- Email: [email protected]
High-Q photonic crystal heterostructure microcavities by tuning air holes
Optics Communications 446 (2019) 88–92
Contents lists available at ScienceDirect
Optics Communications journal homepage: www.elsevier.com/locate/optcom
High-Q photonic crystal heterostructure microcavities by tuning air holes Peng Shi Nanophotonics Research Centre, Shenzhen University, Shenzhen, 518060, Guangdong, China
ARTICLE
INFO
Keywords: Nanophotonics and photonic crystals Microcavity devices Nanostructure fabrication
ABSTRACT An enhanced type of photonic crystal heterostructure microcavity obtained by tuning the radii of air holes close to the photonic crystal waveguide was designed and experimentally verified. The quality factor of the optimized cavity was about 1.73×105 , which is greatly increased compared with that of the original heterostructure cavity. The main imperfections of the cavities were caused by the over-developing and over-etching of the side of the cavity structure.
1. Introduction In the last decades, the study of optical nanocavities based on photonic crystals (PCs) has attracted much attention from researchers. PCs are periodic optical nanostructures that have a photonic bandgap (PBG) and can effectively control light propagation. There are many promising applications of compact and efficient PC nanocavities, such as optical switches [1–4], filters [5–8], modulators [9], ultrasmall lasers [10–13], biological and chemical sensors [14–17] and they also have potential uses in quantum electrodynamics [18–21] and nonlinear optics [22–25]. All these applications require cavities with a high quality factor (Q) and small modal volume (V ). For instance, the operation energy scales as V/Q 2 for bistable devices [2]. The dynamics of strongly coupled atom–photon systems for quantum information processing scales as Q/V 1∕2 [26]. The ratio Q/V also determines the Purcell factor of a cavity, which influences the spontaneous emission rate of quantum optical devices [27]. A two-dimensional (2D) PC waveguide can be constructed by removing one line of air holes from a PC. A waveguide introduced across two PC slabs has different dispersion curves within each PC slab [28]. Within a PBG, there is a mode gap between photonic bands, which means that light can only propagate in the waveguide of the central structure and decays exponentially elsewhere. Song et al. [29,30] first proposed double-heterostructure cavities by combining a PC waveguide with two PC slabs with slightly different lattice constants. These lattices were combined in a similar manner to the design illustrated in Fig. 1(a): in the outer regions (PC1 ), the lattice is hexagonal with a lattice constant (𝑎2 ) of 410 nm. In the central region (PC2 ), the lattice constant (𝑎1 ) is slightly elongated to 420 nm in the horizontal direction, which is orthogonal to the heterostructure and parallel to the PC waveguide. Other dimensions of these two PC slabs are identical. Using this design, Song and co-workers experimentally achieved a Q value of 6 × 105 [30]. The effect of double heterostructures can also be achieved
via lateral hole displacement [31]; using this approach, Kuramochi and colleagues experimentally achieved a Q value of 8 × 105 . In this paper, we propose a novel PC microcavity design in which the radii of air holes in 2D heterostructure PC microcavities are tuned. The cavity contains eight rows of air holes in the direction orthogonal to the waveguide. We label the lattices surrounding the waveguide as layers, as shown in Fig. 1(a). Moreover, there are 22 columns of air holes in the lateral direction. The radii of air holes in the layers adjacent to the central waveguide are adjusted to maximize Q. As we carefully tune the radii of the air holes of the neighboring four layers, the theoretical Q increases from 4 × 105 to 15 × 105 . We also fabricate the optimized structure and obtain an experimental Q value of 1.73 × 105 . 2. Design Our model is a PC slab composed of a hexagonal array of cylindrical air holes in a silicon slab. A finite PC slab with 22 periods in the x-direction and 18 periods in the y-direction was considered, as illustrated in Fig. 1(a). The slab includes two components: PC1 and PC2 . The structure has holes of radius R and h is the thickness of the slab. There is a line defect of a W0.90 √ waveguide√(it indicates the width of waveguide decreases to 0.90* 3*𝑎2 , where 3*𝑎2 denotes the original width of PC waveguide) across the PC slab in the 𝛤 -K direction [32–34]. We began our analysis by considering a cavity PC2 with a lattice constant of 𝑎2 , which was analogous to the structure described by Song et al. [30] except for h and the width of the PC waveguide. In this cavity, 𝑎2 was 420 nm, R was 0.26𝑎2 , and h was 260 nm, which were kept constant. The length of PC1 is denoted by d, where 𝑑 = 2𝑎1 and 𝑎1 was 410 nm. The refractive index of silicon was set to 3.476. The simulation and optimization of Q were carried out by the finitedifference time-domain method combined with fast harmonic analysis using the Qfinder model in Rsoft software. The grid size was 10 nm in the x- and y-directions and 13 nm in the z-direction because the
E-mail address: [email protected]. https://doi.org/10.1016/j.optcom.2019.04.072 Received 8 November 2018; Received in revised form 22 April 2019; Accepted 24 April 2019 Available online 28 April 2019 0030-4018/© 2019 Elsevier B.V. All rights reserved.
P. Shi
Optics Communications 446 (2019) 88–92
Fig. 1. (a) Schematic diagram of the proposed cavity and (b) SEM image of device 1.
Fig. 2. Calculated variations of (a) resonance wavelength and (b) Q factor versus 𝑟1 when 𝑟𝑛 = 0.125 μm. Calculated variations of (c) resonance wavelength and (c) Q factors versus 𝑟1 when 𝑟𝑛 = 0.130 μm. The red, blue, and black dotted lines denote the change of 𝑟1 calculated using linear, quadratic, and cubic equations, respectively. The number of layers was 3 . (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
structure was homogeneous in the z-direction. Details of the numerical parameters used for the calculations can be found in Ref. [27]. Satisfactory convergence was obtained by using 41 points per period. The calculated Q factor of this structure was 4 × 105 and its resonance wavelength was 𝜆0 = 1585.86 nm. Because h and the width of the PC waveguide were different in the theoretical design and experimental device, the Q factor was decreased compared with that in Ref. [30]. To enhance Q of the device, we then adjusted R in the first three layers adjacent to the waveguide. The R values of the air holes were gradually changed using (linear, quadratic, and cubic equations. The ( ) ( 𝑖−1 )𝑥 ) equation is given by 𝑟𝑖 = 𝑟1 + 𝑟𝑛 − 𝑟1 ⋅ 𝑛−1 , where n is the total
R increased, the defect mode moved to higher frequency, which caused the resonance wavelength to shorten, as illustrated in Fig. 2(a) and (c). The maximum Q factor was around 15 × 105 at 𝑟1 = 0.114 μm. The maximum calculated Q factor is about one order of magnitude larger than that of the normal structure. In addition, the Q factor exceeded 106 when 𝑟1 was varied from 0.110 μm to 0.118 μm, which gives us substantial tolerance for fabrication error. Next, the number of adjusted layers was varied from 1 to 4 when R of each layer was changed using the cubic equation. The results are given in Fig. 3. The frequency of the defect mode decreased as R increased. The maximum Q factor was also about 15 × 105 .
number of adjusted layers, which is 3 here, and i indicates the number of layers between 1 and n (Note here that the second term vanishes when n = 1). In addition, 𝑟𝑖 , 𝑟1 , and 𝑟𝑛 are the radii of the air holes of the 𝑖th, 1st, and 𝑛th layers, respectively, and x denotes the order of the equation. Note that two devices denoted as device 1 and 2 and shown in Figs. 1(b) and 4(b) respectively are measured experimentally here. The radii of 𝑛th layers are 𝑟𝑛 = 0.130 μm and 0.125 μm for the device 1 and 2, respectively. We conducted a series of simulations to obtain results for scanning 𝑟1 from 0.106 μm to 0.118 μm when 𝑟𝑛 was 0.125 μm or 0.13 μm. Then, we obtained the changes of resonance wavelength and Q factor against 𝑟1 using linear, quadratic, and cubic equations, as shown in Fig. 2. As
3. Fabrication process Devices were fabricated on silicon-on-insulator (SOI) wafers consisting of a 260 nm-thick device (silicon) layer and 2 μm-thick silicon dioxide layer. An electron-beam resist layer of ZEP 520A-7 with a thickness of 260 to 280 nm was coated on the SOI wafer. The cavity patterns were fabricated by electron-beam lithography (EBL). The writing current was 200 pA and the exposure dose was 320 μC/cm2 . The device pattern was transferred to the device layer of the SOI wafer with an inductively coupled plasma reactive ion etching (ICP-RIE) system, which used plasma produced from 𝐶4 F8 /SF6 gas. The etching depth 89
P. Shi
Optics Communications 446 (2019) 88–92
Fig. 3. Calculated (a) resonance wavelength and (b) Q factor versus 𝑟1 when 𝑟𝑛 = 0.125 𝜇m. Calculated (c) resonance wavelength and (c) Q factor versus 𝑟1 when 𝑟𝑛 = 0.13 μm. The red, blue, black, and cyan dotted lines show results when the number of adjusted layers is 1, 2, 3, and 4, respectively. The change of the radii of air holes was quadratic . (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 4. SEM image of the (a) grating coupler and (b) PC cavity of device 2.
of this step was 260 nm; i.e., the silicon layer was etched through. The residual electron-beam photoresist was removed using Microposit 1165 remover. Further EBL and ICP-RIE steps were conducted to fabricate rib waveguides and grating couplers; in this case, the etching depth was controlled to 80 nm. The residual electron-beam photoresist was also removed using Microposit 1165. The other structures needed to characterize the devices, including an isolation trench and electrodes, were fabricated through a series of lithography, RIE, metal electronbeam evaporation, and lift-off processes. Finally, the wafer was sliced into 6 × 6 mm chips, and the chips were suspended in hydrofluoric acid vapor to etch the silicon dioxide below the cavities and actuators. Scanning electron microscopy (SEM) images of the grating coupler and cavity are shown in Fig. 4(a) and (b), respectively.
Fig. 5. Schematic of the setup used to characterize the tunable 2D cavity. TLS, tunable laser source; FPC, fiber polarization controller; OSA, optical spectrum analyzer.
to the cavity and the cavity’s output was launched into a multi-mode fiber through the output grating coupler. Finally, the light signal was recorded by an optical spectrum analyzer (OSA; ANDO AQ6317C). The TLS and OSA could synchronously sweep through wavelengths from 1520 to 1620 nm with a resolution of 1 pm. Two types of PC cavity devices were fabricated. The parameters of these two devices were the same except that 𝑟𝑛 = 0.130 μm for device 1 and 𝑟𝑛 = 0.125 μm for device 2. The other parameters were 𝑛 = 4, 𝑥 = 3, and 𝑟1 = 0.116 μm. The simulated resonance wavelength and Q factor were 1553.236 nm and 12.8 × 105 for a device with 𝑟𝑛 = 0.130 μm (an SEM image of the actual device 1 is shown in Fig. 1(b)). The experimental data for device 1 is given in Fig. 6(a) and a magnified view of the region near the resonance peak including detailed data and
4. Experimental results and discussion Fig. 5 shows a schematic of the setup used to test the 2D cavity. Light from a tunable laser source (TLS) was launched into a singlemode fiber. A fiber polarization controller was used to selectively excite the transverse electric-like modes of the split cavity. A pair of XYZstages controlling the coupling fibers was tilted 10◦ from the normal direction to the device surface. The fibers were aligned manually under a microscope with the grating couplers on the device. Light coupled into the waveguide through the input grating coupler was directed 90
P. Shi
Optics Communications 446 (2019) 88–92
Fig. 6. (a) Measured signal and (b) detailed and Lorentz-fitted data for device 1. The FWHM of the resonance is 11.58 pm and the Q factor is 1.3 × 105 . (c) Measured signal and (d) detailed and Lorentz-fitted data for device 2. The FWHM of the resonance is 8.94 pm and the Q factor is 1.73 × 105 .
Acknowledgment
the fitted curve is shown in Fig. 6(b). From the Lorentz fitting curve, the resonance wavelength and full width at half maximum (FWHM) of device were calculated to be 1543.451 nm and 11.58 pm, respectively. Therefore, the experimental Q factor of device 1 is 1.3 × 105 . For a device with 𝑟𝑛 = 0.125 μm (an SEM image of the actual device 2 is shown in Fig. 4(b)), the simulated resonance wavelength and Q factor are 1553.705 nm and 13.4 × 105 , respectively. The experimental data for device 2 is presented in Fig. 6(c), along with the detailed resonance data and the fitting curve in Fig. 6(d). From the Lorentz fitting curve, the resonance wavelength and FWHM of device 2 are calculated to be 1551.777 nm and 8.94 pm, respectively. Thus, the calculated experimental Q factor for device 2 is 1.73 × 105 . Comparing the simulation and experimental results revealed that the experimental Q factor is considerably lower than the simulated values. This decrease is mainly caused by two reasons: imperfect the cavity shape and imperfect cavity material. Current processes to realize high-Q cavities typically rely on extremely precise control of hole size and position using EBL. In our devices, the main factor limiting the Q value of the cavity is the excess development and side etching of the air holes. As a result, the measured resonance wavelengths of the cavities are shifted to higher frequencies compared with the simulated values.
This work was funded by the National Natural Science Foundation of China (NSFC) (grant No. 61705135). References [1] M.F. Yanik, S. Fan, M. Soljacic, High-contrast all-optical bistable switching in photonic crystal microcavities, Appl. Phys. Lett. 83 (14) (2003) 2739–2741. [2] T. Tanabe, M. Notomi, S. Mitsugi, A. Shinya, E. Kuramochi, Fast bistable alloptical switch and memory on a silicon photonic crystal on-chip, Opt. Lett. 30 (19) (2005) 2575–2577. [3] K. Nozaki, T. Tanabe, A. Shinya, S. Matsuo, T. Sato, H. Taniyama, M. Notomi, Sub-femtojoule all-optical switching using a photonic-crystal nanocavity, Nat. Photonics 4 (7) (2010) 477–483. [4] Feng Tian, Guangya Zhou, Yu Du, Fook Siong Chau, Jie Deng, Siew Lang Teo, Ramam Akkipeddi, Nanoelectromechanical-systems-controlled bistability of double-coupled photonic crystal cavities, Opt. Lett. 38 (17) (2013) 3394–3397. [5] M. Qiu, B. Jaskorzynska, Design of a channel drop filter in a two-dimensional triangular photonic crystal, Appl. Phys. Lett. 83 (6) (2003) 1074–1076. [6] Z. Qiang, W. Zhou, R.A. Soref, Optical add-drop filters based on photonic crystal ring resonators, Opt. Express 15 (4) (2007) 1823–1831. [7] P.B. Deotare, I. Bulu, I.W. Frank, Q. Quan, Y. Zhang, R. Ilic, M. Loncar, All optical reconfiguration of optomechanical filters, Nature Commun. 3 (2012) 846. [8] T. Tanabe, K. Nishiguchi, E. Kuramochi, M. Notomi, Highly efficient optical filter based on vertically coupled photonic crystal cavity and bus waveguide, Opt. Express 17 (25) (2009) 22505–22513. [9] J.H. Wülbern, A. Petrov, M. Eich, Electro-optical modulator in a polymerinfiltrated silicon slotted photonic crystal waveguide heterostructure resonator, Opt. Express 17 (1) (2009) 304–313. [10] O. Painter, R.K. Lee, A. Scherer, A. Yariv, J.D. O’Brien, P.D. Dapkus, I. Kim, Two-dimensional photonic crystal defect laser, Science 284 (5421) (1999) 1819–1821. [11] Peng Shi, Kun Huang, Xue-liang Kang, Yong-ping Li, Creation of large band gap with anisotropic annular photonic crystal slab structure, Opt. Express 18 (5) (2010) 5221–5228. [12] Peng Shi, Kun Huang, Yong-ping Li, Photonic crystal with complex unit cell for large complete band gap, Opt. Commun. 285 (3128–3132) (2012). [13] Peng Shi, Han Du, Fook Siong Chau, Guangya Zhou, Jie Deng, Tuning the quality factor of split nanobeam cavity by nanoelectromechanical systems, Opt. Express 23 (15) (2015) 19338–19347. [14] M. Lončar, A. Scherer, Y. Qiu, Photonic crystal laser sources for chemical detection, Appl. Phys. Lett. 82 (26) (2003) 4648–4650. [15] S. Mandal, D. Erickson, Nanoscale optofluidic sensor arrays, Opt. Express 16 (3) (2008) 1623–1631.
5. Conclusion We optimized a PC heterostructure microcavity by tuning the radii of air holes close to the PC waveguide. The radii of air holes in the three layers adjacent to the waveguide were gradually changed using linear, quadratic, and cubic equations. Then, the number of adjusted layers was varied from 1 to 4 as the radii of air holes in each layer was changed quadratically. The maximum simulated Q factor was 15 × 105 . The microcavities were fabricated by EBL and ICP-RIE. The measured Q factor of the actual device was about 1.73 × 105 . Because the measured resonance wavelengths of cavities were shifted to higher frequencies compared to the simulated results, we conclude that the main factor limiting the Q value of the cavities is the excess development and side etching of the air holes. The Q factor of such structures can be further increased via stepwise lateral air-hole displacement. 91
P. Shi
Optics Communications 446 (2019) 88–92 [25] Peng Shi, Kun Huang, Yong-ping Li, Subwavelength imaging by a graded-index photonic-crystal flat lens in a honeycomb lattice, J. Opt. Soc. Amer. A 28 (10) (2011) 2171–2175. [26] D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, J. Vuckovic, Controlling the spontaneous emission rate of single quantum dots in a two-dimensional photonic crystal, Phys. Rev. Lett. 95 (2005) 013904–013907. [27] S. Tomljenovic-Hanic, M.J. Steel, C.M. de Sterke, J. Salzman, Diamond based photonic crystal microcavities, Opt. Express 14 (2006) 3556–3562. [28] B.S. Song, T. Asano, Y. Akahane, Y. Tanaka, S. Noda, Transmission and reflection characteristics of in-plane hetero-photonic crystals, Appl. Phys. Lett. 85 (2004) 4591–4593. [29] Y. Akahane, T. Asano, B.S. Song, S. Noda, Ultrahigh- nanocavities in two-dimensional photonic crystal slabs, Nature 425 (2003) 944–947. [30] B.S. Song, S. Noda, T. Asano, Y. Akahane, Ultra-high-Q photonic doubleheterostructure nanocavity, Nature Mater. 4 (2005) 207–210. [31] E. Kuramochi, M. Natomi, S. Mitsugi, A. Shinya, T. Tanabe, Ultrahigh-Q photonic crystal nanocavities realized by the local width modulation of a line defect, Appl. Phys. Lett. 88 (2006) 041112–041114. [32] M.D. Birowosuto, A. Yokoo, G. Zhang, K. Tateno, E. Kuramochi, H. Taniyama, M. Takiguchi, M. Notomi, Movable high-Q nanoresonators realized by semiconductor nanowires on a si photonic crystal platform, Nature Mater. 13 (2014) 279–285. [33] Kazuaki Sakoda, Optical Properties of Photonic Crystals, second ed., Springer, New York, 2005, p. 58. [34] J.D. Joannopoulos, R.D. Meade, J.N. Winn, Photonic Crystals: Molding the Flow of Light, Princeton, New Jersey, 1995, p. 76.
[16] T. Sünner, T. Stichel, S.H. Kwon, T.W. Schlereth, S. Hofling, M. Kamp, A. Forchel, Photonic crystal cavity based gas sensor, Appl. Phys. Lett. 92 (26) (2008) 261112–261114. [17] Xingwang Zhang, Guangya Zhou, Peng Shi, Han Du, Tong Lin, Jinghua Teng, Fook Siong Chau, On-chip integrated optofluidic complex refractive index sensing using silicon photonic crystal nanobeam cavities, Opt. Lett. 41 (6) (2016) 1197–1200. [18] K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E.L. Hu, A. Imamoğlu, Quantum nature of a strongly coupled single quantum dot–cavity system, Nature 445 (7130) (2007) 896–899. [19] Peng Shi, Guangya Zhou, Jie deng, Feng Tian, Fook Siong Chau, Tuning alloptical analog to electromagnetically induced transparency in nanobeam cavities using nanoelectromechanical system, Sci. Rep. 5 (2015) 14379. [20] Tong Lin, Feng Tian, Peng Shi, Fook Siong Chau, Guangya Zhou, Xiaosong Tang, Jie Deng, Design of mechanically-tunable photonic crystal split-beam nanocavity, Opt. Lett. 40 (15) (2015) 3504–3507. [21] M. Toishi, D. Englund, A. Faraon, J. Vucković, High-brightness single photon source from a quantum dot in a directional-emission nanocavity, Opt. Express 17 (17) (2009) 14618–14626. [22] P. Barclay, K. Srinivasan, O. Painter, Nonlinear response of silicon photonic crystal microresonators excited via an integrated waveguide and fiber taper, Opt. Express 13 (3) (2005) 801–820. [23] T. Uesugi, B.S. Song, T. Asano, S. Noda, Investigation of optical nonlinearities in an ultra-high-q si nanocavity in a two-dimensional photonic crystal slab, Opt. Express 14 (1) (2006) 377–386. [24] Peng Shi, Kun Huang, Yong-ping Li, Enhance the resolution of photonic crystal negative refraction imaging by metal grating, Opt. Lett. 37 (3) (2012) 359–361.
92
Contents lists available at ScienceDirect
Optics Communications journal homepage: www.elsevier.com/locate/optcom
High-Q photonic crystal heterostructure microcavities by tuning air holes Peng Shi Nanophotonics Research Centre, Shenzhen University, Shenzhen, 518060, Guangdong, China
ARTICLE
INFO
Keywords: Nanophotonics and photonic crystals Microcavity devices Nanostructure fabrication
ABSTRACT An enhanced type of photonic crystal heterostructure microcavity obtained by tuning the radii of air holes close to the photonic crystal waveguide was designed and experimentally verified. The quality factor of the optimized cavity was about 1.73×105 , which is greatly increased compared with that of the original heterostructure cavity. The main imperfections of the cavities were caused by the over-developing and over-etching of the side of the cavity structure.
1. Introduction In the last decades, the study of optical nanocavities based on photonic crystals (PCs) has attracted much attention from researchers. PCs are periodic optical nanostructures that have a photonic bandgap (PBG) and can effectively control light propagation. There are many promising applications of compact and efficient PC nanocavities, such as optical switches [1–4], filters [5–8], modulators [9], ultrasmall lasers [10–13], biological and chemical sensors [14–17] and they also have potential uses in quantum electrodynamics [18–21] and nonlinear optics [22–25]. All these applications require cavities with a high quality factor (Q) and small modal volume (V ). For instance, the operation energy scales as V/Q 2 for bistable devices [2]. The dynamics of strongly coupled atom–photon systems for quantum information processing scales as Q/V 1∕2 [26]. The ratio Q/V also determines the Purcell factor of a cavity, which influences the spontaneous emission rate of quantum optical devices [27]. A two-dimensional (2D) PC waveguide can be constructed by removing one line of air holes from a PC. A waveguide introduced across two PC slabs has different dispersion curves within each PC slab [28]. Within a PBG, there is a mode gap between photonic bands, which means that light can only propagate in the waveguide of the central structure and decays exponentially elsewhere. Song et al. [29,30] first proposed double-heterostructure cavities by combining a PC waveguide with two PC slabs with slightly different lattice constants. These lattices were combined in a similar manner to the design illustrated in Fig. 1(a): in the outer regions (PC1 ), the lattice is hexagonal with a lattice constant (𝑎2 ) of 410 nm. In the central region (PC2 ), the lattice constant (𝑎1 ) is slightly elongated to 420 nm in the horizontal direction, which is orthogonal to the heterostructure and parallel to the PC waveguide. Other dimensions of these two PC slabs are identical. Using this design, Song and co-workers experimentally achieved a Q value of 6 × 105 [30]. The effect of double heterostructures can also be achieved
via lateral hole displacement [31]; using this approach, Kuramochi and colleagues experimentally achieved a Q value of 8 × 105 . In this paper, we propose a novel PC microcavity design in which the radii of air holes in 2D heterostructure PC microcavities are tuned. The cavity contains eight rows of air holes in the direction orthogonal to the waveguide. We label the lattices surrounding the waveguide as layers, as shown in Fig. 1(a). Moreover, there are 22 columns of air holes in the lateral direction. The radii of air holes in the layers adjacent to the central waveguide are adjusted to maximize Q. As we carefully tune the radii of the air holes of the neighboring four layers, the theoretical Q increases from 4 × 105 to 15 × 105 . We also fabricate the optimized structure and obtain an experimental Q value of 1.73 × 105 . 2. Design Our model is a PC slab composed of a hexagonal array of cylindrical air holes in a silicon slab. A finite PC slab with 22 periods in the x-direction and 18 periods in the y-direction was considered, as illustrated in Fig. 1(a). The slab includes two components: PC1 and PC2 . The structure has holes of radius R and h is the thickness of the slab. There is a line defect of a W0.90 √ waveguide√(it indicates the width of waveguide decreases to 0.90* 3*𝑎2 , where 3*𝑎2 denotes the original width of PC waveguide) across the PC slab in the 𝛤 -K direction [32–34]. We began our analysis by considering a cavity PC2 with a lattice constant of 𝑎2 , which was analogous to the structure described by Song et al. [30] except for h and the width of the PC waveguide. In this cavity, 𝑎2 was 420 nm, R was 0.26𝑎2 , and h was 260 nm, which were kept constant. The length of PC1 is denoted by d, where 𝑑 = 2𝑎1 and 𝑎1 was 410 nm. The refractive index of silicon was set to 3.476. The simulation and optimization of Q were carried out by the finitedifference time-domain method combined with fast harmonic analysis using the Qfinder model in Rsoft software. The grid size was 10 nm in the x- and y-directions and 13 nm in the z-direction because the
E-mail address: [email protected]. https://doi.org/10.1016/j.optcom.2019.04.072 Received 8 November 2018; Received in revised form 22 April 2019; Accepted 24 April 2019 Available online 28 April 2019 0030-4018/© 2019 Elsevier B.V. All rights reserved.
P. Shi
Optics Communications 446 (2019) 88–92
Fig. 1. (a) Schematic diagram of the proposed cavity and (b) SEM image of device 1.
Fig. 2. Calculated variations of (a) resonance wavelength and (b) Q factor versus 𝑟1 when 𝑟𝑛 = 0.125 μm. Calculated variations of (c) resonance wavelength and (c) Q factors versus 𝑟1 when 𝑟𝑛 = 0.130 μm. The red, blue, and black dotted lines denote the change of 𝑟1 calculated using linear, quadratic, and cubic equations, respectively. The number of layers was 3 . (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
structure was homogeneous in the z-direction. Details of the numerical parameters used for the calculations can be found in Ref. [27]. Satisfactory convergence was obtained by using 41 points per period. The calculated Q factor of this structure was 4 × 105 and its resonance wavelength was 𝜆0 = 1585.86 nm. Because h and the width of the PC waveguide were different in the theoretical design and experimental device, the Q factor was decreased compared with that in Ref. [30]. To enhance Q of the device, we then adjusted R in the first three layers adjacent to the waveguide. The R values of the air holes were gradually changed using (linear, quadratic, and cubic equations. The ( ) ( 𝑖−1 )𝑥 ) equation is given by 𝑟𝑖 = 𝑟1 + 𝑟𝑛 − 𝑟1 ⋅ 𝑛−1 , where n is the total
R increased, the defect mode moved to higher frequency, which caused the resonance wavelength to shorten, as illustrated in Fig. 2(a) and (c). The maximum Q factor was around 15 × 105 at 𝑟1 = 0.114 μm. The maximum calculated Q factor is about one order of magnitude larger than that of the normal structure. In addition, the Q factor exceeded 106 when 𝑟1 was varied from 0.110 μm to 0.118 μm, which gives us substantial tolerance for fabrication error. Next, the number of adjusted layers was varied from 1 to 4 when R of each layer was changed using the cubic equation. The results are given in Fig. 3. The frequency of the defect mode decreased as R increased. The maximum Q factor was also about 15 × 105 .
number of adjusted layers, which is 3 here, and i indicates the number of layers between 1 and n (Note here that the second term vanishes when n = 1). In addition, 𝑟𝑖 , 𝑟1 , and 𝑟𝑛 are the radii of the air holes of the 𝑖th, 1st, and 𝑛th layers, respectively, and x denotes the order of the equation. Note that two devices denoted as device 1 and 2 and shown in Figs. 1(b) and 4(b) respectively are measured experimentally here. The radii of 𝑛th layers are 𝑟𝑛 = 0.130 μm and 0.125 μm for the device 1 and 2, respectively. We conducted a series of simulations to obtain results for scanning 𝑟1 from 0.106 μm to 0.118 μm when 𝑟𝑛 was 0.125 μm or 0.13 μm. Then, we obtained the changes of resonance wavelength and Q factor against 𝑟1 using linear, quadratic, and cubic equations, as shown in Fig. 2. As
3. Fabrication process Devices were fabricated on silicon-on-insulator (SOI) wafers consisting of a 260 nm-thick device (silicon) layer and 2 μm-thick silicon dioxide layer. An electron-beam resist layer of ZEP 520A-7 with a thickness of 260 to 280 nm was coated on the SOI wafer. The cavity patterns were fabricated by electron-beam lithography (EBL). The writing current was 200 pA and the exposure dose was 320 μC/cm2 . The device pattern was transferred to the device layer of the SOI wafer with an inductively coupled plasma reactive ion etching (ICP-RIE) system, which used plasma produced from 𝐶4 F8 /SF6 gas. The etching depth 89
P. Shi
Optics Communications 446 (2019) 88–92
Fig. 3. Calculated (a) resonance wavelength and (b) Q factor versus 𝑟1 when 𝑟𝑛 = 0.125 𝜇m. Calculated (c) resonance wavelength and (c) Q factor versus 𝑟1 when 𝑟𝑛 = 0.13 μm. The red, blue, black, and cyan dotted lines show results when the number of adjusted layers is 1, 2, 3, and 4, respectively. The change of the radii of air holes was quadratic . (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 4. SEM image of the (a) grating coupler and (b) PC cavity of device 2.
of this step was 260 nm; i.e., the silicon layer was etched through. The residual electron-beam photoresist was removed using Microposit 1165 remover. Further EBL and ICP-RIE steps were conducted to fabricate rib waveguides and grating couplers; in this case, the etching depth was controlled to 80 nm. The residual electron-beam photoresist was also removed using Microposit 1165. The other structures needed to characterize the devices, including an isolation trench and electrodes, were fabricated through a series of lithography, RIE, metal electronbeam evaporation, and lift-off processes. Finally, the wafer was sliced into 6 × 6 mm chips, and the chips were suspended in hydrofluoric acid vapor to etch the silicon dioxide below the cavities and actuators. Scanning electron microscopy (SEM) images of the grating coupler and cavity are shown in Fig. 4(a) and (b), respectively.
Fig. 5. Schematic of the setup used to characterize the tunable 2D cavity. TLS, tunable laser source; FPC, fiber polarization controller; OSA, optical spectrum analyzer.
to the cavity and the cavity’s output was launched into a multi-mode fiber through the output grating coupler. Finally, the light signal was recorded by an optical spectrum analyzer (OSA; ANDO AQ6317C). The TLS and OSA could synchronously sweep through wavelengths from 1520 to 1620 nm with a resolution of 1 pm. Two types of PC cavity devices were fabricated. The parameters of these two devices were the same except that 𝑟𝑛 = 0.130 μm for device 1 and 𝑟𝑛 = 0.125 μm for device 2. The other parameters were 𝑛 = 4, 𝑥 = 3, and 𝑟1 = 0.116 μm. The simulated resonance wavelength and Q factor were 1553.236 nm and 12.8 × 105 for a device with 𝑟𝑛 = 0.130 μm (an SEM image of the actual device 1 is shown in Fig. 1(b)). The experimental data for device 1 is given in Fig. 6(a) and a magnified view of the region near the resonance peak including detailed data and
4. Experimental results and discussion Fig. 5 shows a schematic of the setup used to test the 2D cavity. Light from a tunable laser source (TLS) was launched into a singlemode fiber. A fiber polarization controller was used to selectively excite the transverse electric-like modes of the split cavity. A pair of XYZstages controlling the coupling fibers was tilted 10◦ from the normal direction to the device surface. The fibers were aligned manually under a microscope with the grating couplers on the device. Light coupled into the waveguide through the input grating coupler was directed 90
P. Shi
Optics Communications 446 (2019) 88–92
Fig. 6. (a) Measured signal and (b) detailed and Lorentz-fitted data for device 1. The FWHM of the resonance is 11.58 pm and the Q factor is 1.3 × 105 . (c) Measured signal and (d) detailed and Lorentz-fitted data for device 2. The FWHM of the resonance is 8.94 pm and the Q factor is 1.73 × 105 .
Acknowledgment
the fitted curve is shown in Fig. 6(b). From the Lorentz fitting curve, the resonance wavelength and full width at half maximum (FWHM) of device were calculated to be 1543.451 nm and 11.58 pm, respectively. Therefore, the experimental Q factor of device 1 is 1.3 × 105 . For a device with 𝑟𝑛 = 0.125 μm (an SEM image of the actual device 2 is shown in Fig. 4(b)), the simulated resonance wavelength and Q factor are 1553.705 nm and 13.4 × 105 , respectively. The experimental data for device 2 is presented in Fig. 6(c), along with the detailed resonance data and the fitting curve in Fig. 6(d). From the Lorentz fitting curve, the resonance wavelength and FWHM of device 2 are calculated to be 1551.777 nm and 8.94 pm, respectively. Thus, the calculated experimental Q factor for device 2 is 1.73 × 105 . Comparing the simulation and experimental results revealed that the experimental Q factor is considerably lower than the simulated values. This decrease is mainly caused by two reasons: imperfect the cavity shape and imperfect cavity material. Current processes to realize high-Q cavities typically rely on extremely precise control of hole size and position using EBL. In our devices, the main factor limiting the Q value of the cavity is the excess development and side etching of the air holes. As a result, the measured resonance wavelengths of the cavities are shifted to higher frequencies compared with the simulated values.
This work was funded by the National Natural Science Foundation of China (NSFC) (grant No. 61705135). References [1] M.F. Yanik, S. Fan, M. Soljacic, High-contrast all-optical bistable switching in photonic crystal microcavities, Appl. Phys. Lett. 83 (14) (2003) 2739–2741. [2] T. Tanabe, M. Notomi, S. Mitsugi, A. Shinya, E. Kuramochi, Fast bistable alloptical switch and memory on a silicon photonic crystal on-chip, Opt. Lett. 30 (19) (2005) 2575–2577. [3] K. Nozaki, T. Tanabe, A. Shinya, S. Matsuo, T. Sato, H. Taniyama, M. Notomi, Sub-femtojoule all-optical switching using a photonic-crystal nanocavity, Nat. Photonics 4 (7) (2010) 477–483. [4] Feng Tian, Guangya Zhou, Yu Du, Fook Siong Chau, Jie Deng, Siew Lang Teo, Ramam Akkipeddi, Nanoelectromechanical-systems-controlled bistability of double-coupled photonic crystal cavities, Opt. Lett. 38 (17) (2013) 3394–3397. [5] M. Qiu, B. Jaskorzynska, Design of a channel drop filter in a two-dimensional triangular photonic crystal, Appl. Phys. Lett. 83 (6) (2003) 1074–1076. [6] Z. Qiang, W. Zhou, R.A. Soref, Optical add-drop filters based on photonic crystal ring resonators, Opt. Express 15 (4) (2007) 1823–1831. [7] P.B. Deotare, I. Bulu, I.W. Frank, Q. Quan, Y. Zhang, R. Ilic, M. Loncar, All optical reconfiguration of optomechanical filters, Nature Commun. 3 (2012) 846. [8] T. Tanabe, K. Nishiguchi, E. Kuramochi, M. Notomi, Highly efficient optical filter based on vertically coupled photonic crystal cavity and bus waveguide, Opt. Express 17 (25) (2009) 22505–22513. [9] J.H. Wülbern, A. Petrov, M. Eich, Electro-optical modulator in a polymerinfiltrated silicon slotted photonic crystal waveguide heterostructure resonator, Opt. Express 17 (1) (2009) 304–313. [10] O. Painter, R.K. Lee, A. Scherer, A. Yariv, J.D. O’Brien, P.D. Dapkus, I. Kim, Two-dimensional photonic crystal defect laser, Science 284 (5421) (1999) 1819–1821. [11] Peng Shi, Kun Huang, Xue-liang Kang, Yong-ping Li, Creation of large band gap with anisotropic annular photonic crystal slab structure, Opt. Express 18 (5) (2010) 5221–5228. [12] Peng Shi, Kun Huang, Yong-ping Li, Photonic crystal with complex unit cell for large complete band gap, Opt. Commun. 285 (3128–3132) (2012). [13] Peng Shi, Han Du, Fook Siong Chau, Guangya Zhou, Jie Deng, Tuning the quality factor of split nanobeam cavity by nanoelectromechanical systems, Opt. Express 23 (15) (2015) 19338–19347. [14] M. Lončar, A. Scherer, Y. Qiu, Photonic crystal laser sources for chemical detection, Appl. Phys. Lett. 82 (26) (2003) 4648–4650. [15] S. Mandal, D. Erickson, Nanoscale optofluidic sensor arrays, Opt. Express 16 (3) (2008) 1623–1631.
5. Conclusion We optimized a PC heterostructure microcavity by tuning the radii of air holes close to the PC waveguide. The radii of air holes in the three layers adjacent to the waveguide were gradually changed using linear, quadratic, and cubic equations. Then, the number of adjusted layers was varied from 1 to 4 as the radii of air holes in each layer was changed quadratically. The maximum simulated Q factor was 15 × 105 . The microcavities were fabricated by EBL and ICP-RIE. The measured Q factor of the actual device was about 1.73 × 105 . Because the measured resonance wavelengths of cavities were shifted to higher frequencies compared to the simulated results, we conclude that the main factor limiting the Q value of the cavities is the excess development and side etching of the air holes. The Q factor of such structures can be further increased via stepwise lateral air-hole displacement. 91
P. Shi
Optics Communications 446 (2019) 88–92 [25] Peng Shi, Kun Huang, Yong-ping Li, Subwavelength imaging by a graded-index photonic-crystal flat lens in a honeycomb lattice, J. Opt. Soc. Amer. A 28 (10) (2011) 2171–2175. [26] D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, J. Vuckovic, Controlling the spontaneous emission rate of single quantum dots in a two-dimensional photonic crystal, Phys. Rev. Lett. 95 (2005) 013904–013907. [27] S. Tomljenovic-Hanic, M.J. Steel, C.M. de Sterke, J. Salzman, Diamond based photonic crystal microcavities, Opt. Express 14 (2006) 3556–3562. [28] B.S. Song, T. Asano, Y. Akahane, Y. Tanaka, S. Noda, Transmission and reflection characteristics of in-plane hetero-photonic crystals, Appl. Phys. Lett. 85 (2004) 4591–4593. [29] Y. Akahane, T. Asano, B.S. Song, S. Noda, Ultrahigh- nanocavities in two-dimensional photonic crystal slabs, Nature 425 (2003) 944–947. [30] B.S. Song, S. Noda, T. Asano, Y. Akahane, Ultra-high-Q photonic doubleheterostructure nanocavity, Nature Mater. 4 (2005) 207–210. [31] E. Kuramochi, M. Natomi, S. Mitsugi, A. Shinya, T. Tanabe, Ultrahigh-Q photonic crystal nanocavities realized by the local width modulation of a line defect, Appl. Phys. Lett. 88 (2006) 041112–041114. [32] M.D. Birowosuto, A. Yokoo, G. Zhang, K. Tateno, E. Kuramochi, H. Taniyama, M. Takiguchi, M. Notomi, Movable high-Q nanoresonators realized by semiconductor nanowires on a si photonic crystal platform, Nature Mater. 13 (2014) 279–285. [33] Kazuaki Sakoda, Optical Properties of Photonic Crystals, second ed., Springer, New York, 2005, p. 58. [34] J.D. Joannopoulos, R.D. Meade, J.N. Winn, Photonic Crystals: Molding the Flow of Light, Princeton, New Jersey, 1995, p. 76.
[16] T. Sünner, T. Stichel, S.H. Kwon, T.W. Schlereth, S. Hofling, M. Kamp, A. Forchel, Photonic crystal cavity based gas sensor, Appl. Phys. Lett. 92 (26) (2008) 261112–261114. [17] Xingwang Zhang, Guangya Zhou, Peng Shi, Han Du, Tong Lin, Jinghua Teng, Fook Siong Chau, On-chip integrated optofluidic complex refractive index sensing using silicon photonic crystal nanobeam cavities, Opt. Lett. 41 (6) (2016) 1197–1200. [18] K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E.L. Hu, A. Imamoğlu, Quantum nature of a strongly coupled single quantum dot–cavity system, Nature 445 (7130) (2007) 896–899. [19] Peng Shi, Guangya Zhou, Jie deng, Feng Tian, Fook Siong Chau, Tuning alloptical analog to electromagnetically induced transparency in nanobeam cavities using nanoelectromechanical system, Sci. Rep. 5 (2015) 14379. [20] Tong Lin, Feng Tian, Peng Shi, Fook Siong Chau, Guangya Zhou, Xiaosong Tang, Jie Deng, Design of mechanically-tunable photonic crystal split-beam nanocavity, Opt. Lett. 40 (15) (2015) 3504–3507. [21] M. Toishi, D. Englund, A. Faraon, J. Vucković, High-brightness single photon source from a quantum dot in a directional-emission nanocavity, Opt. Express 17 (17) (2009) 14618–14626. [22] P. Barclay, K. Srinivasan, O. Painter, Nonlinear response of silicon photonic crystal microresonators excited via an integrated waveguide and fiber taper, Opt. Express 13 (3) (2005) 801–820. [23] T. Uesugi, B.S. Song, T. Asano, S. Noda, Investigation of optical nonlinearities in an ultra-high-q si nanocavity in a two-dimensional photonic crystal slab, Opt. Express 14 (1) (2006) 377–386. [24] Peng Shi, Kun Huang, Yong-ping Li, Enhance the resolution of photonic crystal negative refraction imaging by metal grating, Opt. Lett. 37 (3) (2012) 359–361.
92