A Trade-Off Between Propagation Length and Light Confinement in Cylindrical Metal-Dielectric Waveguides *

ISSN: 0256-307X 中国物理快报 Chinese Physics Letters

Volume 28 Number 5 May 2011 A Series Journal of the Chinese Physical Society Distributed by IOP Publishing Online: http://iopscience.iop.org/cpl http://cpl.iphy.ac.cn

C HINESE P HYSICAL S OCIETY

Institute of Physics PUBLISHING CHIN. PHYS. LETT. Vol. 28, No. 5 (2011) 057303 A Trade-off between Propagation Length and Light Confinement in Cylindrical Metal-Dielectric Waveguides *

SUN Bao-Qing(孙宝清), GU Ying(古英)**, HU Xiao-Yong(胡小永), GONG Qi-Huang(龚旗煌)** State Key Laboratory for Mesoscopic Physics, Department of Physics, Peking University, Beijing 100871

(Received 17 April 2010) We theoretically investigate the hybrid plasmonic modes of cylindrical nanocables with gold nanocore and two dielectric nanolayers (SiO2 and BN). By solving a complete set of Maxwell’s equations, the propagation constants and effective radii depending on geometrical parameters are numerically calculated. By declining atrade-off between propagation length and light confinement, high quality hybrid modes which can travel a long range of 120–200휆 with a subwavelength effective radius are obtained at the optical wavelength. These modesin one-dimensional cylindrical waveguides should have potential applications in nanoscale optical device designs. PACS: 73.20.Mf, 78.67.−n DOI: 10.1088/0256-307X/28/5/057303

Surface plasmon polaritons (SPPs) are light waves the propagating and evanescent modes and generally coupled to free electron oscillations in metal-dielectric the evanescent part dominated. Due to the Ohmic interfaces. These waves are evanescent near surfaces, loss, the propagation lengths of these nanoscale 1D which makes it possible to localize and guide light in metallic waveguides were decreased to a small range, a subwavelength scale.[1,2] To guide SPPs, researchers which greatly limits the applications in nanoscale opti- have explored many plasmonic waveguide structures cal devices. The aim of this work is to find hybrid SPP such as thin metal films,[3−5] metal stripes,[6−8] two di- modes with a long range propagation length and good mensional metal-dielectric multilayers,[9,10] subwave- light confinement in 1D metallic-dielectric waveguides. length metal grooves,[11−13] nanoparticle chains,[14] In this work, a hybrid plasmonic waveguide com- and cylindrical waveguides.[15−20] Although the op- posed of a gold nanocore and two dielectric nanolayers tical energy is well confined, the propagation length is proposed, as shown in Fig. 1. The inner dielectric will be greatly reduced because of the Ohmic loss in layer SiO2 has a low dielectric constant and the outer metals. In fact, there is a trade-off between light con- dielectric layer BN has a high dielectric constant. The finement and propagation length in all kinds ofSPP whole system can be regarded as a gold nanocore nest- waveguides. To solve this problem, a hybrid waveg- ing in a BN nanotube, so the SPP modes in a metallic uide combining the advantages of both SPP modes nanowire can couple to the waveguide modes in a nan- and dielectric waveguide modes is suggested. With otube, leading to some hybrid SPP modes. By adjust- the coupling of plasmonic and dielectric waveguides, ing thicknesses of the layers, the high quality hybrid hybrid modes can be improved to achieve a long prop- modes which can travel a long range of 120–200휆 and agating length while keeping moderate light confine- have a subwavelength effective radius can be achieved ment in a ‘capacitor-like’ structure.[21,22] at the optical wavelength. These modes in 1D cylin- SPPs in one-dimensional (1D) metallic cylindri- drical waveguides should have potential applications cal waveguides have been extensively studied. In the in nanoscale optical device designs. 1970s, the first experiment using light scattering to The solution of Maxwell’s equations in a cylindri- excite SPP modes in 50 µm metallic cylinders was cal structure is well documented in the textbook.[23] performed[15] and also explained by means of the vir- Electromagnetic fields of the eigenmodes in the cylin- tual radiative modes with a complex frequency.[16] drical coordinates (푟, 휃, 푧) can be expressed as Then, a clear mode classification in two-layer cylindrical waveguide structures was thoroughly investi- [︁푖푘푧 푗 ′ 휇푗휔푛 푗 ]︁ gated where only negative real dielectric constant was 퐸푟 = 푓푛 (훾푗푟) − 2 푔푛(훾푗푟) 푆푛, 훾푗 훾 푟푐 considered.[17] The SPP modes in a lossy cylindrical 푗 [︁ ]︁ metallic nanotube with a dielectric core were used to 푛푘푧 푗 푖휇푗휔 푗 ′ 퐸휑 = − 2 푓푛(훾푗푟) − 2 푔푛 (훾푗푟) 푆푛, model light propagation of a scanning near field op- 훾푗 푟 훾푗 푐 tical microscope (SNOM).[18,19] Mode coupling and 푗 퐸푧 = 푓푛(훾푗푟)푆푛, transformation of SPPs in a lossy metallic cylindri- [︁푛휀 휔 푖푘 ]︁ cal nanocable were also studied.[20] However, in the 퐻 = 푗 푓 푗 (훾 푟) + 푧 푔푗 ′(훾 푟) 푆 , 푟 훾2푟푐 푛 푗 훾 푛 푗 푛 above-mentioned works (Refs. [18–20]), instead of a 푗 푗 clear distinction between pure propagating modes and [︁푖휀푗휔 푗 ′ 푛푘푧 푗 ]︁ 퐻휑 = 푓푛 (훾푗푟) − 2 푔푛(훾푗푟) 푆푛, evanescent modes, the SPP modes mediated between 훾푗푐 훾푗 푟

*Supported by the National Natural Science Foundation of China under Grant Nos 10874004 and 10821062 and the National Basic Research Program of China under Grant No 2007CB307001. **To whom correspondence should be addressed. Email: [email protected]; [email protected] © 2011 Chinese Physical Society and IOP Publishing Ltd

057303-1 CHIN. PHYS. LETT. Vol. 28, No. 5 (2011) 057303

푗 퐻푧 = 푔푛(훾푗푟)푆푛, (1) good confinement of 푅eff = 100 nm (the calculations related to this part are not shown). To overcome this where 푖 is the imaginary unit, 푛 is an integer (푛 = 0, dilemma that the SPP mode in nanowire has either a 1, 2, ···), 푘푧 is the propagation constant along the 푧 long range with bad confinement or good confinement direction (the cylinder axis) and here it is complex due with a short traveling length, we set the gold nanowire to the loss of metal, 휀푗 is the dielectric constant of the in a high-permittivity dielectric nanotube, forming a medium 푗 and 푐 is the speed of light in vacuum. As we metallic-dielectric nanocable as shown in Fig. 1. The are not dealing with magnetic materials, the magnetic waveguide modes of the nanotube will pull the elec- permeability 휇 is set as unity. 푆푛 is the exponential tromagnetic energy of the SPP mode of the nanowire factor, into the low-permittivity middle layer, leading to some 푆푛 = exp(푖푛휑 + 푖푘푧푧 − 푖휔푡), (2) hybrid SPP modes. Then, by carefully choosing the 훾푗 is the transverse wave number in the 푗th medium, geometric parameters, compared to the SPP modes in nanowires, higher quality hybrid modes with both 2 2 2 훾푗 = 휇푗휀푗(휔/푐) − 푘푧 , (3) long propagation lengths and small effective radii are achieved. and 푓 푗 , 푔푗 are the superposition of Bessel functions. 푛 푛

2.8

2.7 )

2.0

Fig. 1. The schematic diagram of a hybrid cylindrical Re( metal-dielectric waveguide. 1.5

(a) By applying the boundary conditions that the tan-

1.0 gential components of 퐸 and 푏푚퐻 must be continu- 0.20

ous at the interface, a homogeneous system of linear HE Nanowire in SiO

0.16 11 2

푗 푗 HE Nanowire in BN ) equations for the expansion coefficients of 푓푛 and 푔푛 is 12 HE

0.12

EH obtained. The existence of the nontrivial solutions is 11 guaranteed by letting the determinant of the system 0.08 Im(

vanish. Then we obtain the transcendental equation 0.04

(b) det[푀(푘푧)] = 0 for the complex propagation constant [20] 0.00 푘푧. Using a numerical method, we can solve the 푘 100 200 300 400 value of 푧 for a specific mode. With the propaga- (nm) tion constant, all the information of this mode can be obtained, including the EM fields, propagation length Fig. 2. Dispersion relations of nanocable versus the thickness 푑1 of the SiO2 middle layer. Here the gold nanocore and Poynting vector. is in size 푟0 = 40 nm and the BN outer layer is in thickness Propagation length is defined as the length 퐿푚 = 푑2 = 40 nm. (2Im(푘 ))−1 푧 after which the intensity of SPPs decreases to 1/푒.[1] Light confinement in the radial direc- 1.0

HE mode EH mode

11 11 tion is described by the effective radius 푅eff , defined 6

0.5 as a hypothetic radius inside which 86.5% of the power 3

0.0

0 is confined,

∫︀ 푅eff

푆 푑퐴 -0.5 푧 -3 0 ∫︀ ∞ = 86.5%, (4)

-6 푆푧푑퐴 -1.0

HE mode 푆 HE mode 9 푧 12 where is the Poynting vector in the axis direction 4 [25] 13 푆푧 = (퐸푟 * 퐻휑 − 퐸휑 * 퐻푟). 3 In a gold nanowire embedded in a dielectric host, 6 2

3 Electromagnetic fields low-permittivity dielectric tends to guide a long-range 1

SPP mode but with a large effective radius, while 0

0 high-permittivity dielectric tends to channel a short -3

-1 SPP mode but with a small effective radius. As an

0 200 400 600 0 200 400 600

(nm) example, we consider the 푛 = 1 mode in the gold (nm) nanowire of 푟0 = 40 nm. The gold dielectric permit- Fig. 3. Field distribution at 푟0 = 40 nm, 푑1 = 260 nm, tivity of 휀푚 = −11.75 + 1.25푖 at the wavelength of 푑2 = 40 nm. (a) HE11 mode, (b) HE12 mode, (c) EH11 휆 = 632.8 nm is taken from Ref. [24]. With infinite mode, (d) HE13 mode. SiO2 cladding of 휀1 = 2.25, it has a long propagation length of 퐿푚 = 45.8 µm and a large effective ra- In the following, the three-layer nanocable has a dius of 푅eff = 467.6 nm; while with BN cladding of gold core of 푟0 = 40 nm, a varying SiO2 middle layer 휀2 = 4.41, it has a short length of 퐿푚 = 1.66 µm and of 푑1 = 50–400 nm and an outer BN layer of 푑2 = 30– 057303-2 CHIN. PHYS. LETT. Vol. 28, No. 5 (2011) 057303

60 nm. We first explore the dispersion relations ofthe SiO2 and BN claddings, which means that they do nanocable for 푛 = 1 modes by varying 푑1 in Fig.2. not have a longer-range propagation length than that The corresponding field distribution is shown in Fig. 3. in gold nanowires. Only the imaginary part of the Then we choose the best quality hybrid mode HE13 HE13 mode is less than that in the nanowire with SiO2 by comparing their propagation lengths and effective cladding. We note that this mode appears when 푑1 is radii, as shown in Fig. 4. Finally, in Figs. 5 and 6, larger than 260 nm. It is a hybridizing result of the a trade-off between propagation length and effective SPP modes in the gold nanocore and the waveguide radius with varying geometrical and material param- mode in BN nanocladding, where the high quality in eters are clearly shown. the propagation length and effective radius is further

proved in Fig. 4.

(a) HE

120

EH m)

11 (a)

120 m

90 m)

13 m

Nanowire in SiO

Nanowire in BN

60 100

30 length ( Propagation

60 600 (b)

500

40 Propagation length (

(b)

400

=30 nm

650

=40 nm

300

=50 nm

2 (nm)

=60 nm 600 2

200 Nanowire in SiO

550 100 Effective radius (nm)

100 200 300 400

(nm) 500

Fig. 4. Effective radius Propagation length and effective radius of the 450

HE13 mode versus the thickness 푑1 of the SiO2 layer. 200 250 300 350 400

(nm)

Figure2 displays the dispersion relations of the hy- Fig. 5. (a) Propagation length and (b) effective radius of brid modes gold nanocable as a function of the middle HE13 mode with varying the thickness 푑2 of the BN outer layer. layer thickness 푑1. Here 푑2 = 40 nm. For comparison, the dispersion relations of a gold nanowire with infinite SiO2 and BN cladding are also shown. For a m)

(a) m multi-interface cylindrical waveguide structure, such 100 as nanotube or nanocable, there are no rigorous def- initions about EH and HE modes. The classification 80 of modes can refer to Ref. [17]. By comparing the am-

60 plitudes of 퐸푧 and 퐻푧, if |퐸푧| > |퐻푧|, the mode is

regarded as TM-like and designated as an EH mode; 40

in the contrast, if |퐸푧| < |퐻푧|, this mode is TE-like Propagation length ( and an HE mode. The adoption of this designation is (b)

=4.41

600

=6.0 only for the convenience of modes citing and it is some- 2

=8.0 what arbitrary. Here TM modes for 푛 = 0, which also 2

500 exist in the nanocable, are not considered. Due to the coupling of the SPP mode of the gold nanowire and waveguide modes of the BN nanotube, four modes are 400

obtained. Each hybrid mode has a distinct propaga- Effective radius (nm) tion constant, which corresponds to its field distribu- 2.0 2.5 3.0 3.5 4.0 tion (Fig. 3). The feature of the field distribution for 1 each mode is also responsible for the variation trend of Fig. 6. (a) Propagation length and (b) effective radius of the propagation constant. Among all the four modes, the HE13 mode with varying the permittivities 휀1 and 휀2. the field of the13 HE mode has a distinguished distribution pattern compared to the other three modes. In Fig.4, we can see that the qualities of modes For the HE13 mode, the distribution in the SiO2 layer HE11, HE12 and EH11 are not substantially improved. has a pattern similar to that of a waveguide mode, However, mode HE13 overcomes the trade-off between which means that more energy locates in the SiO2 the propagation length and effective radius in some layer and the loss will thereby decrease. By varying 푑1, degree. It can travel 80–130 µm or 120–200휆 with an the imaginary parts of propagation constants of HE11, effective radius of only 500–600 nm. Especially, when HE12 and EH11 lie between that of two nanowires with 푑1 = 400 nm, it has a propagation length of 128 µm 057303-3 CHIN. PHYS. LETT. Vol. 28, No. 5 (2011) 057303 and an effective radius of 497 nm. The propagation tion length of 120–200휆 and a small effective radius of length has been increased to more than two times of subwavelength scale. It has also shown that the geo- the original value compared to that in the nanowire metrical parameters as well as material permittivities with SiO2 cladding, at a sacrifice of a little increase can effectively adjust the propagation length and ef- of the effective radius. It demonstrates the combina- fective radius of the hybrid SPP mode. It should be tion of the advantages of both the SPP mode and the confessed that the trade-off between the propagation waveguide mode in the hybrid mode HE13. length and effective radius still exists. However, with Figure5 shows the details of the property of hybrid the combination of the mode coupling and the dielec- mode HE13. We can see that with an increment of 푑2, tric contrast effect, this hybrid mode method improves both the propagation length and the effective radius dramatically the properties of SPP modes in 1D cylin- decreases, showing a clear trade-off between them. For drical nanocables compared to that in nanowires with the same 푑2, with a change of 푑1, however there ex- homogeneous dielectric cladding. With the develop- ists a minimum in the curves of propagation length. ment of fabrication technology, this hybrid waveguide Especially, when 푑1 is larger than the value at the structure can find applications in nanoscale optical de- minimum point, the effective radius of the mode stays vices such as SPP waveguides, spaser and SPP sensors. in a relative constant value as the propagation length We thank Pengfei Yang for the useful discussions. increases. This means that the trade-off between the propagation length and the effective radius in this region is overcome. This improvement can be attributed References to the advantage of the coupling between SPP modes [1] Raether H 1988 Surface Plasmons (Berlin: Springer- and the waveguide modes. Verlag) Finally, we explore the effect of different permit- [2] Barnes W L et al 2003 Nature 424 824 tivities of dielectric layers on the propagation length [3] Economou E N 1969 Phys. Rev. 182 539 휀 [4] Sarid D 1981 Phys. Rev. Lett. 47 1927 and effective radius. As shown in Fig. 6, we change 1 [5] Charbonneau R et al 2000 Opt. Lett. 25 844 from 2.0 to 4.0, with which the material can be easily [6] Lamprecht B et al 2001 App. Phys. Lett. 79 51 selected in optical frequencies. Here 휀2 is set as 4.41 [7] Zia R, Selker M D et al 2005 Phys. Rev. B 71 165431 Phys. Rev. 77 (BN), 6.0 (BaTiO3 or SrTiO3) and 8.0 (Sb2O3 and [8] Degiron A et al 2008 A 021804(R) [26] 휀 휀 [9] Dionne J A et al 2006 Phys. Rev.B 73 035407 SiO2). Generally speaking, when 1 and 2 are in- [10] Guo J and Adato R 2006 Opt. Express 14 12409 creased, both propagation length and effect radius are [11] Bozhevolnyi S B, Volkov V S, Devaux E and Ebbesen T W decreasing, which can be correspondingly explained as 2005 Phys. Rev. Lett. 95 046802 a decrease of optical propagation length with an in- [12] Pile D F P and Gramotnev D K 2004 Opt. Lett. 29 1069 휀 휀 [13] Novikov I V and Maradudin A A 2002 Phys. Rev. B 66 crement of dielectric permittivity. When 1 (or 2) is 035403 fixed, with increasing 휀2 (or 휀1), both its propagation [14] Maier S A et al 2005 Appl. Phys. Lett. 86 071103 length and effective radius are decreased. In this situ- [15] Miziumski C 1972 Phys. Lett. A 40 187 ation, a trade-off between them is still seen. Thus this [16] Peeiffer C A and Economou E N 1974 Phys. Rev. B 10 3038 permittivitiy contraction can also effectively control [17] Prade B and Vinet J Y 1994 J. Lighwave Technol. 12 6 the propagation properties of this hybrid SPP waveg- [18] Schroter U and Dereux A 2001 Phys. Rev. B 64 125420 uide. Generally, for a specialized plasmonic waveg- [19] Novotny L and Hafner C 1994 Phys. Rev. E 50 4094 uide structure, by releasing some propagation length [20] Yang P F, Gu Y and Gong Q H 2008 Chin. Phys. B 17 3880 we can reach good light confinement and vice versa. [21] Maier S A 2008 Nature Photon. 2 460 In summary, by the coupling of SPP modes and [22] Oulton R F, Sorger V J, Genov D A, Pile D F P and Zhang waveguide modes, we have theoretically found a hy- X 2008 Nature Photon. 2 496 Electromagnetic Theory brid plasmonic mode with a long propagation length [23] Stratton J A 1941 (New York: McGraw-Hill) and good light confinement in a cylindrical metal- [24] Palik E D 1985 Handbook of Optical Constants of Solids dielectric waveguide. At the optical wavelength of (Orlando: Academic) 휆 = 632.8 nm, in a nanocable with the gold nanocore [25] Snyder A W, Love J D 1983 Optical Waveguide Theory (New York: Chapman and Hall) of 40 nm, a SiO2 middle layer of 260–400 nm and a [26] Lide D R 2005–2006 CRC Handbook of Chemistry and BN outer layer of 40 nm, we obtain the long propaga- Physics 86th edn (Florida: Taylor & Francis)

057303-4 Chinese Physics Letters Volume 28 Number 5 May 2011

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(Continued on inside back cover) NUCLEAR PHYSICS 052101 An Alternative Interacting Boson Model Description of The N = 90 Nuclei DAI Lian-Rong, TENG Wei-Xin, PAN Feng, WANG Sheng-Hua 052102 Astrophysical Rates for the 6He(p, γ)7Li Reaction LI Er-Tao, LI Zhi-Hong, SU Jun, GUO Bing, LI Yun-Ju, YAN Sheng-Quan, BAI Xi-Xiang, WANG You-Bao, WANG Bao-Xiang, LIAN Gang, ZENG Sheng, FANG Xiao, ZHAO Wei-Juan, LIU Wei-Ping 052103 Description of the Chiral Doublet Bands in 135Nd and 136Nd ZHANG Da-Li, DING Bin-Gang ATOMIC AND MOLECULAR PHYSICS 053201 A Phenomenological Model for Decay Process of Long-Persistent Phosphorescence CHEN Bin, HAO Hong-Chen, ZHU Jiang, LU Ming 053202 Simulation of Hydrogen Emission Spectrum in Debye Plasmas DING Qi-Yong, ZHANG Song-Bin, WANG Jian-Guo 053301 Relationship between Fermi Resonance and Solvent Effects JIANG Xiu-Lan, LI Dong-Fei, SUN Cheng-Lin, LI Zhan-Long, YANG Guang, ZHOU Mi, LI Zuo-Wei, GAO Shu-Qin 053401 Inner-Shell Excitations of 2p Electrons of Argon Investigated by Fast Electron Impact with High Resolution REN Lin-Mao, WANG You-Yan, LI Dong-Dong, YUAN Zhen-Sheng, ZHU Lin-Fan 053402 Potential and Kinetic Electron Emissions from HOPG Surface Irradiated by Highly Charged Xenon and Neon Ions WANG Yu-Yu, ZHAO Yong-Tao, SUN Jian-Rong, LI De-Hui, QAYYUM Abdul , LI Jin-Yu, WANG Ping-Zhi, XIAO Guo-Qing 053601 Diffusion of Six-Atom Cu Islands on Cu(111) and Ag(111) Sardar Sikandar Hayat, I. Ahmad, M. Arshad Choudhry 053701 A Simplified Cold Atom Source for 3-D MOT Loading WANG Xiao-Long, CHENG Bing, WU Bin, WANG Zhao-Ying, LIN Qiang FUNDAMENTAL AREAS OF PHENOMENOLOGY(INCLUDING APPLICATIONS) 054201 Repulsive and Restoring Casimir Forces Based on Magneto-Optical Effect ZENG Ran, YANG Ya-Ping

054202 Compact Continuous-Wave Nd:YVO4 Laser with Self-Raman Conversion and Sum Frequency Generation ZHU Hai-Yong, ZHANG Ge, DUAN Yan-Min, HUANG Cheng-Hui, WEI Yong 054203 All-Optical Format Conversion from RZ-DPSK to NRZ-DPSK at 40 Gbit/s ZHANG Zheng, PAN Di, YU Yu, ZHANG Xin-Liang 054204 Propagation of Coherent Gaussian Schell-Model Beam Array in a Misaligned Optical System ZHOU Pu, WANG Xiao-Lin, MA Yan-Xing, MA Hao-Tong, XU Xiao-Jun, LIU Ze-Jin 054205 High-Resolution Plasmonic Refractive-Index Sensor Based on a Metal-Insulator-Metal Structure ZHU Jia-Hu, HUANG Xu-Guang, MEI Xian 054206 Luminance Eﬀects on Neural Mechanism at Photopic Level GE Jing-Jing, WANG Zhao-Qi 054207 A New Type of Absorbance Sensors Based on Long-Period Fiber Gratings LUO Tao, GU Zheng-Tian 054208 Slow-Light Propagation in a Tapered Dielectric Periodic Waveguide over Broad Frequency Range FANG Yi-Jiao, CHEN Zhuo, WANG Zhen-Lin 054209 Simulation of Far-Field Superresolution Fluorescence Imaging with Two-Color One-Photon Excitation of Reversible Photoactivatable Protein WANG Chen, QIAO Ling-Ling, MAO Zheng-Le

054210 Efficient Tunable Mid-Wave Infrared Laser from 2 µm Tm,Ho:YVO4 Pumped Gain-Switched Cr2+:ZnSe Laser MENG Pei-Bei, YAO Bao-Quan, LI Gang, JU You-Lun, WANG Yue-Zhu 054211 A Novel Method for Heightening Sensitivity of Prism Coupler-Based SPR Sensor ZHANG Zhi-Wei, WEN Ting-Dun, WU Zhi-Fang 054212 High Power Passive Phase Locking of Four Yb-Doped Fiber Amplifiers by an All-Optical Feedback Loop XUE Yu-Hao, HE Bing, ZHOU Jun, LI Zhen, FAN Yuan-Yuan, QI Yun-Feng, LIU Chi, YUAN Zhi-Jun, ZHANG Hai-Bo, LOU Qi-Hong 054213 Enhancement of Light Absorption in Thin Film Silicon Solar Cells with Metallic Grating and One-Dimensional Photonic Crystals ZHENG Gai-Ge, XIAN Feng-Lin, LI Xiang-Yin 054214 Enhanced Visible Light Generation from 1 µm Femtosecond Pulses within High-∆ Photonic Crystal Fibers ZHANG Xin-Ben, ZHU Xian, CHEN Xiang, PENG Jing-Gang, DAI Neng-Li, LI Jin-Yan 054215 Analysis of Optical Vortices in the Near Field of a Thin Metal Film ZHANG Jin-Long 054216 Light Extraction Enhancement of GaN LED with a Two-Dimensional Photonic Crystal Slab LIU Hong-Wei, KAN Qiang, WANG Chun-Xia, HU Hai-Yang, XU Xing-Sheng, CHEN Hong-Da 054401 A Hemispherical-Involute Cavity Receiver for Stirling Engine Powered by a Xenon Arc Solar Simulator LI Zhi-Gang, TANG Da-Wei, LI Tie, DU Jing-Long 054701 Exact Solutions on MHD Flow Past an Accelerated Porous Plate in a Rotating Frame T. Hayat Liaqat Ali. Khan, R. Ellahi, S. Obaidat 054702 TR PIV Experimental Investigation on Bypass Transition Induced by a Cylinder Wake TANG Zhan-Qi, JIANG Nan 054703 Transient Growth of Perturbation Energy in the Taylor–Couette Problem with Radial Flow CHEN Cheng, GUO Zhi-Wei, WANG Bo-Fu, SUN De-Jun PHYSICS OF GASES, PLASMAS, AND ELECTRIC DISCHARGES 055201 Lifetime Calculations on Collector Optics from Laser Plasma Extreme Ultraviolet Sources with Minimum Mass WU Tao, WANG Xin-Bing 055202 Similar Rayleigh–Taylor Instability of Shock Fronts Perturbed by Corrugated Interfaces HE Yong, HU Xi-Wei, JIANG Zhong-He CONDENSED MATTER: STRUCTURE, MECHANICAL AND THERMAL PROPERTIES 056101 A Transition Phase in the Transformation from α-, β- and ε- to δ-Bismuth Oxide DENG Hong-Yan, HAO Wei-Chang, XU Huai-Zhe 056201 Superlubricity of a Mixed Aqueous Solution MA Zhi-Zuo, ZHANG Chen-Hui, LUO Jian-Bin, LU Xin-Chun, WEN Shi-Zhu 056801 Preparation of Curled Microfibers by Electrospinning with Tip Collector TANG Cheng-Chun, CHEN Jun-Chi, LONG Yun-Ze, YIN Hong-Xing, SUN Bin, ZHANG Hong-Di 056802 Explosive Synchronization and Emergence of Assortativity on Adaptive Networks JIANG Hui-Jun, WU Hao, HOU Zhong-Huai CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES

057101 Prediction of a Low-Dense BC2N Phase SHAO Xi 057102 Improved AlGaN/GaN HEMTs Grown on Si Substrates Using Stacked AlGaN/AlN Interlayer by MOCVD WANG Yong, YU Nai-Sen, LI Ming, LAU Kei-May 057201 Frequency-Dependent Electrical Transport Properties of 4, 40, 400-Tri(N-carbazolyl)-Triphenylamine Investigated by Impedance Spectroscopy LI Bi-Xin, CHEN Jiang-Shan, ZHAO Yong-Biao, MA Dong-Ge 057301 Photocatalysis of InGaN Nanodots Responsive to Visible Light WANG Lai, ZHAO Wei, HAO Zhi-Biao, LUO Yi 057302 Pure Electric and Pure Magnetic Resonances in Near-Infrared Metal Double-Triangle Metamaterial Arrays CAO Zhi-Shen, PAN Jian, CHEN Zhuo, ZHAN Peng , MIN Nai-Ben, WANG Zhen-Lin 057303 A Trade-oﬀ between Propagation Length and Light Conﬁnement in Cylindrical Metal-Dielectric Waveguides SUN Bao-Qing, GU Ying, HU Xiao-Yong, GONG Qi-Huang

057401 Growth, Characterization and Fermi Surface of Heavy Fermion CeCoIn5 Superconductor JIA Xiao-Wen, LIU Yan, YU Li, HE Jun-Feng, ZHAO Lin, ZHANG Wen-Tao, LIU Hai-Yun, LIU Guo-Dong, HE Shao-Long, ZHANG Jun, LU Wei, WU Yue, DONG Xiao-Li, SUN Li-Ling, WANG Gui-Ling, ZHU Yong, WANG Xiao-Yang, PENG Qin-Jun, WANG Zhi-Min, ZHANG Shen-Jin, YANG Feng, XU Zu-Yan, CHEN Chuang-Tian, ZHOU Xing-Jiang

057402 Electronic Structure of KFe2Se2 from First-Principles Calculations CAO Chao, DAI Jian-Hui

057501 Magnetism and Substrate Eﬀects of Mn3 Clusters on Cu(111), Pd(111) and Ne(111) ZHONG Ke-Hua, WENG Zhen-Zhen, FENG Qian, YANG Yan-Min, HUANG Zhi-Gao 057502 Thermal Decay and Reversal of Exchange Bias Field of CoFe/PtMn Bilayer after Ga+ Irradiation ZHOU Guang-Hong, ZHU Yu-Fu, LIN Yue-Bin 057701 Nonresonant Metamaterials with an Ultra-High Permittivity HE Xiao-Yang, CHEN Qi, LI Lin-Cui, YANG Chun, LI Biao, ZHOU Bang-Hua, TANG Chuan-Xiang

057702 L-cystine-Assisted Growth and Mechanism of CuInS2 Nanocrystallines via Solvothermal Process LIU Hai-Tao, ZHONG Jia-Song, LIU Bing-Feng, LIANG Xiao-Juan, YANG Xin-Yu, JIN Huai-Dong, YANG Fan, XIANG Wei-Dong 057801 Ordered Gold Nanobowl Arrays as Substrates for Surface-Enhanced Raman Spectroscopy CHEN Ling, LIU Fan-Xin, ZHAN Peng, PAN Jian, WANG Zhen-Lin 057802 AlGaN/GaN Ultraviolet Detector with Dual Band Response GAO Bo, LIU Hong-Xia, WANG Shu-Long 057803 Localized Surface Plasmons Enhanced Ultraviolet Emission of ZnO Films LIU Yan-Song, LU Hai-Fei, XU Xiao-Liang, GONG Mao-Gang, LIU Ling, YANG Zhou 057804 Gallium Nitride Nanowires Grown by Hydride Vapor Phase Epitaxy LIU Zhan-Hui, XIU Xiang-Qian, YAN Huai-Yue, ZHANG Rong, XIE Zi-Li, HAN Ping, SHI Yi, ZHENG You-Dou 057805 Linear and Nonlinear Optical Properties of Micrometer-Scale Gold Nanoplates LIU Xiao-Lan, PENG Xiao-Niu, YANG Zhong-Jian, LI Min, ZHOU Li CROSS-DISCIPLINARY PHYSICS AND RELATED AREAS OF SCIENCE AND TECHNOLOGY 058101 Measurement of Beta Particles Induced Electron-Hole Pairs Recombination in Depletion Region of GaAs PN Junction CHEN Hai-Yang, JIANG Lan, LI Da-Rang 058201 Interaction of a Spherical Colloid and a Porous Membrane in a Bulk Electrolyte LIAN Zeng-Ju 058901 Analysis of Imaging Contrast of Small Cracks in FNR Specimens DOU Hai-Feng, TANG Bin, WU Yang 058902 Effect of Adaptive Delivery Capacity on Networked Traffic Dynamics CAO Xian-Bin, DU Wen-Bo, CHEN Cai-Long, ZHANG Jun 058903 Effects of Variant Rates and Noise on Epidemic Spreading LI Wei, GAO Zong-Mao, GU Jiao 058904 Attack Robustness of Scale-Free Networks Based on Grey Information LI Jun, WU Jun, LI Yong, DENG Hong-Zhong, TAN Yue-Jin GEOPHYSICS, ASTRONOMY, AND ASTROPHYSICS 059101 Electrical Properties of Hydrous Forsterite Derived from First-Principles Calculations WANG Duo-Jun, LIU Zai-Yang, YI Li, SHI Bao-Ping 059201 A Three-Box Model of Thermohaline Circulation under the Energy Constraint SHEN Yang, GUAN Yu-Ping, LIANG Chu-Jin, CHEN Da-Ke 059601 Standing Shocks in the Inner Slow Solar Wind LI Bo, CHEN Yan-Jun, LI Xing