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Multi-band transmission color filters for multi-color white LEDs based visible light communication
Optics Communications 403 (2017) 330–334
Contents lists available at ScienceDirect
Optics Communications journal homepage: www.elsevier.com/locate/optcom
Multi-band transmission color filters for multi-color white LEDs based visible light communication Qixia Wang a , Zhendong Zhu a,b , Huarong Gu a , Mengzhu Chen a , Qiaofeng Tan a, * a b
State Key Laboratory of Precision Measurement Technology and Instruments, Department of Precision Instrument, Tsinghua University, Beijing 100084, China National Institute of Metrology, Beijing, 100018, China
a r t i c l e
i n f o
Keywords: Diffraction gratings Wavelength filtering devices Visible light communication
a b s t r a c t Light-emitting diodes (LEDs) based visible light communication (VLC) can provide license-free bands, high data rates, and high security levels, which is a promising technique that will be extensively applied in future. Multiband transmission color filters with enough peak transmittance and suitable bandwidth play a pivotal role for boosting signal-noise-ratio in VLC systems. In this paper, multi-band transmission color filters with bandwidth of dozens nanometers are designed by a simple analytical method. Experiment results of one-dimensional (1D) and two-dimensional (2D) tri-band color filters demonstrate the effectiveness of the multi-band transmission color filters and the corresponding analytical method. © 2017 Elsevier B.V. All rights reserved.
1. Introduction Visible light communication (VLC), which can provide free license with a new broad band, high data rates and high security, has attracted many attentions [1–3]. VLC is considered as a promising solution for the next-generation 5G wireless communications since it uses the visible spectrum to solve the congested radio-frequency communication spectrum [4]. The multi-color white light light-emitting diodes (LEDs) have been demonstrated to mitigate the LEDs nonlinearity when using orthogonal frequency division multiplexing modulations [5]. Usually, two major types of commercially multi-color white light LEDs, red– green–blue (RGB) LEDs and red–green–blue–amber (RGBA) LEDs, are available. Considering that noise usually comes from background light, multi-band transmission color filters are key components for filtering out the wanted light, whose central wavelengths and bandwidths correspond to the multi-color LEDs. Multi-band transmission color filters with bandwidth of dozens nanometers can be achieved by using multilayered thin films, however such multilayered thin films require high precision of thickness and refractive indices [6]. Multi-band filters can also be realized by onedimensional photonic crystals with multiple defects [7–12], which also require high precision of thickness and refractive indices. The guidedmode resonance of diffraction grating is introduced to design the multiband filter, however the bandwidth is very narrow [13]. Metallic grating was introduced to enlarge the bandwidth. The transmission * Corresponding author.
E-mail address: [email protected] (Q. Tan). http://dx.doi.org/10.1016/j.optcom.2017.07.065 Received 19 March 2017; Received in revised form 27 June 2017; Accepted 23 July 2017 Available online 4 August 2017 0030-4018/© 2017 Elsevier B.V. All rights reserved.
color filters with tunable transmission bandwidth of 13–100 nm were designed, which based on the hybridization between plasmonic mode and waveguide mode [14–20]. But such color filters have only one single transmission band and were designed based on optimization. Nevertheless, there is rare research on tri-band or multi-band transmission filters with bandwidth of dozens nanometers. Most recently, a dualband bandpass filter with 70 nm bandwidth was proposed based on the hybridization of waveguide resonance mode and the SPP mode [21]. Though the filter was designed for resonance wavelength in the infrared band. The structure with a groove carved on the metal strip of a subwavelength grating is difficult to fabricate, and the experimental results were not given. In this paper, multi-band transmission filters with bandwidth of dozens nanometers, where dielectric waveguide is loaded with a onedimensional (1D) or two-dimensional (2D) subwavelength metallic grating, are proposed. A simple analytical method is presented to design the tri-band and quad-band transmission filter. The 1D multi-band color filters have peak transmittance up to or close to 80% for TM polarization, as well as a good performance down to near zero for the valley transmittances of the stop-bands. The 2D tri-band filter has peak transmittance up to 60% for both TE and TM polarization. Both 1D and 2D tri-band color filters are fabricated. The experiment results demonstrate the effectiveness of the proposed analytical method and the potential of designing multi-band transmission color filters.
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Optics Communications 403 (2017) 330–334
Fig. 1. Configuration of the proposed 1D tri-band color filter. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
2. Design and experiment 2.1. Design of 1D multi-band color filters The configuration of the proposed 1D tri-band color filter is illustrated in Fig. 1. One-dimensional subwavelength metallic grating is mounted on a planar waveguide layer. The parameters of the grating are denoted as the period 𝛬, the height 𝑑 and the duty cycle ratio 𝑓 . The device is incident under TM polarization light from the top side, where the magnetic field (𝐻z ) is perpendicular to the plane of the grating vector. The dielectric planar waveguide layer with the thickness ℎ is deposited on silica substrate (SiO2 ). It is necessary to introduce a dielectric material with enough high refractive index, in which visible light can be concentrated. Here, titanium dioxide (TiO2 ) is used as the waveguide layer, because of its high transmission efficiency and ∼2.1 refractive index in visible range. The permittivities of the air, the waveguide layer and the substrate are assumed to be 𝜀0 , 𝜀1 and 𝜀2 , respectively. To achieve a multi-band transmission color filter at particular wavelengths for multi-color white LEDs, the resonant modes are analyzed, including the plasmonic mode and waveguide modes. Both modes can be excited when phase-matching condition between the incident beams and the modes is satisfied [22]. Either plasmonic mode or waveguide modes can be characterized by effective index 𝑛𝑒𝑓 𝑓 of the mode, and phase-matching equation can be written as
Fig. 2. Transmission spectra of two designed 1D tri-band color filters. The blue dash line is designed with 𝜆3 and 𝜆2 . The black dash dot line is design with 𝜆3 and 𝜆1 are selected. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
of waveguide, which is difficult to get an analytical solution of the structure parameters via Eq. (2), needs to be solved. The 1D multi-band color filter is designed with an analytic method based on wave vector matching. Arising out of the real spectrum of the RGB LEDs, measured by the spectrometer Maya 2000 pro, the triband color filter is desired with central wavelength of 𝜆1 (462 nm), 𝜆2 (554 nm) and 𝜆3 (658 nm). For a tri-band color filter, the waveguide should sustain two modes, 𝑚 = 0 and 1, which respond primarily to the largest resonance wavelength 𝜆3 and a higher order mode at 𝜆2 or 𝜆1 , respectively. The plasmonic mode responds primarily to the third resonance wavelength 𝜆1 or 𝜆2 . Both silver (Ag) and aluminum (Al) enable strong plasmon resonances spanning much of the visible region [24]. Due to the advantage of lower cost compared to Ag, Al is chosen as the grating in this paper. The Lorentz–Drude model [25] is applied for fitting the permittivity of Al. Without loss of generality, 𝑓 is given as 0.5. When such a structure is illuminated with incident light as shown in Fig. 1, part of the beam is reflected, part is directly transmitted and part is diffracted, exciting waveguide modes that trapped inside the waveguide layer. The 𝑦-component of the wave vector 𝛹 in the ( )1∕2 waveguide layer can be written as 𝛹 = 𝑘2𝑖 𝜀1 − 𝛽 2 . To ensure peak transmittance and cut down the energy reflected by the interface as much as possible, the 𝑦-component of the wave vector should be made as close as possible to the wave vector in the air or substrate [26]. When 𝛹 is made similarly to wave vector either at the top or the bottom interface of the waveguide layer, 𝛽 will be the particular solution of Eq. (2). Here, 𝜆2 and 𝜆3 are selected to be the two modes sustained in the waveguide, then (( ) )1∕2 2 ⎧ √ 2𝜋 2𝜋 2 𝜀 − 𝛽 = 𝜀2 (for bottom interface) ⎪ 1 𝜆3 𝜆3 ⎪ (3) ⎨(( ) )1∕2 2 ⎪ √ 2𝜋 2𝜋 2 𝜀1 − 𝛽 = 𝜀0 (for top interface) . ⎪ 𝜆2 𝜆2 ⎩
2𝜋 = 𝑘𝑖 𝑛𝑒𝑓 𝑓 (1) 𝛬 where 𝜆𝑖 is the desired resonance wavelength, 𝑘𝑖 = 2𝜋∕𝜆𝑖 is the propagation constant in free space, 𝜃 is the incident angle, 𝑝 is the diffraction order. Considering that the period 𝛬 of the grating is less than the resonance wavelength, the diffraction order 𝑝 is only considered as 1. The plasmonic resonance would be produced at the metal–dielectric and metal–air interfaces [23]. The 𝑛𝑒𝑓 𝑓 of planar waveguide can be solved by the eigen-equation of the waveguide [15]. The metallic grating, whose height 𝑑 is thin enough, produces a small perturbation on the resonance wavelength of the guided mode in the waveguide layer that can be ignored. Therefore, the eigen-equation for TM modes of the planar waveguide can be written as ( )1∕2 ( 2 ) 𝜀1 𝛽 2 − 𝑘2𝑖 𝜀0 2 1∕2 𝑘𝑖 𝜀 1 − 𝛽 ℎ = 𝑚𝜋 + arctan 𝜀0 𝑘2 𝜀1 − 𝛽 2 𝑖 )1∕2 ( 2 − 𝑘2 𝜀 𝛽 𝜀1 𝑖 2 + arctan (2) 𝜀2 𝑘2 𝜀1 − 𝛽 2
𝑘𝑖 sin 𝜃 + 𝑝
𝑖
where 𝑚 is the number of the waveguide mode, 𝛽 is the propagation constant of the guided modes which can be written as 𝛽 = 𝑘𝑖 𝑛𝑒𝑓 𝑓 . Since the guided modes can be excited by the first order diffraction of incident light by the metal grating given by Eq. (1), we can choose the proper parameters of metallic grating and waveguide to efficiently couple the incident light into waveguide modes at multiple specific resonance wavelengths 𝜆𝑖 . The resonances should take place at the particular solutions of 𝑛𝑒𝑓 𝑓 in Eq. (2). That means an inverse problem 331
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Optics Communications 403 (2017) 330–334
Fig. 3. (a) Comparison of the transmission spectrum of the designed 1D tri-band color filter (𝛬 = 350 nm, ℎ = 280 nm, 𝑓 = 0.5 and 𝑑 = 50 nm) and the spectrum of RGB LEDs. (b) The measured transmission spectrum. (c) The SEM image of the filter. (d) The re-calculated transmission spectrum with the parameters measured by the SEM. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
When the period 𝛬 is determined, Eq. (2) tells that ℎ is only associated with 𝑚, namely the sustaining mode number 𝑚 of the waveguide. In other words, the thickness ℎ is defined by the mode number 𝑚 of the waveguide. As far as a tri-band color filter, 𝑚 is determined by the number of bands. For tri-band color filter, the waveguide should sustain two modes, 𝑚 = 0 and 1. Then we can get the value range of waveguide thickness ℎ from Eq. (2). Furthermore, ℎ can be optimized in a small range by rigorous coupled wave analysis based on the software RSOFT. The plasmonic mode responds to the first resonance wavelength 𝜆1 , which is sensitive to the height 𝑑 of the grating. For normal incidence and 𝜆1 = 460 nm, 𝑑 is chosen as 50 nm [17]. All parameters of the designed tri-band color filter are 𝛬 = 350 nm, ℎ = 280 nm, 𝑓 = 0.5 and 𝑑 = 50 nm. If 𝜆1 and 𝜆3 are selected in Eq. (3), then another filter is designed which parameters are 𝛬 = 325 nm, ℎ = 285 nm, 𝑓 = 0.5 and 𝑑 = 50 nm. The corresponding far field transmission spectra of the designed tri-band color filters have been calculated and plotted in Fig. 2. The transmission is defined by the ratio of intensity of TM or TE wave that pass through the filter and intensity of incident in the same polarization. As shown in Fig. 2, the wavelengths 𝜆2 and 𝜆3 should be chosen to be sustained in the waveguide to get the better color filter. The far field spectrum of the designed tri-band filter is simulated by RSOFT in blue dash line in Fig. 3(a). The peak transmittances of the resonant bands are all over 80% and the valley transmittances of the stop-bands are all down to near zero except the shortest resonant wavelength. The bandwidths are dozens nanometers as expected. Additionally, the resonant wavelengths are only a little different to that of RGB LEDs. To demonstrate the proposed method, the designed 1D triband color filters were fabricated. The far field spectrum was measured with spectroscopic ellipsometry (WVASE, J.A. Woollam Co.) incident with a TM polarized plane wave illuminating from the top side by normal incidence (in the −𝑦 axis direction). The measured results are shown in Fig. 3(b). The properties of the measured spectrum basically agree with the simulated results including the central wavelengths and bandwidths of the resonant peaks, while small deviation exists in the central wavelengths. To track the origin of the small deviation, the cross sectional of the fabricated filter was scan by the scanning electron microscope (SEM). As shown in Fig. 3(c), the thickness of the TiO2 layer is about 280 nm, the period and the height of the grating respectively are 350 nm and 50 nm, but the duty cycle ratio is 0.6. We re-calculate the far field transmission spectrum of the filter by RSOFT with the parameters
Fig. 4. Comparison of the spectrum of the designed quad-band filter (𝛬 = 325 nm, ℎ = 480 nm, 𝑓 = 0.5 and 𝑑 = 50 nm) and the measured spectrum of one RGBA LEDs. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Combining Eq. (3) with Eq. (1), we can obtain two grating period 𝛬1 and 𝛬2 , as shown in Eq. (4). ⎧ 2𝜋 2𝜋 ⎪𝛽 = 𝜆 sin 𝜃 + 𝛬 3 1 ⎪( )1∕2 ⎨ ( )2 √ 2𝜋 2𝜋 ⎪ 𝜀1 − 𝛽 2 = 𝜀2 ⎪ 𝜆3 𝜆3 ⎩
(4a)
⎧ 2𝜋 2𝜋 ⎪𝛽 = 𝜆 sin 𝜃 + 𝛬 2 2 ⎪( )1∕2 ⎨ ( )2 √ 2𝜋 2𝜋 ⎪ 𝜀1 − 𝛽 2 = 𝜀0 . ⎪ 𝜆2 𝜆2 ⎩
(4b)
Then, without loss of generality, the 𝛬 takes the average value of these two periods instead the parameters were obtained via Eqs. (1) and (2). ( ) 𝛬 = 𝛬1 + 𝛬2 ∕2.
(5) 332
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Optics Communications 403 (2017) 330–334
Fig. 5. (a) Configuration of the proposed 2D tri-band color filter. (b) The transmission spectra of the filter (𝛬𝑥 = 𝛬𝑧 = 350 nm, 𝑓𝑥 = 𝑓𝑧 = 0.7, ℎ = 280 nm and 𝑑 = 50 nm). (c) The measured transmission spectra. (d) The SEM image of the filter. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
measured by the SEM. The re-simulation results are respectively shown in Fig. 3(d), and which is more consistent with the experimental results. Al, with strong absorption of near UV spectrum, shows strong absorption at the first resonance. The peak transmittance of the first resonance is approximately 40%, which is lower than the simulated results. There are several other types of multi-color white LEDs, such as red– green–blue–amber (RGBA) LEDs. Arising out of the real spectrum of the RGBA LEDs, four center wavelengths of the quad-band color filter are 𝜆1 = 456 nm, 𝜆2 = 532 nm, 𝜆3 = 597 nm and 𝜆4 = 663 nm, respectively, as shown in Fig. 4, in red solid line. Compared with the tri-band color filter, more complicated electromagnetic field will arise for quad-band color filter and will bring more difficulty to solve Eq. (2). However, the proposed method can also overcome such difficulty. The quad-band color filter can be realized by only changing the mode number of the waveguide, 𝑚 = 0, 1 and 2, respectively. Two periods are obtained by substituting two sets of center wavelengths 𝜆4 , 𝜆3 and 𝜆2 , 𝜆1 into Eqs. (4) and (5). Then the 𝛬 takes the average value of two periods without loss of generality. Similarly, the waveguide should sustain three modes. Under this condition, the value range of ℎ also can be calculated from the Eq. (2). For normal incidence, the geometric parameters of quad-band color filter are 𝑓 = 0.5, 𝛬 = 325 nm, ℎ = 480 nm, and 𝑑 = 50 nm. The far field spectrum of the designed quad-band filter simulated by RSOFT is shown in Fig. 4, in blue dash line. The peak transmittances of the resonant bands are up to or close to 80%, and the valley transmittances of the stop-bands are all down to near zero except the shortest resonant wavelength.
WVASE was shown in Fig. 5(c), and the top view of the fabricated 2D tri-band was shown in Fig. 5(d). Experimental results basically agree with the simulated results, and the transmission spectrum of TE wave almost equal with that of TM wave. Similar to 1D case, due to the strong absorption, the peak transmittance of the first resonance is approximately 40%, which is also lower than the simulated results. 3. Conclusions In summary, multi-band transmission color filters, with bandwidths of dozens nanometers are successfully designed with the proposed analytical method. The 1D multi-band filters have peak transmittance up to or close to 80% for TM polarization, as well as a good performance down to near zero for the valley transmittances of the stop-bands. The 2D multi-band filter has peak transmittance close to 60% for both TE and TM polarization. The central wavelength of the multi-band color filters can be modulated by the thickness of the planar waveguide and height of the grating to meet the real spectra of multi-color white LEDs. Experimental results of the 1D and 2D tri-band filter demonstrate the effectiveness of the proposed analytical method and show its potential to design the multi-band transmission color filters with high peak transmittance and dozens nanometers bandwidths. The bandwidths of the multi-band color filters are dozens nanometers, but not controlled in the design. Nevertheless, the analytical method need to be further improved by analyzing the hybridization to design multi-band filter with better performances, including higher peak transmittance and more matched bandwidths.
2.2. Design of 2D Tri-band color filter
Acknowledgments
Due to the plasmonic mode is excited only by TM polarized radiation, the 1D filter is polarization dependent. To decrease such polarization dependence, one 2D tri-band color filter is designed. As shown in Fig. 5(a), a 2D subwavelength metallic grating is mounted on the planar waveguide layer which is same as that in the 1D multi-band filter. The parameters of the designed 2D tri-band color filter are almost entirely consistent with those of the designed 1D tri-band color filter except with duty cycle of 0.7. The transmission spectra of the 2D tri-band color filter have been calculated for both TE and TM incident light (𝐻z is along the 𝑥 or 𝑧 axis, respectively). As shown in Fig. 5(b), the transmission spectra under TE and TM incident light are almost the same. The peak transmittances are close to 60% and the valley transmittances of the stop-bands are down to near zero. The far field spectra measured by
This work was supported by the National Key Basic Research Program of China (No. 2013CB329202) and National Natural Science Foundation of China (No. 61675109). References [1] K. Cui, J. Quan, et al., Performance of indoor optical femtocell by visible light communication, Opt. Commun. 298–299 (7) (2013) 59–66. [2] J. Li, Z. Huang, et al., Hybrid time-frequency domain equalization for LED nonlinearity mitigation in OFDM-based VLC systems, Opt. Express 23 (1) (2015) 611–619. [3] C. Tang, M. Jiang, H. Shen, C. Zhao, Analysis and optimization of P-LDPC coded RGB-LED-based VLC systems, IEEE Photonics J. 7 (6) (2015) 1–13. [4] C. Hsu, G. Chen, et al., Adaptive filtering for white-light LED visible light communication, Opt. Eng. 56 (1) (2017) 016115.
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Q. Wang et al.
Optics Communications 403 (2017) 330–334 [15] T. Xu, H. Shi, et al., Structural colors: From plasmonic to carbon nanostructures, Small 7 (22) (2011) 3128–3136. [16] A.F. Kaplan, T. Xu, et al., High efficiency resonance-based spectrum filters with tunable transmission bandwidth fabricated using nanoimprint lithography, Appl. Phys. Lett. 99 (14) (2011) 143111. [17] Y. Yoon, C. Park, et al., Highly efficient color filter incorporating a thin metal– dielectric resonant structure, Appl. Phys. Express 5 (2) (2012) 02250. [18] A.F. Kaplan, T. Xu, Y.-K. Wu, L.J. Guo, Multilayer pattern transfer for plasmonic color filter applications, J. Vac. Sci. Technol. B 28 (6) (2010) C6O60–C6O63. [19] Y. Xue, C. Wang, et al., Compound polarized wavelength filters with a single subwavelength structure, Opt. Commun. 284 (1) (2011) 501–509. [20] N. Nguyen-Huu, Y.L. Lo, et al., Color filters featuring high transmission efficiency and broad bandwidth based on resonant waveguide-metallic grating, Opt. Commun. 284 (10–11) (2011) 2473–2479. [21] R. Hu, Y. Liang, et al., Dual-band bandpass filter based on compound metallic grating waveguide structure, Opt. Commun. 336 (2015) 110–115. [22] C. Tan, J. Simonen, et al., Hybrid waveguide-surface plasmon polariton modes in a guided-mode resonance grating, Opt. Commun. 285 (21–22) (2012) 4381–4386. [23] Y. Chen, H. Ming, Review of surface plasmon resonance and localized surface plasmon resonance sensor, Photonic Sens. 2 (1) (2012) 37–49. [24] M.W. Knight, N.S. King, et al., Aluminum for plasmonics, ACS Nano 8 (1) (2014) 834–840. [25] E.D. Pauk, Handbook of Optical Constants of Solids III, Academic Press, 1998. [26] J. Ji, Tutorial of Advanced Optics, Science Press, 2009.
[5] J. Sung, C. Chow, et al., Is blue optical filter necessary in high speed phosphor-based white light LED visible light communications?, Opt. Express 22 (17) (2014) 20646– 20651. [6] A.V. Tikhonravov, M.K. Trubetskov, et al., Application of the needle optimization technique to the design of optical coatings, Appl. Opt. 35 (28) (1996) 5493–5508. [7] A. Belardini, A. Bosco, et al., Femtosecond pulses chirping compensation by using one-dimensional compact multiple-defect photonic crystals, Appl. Phys. Lett. 89 (3) (2006) 031111. [8] G. Shambat, M.S. Mirotznik, et al., Photonic crystal filters for tri-band optical filtering on a monolithic substrate, J. Nanophotonics 3 (1) (2009) 031506–03150611. [9] F. Biancalana, All-optical diode action with quasiperiodic photonic crystals, J. Appl. Phys. 104 (9) (2008) 093113. [10] S. Wang, X. Chen, et al., Fractal independently tunable multichannel filters, Appl. Phys. Lett. 90 (21) (2007) 211113. [11] G.A.F.B. Victor, Bistability, multistability and non-reciprocal light propagation in Thue–Morse multilayered structures, New J. Phys. 12 (5) (2010) 053041. [12] S. Kozhukh, S. Zhukovsky, et al., Design of high-transmission multiband multilayer filters for Raman spectroscopy, J. Nanophotonics 6 (1) (2012) 061704. [13] S. Tibuleac, R. Magnusson, Reflection and transmission guided-mode resonance filters, J. Opt. Soc. Am. A 14 (7) (1997) 1617–1626. [14] C. Park, Y. Yoon, et al., Polarization-independent visible wavelength filter incorporating a symmetric metal–dielectric resonant structure, Opt. Express 20 (21) (2012) 23769–23777.
334
Contents lists available at ScienceDirect
Optics Communications journal homepage: www.elsevier.com/locate/optcom
Multi-band transmission color filters for multi-color white LEDs based visible light communication Qixia Wang a , Zhendong Zhu a,b , Huarong Gu a , Mengzhu Chen a , Qiaofeng Tan a, * a b
State Key Laboratory of Precision Measurement Technology and Instruments, Department of Precision Instrument, Tsinghua University, Beijing 100084, China National Institute of Metrology, Beijing, 100018, China
a r t i c l e
i n f o
Keywords: Diffraction gratings Wavelength filtering devices Visible light communication
a b s t r a c t Light-emitting diodes (LEDs) based visible light communication (VLC) can provide license-free bands, high data rates, and high security levels, which is a promising technique that will be extensively applied in future. Multiband transmission color filters with enough peak transmittance and suitable bandwidth play a pivotal role for boosting signal-noise-ratio in VLC systems. In this paper, multi-band transmission color filters with bandwidth of dozens nanometers are designed by a simple analytical method. Experiment results of one-dimensional (1D) and two-dimensional (2D) tri-band color filters demonstrate the effectiveness of the multi-band transmission color filters and the corresponding analytical method. © 2017 Elsevier B.V. All rights reserved.
1. Introduction Visible light communication (VLC), which can provide free license with a new broad band, high data rates and high security, has attracted many attentions [1–3]. VLC is considered as a promising solution for the next-generation 5G wireless communications since it uses the visible spectrum to solve the congested radio-frequency communication spectrum [4]. The multi-color white light light-emitting diodes (LEDs) have been demonstrated to mitigate the LEDs nonlinearity when using orthogonal frequency division multiplexing modulations [5]. Usually, two major types of commercially multi-color white light LEDs, red– green–blue (RGB) LEDs and red–green–blue–amber (RGBA) LEDs, are available. Considering that noise usually comes from background light, multi-band transmission color filters are key components for filtering out the wanted light, whose central wavelengths and bandwidths correspond to the multi-color LEDs. Multi-band transmission color filters with bandwidth of dozens nanometers can be achieved by using multilayered thin films, however such multilayered thin films require high precision of thickness and refractive indices [6]. Multi-band filters can also be realized by onedimensional photonic crystals with multiple defects [7–12], which also require high precision of thickness and refractive indices. The guidedmode resonance of diffraction grating is introduced to design the multiband filter, however the bandwidth is very narrow [13]. Metallic grating was introduced to enlarge the bandwidth. The transmission * Corresponding author.
E-mail address: [email protected] (Q. Tan). http://dx.doi.org/10.1016/j.optcom.2017.07.065 Received 19 March 2017; Received in revised form 27 June 2017; Accepted 23 July 2017 Available online 4 August 2017 0030-4018/© 2017 Elsevier B.V. All rights reserved.
color filters with tunable transmission bandwidth of 13–100 nm were designed, which based on the hybridization between plasmonic mode and waveguide mode [14–20]. But such color filters have only one single transmission band and were designed based on optimization. Nevertheless, there is rare research on tri-band or multi-band transmission filters with bandwidth of dozens nanometers. Most recently, a dualband bandpass filter with 70 nm bandwidth was proposed based on the hybridization of waveguide resonance mode and the SPP mode [21]. Though the filter was designed for resonance wavelength in the infrared band. The structure with a groove carved on the metal strip of a subwavelength grating is difficult to fabricate, and the experimental results were not given. In this paper, multi-band transmission filters with bandwidth of dozens nanometers, where dielectric waveguide is loaded with a onedimensional (1D) or two-dimensional (2D) subwavelength metallic grating, are proposed. A simple analytical method is presented to design the tri-band and quad-band transmission filter. The 1D multi-band color filters have peak transmittance up to or close to 80% for TM polarization, as well as a good performance down to near zero for the valley transmittances of the stop-bands. The 2D tri-band filter has peak transmittance up to 60% for both TE and TM polarization. Both 1D and 2D tri-band color filters are fabricated. The experiment results demonstrate the effectiveness of the proposed analytical method and the potential of designing multi-band transmission color filters.
Q. Wang et al.
Optics Communications 403 (2017) 330–334
Fig. 1. Configuration of the proposed 1D tri-band color filter. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
2. Design and experiment 2.1. Design of 1D multi-band color filters The configuration of the proposed 1D tri-band color filter is illustrated in Fig. 1. One-dimensional subwavelength metallic grating is mounted on a planar waveguide layer. The parameters of the grating are denoted as the period 𝛬, the height 𝑑 and the duty cycle ratio 𝑓 . The device is incident under TM polarization light from the top side, where the magnetic field (𝐻z ) is perpendicular to the plane of the grating vector. The dielectric planar waveguide layer with the thickness ℎ is deposited on silica substrate (SiO2 ). It is necessary to introduce a dielectric material with enough high refractive index, in which visible light can be concentrated. Here, titanium dioxide (TiO2 ) is used as the waveguide layer, because of its high transmission efficiency and ∼2.1 refractive index in visible range. The permittivities of the air, the waveguide layer and the substrate are assumed to be 𝜀0 , 𝜀1 and 𝜀2 , respectively. To achieve a multi-band transmission color filter at particular wavelengths for multi-color white LEDs, the resonant modes are analyzed, including the plasmonic mode and waveguide modes. Both modes can be excited when phase-matching condition between the incident beams and the modes is satisfied [22]. Either plasmonic mode or waveguide modes can be characterized by effective index 𝑛𝑒𝑓 𝑓 of the mode, and phase-matching equation can be written as
Fig. 2. Transmission spectra of two designed 1D tri-band color filters. The blue dash line is designed with 𝜆3 and 𝜆2 . The black dash dot line is design with 𝜆3 and 𝜆1 are selected. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
of waveguide, which is difficult to get an analytical solution of the structure parameters via Eq. (2), needs to be solved. The 1D multi-band color filter is designed with an analytic method based on wave vector matching. Arising out of the real spectrum of the RGB LEDs, measured by the spectrometer Maya 2000 pro, the triband color filter is desired with central wavelength of 𝜆1 (462 nm), 𝜆2 (554 nm) and 𝜆3 (658 nm). For a tri-band color filter, the waveguide should sustain two modes, 𝑚 = 0 and 1, which respond primarily to the largest resonance wavelength 𝜆3 and a higher order mode at 𝜆2 or 𝜆1 , respectively. The plasmonic mode responds primarily to the third resonance wavelength 𝜆1 or 𝜆2 . Both silver (Ag) and aluminum (Al) enable strong plasmon resonances spanning much of the visible region [24]. Due to the advantage of lower cost compared to Ag, Al is chosen as the grating in this paper. The Lorentz–Drude model [25] is applied for fitting the permittivity of Al. Without loss of generality, 𝑓 is given as 0.5. When such a structure is illuminated with incident light as shown in Fig. 1, part of the beam is reflected, part is directly transmitted and part is diffracted, exciting waveguide modes that trapped inside the waveguide layer. The 𝑦-component of the wave vector 𝛹 in the ( )1∕2 waveguide layer can be written as 𝛹 = 𝑘2𝑖 𝜀1 − 𝛽 2 . To ensure peak transmittance and cut down the energy reflected by the interface as much as possible, the 𝑦-component of the wave vector should be made as close as possible to the wave vector in the air or substrate [26]. When 𝛹 is made similarly to wave vector either at the top or the bottom interface of the waveguide layer, 𝛽 will be the particular solution of Eq. (2). Here, 𝜆2 and 𝜆3 are selected to be the two modes sustained in the waveguide, then (( ) )1∕2 2 ⎧ √ 2𝜋 2𝜋 2 𝜀 − 𝛽 = 𝜀2 (for bottom interface) ⎪ 1 𝜆3 𝜆3 ⎪ (3) ⎨(( ) )1∕2 2 ⎪ √ 2𝜋 2𝜋 2 𝜀1 − 𝛽 = 𝜀0 (for top interface) . ⎪ 𝜆2 𝜆2 ⎩
2𝜋 = 𝑘𝑖 𝑛𝑒𝑓 𝑓 (1) 𝛬 where 𝜆𝑖 is the desired resonance wavelength, 𝑘𝑖 = 2𝜋∕𝜆𝑖 is the propagation constant in free space, 𝜃 is the incident angle, 𝑝 is the diffraction order. Considering that the period 𝛬 of the grating is less than the resonance wavelength, the diffraction order 𝑝 is only considered as 1. The plasmonic resonance would be produced at the metal–dielectric and metal–air interfaces [23]. The 𝑛𝑒𝑓 𝑓 of planar waveguide can be solved by the eigen-equation of the waveguide [15]. The metallic grating, whose height 𝑑 is thin enough, produces a small perturbation on the resonance wavelength of the guided mode in the waveguide layer that can be ignored. Therefore, the eigen-equation for TM modes of the planar waveguide can be written as ( )1∕2 ( 2 ) 𝜀1 𝛽 2 − 𝑘2𝑖 𝜀0 2 1∕2 𝑘𝑖 𝜀 1 − 𝛽 ℎ = 𝑚𝜋 + arctan 𝜀0 𝑘2 𝜀1 − 𝛽 2 𝑖 )1∕2 ( 2 − 𝑘2 𝜀 𝛽 𝜀1 𝑖 2 + arctan (2) 𝜀2 𝑘2 𝜀1 − 𝛽 2
𝑘𝑖 sin 𝜃 + 𝑝
𝑖
where 𝑚 is the number of the waveguide mode, 𝛽 is the propagation constant of the guided modes which can be written as 𝛽 = 𝑘𝑖 𝑛𝑒𝑓 𝑓 . Since the guided modes can be excited by the first order diffraction of incident light by the metal grating given by Eq. (1), we can choose the proper parameters of metallic grating and waveguide to efficiently couple the incident light into waveguide modes at multiple specific resonance wavelengths 𝜆𝑖 . The resonances should take place at the particular solutions of 𝑛𝑒𝑓 𝑓 in Eq. (2). That means an inverse problem 331
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Fig. 3. (a) Comparison of the transmission spectrum of the designed 1D tri-band color filter (𝛬 = 350 nm, ℎ = 280 nm, 𝑓 = 0.5 and 𝑑 = 50 nm) and the spectrum of RGB LEDs. (b) The measured transmission spectrum. (c) The SEM image of the filter. (d) The re-calculated transmission spectrum with the parameters measured by the SEM. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
When the period 𝛬 is determined, Eq. (2) tells that ℎ is only associated with 𝑚, namely the sustaining mode number 𝑚 of the waveguide. In other words, the thickness ℎ is defined by the mode number 𝑚 of the waveguide. As far as a tri-band color filter, 𝑚 is determined by the number of bands. For tri-band color filter, the waveguide should sustain two modes, 𝑚 = 0 and 1. Then we can get the value range of waveguide thickness ℎ from Eq. (2). Furthermore, ℎ can be optimized in a small range by rigorous coupled wave analysis based on the software RSOFT. The plasmonic mode responds to the first resonance wavelength 𝜆1 , which is sensitive to the height 𝑑 of the grating. For normal incidence and 𝜆1 = 460 nm, 𝑑 is chosen as 50 nm [17]. All parameters of the designed tri-band color filter are 𝛬 = 350 nm, ℎ = 280 nm, 𝑓 = 0.5 and 𝑑 = 50 nm. If 𝜆1 and 𝜆3 are selected in Eq. (3), then another filter is designed which parameters are 𝛬 = 325 nm, ℎ = 285 nm, 𝑓 = 0.5 and 𝑑 = 50 nm. The corresponding far field transmission spectra of the designed tri-band color filters have been calculated and plotted in Fig. 2. The transmission is defined by the ratio of intensity of TM or TE wave that pass through the filter and intensity of incident in the same polarization. As shown in Fig. 2, the wavelengths 𝜆2 and 𝜆3 should be chosen to be sustained in the waveguide to get the better color filter. The far field spectrum of the designed tri-band filter is simulated by RSOFT in blue dash line in Fig. 3(a). The peak transmittances of the resonant bands are all over 80% and the valley transmittances of the stop-bands are all down to near zero except the shortest resonant wavelength. The bandwidths are dozens nanometers as expected. Additionally, the resonant wavelengths are only a little different to that of RGB LEDs. To demonstrate the proposed method, the designed 1D triband color filters were fabricated. The far field spectrum was measured with spectroscopic ellipsometry (WVASE, J.A. Woollam Co.) incident with a TM polarized plane wave illuminating from the top side by normal incidence (in the −𝑦 axis direction). The measured results are shown in Fig. 3(b). The properties of the measured spectrum basically agree with the simulated results including the central wavelengths and bandwidths of the resonant peaks, while small deviation exists in the central wavelengths. To track the origin of the small deviation, the cross sectional of the fabricated filter was scan by the scanning electron microscope (SEM). As shown in Fig. 3(c), the thickness of the TiO2 layer is about 280 nm, the period and the height of the grating respectively are 350 nm and 50 nm, but the duty cycle ratio is 0.6. We re-calculate the far field transmission spectrum of the filter by RSOFT with the parameters
Fig. 4. Comparison of the spectrum of the designed quad-band filter (𝛬 = 325 nm, ℎ = 480 nm, 𝑓 = 0.5 and 𝑑 = 50 nm) and the measured spectrum of one RGBA LEDs. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Combining Eq. (3) with Eq. (1), we can obtain two grating period 𝛬1 and 𝛬2 , as shown in Eq. (4). ⎧ 2𝜋 2𝜋 ⎪𝛽 = 𝜆 sin 𝜃 + 𝛬 3 1 ⎪( )1∕2 ⎨ ( )2 √ 2𝜋 2𝜋 ⎪ 𝜀1 − 𝛽 2 = 𝜀2 ⎪ 𝜆3 𝜆3 ⎩
(4a)
⎧ 2𝜋 2𝜋 ⎪𝛽 = 𝜆 sin 𝜃 + 𝛬 2 2 ⎪( )1∕2 ⎨ ( )2 √ 2𝜋 2𝜋 ⎪ 𝜀1 − 𝛽 2 = 𝜀0 . ⎪ 𝜆2 𝜆2 ⎩
(4b)
Then, without loss of generality, the 𝛬 takes the average value of these two periods instead the parameters were obtained via Eqs. (1) and (2). ( ) 𝛬 = 𝛬1 + 𝛬2 ∕2.
(5) 332
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Fig. 5. (a) Configuration of the proposed 2D tri-band color filter. (b) The transmission spectra of the filter (𝛬𝑥 = 𝛬𝑧 = 350 nm, 𝑓𝑥 = 𝑓𝑧 = 0.7, ℎ = 280 nm and 𝑑 = 50 nm). (c) The measured transmission spectra. (d) The SEM image of the filter. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
measured by the SEM. The re-simulation results are respectively shown in Fig. 3(d), and which is more consistent with the experimental results. Al, with strong absorption of near UV spectrum, shows strong absorption at the first resonance. The peak transmittance of the first resonance is approximately 40%, which is lower than the simulated results. There are several other types of multi-color white LEDs, such as red– green–blue–amber (RGBA) LEDs. Arising out of the real spectrum of the RGBA LEDs, four center wavelengths of the quad-band color filter are 𝜆1 = 456 nm, 𝜆2 = 532 nm, 𝜆3 = 597 nm and 𝜆4 = 663 nm, respectively, as shown in Fig. 4, in red solid line. Compared with the tri-band color filter, more complicated electromagnetic field will arise for quad-band color filter and will bring more difficulty to solve Eq. (2). However, the proposed method can also overcome such difficulty. The quad-band color filter can be realized by only changing the mode number of the waveguide, 𝑚 = 0, 1 and 2, respectively. Two periods are obtained by substituting two sets of center wavelengths 𝜆4 , 𝜆3 and 𝜆2 , 𝜆1 into Eqs. (4) and (5). Then the 𝛬 takes the average value of two periods without loss of generality. Similarly, the waveguide should sustain three modes. Under this condition, the value range of ℎ also can be calculated from the Eq. (2). For normal incidence, the geometric parameters of quad-band color filter are 𝑓 = 0.5, 𝛬 = 325 nm, ℎ = 480 nm, and 𝑑 = 50 nm. The far field spectrum of the designed quad-band filter simulated by RSOFT is shown in Fig. 4, in blue dash line. The peak transmittances of the resonant bands are up to or close to 80%, and the valley transmittances of the stop-bands are all down to near zero except the shortest resonant wavelength.
WVASE was shown in Fig. 5(c), and the top view of the fabricated 2D tri-band was shown in Fig. 5(d). Experimental results basically agree with the simulated results, and the transmission spectrum of TE wave almost equal with that of TM wave. Similar to 1D case, due to the strong absorption, the peak transmittance of the first resonance is approximately 40%, which is also lower than the simulated results. 3. Conclusions In summary, multi-band transmission color filters, with bandwidths of dozens nanometers are successfully designed with the proposed analytical method. The 1D multi-band filters have peak transmittance up to or close to 80% for TM polarization, as well as a good performance down to near zero for the valley transmittances of the stop-bands. The 2D multi-band filter has peak transmittance close to 60% for both TE and TM polarization. The central wavelength of the multi-band color filters can be modulated by the thickness of the planar waveguide and height of the grating to meet the real spectra of multi-color white LEDs. Experimental results of the 1D and 2D tri-band filter demonstrate the effectiveness of the proposed analytical method and show its potential to design the multi-band transmission color filters with high peak transmittance and dozens nanometers bandwidths. The bandwidths of the multi-band color filters are dozens nanometers, but not controlled in the design. Nevertheless, the analytical method need to be further improved by analyzing the hybridization to design multi-band filter with better performances, including higher peak transmittance and more matched bandwidths.
2.2. Design of 2D Tri-band color filter
Acknowledgments
Due to the plasmonic mode is excited only by TM polarized radiation, the 1D filter is polarization dependent. To decrease such polarization dependence, one 2D tri-band color filter is designed. As shown in Fig. 5(a), a 2D subwavelength metallic grating is mounted on the planar waveguide layer which is same as that in the 1D multi-band filter. The parameters of the designed 2D tri-band color filter are almost entirely consistent with those of the designed 1D tri-band color filter except with duty cycle of 0.7. The transmission spectra of the 2D tri-band color filter have been calculated for both TE and TM incident light (𝐻z is along the 𝑥 or 𝑧 axis, respectively). As shown in Fig. 5(b), the transmission spectra under TE and TM incident light are almost the same. The peak transmittances are close to 60% and the valley transmittances of the stop-bands are down to near zero. The far field spectra measured by
This work was supported by the National Key Basic Research Program of China (No. 2013CB329202) and National Natural Science Foundation of China (No. 61675109). References [1] K. Cui, J. Quan, et al., Performance of indoor optical femtocell by visible light communication, Opt. Commun. 298–299 (7) (2013) 59–66. [2] J. Li, Z. Huang, et al., Hybrid time-frequency domain equalization for LED nonlinearity mitigation in OFDM-based VLC systems, Opt. Express 23 (1) (2015) 611–619. [3] C. Tang, M. Jiang, H. Shen, C. Zhao, Analysis and optimization of P-LDPC coded RGB-LED-based VLC systems, IEEE Photonics J. 7 (6) (2015) 1–13. [4] C. Hsu, G. Chen, et al., Adaptive filtering for white-light LED visible light communication, Opt. Eng. 56 (1) (2017) 016115.
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Q. Wang et al.
Optics Communications 403 (2017) 330–334 [15] T. Xu, H. Shi, et al., Structural colors: From plasmonic to carbon nanostructures, Small 7 (22) (2011) 3128–3136. [16] A.F. Kaplan, T. Xu, et al., High efficiency resonance-based spectrum filters with tunable transmission bandwidth fabricated using nanoimprint lithography, Appl. Phys. Lett. 99 (14) (2011) 143111. [17] Y. Yoon, C. Park, et al., Highly efficient color filter incorporating a thin metal– dielectric resonant structure, Appl. Phys. Express 5 (2) (2012) 02250. [18] A.F. Kaplan, T. Xu, Y.-K. Wu, L.J. Guo, Multilayer pattern transfer for plasmonic color filter applications, J. Vac. Sci. Technol. B 28 (6) (2010) C6O60–C6O63. [19] Y. Xue, C. Wang, et al., Compound polarized wavelength filters with a single subwavelength structure, Opt. Commun. 284 (1) (2011) 501–509. [20] N. Nguyen-Huu, Y.L. Lo, et al., Color filters featuring high transmission efficiency and broad bandwidth based on resonant waveguide-metallic grating, Opt. Commun. 284 (10–11) (2011) 2473–2479. [21] R. Hu, Y. Liang, et al., Dual-band bandpass filter based on compound metallic grating waveguide structure, Opt. Commun. 336 (2015) 110–115. [22] C. Tan, J. Simonen, et al., Hybrid waveguide-surface plasmon polariton modes in a guided-mode resonance grating, Opt. Commun. 285 (21–22) (2012) 4381–4386. [23] Y. Chen, H. Ming, Review of surface plasmon resonance and localized surface plasmon resonance sensor, Photonic Sens. 2 (1) (2012) 37–49. [24] M.W. Knight, N.S. King, et al., Aluminum for plasmonics, ACS Nano 8 (1) (2014) 834–840. [25] E.D. Pauk, Handbook of Optical Constants of Solids III, Academic Press, 1998. [26] J. Ji, Tutorial of Advanced Optics, Science Press, 2009.
[5] J. Sung, C. Chow, et al., Is blue optical filter necessary in high speed phosphor-based white light LED visible light communications?, Opt. Express 22 (17) (2014) 20646– 20651. [6] A.V. Tikhonravov, M.K. Trubetskov, et al., Application of the needle optimization technique to the design of optical coatings, Appl. Opt. 35 (28) (1996) 5493–5508. [7] A. Belardini, A. Bosco, et al., Femtosecond pulses chirping compensation by using one-dimensional compact multiple-defect photonic crystals, Appl. Phys. Lett. 89 (3) (2006) 031111. [8] G. Shambat, M.S. Mirotznik, et al., Photonic crystal filters for tri-band optical filtering on a monolithic substrate, J. Nanophotonics 3 (1) (2009) 031506–03150611. [9] F. Biancalana, All-optical diode action with quasiperiodic photonic crystals, J. Appl. Phys. 104 (9) (2008) 093113. [10] S. Wang, X. Chen, et al., Fractal independently tunable multichannel filters, Appl. Phys. Lett. 90 (21) (2007) 211113. [11] G.A.F.B. Victor, Bistability, multistability and non-reciprocal light propagation in Thue–Morse multilayered structures, New J. Phys. 12 (5) (2010) 053041. [12] S. Kozhukh, S. Zhukovsky, et al., Design of high-transmission multiband multilayer filters for Raman spectroscopy, J. Nanophotonics 6 (1) (2012) 061704. [13] S. Tibuleac, R. Magnusson, Reflection and transmission guided-mode resonance filters, J. Opt. Soc. Am. A 14 (7) (1997) 1617–1626. [14] C. Park, Y. Yoon, et al., Polarization-independent visible wavelength filter incorporating a symmetric metal–dielectric resonant structure, Opt. Express 20 (21) (2012) 23769–23777.
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