia Yi 621, Taiwan * Email: ledactuyen@humg.edu.vn Received: 5 September 2015; Accepted for publication: 29 October 2015 ABSTRACT High-quality opal photonic crystals were fabricated by self-assembling of monodispersed SiO2 nanospheres with a thermal-assistant cell method. The angle- and polarization-resolved optical reflection and transmission of an artificial opal were studied. A strong anisotropy in the intensity and the full width at half maximum of reflection and transmission spectra of the s- and p-polarized light was observed along the L-U (L-K) direction of the first Brillouin zone, and these differences become more pronounced in the vicinity U (K) point. The observed polarization anisotropy of optical properties is caused by symmetry characterization of polarized light and opal structure. The obtained results agree fairly well with calculated photonic band structure, which is also compared with predictions based on the group theory. Keywords: photonic crystals, opal, polarization. 1. INTRODUCTION Photonic crystals (PhCs) have been attracted intense interest due to a variety of possible applications in optoelectronics [1 - 4]. Interaction of an electromagnetic field with PhCs is accompanied by remarkable optical diffraction phenomena, which can be assigned to strong modification of the photon energy spectrum inside the structure [5, 6]. PhCs allow one to create photonic band gaps (PBG) to prohibit photons with photon energy within the gaps, resulting in high reflectivity or low transmissivity [5, 6]. PhCs have been demonstrated unique properties in ability to control light. Moreover, such structures are novel nontrivial objects that can be used to explore fundamental aspects of the interaction of light with condensed media [7, 8]. Opal structure is convenient objects available for studying three-dimensional PhCs, which consists of identical dielectric spheres ordered into a close-packed face-centered cubic (fcc) Le Dac Tuyen, Do Danh Bich, Du Thi Xuan Thao, Le Quoc Minh, Chia Chen Hsu 144 lattice [8, 9]. The photonic stop band of opal can be precisely tuned through the diameter of spheres [10, 11]. The optical properties of opals have been the subject of numerous theoretical and experimental studies in recent years [11 - 25]. However, there are only few reports on polarization-resolved spectroscopy [12 - 16]. In this work, we present experimental studies on optical properties of silica (SiO2) opal PhC fabricated by self-assembling of monodispersed SiO2 nanospheres with a thermal-assistant cell method. The angle- and polarization-resolved reflection and transmission measurements were carried out along the L-U (L-K) orientation of the first Brillouin zone (FBZ). It shows that the relative intensity and full width at half maximum (FWHM) of reflection and transmission spectra are dependent on polarization of light illumination. The difference is more pronounced in the vicinity of U (K) point. The experimental results agree fairly well with photonic band structure, and predictions based on group theory. 2. EXPERIMENT Through the hydrolysis and condensation of tetraethoxysilane (TEOS - Si(OC2H5)4) in mixtures of aqueous ammonia (NH4OH), water (H2O), and alcohol (C2H5OH), colloidal silica nanospheres were synthesized following a method developed by Stöber et al. [11,26]. 0.65 ml of TEOS (Aldrich), 2.15 ml of deionized water (18.2 M cm -1 , Millipore), and 1.35 ml of NH4OH (Acrôs) were added sequence in 17 ml of C2H5OH (Acrôs) solution, respectively. The mixture was stirred vigorously for 4 h to obtain a white turbid suspension, and the ambient temperature was kept at 30 0 C. Subsequently, nanospheres, separated from the mother liquid by centrifugation (3000 rpm), were purified and repeated with deionized water three times. Monodispersed nanospheres were obtained by partial aggregation of different sedimentation regions [27]. Finally, the high quality opal PhCs were fabricated by self-assembling processes with a thermal-assistant cell method [11]. Figure 1. (a) Schematic of experimental setup for angle- and polarization-resolved reflection and transmission spectra on the opal sample. is incident angle (angle between the incident beam and the normal to sample surface), and is polarization orientation angle (angle is adjusted by a polarizer for the choice of polarized light illumination). (b) The first Brillouin zone of the fcc structure and symmetric points. Polarization dependence in optical reflection and transmission of opal photonic crystals 145 The morphology of the opal PhC was determined by field emission scanning electron microscopy (FE-SEM, Hitachi 4800I). Diffraction pattern of the opal PhC was generated by a He-Cd Laser with the wavelength at 325 nm. The reflection and transmission spectra of the opal PhC were measured using an Ocean- optic fiber spectrometer (S2000). Figure 1(a) shows the schematic of reflection and transmission measurement setup. A tungsten halogen lamp (OSRAM) was used as a light source that can produce broadband spectrum in the visible region. The p- and s-polarization of the collimated light were controlled by using a prism polarizer to adjust electric field vector as parallel (Ep, = 0 0 ) and perpendicular (Es, = 90 0 ) to the plane of incidence, respectively. The cross section of the light beam was about 2 mm 2 . The reflected or transmitted light beam was collected by a lens and focused to a fiber bundle which was connected to spectrometer. The sample was rotated by a rotation stage with an angular step of 1 0 . Fig. 1(b) shows the FBZ of the fcc structure. Highly symmetric points are denoted by the standard notations in this figure. We carried out s- and p- polarized reflection and transmission measurements with the incident angle varying from 0 0 to 55 0 along the L-U (L-K) orientation of the FBZ. 1. RESULTS AND DISCUSSION The SEM images with different magnifications of the top surface of a SiO2 opal PhC are shown in Figs. 2(a) and 2(b). Monodispersed SiO2 nanospheres with a diameter of 424 nm were closely packed on the glass substrate by gravity sedimentation during solvent evaporation. The thickness of the sample was about 20 m. Figure 2(c) shows the photograph of the diffraction pattern of the opal sample at wavelength = 325 nm. Six diffraction spots were observed on a screen behind the sample when a laser beam illuminated perpendicular onto the sample surface with a beam diameter of 1 mm. The orientation of the spots is unchanged when the illumination position is changed. The clear diffraction spots shown in the photograph indicate the existence of symmetric lattice order in long range [28]. It allows us to identify the orientation of samples. Figure 2. (a) and (b) Top view SEM images of the opal surface structure made of 424 nm silica spheres. (c) Diffraction pattern of reflected beams projected on a screen behind the surface of the opal structure for λ = 325 nm. Figs. 3(a) and 3(b) show the s- and p-polarization reflection spectra with different angles of incidence, respectively. We can clearly see reflection resonances in these spectra throughout the range of incident angles covered, thus permitting adequate evaluation of the angular dependence of polarization anisotropy. For small angles of incidence, the peak position and FWHM of s- and p-polarization reflection spectra associated with the (111) plane are very similar. There is small Le Dac Tuyen, Do Danh Bich, Du Thi Xuan Thao, Le Quoc Minh, Chia Chen Hsu 146 change in the reflection intensity and FWHM of s-polarized light when incident angle increases, whereas the correlative p-polarized light becomes weaker and narrower. As the angle of incidence is in the range from 45 0 to 55 0 , a new reflection peak appears in the short wavelength side for the s-polarized reflection, and it becomes to predominate while the long wavelength peak disappears at larger incident angles. This effect has been observed for opal PhCs [12,19,24]. The phenomenon was attributed to simultaneous diffraction by the (111) and (200) sets of planes (i.e., the U point) or the (111) and (-100) sets of planes (i.e., the K point), while the p-polarized light is only reflected by (111) planes [12,19,24]. Figure 3. Angle-resolved reflection (a, b) and transmission (c, d) spectra for s polarization (a, c) and (b, d) p polarization of light. Reflection (e) and transmission (f) spectra at incident angle of = 49 0 with various polarization orientation angle . Polarization dependence in optical reflection and transmission of opal photonic crystals 147 Figures 3(c) and 3(d) show the s- and p-polarization transmission spectra with different angles of incidence, respectively. The most pronounced dips observed are due to the (111) planes. The dip positions in transmission spectra coincide with peak positions in the corresponding reflection spectra at the same incident angle. It indicates that high reflectivity or low transmissivity is caused by the photonic stop band. Moreover, the transmission dips in s-polarized light associated with (200) or (-111) family planes exist with angle of incidence from 45 0 to 55 0 [13]. The physical origin of the observation can be explained by multiple diffractions inside the PhC. The reflection spectra are sum of diffraction results of selected planes determined by the geometry of the scattering. On the other hand, the transmission spectra are gathered on all possible diffraction processes which results in a reduction of transmitted intensity. The observation indicates that the optical properties at small incident angle are nearly isotropic, and the different orientation of lattice symmetry is manifested at large incident angle. Figures 3(e) and 3(f) show sets of reflection and transmission spectra, respectively, measured at incident angle = 49 0 with a variety of polarization orientation angle from 0 0 to 90 0 . Here, we can clearly observe the changes in spectra of differently polarized light. In Fig. 3(e), when polarization orientation angle is adjusted from 0 0 (p-polarization) to 90 0 (s- polarization), the reflection spectra start from one peak to split to two peaks, and the FWHM and intensity become wider and stronger. The same thing is found on transmission spectra as shown in Fig. 3(f). The differences in the reflection and transmission spectra between s- and p-polarized light indicate that the photonic band structure of the opal PhC is polarization dependent. The FWHM of experimental reflection peaks is compared with the edges of the simulated photonic stop band obtained by the plane expansion method (Rsoft). Fig. 4 shows the experimental FWHM results for s- and p-polarized light corresponding to squares (blue, yellow) and circles (red), respectively, plotted on the calculated bands (lines) along L-U direction of the FBZ. The photonic band calculation result was obtained by using diameter of silica spheres D = 424 nm (lattice constant a = 600 nm), refractive index of silica n = 1.45, and refractive index of air = 1.00. The FWHM values of reflection peaks were obtained by using Gaussian fitting. The abscissa represents the wave vector in the FBZ of the fcc structure (Fig. 1(b)). The ordinate is the normalized frequency where a and c stand for the lattice constant and the light velocity in free space. For this structure, there is no complete band gap that extends throughout the Brillouin zone. As shown in Fig. 4, the first-order stop band, where the wavelength of light is greater than the lattice constant (a/ < 1), is a function of the incident angle. A fair agreement between experimental and calculated values can be found in both cases of s- and p-polarization. The anisotropic effect on the peak widths becomes more pronounced as the incident angle increases. In the case of the p-polarized light, the Ep field is confined in the same plane of incidence, and the specular reflection with respect to that plane leaves the field vector unchanged. While, for s-polarized light, the Es field is perpendicular to the plane of incidence so that the symmetry operation changes Es into -Es (Fig. 1(a)). Thus, the symmetric p-polarized fields can only couple with the symmetric (A’) eigenstates along the L-U direction, whereas the s-polarized fields can only couple with the antisymmetric (A’’) eigenstates [21]. So, the reflection peak widths obtained at different incident angles determined from band structure simulation should be polarization-dependent. According to the previous analysis [21], the polarized light interacts with opal structure depending on the symmetry properties of eigenstates. The stop band width of p-polarized light is narrower because it is associated with the pair inner bands (2 nd and 3 rd ). While the outer bands Le Dac Tuyen, Do Danh Bich, Du Thi Xuan Thao, Le Quoc Minh, Chia Chen Hsu 148 (1 st and 4 th ) are coupled to s-polarized light and that is why it yields larger stop band width. For the experiments using unpolarized light [19,24], the observations are very similar to that of s- polarized light. In this case, the s-polarization (outer bands) would be probed, while the p- polarization (inner ones) would remain hidden since the broader peaks contain the narrower one and the stronger intensities predominate weaker. Figure 4. Comparison of photonic band calculation (lines) with FWHM of reflection spectra measurement of s- and p-polarized light corresponding squares (blue, yellow) and circles (red). Photonic bands obtained by the plane expansion method using diameter of silica spheres D = 424 nm (lattice constant a = 600 nm) and refractive index of silica n = 1.45. FWHM values of reflection peaks obtained by using Gaussian fitting. 2. CONCLUSIONS We have measured angle- and polarization-resolved reflection and transmission from artificial opals to investigate the complex interaction of light with photonic crystals. We have observed experimentally strong polarization dependence in the s- and p-polarized light. 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TÓM TẮT SỰ PHỤ THUỘC PHÂN CỰC ÁNH SÁNG TRONG PHẢN XẠ VÀ TRUYỀN QUA CỦA TINH THỂ QUANG TỬ OPAL Le Dac Tuyen 1, * , Do Danh Bich 2 , Du Thi Xuan Thao 1 , Le Quoc Minh 3 , Chia Chen Hsu 4 1 Bộ môn Vật lý, Trường Đại học Mỏ - Địa chất, 18 Phố Viên, Hà Nội, Việt Nam 2 Khoa Vật lý, Trường Đại học Sư phạm Hà Nội, 136 Xuân Thủy, Hà Nội, Việt Nam 3 Viện Khoa học Vật liệu, Viện HLKHCNVN, 18 Hoàng Quốc Việt, Hà Nội, Việt Nam 4 Khoa Vật lý, Trường Đại học Quốc gia Chung Cheng, 168 Đường Đại học, Chia Yi, Đài Loan * Email: ledactuyen@humg.edu.vn Tinh thể quang tử opal có chất lượng cao được chế tạo từ các quả cầu silica đồng nhất bằng phương pháp tự sắp xếp với sự hỗ trợ của nhiệt độ. Chúng tôi nghiên cứu phổ phản xạ và truyền qua phân giải theo góc của ánh sáng phân cực s và p. Sự khác biệt lớn về cường độ và độ bán rộng (FWHM) trong phổ phản xạ và truyền qua của ánh sáng phân cực s và p đã được quan sát theo phương L-U (L-K) của vùng Brillouin thứ nhất, và những khác biệt này rõ rệt hơn tại lân cận điểm U (K). Kết quả thực nghiệm chứng tỏ tính chất quang của tinh thể quang tử opal phụ thuộc ánh sáng phân cực là do tính đối xứng của cấu trúc. Kết quả thu được khá phù hợp với tính toán cấu trúc vùng năng lượng và các dự đoán dựa trên cơ sở lí thuyết nhóm. Từ khóa: tinh thể quang tử, opal, phân cực.