Open Access
Add to BibSonomy
Abstract
We report the design of broadband highly reflective subwavelength high-index-contrast gratings (HCGs) for both TE and TM polarizations in the visible regime. Results show that high reflectivity above 99% covering 544–726 nm or 510–666 nm can be achieved, corresponding to a fractional bandwidth of Δλ/λ0 = 28.7% or 26.5% for the TM or TE polarization, respectively. We reveal that these broad high-reflectivity bands originate from a blend of multiple leaky modes, similar to the counterparts operating in the near-infrared regime. By investigating the effects of the grating height, period, and width, we find that the broadband high reflectivity requires careful optimization. We expect that this work will advance the engineering of broadband HCG reflectors and promote their applications in the visible regime.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Highly reflective and broadband mirrors are essential optical components in a diverse range of applications. Although aluminum or silver coated mirrors can be used over a very broad spectral range (from 450 nm to 20 $\mu$m), they have an intrinsically lower laser-induced damage threshold than all-dielectric mirrors, and suffer from relatively high absorption loss. As a result, metallic coated mirrors are not suitable for high-power ultra-short laser applications [1] and transmission-type devices such as etalon filters used in hyper-spectral imaging [2,3]. Commercially available broadband mirrors made of fused silica have negligible loss and high reflectivity, but they are too thick (usually $\sim$ mm) to be integrated. Distributed Bragg reflectors (DBRs) formed from multiple layers of alternating high- and low-index all-dielectric materials are lossless and highly reflective, but these reflectors have limited bandwidth [3] and require a lengthy deposition process which adds the cost [4].
In 2004, Mateus et al. [3,5] demonstrated that a subwavelength high-index-contrast grating (HCG), which consists of periodic high-index bars surrounded by low-index environment, has a high reflectivity exceeding 95% over a broad spectral range (the fractional bandwidth reaches $\Delta \lambda /\lambda _0\approx 50\%$). Since then, HCGs as well as their two-dimensional (2D) counterparts, high-index metamaterials or metasurfaces, have attracted increasing attentions because of their broadband and high reflectivity [6,7]. Taking advantages of the attractive merits of HCGs compared to DBRs, such as the one tenth thickness, one thousandth weight, ten times wider bandwidth, and increased fabrication tolerance, many groups [8–12] have demonstrated highly integrated and wavelength tunable vertical-cavity surface-emitting lasers (VCSELs) incorporating HCG mirrors. Highly reflective HCGs have also been used in many other applications, such as high-Q factor optical resonators [13], hollow-core waveguides [14], nonlinear optical applications [15], and sensors [16].
To date, HCGs in most literature have been designed or analyzed for the near-infrared or longer wavelength regime. It has been showed that the ultra-broad reflection spectrum can be easily scaled to longer wavelength ranges by simply multiplying the dimensions by a constant [3,17]. However, when HCGs are scaled to shorter wavelengths such as the visible regime, the bandwidth is not as broad as expected. This is partially because large refractive index contrast between the HCG and the surrounding environment is vital for achieving large high-reflectivity bandwidth [3,18], whereas materials that are transparent in the visible regime usually have relatively low refractive index. Although Ahmed et al. [19] designed a broadband HCG reflector of reflectivity above 99% over 500-700 nm, the intrinsic loss of the high-index semiconductor material AlGaAs is not considered. By using lossless TiO$_2$ HCGs suspended in air, Hashemi et al. [20] achieved only 80 nm bandwidth in the visible regime. Yao and Wu [21] achieved reflectivity above 90% over 640-790 nm, corresponding to 150 nm bandwidth, but the gratings are made of heterogeneous amorphous silicon, silicon nitride, and silicon dioxide. Quite recently, He et al. [22] made use of particle swarm optimization and designed a broadband GaN HCG reflector, but the bandwidth for 99% reflectance is only 84 nm in the visible regime. In other words, it remains challenging to achieve broadband and highly reflective HCGs in the visible regime.
In this work, we address this challenge and report the design of broadband highly reflective subwavelength HCGs in the visible regime. By exploring the geometric parameters under normal incidence, we show that high reflectivity above 99% covering 544–726 nm (or 510–666 nm), corresponding to $\Delta \lambda /\lambda _0\approx 28.7\%$ (or 26.5%) can be achieved for the TM (or TE) polarization. Strikingly, the obtained bandwiths for both polarizations are larger than those of previously reported HCGs [19–22] or DBRs [23] operating in the visible regime. Moreover, these fractional bandwidths are comparable to those of HCGs operating in the near-infrared or longer wavelength regimes [6]. By systematically investigating the effects of the grating bar height, period and duty factor, we will show that the HCGs operating in the visible regime have stringent performance tolerance on the structure sizes, which partially explains the relatively narrow bandwidth for high reflectivity in the literature.
2. Simulation setup
Figure 1 illustrates the HCG designed for broadband high reflectivity in the visible regime. It consists of periodic TiO$_2$ grating bars suspended in air with a SiO$_2$ substrate. The grating bar has height $h$, width $w$, and period $p$. The duty cycle is defined as the ratio of the high-index bar width to the period, i.e., $w/p$. Here we adopt TiO$_2$ since it is transparent and has large refractive index in the visible regime.
This HCG structure could be fabricated with the state-of-the-art nanofabrication processes following [20]. A thin film of TiO$_2$ layer is first deposited on a SiO$_2$ substrate by sputtering. The TiO$_2$ grating is patterned using electron-beam lithography followed by reactive ion etching. The underlying SiO$_2$ is then etched with a controlled thickness $d$.
Fig. 1. Schematic of a TiO$_2$/air HCG with a SiO$_2$ substrate. $h$, $w$, and $p$ are the grating bar height, width, and period, respectively. $d$ is the distance between the HCG grating bars and the SiO$_2$ substrate. Plane wave light with TM (polarized in $x$ direction) or TE (polarized in $y$ direction) polarization normally impinges onto the grating.
In order to design HCGs with high reflectivity and broad bandwith in the visible regime, we performed extensive calculations by exploring all the geometric parameters, i.e., the grating height, period and duty cycle, for both TM and TE polarizations. Here the TM or TE polarization indicates that the electric field of the normally incident plane wave is polarized in the $x$ or $y$ direction. We aim to achieve high reflectivity above 99% over the widest spectral range in the visible regime. All the calculations were performed with a home-developed package for fully vectorial rigorous coupled-wave analysis (RCWA) following [24]. With the RCWA technique, the diffracted reflectance and transmittance efficiencies as well as the electric and magnetic fields can be obtained. In all our simulations, the wavelength-dependent refractive indices of TiO$_2$ are tabulated in [25], and the refractive index of SiO$_2$ is taken to be $n_\textrm {sub}=1.45$. The distance between the HCG and the SiO$_2$ substrate is taken to be large enough ($d=800$ nm), so that the SiO$_2$ substrate has little influence on the reflectance performance because the reflectivity of the air/SiO$_2$ interface is very small ($<4\%$).
3. Results and discussion
3.1 TM polarization
Figure 2 shows the zeroth-order reflectance and transmittance spectra of the optimized broadband and highly reflective HCG reflector for the TM polarization. The design parameters are $h=241$ nm, $p=360$ nm, and $w/p=0.69$. Since the visible wavelengths are larger than the structure’s Rayleigh wavelength, $\lambda _\textrm {R}=n_\textrm {air}p=360$ nm with $n_\textrm {air}=1$ (air), only the zeroth-order diffraction exists. High reflectivity above 99% (i.e., $R_0>99\%$) spans over 544–726 nm, corresponding to a bandwidth of $\Delta \lambda = 182$ nm and a fractional bandwidth of $\Delta \lambda /\lambda _0\approx 28.7\%$. This fractional bandwidth is much wider than those of reported HCGs operating in the visible regime [20,21], and is comparable to those of HCGs in the near-infrared regime or longer wavelengths [3,5,26].
In order to understand the physics underlying the broadband reflectivity, we re-plot the zeroth-order reflectance and transmittance spectra on a logarithmic scale. Figure 2 also shows that there are three transmittance dips inside the high-reflectivity band, which locate at 560 nm, 631 nm and 697 nm, respectively, and each of which corresponds to almost 100% reflection. This phenomenon is consistent with the results of HCGs operating in the near-infrared regime [26,27]. As clarified by Magnusson et al. [26,27], each of these transmittance dips corresponds to a leaky-mode resonance.
Fig. 2. Zeroth-order reflectance and transmittance spectra on (a) linear and (b) logarithmic scales of the optimal HCG-based broadband reflector for TM polarization. The optimized design parameters are $h=241$ nm, $p=360$ nm and $w/p=0.69$. The three dips locating at $\lambda =561$ nm, 631 nm and 697 nm correspond to almost perfect (near 100%) reflection.
The magnetic field distributions for the wavelengths of the three transmittance dips as well as those for another three wavelengths off these dips are shown in Fig. 3. Figure 3(a) shows that, at $\lambda =473$ nm for $T\approx 100\%$, the magnetic field is completely localized at the center of the grating bar. At the wavelengths for the three transmittance dips and for the two peaks between these dips, the magnetic fields are similar, but are quite different from Fig. 3(a): the field is mainly localized at the bottom of the grating bar, and has strong coupling between neighboring bars. The similar field distributions for wavelengths of the three transmittance dips and of the two intermediate peaks show that, the broadband spectrum with high reflectivity originates from the co-existence and interaction of three leaky modes. This is consistent with the HCGs operating in the near-infrared regime [26,27].
Fig. 3. Magnetic field distributions at (a)–(c) three wavelengths off the transmittance dips and (d)–(f) the three wavelengths of the transmittance dips in Fig. 2: (a) $\lambda =473$ nm for $T_0\approx 1$, (b) 600 nm and (c) 658 nm for the two transmittance peaks between the three dips, (d) 561 nm, (e) 631 nm, and (f) 697 nm. $|H_{0y}|$ is the magnetic field amplitude of the incident plane wave. The high-index TiO$_2$ bars are outlined by pink squares.
We further investigated the effects of the grating height $h$, period $p$ and duty factor $w/p$ on the broadband high reflectivity. Figures 4(a)–4(c) show that there exist S-shaped high reflection regions, which indicates the evolution of the reflectance spectra from narrow to broad bands. In general, these behaviors are very similar to HCGs that operate in the near-infrared regime. However, unlike the near-infrared HCGs, we find that the parameter ranges for the 99% contours extending over wide spectral ranges are extremely limited. In order to achieve broadband high reflectivity above 99%, Figs. 4(a)–4(c) respectively show that the grating height should be $240~\textrm {}\leq h \leq 243$ nm for $w/p=0.7$ and $p=360$ nm, that the period should be $358~\textrm {nm}\leq p \leq 361$ nm for $w/p=0.7$ and $h=241$ nm, and that the duty cycle should be $0.69 \leq w/p \leq 0.7$ for $h=241$ nm and $p=360$ nm. These results suggest that the HCGs operating in the visible regime have much more stringent tolerance on the structural sizes (only $1\sim 2\%$ variation) than those operating in the near-infrared regime, most parameters of which have a large tolerance range, sometimes up to 10% variation [3]. In other words, in order to achieve high reflectivity above 99% over a broad spectral band in the visible regime, all the geometric parameters ($h$, $p$ and $w/p$) should be designed with great care, imposing challenges on the fabrication. This explains why the previously reported designs of highly reflective TiO$_2$ HCGs have relatively narrow bandwidths [20].
Fig. 4. Dependence of calculated reflectance spectra for TM polarization on (a) bar height (b) period, and (c) duty cycle. (d)–(f) Associated transmittance spectra on a logarithmic scale. The horizontal dashed lines indicate the optimized design parameters used in Fig. 2. The white solid curves indicates the 99% contour.
Figures 4(d)–4(f) show the transmittance spectra on a logarithmic scale as functions of the grating height, period and duty cycle. These results show the zero-transmittance or the full-reflectance locus. For the optimized parameters indicated by the horizontal dashed lines, the high-reflectivity bandwidth is maximized and three leaky-mode resonances exist to achieve the broadest reflectance.
3.2 TE polarization
We also designed broadband highly reflective HCGs for TE-polarized incident light. The optimized design parameters are found to be $h=129$ nm, $p=510$ nm and $w/p=0.45$, and the resulting high reflectivity above 99% spans over 510–666 nm, corresponding to a bandwidth of $\Delta \lambda = 156$ nm and a fractional bandwidth of $\Delta \lambda /\lambda = 26.5\%$, as shown in Fig. 5(a). The obtained fractional bandwith for high reflectivity above 99% is slightly smaller than the optimized HCG for the TM polarization, but is wider than the reported HCG for the TE polarization [19], and comparable to those operating in the near-infrared regime [20,21,28].
Fig. 5. (a) Zeroth-order reflectance and transmittance spectra on both linear and logarithmic scales of an optimal HCG broadband reflector for TE polarization. The optimized design parameters are $h=129$ nm, $p=510$ nm and $w/p=0.45$. (b)-(d) Dependence of reflectivity spectra on (a) bar height (b) period, and (c) duty cycle. The horizontal dashed lines indicate the optimized design parameters used in (a). The white solid curves indicates the 99% contour.
By re-plotting the reflectance and transmittance spectra on a logarithmic scale in Fig. 5(a), we find that there are also three transmission dips within the broad high-reflectivity spectral band, which locate at $\lambda =518$ nm, 591 nm, and 645 nm, respectively. Although the wavelengths of these transmission dips for the TE polarization are different from those for the TM polarization, the underlying physics is similar: each transmission dip corresponds to a leaky-mode resonance, and the associated electric field is also localized at the bottom of the grating bar with strong coupling between neighboring bars (not shown here for the sake of concision). Therefore, the broadband high reflectivity for the TE polarization also originates from a blend of leaky-mode resonances.
Figures 5(b)–5(d) show the performance tolerance of the reflection spectra on the geometric parameters. Results show that, similar to the case of TM polarization, the parameter ranges for achieving broadband high reflectivity are also very limited. For $w/p=0.45$ and $p=510$ nm, the height should be $127~\textrm {nm}\leq h \leq 131$ nm; for $w/p=0.45$ and $h=129$ nm, the period should be $501~\textrm {nm}\leq p \leq 514$ nm; and for $p=510$ nm and $h=129$ nm, the duty cycle should be $0.446\leq w/p \leq 0.455$. These results suggest that the tolerance on the geometric parameters is also stringent, requiring careful design and fabrication for the TE polarization.
4. Conclusions
In conclusions, we have shown that broadband HCGs with reflectivity above 99% over 544–726 nm (or 510–666 nm), corresponding to a fractional bandwidth of $\Delta \lambda /\lambda _0\approx 28.7\%$ (or 26.5%) can be achieved for the TM (or TE) polarization. These high-reflectivity bandwidths are wider than or comparable to those of the previously reported HCGs operating in the visible or near-infrared regime. We have revealed that, similar to the broadband HCG reflectors operating in near-infrared regime, these wide high-reflectivity bandwidth in the visible regime also originates from a blend of multiple leaky modes. By investigating the effects of the geometric parameters, we have found that the broadband high-reflectivity spectra are very sensitive to grating sizes, which indicates that broadband high reflectivity requires careful optimization. We expect this work will promote the applications of HCGs in the visible regime, especially in tunable etalon filters and high power laser systems.
Funding
Key Research Items from the Ministry of Science and Technology of China (2016YFC1400701); Youth Innovation Promotion Association of the Chinese Academy of Sciences (2016320); Shenzhen Fundamental Research and Discipline Layout project (JCYJ20160608153308846, JCYJ20170413152328742).
Disclosures
The authors declare no conflicts of interest.
References
1. B. Wang and L. Gallais, “A theoretical investigation of the laser damage threshold of metal multi-dielectric mirrors for high power ultrashort applications,” Opt. Express 21(12), 14698–14711 (2013). [CrossRef]
2. N. Gat, “Imaging spectroscopy using tunable filters: a review,” Proc. SPIE 4056, 50–64 (2000). [CrossRef]
3. C. F. R. Mateus, M. C. Y. Huang, Y. Deng, A. R. Neureuther, and C. J. Chang-Hasnain, “Ultrabroadband mirror using low-index cladded subwavelength grating,” IEEE Photonics Technol. Lett. 16(2), 518–520 (2004). [CrossRef]
4. P. Moitra, B. A. Slovick, W. Li, I. I. Kravchencko, D. P. Briggs, S. Krishnamurthy, and J. Valentine, “Large-scale all-dielectric metamaterial perfect reflectors,” ACS Photonics 2(6), 692–698 (2015). [CrossRef]
5. C. Mateus, M. Huang, L. Chen, C. J. Chang-Hasnain, and Y. Suzuki, “Broad-band mirror (1.12-1.62 μm) using a subwavelength grating,” IEEE Photonics Technol. Lett. 16(7), 1676–1678 (2004). [CrossRef]
6. C. J. Chang-Hasnain and W. Yang, “High-contrast gratings for integrated optoelectronics,” Adv. Opt. Photonics 4(3), 379–440 (2012). [CrossRef]
7. P. Qiao, W. Yang, and C. J. Chang-Hasnain, “Recent advances in high-contrast metastructures, metasurfaces, and photonic crystals,” Adv. Opt. Photonics 10(1), 180–245 (2018). [CrossRef]
8. M. C. Y. Huang, Y. Zhou, and C. J. Chang-Hasnain, “A surface-emitting laser incorporating a high-index-contrast subwavelength grating,” Nat. Photonics 1(2), 119–122 (2007). [CrossRef]
9. S. Boutami, B. B. Bakir, J.-L. Leclercq, and P. Viktorovitch, “Compact and polarization controlled 1.55 μm vertical-cavity surface emitting laser using single-layer photonic crystal mirror,” Appl. Phys. Lett. 91(7), 071105 (2007). [CrossRef]
10. I.-S. Chung, V. Iakovlev, A. Sirbu, A. Mereuta, A. Caliman, E. Kapon, and J. Mørk, “Broadband mems-tunable high-index-contrast subwavelength grating long-wavelength VCSEL,” IEEE J. Quantum Electron. 46(9), 1245–1253 (2010). [CrossRef]
11. E. Haglund, J. Gustavsson, J. Bengtsson, Å. Haglund, A. Larsson, D. Fattal, W. Sorin, and M. Tan, “Demonstration of post-growth wavelength setting of VCSELs using high-contrast gratings,” Opt. Express 24(3), 1999–2005 (2016). [CrossRef]
12. M. Gebski, J. A. Lott, and T. Czyszanowski, “Electrically injected VCSEL with a composite DBR and MHCG reflector,” Opt. Express 27(5), 7139–7146 (2019). [CrossRef]
13. Y. Zhou, M. Moewe, J. Kern, M. C. Y. Huang, and C. J. Chang-Hasnain, “Surface-normal emission of a high-Q resonator using a subwavelength high-contrast grating,” Opt. Express 16(22), 17282–17287 (2008). [CrossRef]
14. Y. Zhou, V. Karagodsky, B. Pesala, F. G. Sedgwick, and C. J. Chang-Hasnain, “A novel ultra-low loss hollow-core waveguide using subwavelength high-contrast gratings,” Opt. Express 17(3), 1508–1517 (2009). [CrossRef]
15. T. Sun, W. Yang, and C. J. Chang-Hasnain, “Surface-normal coupled four-wave mixing in a high contrast gratings resonator,” Opt. Express 23(23), 29565–29572 (2015). [CrossRef]
16. B. Hogan, L. Lewis, M. McAuliffe, and S. P. Hegarty, “Mid-infrared optical sensing using sub-wavelength gratings,” Opt. Express 27(3), 3169 (2019). [CrossRef]
17. G. G. Zheng, Y. L. Chen, L. H. Xu, W. Su, and Y. Z. Liu, “High reflectivity broadband infrared mirrors with all dielectric subwavelength gratings,” Opt. Commun. 318, 57–60 (2014). [CrossRef]
18. V. Karagodsky, F. G. Sedgwick, and C. J. Chang-Hasnain, “Theoretical analysis of subwavelength high contrast grating reflectors,” Opt. Express 18(16), 16973–16988 (2010). [CrossRef]
19. A. Ahmed, M. Liscidini, and R. Gordon, “Design and analysis of high-index-contrast gratings using coupled mode theory,” IEEE Photonics J. 2(6), 884–893 (2010). [CrossRef]
20. E. Hashemi, J. Bengtsson, J. S. Gustavsson, S. Carlsson, G. Rossbach, and Å. Haglund, “TiO2 membrane high-contrast grating reflectors for vertical-cavity light-emitters in the visible wavelength regime,” J. Vac. Sci. Technol., B: Nanotechnol. Microelectron.: Mater., Process., Meas., Phenom. 33(5), 050603 (2015). [CrossRef]
21. Y. Yao and W. Wu, “All-dielectric heterogeneous metasurface as an efficient ultra-broadband reflector,” Adv. Opt. Mater. 5(14), 1700090 (2017). [CrossRef]
22. S. He, Q. Liu, T. Sa, and Z. Wang, “Design of broadband reflector at the visible wavelengths using particle swarm optimization,” AIP Adv. 9(7), 075301 (2019). [CrossRef]
23. D. Z. Cao, X. K. Yang, L. Y. Shen, C. C. Zhao, C. N. Luan, J. Ma, and H. D. Xiao, “Fabrication and properties of high quality InGaN-based LEDs with highly reflective nanoporous GaN mirrors,” Photonics Res. 6(12), 1144 (2018). [CrossRef]
24. M. G. Moharam, D. A. Pommet, E. B. Grann, and T. K. Gaylord, “Stable implementation of the rigorous coupled-wave analysis for surface-relief gratings: enhanced transmittance matrix approach,” J. Opt. Soc. Am. A 12(5), 1077–1086 (1995). [CrossRef]
25. “Refractive index of TiO2-rutile,” https://www.filmetrics.com/refractive-index-database/TiO2+-+Rutile.
26. M. Shokooh-Saremi and R. Magnusson, “Wideband leaky-mode resonance reflectors: Influence of grating profile and sublayers,” Opt. Express 16(22), 18249–18263 (2008). [CrossRef]
27. R. Magnusson and M. Shokooh-Saremi, “Physical basis for wideband resonant reflectors,” Opt. Express 16(5), 3456–3462 (2008). [CrossRef]
28. T. Khaleque, M. J. Uddin, and R. Magnusson, “Design and fabrication of broadband guided-mode resonant reflectors in TE polarization,” Opt. Express 22(10), 12349–12358 (2014). [CrossRef]
