Polarization conversion based on plasmonic phase control by an ultra-thin metallic nano-strips Helei Wei, Dejiao Hu, Yunsheng Deng, Xuannan Wu, Xiao Xiao, Yidong Hou, Yunjiao Wang, Ruiying Shi, Deqiang Wang, and Jinglei Du Citation: AIP Advances 6, 125304 (2016); doi: 10.1063/1.4971374 View online: http://dx.doi.org/10.1063/1.4971374 View Table of Contents: http://aip.scitation.org/toc/adv/6/12 Published by the American Institute of Physics Articles you may be interested in Phonon interaction with coupled photonic-plasmonic modes in a phoxonic cavity AIP Advances 6, 122001122001 (2016); 10.1063/1.4968615 Multi-frequency acoustic metasurface for extraordinary reflection and sound focusing AIP Advances 6, 121702121702 (2016); 10.1063/1.4968607 Switchable polarization rotation of visible light using a plasmonic metasurface AIP Advances 2, 016103016103 (2016); 10.1063/1.4968840 Band gaps in bubble phononic crystals AIP Advances 6, 121604121604 (2016); 10.1063/1.4968616 AIP ADVANCES 6, 125304 (2016) Polarization conversion based on plasmonic phase control by an ultra-thin metallic nano-strips Helei Wei,1 Dejiao Hu,1 Yunsheng Deng,2 Xuannan Wu,1 Xiao Xiao,1 Yidong Hou,1 Yunjiao Wang,2 Ruiying Shi,1 Deqiang Wang,2 and Jinglei Du1,a College of Physical Science and Technology, Sichuan University, 610064 Chengdu, China Key Lab of Multi-scale Manufacturing Technology, Chongqing Institute of Green and Intelligent Technology, Chinese Academy of Sciences, 400714 Chongqing, China Chongqing (Received 21 August 2016; accepted 20 November 2016; published online December 2016) Ultra-thin metallic nano-strips (thinner than skin depth) can lead to anomalous reflection for a transverse magnetic (TM) incidence of some wave-lengths, due to the phase modulation of localized surface plasmon resonance Based on the principle above, we proposed a method of polarization modulation using ultrathin metallic nano-strips When irradiating nano-strips vertically by light with a given polarized angle, we can utilize the phase difference of the TM transmission and transverse electric (TE) transmission near anomalous reflection region to modulate transmission polarization We have designed and fabricated the ultra-thin metallic nano-strips with the function of quarter-wave plate, the attained transmission Stokes parameter S3 is 0.95 The nano-strips is easy to design and fabricate, also compatible with other optics devices, hence has the potential applications in integrated optics field © 2016 Author(s) All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/) [http://dx.doi.org/10.1063/1.4971374] I INTRODUCTION Traditional polarization modulation devices (like quarter-wave plate) are mainly made of birefringent crystal with accurate thickness, such as quartz etc, which can generate additional optical path difference between the two incident electric field components which parallel to the optical axis and perpendicular to the optical axis Recently, the ultra-thin and novel micro-nano polarization conversion devices have become a research focus, as the increasing demands of micro-nano optics for signal generation, transmission and detection Meta-materials/meta-surfaces has the excellent ability of optical control and some achievements have been gained by utilizing Meta-material/meta-surfaces to make polarization conversion devices.1–9 However, we still face some challenges for the practical application, such as the reflection geometry makes it inconvenient for practical applications due to the interference between incident and reflected waves.10 Besides, the metallic film with a thickness smaller than skin depth is high transparent for visible light and half transparent for infrared light,11–14 but some transmission devices with larger thickness are typically not perfectly transparent for electromagnetic waves,15–18 so the energy loss issues remains unsolved Moreover, due to the complex structure of the meta-materials/meta-surfaces and the fabrication difficulty, they are not suitable for practical applications Previously, we proposed a theoretical model to investigate the anomalous reflection of ultra-thin metallic nano-strips, the simulation shows a reasonable agreements with the corresponding experimental results,19 and the phase modulation was also analyzed.10 Considering that the ultra-thin metallic nano-strips is transparent for visible light, this article puts forward an idea of ultra-thin metallic nano-strips based polarization converter which has a function of traditional quarter-wave plate Based on the accurate control of transmission coefficients and phase difference of a Electronic mail: DuJL@scu.edu.cn 2158-3226/2016/6(12)/125304/7 6, 125304-1 © Author(s) 2016 125304-2 Wei et al AIP Advances 6, 125304 (2016) x polarization (TM) and y polarization (TE), optimization and analysis about the impacts of various nano-strips parameters on the polarization characteristics, we designed and fabricated the ultra-thin metallic nano-strips, and the performance of transmission polarization was also tested Our simulation shows that the optimized nano-strips based polarization converters can obtain higher transmittance And compared with reflective devices, our designed device is easy to fabricate, and convenient to use II ULTRA-THIN METALLIC NANO-STRIPS FOR POLARIZATION CONVERSION AND ITS STRUCTURE PARAMETERS DESIGN Figure 1(a) shows the schematic diagram of ultra-thin metallic nano-strips based quarter-wave plate structure Every strip extends indefinitely in Y direction, and forms periodic structure along X direction with period Λ, width W The gold layer with thickness h (thinner than the skin depth of gold) is deposited on a glass substrate with refractive index ns A linearly polarized light with polarized angle θ was illuminated on the structure vertically In our previous work, the transmission characteristics of ultra-thin metallic nano-strips have been discussed, owe to the Localized Surface Plasmon Resonance (LSPR).10 For a nano-strip with the defined width, x polarized incident light would excite LSPR at a particular wavelength, the transmission is suppressed under the resonant frequency, and a transmission phase variation region exists around resonant frequency; whereas, the resonant wavelength of y polarization light is infinite (the resonant frequency is 0), therefore the suppressed transmission phenomenon does not exist and the phase changes of transmission light is not obvious at limited wavelength range According to Ref 10, the transmission coefficients of ultra-thin metallic nano-strips are expressed in time coupled mode theory formulas as: 2γex j(ω0x − ω) + γ0 + 2γex 2γey ty = − j(ω0y − ω) + γ0 + 2γey tx = − (1) where ω0x (ω0y ) and ω are the resonance frequency of X(Y) direction and incident frequency, γ0 is the intrinsic loss rate, γex and γey are external leakage rate because of radiation to X and Y direction respectively The phase of two polarization transmission coefficients is obtained from equation (1): 2γex (ω0 − ω) (ω0x − ω)2 + γ0 (γ0 + 2γex ) −2γey ω ϕy = arctan (ω0y − ω)2 + γ0 (γ0 + 2γey ) ϕx = arctan (2) We could develop various phase-modulation devices applied to nano-integration optics according to the phase modulation property of ultra-thin metallic nano-strips on transmission coefficients FIG (a) Schematic of ultra-thin metallic nano-strips structure under the vertical illumination of a linearly polarized light with polarized angle θ1 (b) The spectra of transmission coefficients for x and y polarizations and the spectrum of the phase difference from simulation 125304-3 Wei et al AIP Advances 6, 125304 (2016) For an ultra-thin polarization device by one-dimensional (1-D) ultra-thin metallic nano-strips with function like traditional quarter-wave plate, when illuminated vertically under uniform plane wave, the transmission field from the nano-strips can be written as: E˜ x = |tx | E0 cosθ · exp (-iϕx ) E˜ y = ty E0 sinθ · exp -iϕy (3) As for a quarter-wave plate, the transmission is circular polarized light, the phase difference is ∆ϕ = ϕy − ϕx = ±π/2 (plus sign denotes right circular polarized, RCP; and minus sign denotes left circular polarized, LCP) and E˜ x | = E˜ y should be satisfied Combining this condition, the feature polarized angel θ between incident electric field vector and X-axis for certain wavelength is derived as: θ = ±arctan |tx | /|ty | , (4) Hence, the energy transmissivity of incident field at feature polarized direction (θ = θ ) can be calculated as: T = 2tx2 ty2 /(tx2 + ty2 ), (5) The polarization state of the transmitted wave can be measured with the normalized Stokes parameter S3 : S3 = −2 Tx Ty /(Tx + Ty ), (6) Where T x and T y are the transmissivities of x polarization and y polarization respectively t x and t y are closely associated with parameters of surface plasmon ultra-thin metallic nano-strips, and the wavelengths that can obtain circularly polarization transmission are related to device parameter If quartz glass (ns =1.525) is selected as substrate, and the material of nano-strips is gold with thickness 20nm, whose dielectric function is taken from Ref 20 Fig.1(b) shows a spectra sample of the module of the transmission coefficients for x and y polarizations and the spectrum of the phase difference when Λ = 450 nm and W =300nm with Comsol Multiphysics The dash lines and small triangles indicate the specific positions where the phase difference ∆ϕ = −π/2 The left green triangle corresponds to an incident visible wavelength between 600nm-700nm, the transmission coefficients of x polarization and y polarization are 0.64 and 0.71 respectively Taking this parameter, the feature polarized angel θ = 42.29◦ and energy transmissivity T =0.46 can be calculated by the formula (4) and (5) under the condition E˜ x | = E˜ y , and T is higher than the transmissivity of some analogous metamaterial devices.5 In this sample, the right red triangle corresponds to an incident infrared wavelength between 900nm1000nm, and the transmission coefficient of x polarization is smaller which led to extremely low energy transmissivity, of no use value over this To obtain the optimum structure parameters of ultra-thin metallic nano-strips based quarterwave plate for a feature wavelength needed, we have to calculate and analyze the relationship of the phase difference of transmissions and the transmission coefficients to nano-strips period and incident wavelengths While irradiated by x polarization and y polarization respectively, the spectrum of phase difference (ϕy − ϕx ) as a function of the incident wavelength and the grating period is showed in Fig 2(a), here, assuming the duty ratio of nano-strips p = W/Λ = 0.6 is constant Three dash lines correspond to the nano-strips periods and incident wavelengths where |ϕy − ϕx | = π/2 Those results reveal that the energy transmissivity is quite different at the periods where the ultra-thin metallic nano-strips could realize the function of quarter-wave plate: the minimum is close to zero (λ = 1013nm, Λ = 490nm, θ = 0.60◦ ,T =3.263×10-5 ), and the maximum is 0.61 (λ = 610nm, Λ = 400nm, θ = 44.98◦ ) The energy transmissivity can obtain relative high values in the grating period range of 430 nm -550 nm and the incident wavelength range of 600 nm -780 nm, meanwhile, phase difference change slowly in this region So, when a linear polarization light illuminates the device vertically with the feature polarized angel (θ = θ ), if the structure parameters of ultra-thin metallic nano-strips is on the dash line 1(RCP) and dash line 2(LCP), it is expected to obtain circular polarized transmission 125304-4 Wei et al AIP Advances 6, 125304 (2016) FIG (a) The spectra of phase difference ϕy − ϕx The module of the (b) x -polarization and (c) y-polarization transmission coefficients as a function of the wavelength and the grating period The white dashed lines represent the positions where the module of phase difference is equal to π/2 III EXPERIMENTAL RESULTS AND DISCUSSION Besides the theoretical calculation above, here we fabricated an array of nano-strips in a gold film using Focused Ion Beam (FIB, Carl Zeiss, Orion NanoFab), the gold film with the thickness of 21.5nm was deposited by a magnetron sputtering coater (Alliance, Manuals DP 650) deposition system Fig 3(a) shows the image of scanning electron microscopy (SEM, JEOL, JSM-7800F), the measured period and width are 445 and 268nm respectively with a deviation less than 5nm The insert image is FIG (a) SEM image of the ultra-thin metallic nano-strips fabricated by FIB, Inset image is the whole field of nano-strips (b) Scheme of the experimental system (c) The spectra of the transmissivity for different incident wavelength at transmission polarization direction (θ2 ) (d) The spectra of the transmissivity for different polarization incidences(θ1 ) at transmission polarization direction (e) The transmission coefficients for incident wavelength 675 nm and θ1 = 43◦ 125304-5 Wei et al AIP Advances 6, 125304 (2016) the whole field 10 ì 10àm Through the theoretical analysis, we figure out the incident wavelength is 675nm if the transmission is circular polarized light, and θ = 43◦ , T =0.51, S3 =0.99 To measure the transmission performance, a linearly polarized polychromatic light was illuminated to the sample after pouring through polarizer 1, then the transmission light passes through the objective lens and polarizer sequentially prior to reaching the spectrograph (Princeton SP2360), the optical path is shown in Fig 3(b) Fixing polarizer to θ = θ = 43◦ and rotating polarizer 2, the spectra of the transmissivity for different incident wavelengths at transmission polarization directions (θ , modulated by polarizer 2) was obtained, as depicted in Fig.3(c) We found that the transmissivity of incident wavelength 675nm changes the least over θ , compared with that for the incident wavelength 655, 665, 685, and 695nm Fig.3 (d) presents the spectra of transmissivity versus θ for θ = 0◦ (x polarization), θ = 90◦ (y polarization) and θ = 43◦ (the feature direction polarization) The transmissivity of the feature direction polarizations (θ = 43◦ ) exhibits relatively small fluctuation, which suggests the linearly incident light was nearly converted to a circular polarized light And the difference between the feature direction polarization linear response T xx (T =0.31) and T yy (T max =0.58) is the reason the transmission is not perfect circular polarized light The corresponding transmission coefficients also indicate the transmission is closer to circular polarized light, since the Stokes parameter of transmission S3 is as large as 0.95 and the ellipticity is 1.38 The above estimated value is almost consistent with the theoretical calculated value (S3 is 0.99 and ellipticity is 1.03) after the fabrication errors and measurement errors are considered IV FURTHER OPTIMIZATION FOR STOKES PARAMETER AND TRANSMISSIVITY Better polarization conversion characteristics and high transmittance are highly desirable for practical applications Fig.4 show the influence of the deviation of period Λ, duty ratio p and thickness h may cause on the Stokes parameter, which might be a reference for optimizing the performance Fig.4(a) illustrates the effects of period on the S3 is periodically dependent when duty ratio is a constant, experiment of our sample is on the first spike and the amplitude of S3 changes very rapidly Fig.4(b) shows S3 changes gently and remains above 0.93 when duty ratio is within 0.4-0.7 with period is a constant Also when the period and duty ratio are kept the constant, S3 increases slowly to reach a maximum and gradually decreases with the increase of thickness, as depicted in Fig.4(c), and remains above 0.99 when thickness is within 16nm-24.5nm Calculations show that the deviation of duty ratio and thickness within a certain range has small effect on the polarization performance, that is, the duty ratio and thickness have a greater tolerance to the process error While the polarization performance fluctuates cyclically with the variation of period, and the period should be carefully considered in practical application To achieve better circularly polarization characteristics, we suggest the deviation range of duty ratio and thickness are ±0.05 and ±3nm respectively; while associated with the location where the S3 spike is, the deviation range of period may be ±5nm Though, the characteristic of dramatic changes initiated through period may be used to regulate applied wavelengths and performance also Moreover, calculation and analysis indicate thickness is a key factor affecting the transmissivity of metallic nano-strips, and the effects of the other parameters are relatively small Fig.5 shows the spectra of the calculated transmissivity versus thickness, while keeping better circularly polarization transmission (S3 >0.99) corresponds to the different feature wavelengths Here, nano-strips structure FIG S3 as a function of (a) period Λ, (b) duty ratio p and (c) thickness h 125304-6 Wei et al AIP Advances 6, 125304 (2016) FIG T is a function of metallic nano-strips thickness h (Λ = 490nm, p =0.6, S3 >0.99) parameter Λ = 490nm and p =0.6 The point is that the curves of transmissivity look like to present line variety at different thickness If the chosen thickness of metallic nano-strips is within 10nm-25nm, it can be seen the transmissivity increase from 0.45 to 0.74 as the thickness decrease from 25nm to 10nm, increased by approximately 1.64 folds, higher than the transmissivity (30nm) metamaterial.9 So the proper nano-strips thickness may be used to relieve the pressure of demand for high transmissivity, this is easier than the optimization of metamaterial and won’t introduce too much design and fabrication difficulties, of course the metallic film coating technique needed to be strengthened V CONCLUSION This article presents a kind of plasmon resonance phase modulation of ultra-thin metallic nanostrips based polarization conversion technique, which has been proved to be feasible by numerical analysis And we designed an ultra-thin metallic nano-strips based quarter-wave plate for the visible light, the experimental result approaches the theoretical value very well, which can afford the theoretical and experimental proof for developing related nano-integration optical devices The ultrathin metallic nano-strips have simple structure, easy fabrication and integration, which can be mass produced by interference lithography and nanoimprint, and have wide application future ACKNOWLEDGMENTS This work was supported by 51503206 to Y.W, 61504146 to Y.D National Natural Science Foundation of China S Fan, W Suh, and J Joannopoulos, J Opt Soc Am A 20, 569 (2003) Hao, Q Ren, Z An, X Huang, Z Chen, M Qiu, and L Zhou, Phys Rev A 80, 023807 (2009) Y Ye and S He, Appl Phys Lett 96, 203501 (2010) W J Sun, Q He, J M Hao, and L Zhou, Opt Lett 36, 927 (2011) N Yogesh, T Fu, F Lan, and Z Ouyang, IEEE Photonics J 7, (2015) F Shafiei, F Monticone, K Q Le, X.-X Liu, T Hartsfield, A Al` u, and X Li, Nat Nanotechnol 8, 95 (2013) N K Grady, J E Heyes, D R Chowdhury, Y Zeng, M T Reiten, A K Azad, A J Taylor, D A Dalvit, and H.-T Chen, Science 340, 1304 (2013) L M Freeman, L Pang, and Y Fainman, ACS Nano 8, 8383 (2014) Y Zhao and A Al` u, Nano Letters 13, 1086 (2013) 10 D Hu, P Wang, Z Zhang, L Pang, S Kim, and J Du, J Opt Soc Am B 32, 1369 (2015) 11 J Zhang, W Bai, L Cai, X Chen, G Song, and Q Gan, Appl Phys Lett 98, 261101 (2011) 12 D Reibold, F Shao, A Erdmann, and U Peschel, Opt Express 17, 544 (2009) 13 G D’Aguanno, N Mattiucci, A Alu, and M Bloemer, Phys Rev B 83, 035426 (2011) 14 Q Gan, W Bai, S Jiang, Y Gao, W Li, W Wu, and F J Bartoli, Plasmonics 7, 47 (2012) J 125304-7 15 V Wei et al AIP Advances 6, 125304 (2016) R Shrestha, S.-S Lee, E.-S Kim, and D.-Y Choi, Nano Lett 14, 6672 (2014) Spevak, A Y Nikitin, E Bezuglyi, A Levchenko, and A Kats, Phys Rev B 79, 161406 (2009) 17 J Braun, B Gompf, G Kobiela, and M Dressel, Phys Rev Lett 103, 203901 (2009) 18 S Xiao, J Zhang, L Peng, C Jeppesen, R Malureanu, A Kristensen, and N A Mortensen, Appl Phys Lett 97, 071116 (2010) 19 S Kim, L Pang, B Hong, J Ptasinski, and Y Fainman, Opt Lett 41, 1522 (2016) 20 P B Johnson and R W Christy, Phys Rev B 6, 4370 (1972) 16 I ... ADVANCES 6, 125304 (2016) Polarization conversion based on plasmonic phase control by an ultra- thin metallic nano- strips Helei Wei,1 Dejiao Hu,1 Yunsheng Deng,2 Xuannan Wu,1 Xiao Xiao,1 Yidong... designed and fabricated the ultra- thin metallic nano- strips, and the performance of transmission polarization was also tested Our simulation shows that the optimized nano- strips based polarization converters... ultra- thin metallic nanostrips based polarization conversion technique, which has been proved to be feasible by numerical analysis And we designed an ultra- thin metallic nano- strips based quarter-wave