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Plasmonic quarter-wave plate with U-shaped nanopatches
Accepted Manuscript Title: Plasmonic quarter-wave plate with U-shaped nanopatches Authors: Ming Chen, Linzi Chang, Tong Xiuqian, Xiaofei Xiao, Hui Chen PII: DOI: Reference:
S0030-4026(17)30066-9 http://dx.doi.org/doi:10.1016/j.ijleo.2017.01.048 IJLEO 58751
To appear in: Received date: Accepted date:
26-5-2016 17-1-2017
Please cite this article as: Ming Chen, Linzi Chang, Tong Xiuqian, Xiaofei Xiao, Hui Chen, Plasmonic quarter-wave plate with U-shaped nanopatches, Optik - International Journal for Light and Electron Optics http://dx.doi.org/10.1016/j.ijleo.2017.01.048 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Plasmonic quarter-wave plate with U-shaped nanopatches Ming Chena,b,* , Linzi Changb , Tong Xiuqianb, Xiaofei Xiaob, Hui Chenb a
Guangxi key laboratory of precision navigation technology and application, Guilin University of Electronic Technology, Guilin 541004, Guangxi, China b
Guilin University of Electronic Technology, Guilin 541004, Guangxi, China * Corresponding Author: [email protected]
Abstract: a plasmonic quarter-wave plate which is based on U-shaped silver nanopatches array in the near-infrared range is designed and presented by us. It utilizes localized surface plasmon resonances with an abrupt phase shift to achieve the desired phase modulation in the transmitted field. The optimized quarter-wave plate can perfectly convert a linearly polarized light to circularly polarized light, whose ellipticity reaches to 1 at the wavelength of 1.55 μm. The bandwidth, in which the ellipticity is larger than 0.83, is 120 nm. This structure offers an enormous potential applications in optical sensor systems, advanced nanophotonic devices and integrated optical circuits. Keywords: Plasmonic; Quarter-wave plate; Polarization conversion; Nanopatches array.
1 Introduction Polarization, one of the important characteristics of light, is crucial in all kinds of optical researches and applications. Researchers have been seeking for an efficient way to completely control the polarization state of light. Conventional optical components usually utilize a piece of birefringent material to produce phase retardation, such as traditional anisotropic waveplates, polarizers, chiral media and prisms, relay on the propagation effect to control the polarization of light. As a result, the conventional optical components are usually bulky and suffer from difficulties in 1
manufacturing configurations, which go against the general trend of integration and miniaturization in photonics. Recently, controlling the polarization of light by ultrathin interface consisting of periodic plasma resonances array has increasingly received researchers’ attention . Various plasmonic metamaterial waveplates based on patterned metallic films [1-5], nanoslits [6-8] or nanoapertures [9-13] arrays have been proposed and demonstrated at microwave [13-16] and optical frequencies [1-3, 6-10]. Those waveplates can be divided into two types: transmission mode [6,8-11] and reflective mode [1-3,9]. Both of them are combined geometrical effects with localized plasmon resonances to produce the phenomenon of extraordinary optical transmission (EOT) of enhanced transmission fields. Therefore, as long as properly adjusting the geometry scale of the local mechanism unit can we obtain the desired polarization or phase properties at particular frequency. However, previous reported works still suffer from limited operation bandwidth or limited thickness of metal film. For example, Pors et al. using subwavelength nanocross array realized quarter-wave plate at wavelength of 1.52 μm and the bandwidth was 85nm [2]. Khoo et al. proposed a quarter-wave plate based on subwavelength nanoslits array, which was realized at wavelength of 802 nm, and the thickness was 200 nm [7]. Zhao et al. proposed a quarter-wave plate comprising of periodic orthogonal nanorods array at wavelength of 650 nm and the bandwidth was 46 nm [6]. Chen et al. used subwavelength rectangular annular arrays to realize quarter-wave plate at wavelength of 1.55 μm and the thickness of metal film was 200 nm [11]. Here, a plasmonic quarter-wave plate (QWP) based on U-shaped silver nanopatches array on silica substrate is proposed by us. It is well known that a QWP can fully convert linearly polarized light (circularly polarized light) into circularly polarized light (linearly polarized light) due to equal transmitted amplitude in two orthogonal directions and phase difference of π/2 between two orthogonal directions. This concept is realized by the changes of resonance of nanopatch via varying the geometry scale of the local mechanism unit. [5-6,9] Because the phase shift of the transmitted field is introduced by the resonant response of noble-metal nanopatch. For 2
a given illumination wavelength，a dipole plasmonic nanopatch shows to a first-order approximation a harmonic oscillator behavior, which means that its electric near field exhibits a phase shift with respect to the driving field, changing from 0° to 180° when the length is varied from below to above the resonance length [15]. Therefore, by properly choosing the side length of nanopatch can obtain the desired characteristics of the transmitted field. Finite-difference time-domain method (FDTD) is used to analyze the relationship between the transmitted field characteristics and the geometric dimensions of nanopatch. By optimizing the design, we obtain the functionalities of QWP with high performance at wavelength of 1.55 μm. Finally, we investigate the polarization conversion efficiency of the designed QWP. Compared to the traditional QWP, the proposed QWP is of high polarization conversion efficiency and high transmittance. In addition, it has prominent merits of ultrawide wavelength range and thin thickness, which makes it more conveniently integrated into advanced optical system.
1. Theory and structure design Fig. 1 shows the schematic of the designed plasmonic QWP. It consists of periodic U-shaped silver nanopatches array on silica substrate with a refractive index of 1.45. The side length of nanopatch along x-axis and y-axis are Lx and Ly, respectively. The lattice constant is denoted by P. The width and thickness of nanopatch are w=50 nm, and h=60 nm. In the simulation, silver is modeled with Drude material with a plasma frequency of p=2.175 PHz, a damping factor of =4.35 THz, and ∞=5. [17] The linearly polarized plane wave, which polarization orientation angle θ relative to the x axis, is normally incident from the substrate. Fig.1 (a) Schematic sketch of the designed plasmonic quarter-wave plate, which is composed of U-shaped Ag nanopatches array with the same geometrical parameters. Wherein P represents the lattice constant，Lx，Ly are the side length of nanopatch along the x and y axis, respectively. The indices w and h denote the thickness and width of the sliver film, respectively. (b) Overall view of the quarter-wave plate. The linearly polarized with an orientation angle θ with respect to x axis is normally incident from 3
the substrate.
In terms of the whole array, one unit cell can be considered as a miniature polarizer. The general relation between the incident electric field Ei and the transmitted field Eo for normal incidence can be expressed by transmission matrix T (Jones matrix) as Txx Txy Exi E TE i Tyx Tyy E y ο
i
(1)
where Tmn represent the complex amplitudes of transmitted wave [6,18]. For a medium, it has no linear polarization conversion effect, i.e., Txy=Tyx=0. Thus, the transmitted field Eo can be expressed as: Exo Txx 0 Exi o i E y 0 Tyy E y
(2)
For equation (2), the phase of the transmitted field along the x and y directions can be defined as:
xx arg(Txx ) yy arg(Tyy )
(3)
The amplitude ratio (R) and phase difference (ΔΦ), respectively, defined as R= Tyy/Txx and ΔΦ=φyy –φxx. For a QWP, the complex amplitudes of transmitted wave should satisfy Txx=±iTyy, i.e., the amplitude ratio R=1 and the phase difference ΔΦ=90o. As we all know, the polarization state of light is determined by amplitude ratio and phase difference of light. Therefore, the work presented here focuses on researching the amplitude and phase of the transmitted field along the x and y directions.
3. Results and Analysis For the purpose of exploring the relationship between the transmitted field characteristics and the geometric parameters, different structural parameters are 4
studied. First, we analyze the properties of transmission spectrum when the period P is 300 nm, 350 nm, 400 nm. For simplicity，the side length of nanopatch is set to Lx=Ly=250 nm. The thickness of nanopatch is h=60 nm and polarization orientation angle of the incident linearly polarized plane wave is θ=45o. As shown in Fig. 2, each transmission spectrum has several resonant dips as result of plasmon resonance [10-11]. It is apparent that the resonance wavelength is insensitive as P increases in the wavelength range from 0.5 μm to 2.2 μm.
Fig. 2 Transmission plotted as a function of wavelength for structures with lattice constant P varying from 300 to 400 nm. Other parameters: Lx=Ly= 250 nm, h=60 nm, w=50 nm, θ=45°.
Then, we investigate the effect of the transmission spectrum when parameters Lx and Ly simultaneously changes from 150 nm to 250 nm while the period is fixed at P=300 nm, as seen in Fig. 3(a). With the increasing side lengths of the nanopatch, the resonant wavelength is significant red-shift due to the behavior of the plasmonic resonance supported by nanorods when their aspect ratio is varied. Fig. 3(b) presents the transmission and phase shift relative to that without Ag film when Lx=Ly= 250 nm. As clearly seen in Fig. 3(b), the resonance is accompanied by abrupt phase change in the vicinity of resonance dips. Therefore, the phase of the transmitted field can be controlled by plasmonic resonance via changing the side length of the nanopatch.
Fig. 3 The period P is fixed at 300 nm. (a) Transmitted fields with different side length of nanopatch parameters. (b) Transmission and phase shift relative to that without Ag film when Lx=Ly= 250 nm. Other parameters: h=60 nm, w=50 nm, θ=45°. 5
To better understand the physical mechanism of the plasmonic resonance induced extraordinary transmission, distribution of the electric fields of the nanopatch is investigated. Fig. 4 shows the electric field distribution at the resonant wavelength 0.82 μm and 1.81 μm, respectively. We can see the strong resonant field occurs at the corners of nanopatch. The electric fields are mainly distributed on the left side corners of the nanopatch at the resonant wavelength of 0.82 μm. However, the electric fields are mainly appeared on the right side corners of the nanopatch when the resonance wavelength is 1.81μm. Fig. 4 Electric field distribution at the resonant wavelength (a) 0.82 μm and (b) 1.81 μm when the Lx = Ly =250 nm, P=300 nm, h=60 nm, w=50 nm, θ=45°.
To further explore the relationship between the transmitted field characteristics and the geometric dimensions of nanopatch, we studied different values of Lx and Ly. Fig. 5 depicts the amplitude ratio (R) and phase difference (ΔΦ) of the transmitted fields when the linearly polarized plane wave illuminate with polarization orientation angle θ=45o. Fig. 5(a) and 5(b) refer to the structures with Ly=250 nm, w=50 nm, h=60 nm, P=300 nm, and with Lx varying from 150 to 250 nm. While Fig. 5(c) and 5(d) related to the structures by only varying Ly ranging from 150 to 250 nm. As can be seen in Fig. 5(a), when the length of Ly is fixed at 250 nm, the amplitude ratio changes slightly with the rise of Lx in the wavelength range from 0.6 μm to 1.7 μm. However, when the value of Lx is fixed, the amplitude ratio is extremely sensitive to the changed value of Ly, shown in Fig. 5(c). As demonstrated in Fig. 5(b), we can obviously observe the phase difference is very sensitive to the changed value of Lx. However, in Fig. 5(d) clarifies the change of phase difference is not obvious as Ly increases when the length of Lx remain unchanged at 250 nm. In conclusion, we can obtain the desired the amplitude ratio and phase difference by adjusting the value of Ly and Lx respectively at a specific frequency. 6
Fig. 5
Amplitude ratio and phase difference of the transmitted fields for the linearly polarized plane
wave with polarization orientation angle θ=45o. (a) Amplitude ratio and (b) phase difference of the transmitted fields for structures with Ly=250 nm, w=50 nm, h=60 nm, P=300 nm, and with Lx varying from 150 to 250 nm. (c)(d) Similar plots for the structures with Lx=250 nm, w=50 nm, h=60 nm, P=300 nm, and with Ly varying from 150 to 250 nm.
In order to construct a QWP，we seek a structure where the transmitted amplitude ratio is equal to 1 and the phase difference is equal to 90° at the designed wavelength. By optimizing, the unit cell is formed by U-shaped nanopatch with Lx=235 nm, Ly=247.8 nm, w=50 nm, h=60 nm, P=300 nm. Fig.6 shows the transmission amplitude and phase difference curve of the optimized QWP when illuminated by the linearly polarized plane wave with polarization orientation angle θ=45°. At the design wavelength (herein 1.55 μm), the transmission amplitude of the orthogonal components along the x and y axis is equal in Fig. 6(a). As can be seen from Fig. 6(b), the phase difference is exactly equal to 90° at 1.55 μm, which is coincident with the wavelength position of amplitude equalization in Txx and Tyy shown in Fig. 6(a). Therefore, an ideal QWP is obtained at 1.55 μm. However, the gray-shaded region in Fig. 6(b) demonstrates the phase difference in the range of 88°~92°, which is still available and acceptable for construction of QWP. Under this condition, the corresponding wavelength range (1.49 μm~1.61 μm) is 120 nm, which covers the major part of the optical communication bandwidth.
Fig. 6 The optimized design of a quarter-wave plate is realized at 1.55 μm for the linearly polarized plane wave with polarization orientation angle θ=45°, where Lx=235 nm, Ly=247.8 nm, w=50 nm, h=60 nm, P=300 nm. (a) Amplitudes of transmitted field along the x and y components as a function of wavelength. (b) The phase difference between transmitted field’s x and y component as a function of wavelength. A gray-shaded area depicts the region of 88° <ΔΦ<92°. 7
To evaluate the performance of the optimized QWP, ellipticity η is used to describe the polarization state of the transmitted light through the QWP, which is described by the ratio of the minor axis a to the major one b [η=tan(β)=a/b]. β represents the deflection angle of the ellipse with respect to the x axis, i.e., the angle between the major axis b of the ellipse and the x-axis. Fig. 7 shows the ellipticity η (black line) and deflection angle β of the ellipse (blue line) of elliptically polarized light transmitted field as function of wavelength for the linearly polarized plane wave with polarization orientation angle θ=45°. The ellipticity of the transmitted field reaches to 1 at the wavelength of 1.55 μm, i.e., linearly polarized light can be perfectly converted to circularly polarized light at 1.55 μm. When the variation of the phase difference in the range of 88°~92°, the ellipticity is larger than 0.83 and the corresponding bandwidth is 120 nm. Fig. 7 The ellipticity η (black line) and deflection angle β of the ellipse (blue line) of elliptically polarized light transmitted field as function of wavelength for the linearly polarized plane wave with polarization orientation angle θ=45°.
Fig. 8 Schematically illustrates the polarization ellipses of the transmitted field at (a) λ=1.49 μm, (b) λ=1.55 μm, (c) λ=1.62 μm. The axes represent the normalized amplitude of the transmitted field along the x and y axes.
Fig. 8 presents the polarization ellipses of the transmitted field at λ=1.49 μm, λ=1.55 μm, λ=1.62 μm, respectively, indicating the transmitted light is a perfect circularly polarized light at the wavelength of 1.55 μm. Additionally, in order to further verify the performance of the optimized QWP at the wavelength of 1.55 μm, respectively, from the silica substrate perpendicularly incident left-handed circularly polarized (LCP) light and right-handed circularly polarized (RCP) light. When illuminated by LCP, the transmitted light is linearly polarized light with the deflection 8
angle β =-45° relative to the x axis, as shown in Fig. 9(a). Similarly, we can obtain the linearly polarized light with the deflection angle β =45° relative to the x axis when the incident light is RCP, shown in Fig. 9(b). It agrees very well with the theoretical prediction.
Fig. 9 Schematically illustrates the polarization ellipses of the transmitted field at λ=1.55 μm. (a) The incident light with left circular polarization (LCP). (b) The incident light with right circular polarization (RCP). The axes represent the normalized amplitude of the transmitted field along the x and y axes.
Finally, Fig. 10 shows the total transmission (T), reflection (R), and absorption spectra (A) for linearly polarized input with polarization orientation angle θ=45°. The relationship among them is T+R+A=1. It can be seen that the transmittance is approximately 46.3% at the wavelength of 1.55 μm. Fig. 10 Transmittance (black line), reflection (red line), and absorption (blue line) spectra for the quarter-wave plate for under linearly polarized input with polarization orientation angle θ=45°.
4. Conclusion In summary, a plasmonic QWP based on U-shaped silver nanopatches array on silica substrate in the near-infrared frequency is designed and presented by us. It is found that the linearly polarized light can be perfectly converted to circularly polarized light and the circularly polarized light also can be perfectly converted to linearly polarized light at the wavelength of 1.55 μm, which agrees perfectly well with the theoretical prediction. Moreover, the optimized QWP with the thickness is only 60 nm and the transmittance is up to 46.3%. The bandwidth, in which the ellipticity is larger than 0.83, is 120 nm. The QWP fabrication process is also very simple which can be realized by evaporating a thin silver film and then using e-beam lithography 9
followed by reactive ion etching. Such a scheme could potentially be used in optical sensor systems, advanced nanophotonic devices and integrated optical circuits.
References 1. A. Pors, O. Albrektsen, I.P. Radko, S.I. Bozhevolnyi, Gap plasmon-based metasurfaces for total control of reflected light, Sci. Rep. 3(7)(2013) 2155. 2. A. Pors, M.G. Nielsen, G.D. Valle, M. Willatzen, O. Albrektsen, S.I. Bozhevolnyi, Plasmonic metamaterial wave retarders in reflection by orthogonally oriented detuned electrical dipoles, Opt. Lett. 36(9)(2011)1626-1628. 3. F. Wang, A. Chakrabarty, F. Minkowski, K. Sun, Q.H. Wei, Polarization conversion with elliptical patch nanoantennas, Appl. Phys. Lett. 101(2)(2012) 1-6. 4. P. Biagioni, M. Savoini, J.S. Huang, L. Duo, M. Finazzi, B. Hecht, Near-field polarization shaping by a near-resonant plasmonic cross antenna, Phys. Rev. B 80(15)(2009) 153409. 5. J. Yang, J.S. Zhang, Subwavelength Quarter-Waveplate Composed of L-Shaped Metal Nanoparticles, Plasmonics 6 (2)(2011) 251-254. 6. Y. Zhao, A. Alù, Manipulating light polarization with ultrathin plasmonic metasurfaces, Phys. Rev. B 84 (20)(2011)5109-5112. 7. E. H. Khoo, E. P. Li, K. B. Crozier, Plasmonic wave plate based on subwavelength nanoslits, Opt. Lett. 36(13)(2011) 2498-2500. 8. T.Z. Qiao, H.M. Gong, W.B. Ji, Cross-polarization conversion with periodic perforated silver film in the near-infrared spectral range, Optik 127(1)(2016) 371-375. 9. Z.H. Chen, C.H. Wang, F. Xu, Y.M. Lou, B. Cao, X.F. Li, Reflective plasmonic waveplates based on metal-insulator-metal subwavelength rectangular annular arrays, Photonic. Nanostruct. 12(2)(2014) 189-198. 10. A. Roberts, L. Lin, Plasmonic quarter-wave plate, Opt. Lett. 37(11)(2012) 1820-1822. 11. Z.H. Chen, C.H. Wang, Y.M. Lou, B. Cao, X.F. Li, Quarter-wave plate with subwavelength rectangular annular arrays, Opt. Commun. 297(12)(2013) 198-203. 10
12. W.J. Fan, S. Zhang, B. Minhas, K.J. Malloy, S.R.J. Brueck, Enhanced infrared transmission through subwavelength coaxial metallic arrays, Phys. Rev. Lett. 94(3)(2005) 033902. 13. F. Fang, Y.Z. Cheng, H.H. Liao, Giant optical activity and circular dichroism in the terahertz region based on bi-layer Y-shaped chiral metamaterial, Optik 125(20)(2014) 6067-6070. 14. M.X. He, J.G. Han, T. Zhen, J.Q. Gu, Q.R. Xing, Negative refractive index in chiral spiral metamaterials at terahertz frequencies, Optik 122(18)(2011) 1676-1679. 15. N.K. Grady, J.E. Heyes, D.R. Chowdhury, Y.Zeng, M.T. Reiten, A.K. Azad, A.J. Taylor, D.A.R. Dalvit, H.T. Chen, Terahertz metamaterials for linear polarization conversion and anomalous refraction, Science 340(6138)(2013)1304-1307. 16. M.B. Pu, P. Chen, Y.Q. Wang, Z.Y. Zhao, C. Huang, C.T. Wang, X.L. Ma, X.G. Luo, Anisotropic meta-mirror for achromatic electromagnetic polarization manipulation, Appl. Phys. Lett. 102(13)(2013) 131906. 17. P.B. Johnson, R.W. Christy, Optical constants of the noble metals, Phys. Rev. B 6(12)(1972) 4370-4379. 18. M. Kang, T. Feng, H. Wang, J. Li, Wave front engineering from an array of thin aperture antennas, Opt. Express 20(14)(2012) 15882-90.
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S0030-4026(17)30066-9 http://dx.doi.org/doi:10.1016/j.ijleo.2017.01.048 IJLEO 58751
To appear in: Received date: Accepted date:
26-5-2016 17-1-2017
Please cite this article as: Ming Chen, Linzi Chang, Tong Xiuqian, Xiaofei Xiao, Hui Chen, Plasmonic quarter-wave plate with U-shaped nanopatches, Optik - International Journal for Light and Electron Optics http://dx.doi.org/10.1016/j.ijleo.2017.01.048 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Plasmonic quarter-wave plate with U-shaped nanopatches Ming Chena,b,* , Linzi Changb , Tong Xiuqianb, Xiaofei Xiaob, Hui Chenb a
Guangxi key laboratory of precision navigation technology and application, Guilin University of Electronic Technology, Guilin 541004, Guangxi, China b
Guilin University of Electronic Technology, Guilin 541004, Guangxi, China * Corresponding Author: [email protected]
Abstract: a plasmonic quarter-wave plate which is based on U-shaped silver nanopatches array in the near-infrared range is designed and presented by us. It utilizes localized surface plasmon resonances with an abrupt phase shift to achieve the desired phase modulation in the transmitted field. The optimized quarter-wave plate can perfectly convert a linearly polarized light to circularly polarized light, whose ellipticity reaches to 1 at the wavelength of 1.55 μm. The bandwidth, in which the ellipticity is larger than 0.83, is 120 nm. This structure offers an enormous potential applications in optical sensor systems, advanced nanophotonic devices and integrated optical circuits. Keywords: Plasmonic; Quarter-wave plate; Polarization conversion; Nanopatches array.
1 Introduction Polarization, one of the important characteristics of light, is crucial in all kinds of optical researches and applications. Researchers have been seeking for an efficient way to completely control the polarization state of light. Conventional optical components usually utilize a piece of birefringent material to produce phase retardation, such as traditional anisotropic waveplates, polarizers, chiral media and prisms, relay on the propagation effect to control the polarization of light. As a result, the conventional optical components are usually bulky and suffer from difficulties in 1
manufacturing configurations, which go against the general trend of integration and miniaturization in photonics. Recently, controlling the polarization of light by ultrathin interface consisting of periodic plasma resonances array has increasingly received researchers’ attention . Various plasmonic metamaterial waveplates based on patterned metallic films [1-5], nanoslits [6-8] or nanoapertures [9-13] arrays have been proposed and demonstrated at microwave [13-16] and optical frequencies [1-3, 6-10]. Those waveplates can be divided into two types: transmission mode [6,8-11] and reflective mode [1-3,9]. Both of them are combined geometrical effects with localized plasmon resonances to produce the phenomenon of extraordinary optical transmission (EOT) of enhanced transmission fields. Therefore, as long as properly adjusting the geometry scale of the local mechanism unit can we obtain the desired polarization or phase properties at particular frequency. However, previous reported works still suffer from limited operation bandwidth or limited thickness of metal film. For example, Pors et al. using subwavelength nanocross array realized quarter-wave plate at wavelength of 1.52 μm and the bandwidth was 85nm [2]. Khoo et al. proposed a quarter-wave plate based on subwavelength nanoslits array, which was realized at wavelength of 802 nm, and the thickness was 200 nm [7]. Zhao et al. proposed a quarter-wave plate comprising of periodic orthogonal nanorods array at wavelength of 650 nm and the bandwidth was 46 nm [6]. Chen et al. used subwavelength rectangular annular arrays to realize quarter-wave plate at wavelength of 1.55 μm and the thickness of metal film was 200 nm [11]. Here, a plasmonic quarter-wave plate (QWP) based on U-shaped silver nanopatches array on silica substrate is proposed by us. It is well known that a QWP can fully convert linearly polarized light (circularly polarized light) into circularly polarized light (linearly polarized light) due to equal transmitted amplitude in two orthogonal directions and phase difference of π/2 between two orthogonal directions. This concept is realized by the changes of resonance of nanopatch via varying the geometry scale of the local mechanism unit. [5-6,9] Because the phase shift of the transmitted field is introduced by the resonant response of noble-metal nanopatch. For 2
a given illumination wavelength，a dipole plasmonic nanopatch shows to a first-order approximation a harmonic oscillator behavior, which means that its electric near field exhibits a phase shift with respect to the driving field, changing from 0° to 180° when the length is varied from below to above the resonance length [15]. Therefore, by properly choosing the side length of nanopatch can obtain the desired characteristics of the transmitted field. Finite-difference time-domain method (FDTD) is used to analyze the relationship between the transmitted field characteristics and the geometric dimensions of nanopatch. By optimizing the design, we obtain the functionalities of QWP with high performance at wavelength of 1.55 μm. Finally, we investigate the polarization conversion efficiency of the designed QWP. Compared to the traditional QWP, the proposed QWP is of high polarization conversion efficiency and high transmittance. In addition, it has prominent merits of ultrawide wavelength range and thin thickness, which makes it more conveniently integrated into advanced optical system.
1. Theory and structure design Fig. 1 shows the schematic of the designed plasmonic QWP. It consists of periodic U-shaped silver nanopatches array on silica substrate with a refractive index of 1.45. The side length of nanopatch along x-axis and y-axis are Lx and Ly, respectively. The lattice constant is denoted by P. The width and thickness of nanopatch are w=50 nm, and h=60 nm. In the simulation, silver is modeled with Drude material with a plasma frequency of p=2.175 PHz, a damping factor of =4.35 THz, and ∞=5. [17] The linearly polarized plane wave, which polarization orientation angle θ relative to the x axis, is normally incident from the substrate. Fig.1 (a) Schematic sketch of the designed plasmonic quarter-wave plate, which is composed of U-shaped Ag nanopatches array with the same geometrical parameters. Wherein P represents the lattice constant，Lx，Ly are the side length of nanopatch along the x and y axis, respectively. The indices w and h denote the thickness and width of the sliver film, respectively. (b) Overall view of the quarter-wave plate. The linearly polarized with an orientation angle θ with respect to x axis is normally incident from 3
the substrate.
In terms of the whole array, one unit cell can be considered as a miniature polarizer. The general relation between the incident electric field Ei and the transmitted field Eo for normal incidence can be expressed by transmission matrix T (Jones matrix) as Txx Txy Exi E TE i Tyx Tyy E y ο
i
(1)
where Tmn represent the complex amplitudes of transmitted wave [6,18]. For a medium, it has no linear polarization conversion effect, i.e., Txy=Tyx=0. Thus, the transmitted field Eo can be expressed as: Exo Txx 0 Exi o i E y 0 Tyy E y
(2)
For equation (2), the phase of the transmitted field along the x and y directions can be defined as:
xx arg(Txx ) yy arg(Tyy )
(3)
The amplitude ratio (R) and phase difference (ΔΦ), respectively, defined as R= Tyy/Txx and ΔΦ=φyy –φxx. For a QWP, the complex amplitudes of transmitted wave should satisfy Txx=±iTyy, i.e., the amplitude ratio R=1 and the phase difference ΔΦ=90o. As we all know, the polarization state of light is determined by amplitude ratio and phase difference of light. Therefore, the work presented here focuses on researching the amplitude and phase of the transmitted field along the x and y directions.
3. Results and Analysis For the purpose of exploring the relationship between the transmitted field characteristics and the geometric parameters, different structural parameters are 4
studied. First, we analyze the properties of transmission spectrum when the period P is 300 nm, 350 nm, 400 nm. For simplicity，the side length of nanopatch is set to Lx=Ly=250 nm. The thickness of nanopatch is h=60 nm and polarization orientation angle of the incident linearly polarized plane wave is θ=45o. As shown in Fig. 2, each transmission spectrum has several resonant dips as result of plasmon resonance [10-11]. It is apparent that the resonance wavelength is insensitive as P increases in the wavelength range from 0.5 μm to 2.2 μm.
Fig. 2 Transmission plotted as a function of wavelength for structures with lattice constant P varying from 300 to 400 nm. Other parameters: Lx=Ly= 250 nm, h=60 nm, w=50 nm, θ=45°.
Then, we investigate the effect of the transmission spectrum when parameters Lx and Ly simultaneously changes from 150 nm to 250 nm while the period is fixed at P=300 nm, as seen in Fig. 3(a). With the increasing side lengths of the nanopatch, the resonant wavelength is significant red-shift due to the behavior of the plasmonic resonance supported by nanorods when their aspect ratio is varied. Fig. 3(b) presents the transmission and phase shift relative to that without Ag film when Lx=Ly= 250 nm. As clearly seen in Fig. 3(b), the resonance is accompanied by abrupt phase change in the vicinity of resonance dips. Therefore, the phase of the transmitted field can be controlled by plasmonic resonance via changing the side length of the nanopatch.
Fig. 3 The period P is fixed at 300 nm. (a) Transmitted fields with different side length of nanopatch parameters. (b) Transmission and phase shift relative to that without Ag film when Lx=Ly= 250 nm. Other parameters: h=60 nm, w=50 nm, θ=45°. 5
To better understand the physical mechanism of the plasmonic resonance induced extraordinary transmission, distribution of the electric fields of the nanopatch is investigated. Fig. 4 shows the electric field distribution at the resonant wavelength 0.82 μm and 1.81 μm, respectively. We can see the strong resonant field occurs at the corners of nanopatch. The electric fields are mainly distributed on the left side corners of the nanopatch at the resonant wavelength of 0.82 μm. However, the electric fields are mainly appeared on the right side corners of the nanopatch when the resonance wavelength is 1.81μm. Fig. 4 Electric field distribution at the resonant wavelength (a) 0.82 μm and (b) 1.81 μm when the Lx = Ly =250 nm, P=300 nm, h=60 nm, w=50 nm, θ=45°.
To further explore the relationship between the transmitted field characteristics and the geometric dimensions of nanopatch, we studied different values of Lx and Ly. Fig. 5 depicts the amplitude ratio (R) and phase difference (ΔΦ) of the transmitted fields when the linearly polarized plane wave illuminate with polarization orientation angle θ=45o. Fig. 5(a) and 5(b) refer to the structures with Ly=250 nm, w=50 nm, h=60 nm, P=300 nm, and with Lx varying from 150 to 250 nm. While Fig. 5(c) and 5(d) related to the structures by only varying Ly ranging from 150 to 250 nm. As can be seen in Fig. 5(a), when the length of Ly is fixed at 250 nm, the amplitude ratio changes slightly with the rise of Lx in the wavelength range from 0.6 μm to 1.7 μm. However, when the value of Lx is fixed, the amplitude ratio is extremely sensitive to the changed value of Ly, shown in Fig. 5(c). As demonstrated in Fig. 5(b), we can obviously observe the phase difference is very sensitive to the changed value of Lx. However, in Fig. 5(d) clarifies the change of phase difference is not obvious as Ly increases when the length of Lx remain unchanged at 250 nm. In conclusion, we can obtain the desired the amplitude ratio and phase difference by adjusting the value of Ly and Lx respectively at a specific frequency. 6
Fig. 5
Amplitude ratio and phase difference of the transmitted fields for the linearly polarized plane
wave with polarization orientation angle θ=45o. (a) Amplitude ratio and (b) phase difference of the transmitted fields for structures with Ly=250 nm, w=50 nm, h=60 nm, P=300 nm, and with Lx varying from 150 to 250 nm. (c)(d) Similar plots for the structures with Lx=250 nm, w=50 nm, h=60 nm, P=300 nm, and with Ly varying from 150 to 250 nm.
In order to construct a QWP，we seek a structure where the transmitted amplitude ratio is equal to 1 and the phase difference is equal to 90° at the designed wavelength. By optimizing, the unit cell is formed by U-shaped nanopatch with Lx=235 nm, Ly=247.8 nm, w=50 nm, h=60 nm, P=300 nm. Fig.6 shows the transmission amplitude and phase difference curve of the optimized QWP when illuminated by the linearly polarized plane wave with polarization orientation angle θ=45°. At the design wavelength (herein 1.55 μm), the transmission amplitude of the orthogonal components along the x and y axis is equal in Fig. 6(a). As can be seen from Fig. 6(b), the phase difference is exactly equal to 90° at 1.55 μm, which is coincident with the wavelength position of amplitude equalization in Txx and Tyy shown in Fig. 6(a). Therefore, an ideal QWP is obtained at 1.55 μm. However, the gray-shaded region in Fig. 6(b) demonstrates the phase difference in the range of 88°~92°, which is still available and acceptable for construction of QWP. Under this condition, the corresponding wavelength range (1.49 μm~1.61 μm) is 120 nm, which covers the major part of the optical communication bandwidth.
Fig. 6 The optimized design of a quarter-wave plate is realized at 1.55 μm for the linearly polarized plane wave with polarization orientation angle θ=45°, where Lx=235 nm, Ly=247.8 nm, w=50 nm, h=60 nm, P=300 nm. (a) Amplitudes of transmitted field along the x and y components as a function of wavelength. (b) The phase difference between transmitted field’s x and y component as a function of wavelength. A gray-shaded area depicts the region of 88° <ΔΦ<92°. 7
To evaluate the performance of the optimized QWP, ellipticity η is used to describe the polarization state of the transmitted light through the QWP, which is described by the ratio of the minor axis a to the major one b [η=tan(β)=a/b]. β represents the deflection angle of the ellipse with respect to the x axis, i.e., the angle between the major axis b of the ellipse and the x-axis. Fig. 7 shows the ellipticity η (black line) and deflection angle β of the ellipse (blue line) of elliptically polarized light transmitted field as function of wavelength for the linearly polarized plane wave with polarization orientation angle θ=45°. The ellipticity of the transmitted field reaches to 1 at the wavelength of 1.55 μm, i.e., linearly polarized light can be perfectly converted to circularly polarized light at 1.55 μm. When the variation of the phase difference in the range of 88°~92°, the ellipticity is larger than 0.83 and the corresponding bandwidth is 120 nm. Fig. 7 The ellipticity η (black line) and deflection angle β of the ellipse (blue line) of elliptically polarized light transmitted field as function of wavelength for the linearly polarized plane wave with polarization orientation angle θ=45°.
Fig. 8 Schematically illustrates the polarization ellipses of the transmitted field at (a) λ=1.49 μm, (b) λ=1.55 μm, (c) λ=1.62 μm. The axes represent the normalized amplitude of the transmitted field along the x and y axes.
Fig. 8 presents the polarization ellipses of the transmitted field at λ=1.49 μm, λ=1.55 μm, λ=1.62 μm, respectively, indicating the transmitted light is a perfect circularly polarized light at the wavelength of 1.55 μm. Additionally, in order to further verify the performance of the optimized QWP at the wavelength of 1.55 μm, respectively, from the silica substrate perpendicularly incident left-handed circularly polarized (LCP) light and right-handed circularly polarized (RCP) light. When illuminated by LCP, the transmitted light is linearly polarized light with the deflection 8
angle β =-45° relative to the x axis, as shown in Fig. 9(a). Similarly, we can obtain the linearly polarized light with the deflection angle β =45° relative to the x axis when the incident light is RCP, shown in Fig. 9(b). It agrees very well with the theoretical prediction.
Fig. 9 Schematically illustrates the polarization ellipses of the transmitted field at λ=1.55 μm. (a) The incident light with left circular polarization (LCP). (b) The incident light with right circular polarization (RCP). The axes represent the normalized amplitude of the transmitted field along the x and y axes.
Finally, Fig. 10 shows the total transmission (T), reflection (R), and absorption spectra (A) for linearly polarized input with polarization orientation angle θ=45°. The relationship among them is T+R+A=1. It can be seen that the transmittance is approximately 46.3% at the wavelength of 1.55 μm. Fig. 10 Transmittance (black line), reflection (red line), and absorption (blue line) spectra for the quarter-wave plate for under linearly polarized input with polarization orientation angle θ=45°.
4. Conclusion In summary, a plasmonic QWP based on U-shaped silver nanopatches array on silica substrate in the near-infrared frequency is designed and presented by us. It is found that the linearly polarized light can be perfectly converted to circularly polarized light and the circularly polarized light also can be perfectly converted to linearly polarized light at the wavelength of 1.55 μm, which agrees perfectly well with the theoretical prediction. Moreover, the optimized QWP with the thickness is only 60 nm and the transmittance is up to 46.3%. The bandwidth, in which the ellipticity is larger than 0.83, is 120 nm. The QWP fabrication process is also very simple which can be realized by evaporating a thin silver film and then using e-beam lithography 9
followed by reactive ion etching. Such a scheme could potentially be used in optical sensor systems, advanced nanophotonic devices and integrated optical circuits.
References 1. A. Pors, O. Albrektsen, I.P. Radko, S.I. Bozhevolnyi, Gap plasmon-based metasurfaces for total control of reflected light, Sci. Rep. 3(7)(2013) 2155. 2. A. Pors, M.G. Nielsen, G.D. Valle, M. Willatzen, O. Albrektsen, S.I. Bozhevolnyi, Plasmonic metamaterial wave retarders in reflection by orthogonally oriented detuned electrical dipoles, Opt. Lett. 36(9)(2011)1626-1628. 3. F. Wang, A. Chakrabarty, F. Minkowski, K. Sun, Q.H. Wei, Polarization conversion with elliptical patch nanoantennas, Appl. Phys. Lett. 101(2)(2012) 1-6. 4. P. Biagioni, M. Savoini, J.S. Huang, L. Duo, M. Finazzi, B. Hecht, Near-field polarization shaping by a near-resonant plasmonic cross antenna, Phys. Rev. B 80(15)(2009) 153409. 5. J. Yang, J.S. Zhang, Subwavelength Quarter-Waveplate Composed of L-Shaped Metal Nanoparticles, Plasmonics 6 (2)(2011) 251-254. 6. Y. Zhao, A. Alù, Manipulating light polarization with ultrathin plasmonic metasurfaces, Phys. Rev. B 84 (20)(2011)5109-5112. 7. E. H. Khoo, E. P. Li, K. B. Crozier, Plasmonic wave plate based on subwavelength nanoslits, Opt. Lett. 36(13)(2011) 2498-2500. 8. T.Z. Qiao, H.M. Gong, W.B. Ji, Cross-polarization conversion with periodic perforated silver film in the near-infrared spectral range, Optik 127(1)(2016) 371-375. 9. Z.H. Chen, C.H. Wang, F. Xu, Y.M. Lou, B. Cao, X.F. Li, Reflective plasmonic waveplates based on metal-insulator-metal subwavelength rectangular annular arrays, Photonic. Nanostruct. 12(2)(2014) 189-198. 10. A. Roberts, L. Lin, Plasmonic quarter-wave plate, Opt. Lett. 37(11)(2012) 1820-1822. 11. Z.H. Chen, C.H. Wang, Y.M. Lou, B. Cao, X.F. Li, Quarter-wave plate with subwavelength rectangular annular arrays, Opt. Commun. 297(12)(2013) 198-203. 10
12. W.J. Fan, S. Zhang, B. Minhas, K.J. Malloy, S.R.J. Brueck, Enhanced infrared transmission through subwavelength coaxial metallic arrays, Phys. Rev. Lett. 94(3)(2005) 033902. 13. F. Fang, Y.Z. Cheng, H.H. Liao, Giant optical activity and circular dichroism in the terahertz region based on bi-layer Y-shaped chiral metamaterial, Optik 125(20)(2014) 6067-6070. 14. M.X. He, J.G. Han, T. Zhen, J.Q. Gu, Q.R. Xing, Negative refractive index in chiral spiral metamaterials at terahertz frequencies, Optik 122(18)(2011) 1676-1679. 15. N.K. Grady, J.E. Heyes, D.R. Chowdhury, Y.Zeng, M.T. Reiten, A.K. Azad, A.J. Taylor, D.A.R. Dalvit, H.T. Chen, Terahertz metamaterials for linear polarization conversion and anomalous refraction, Science 340(6138)(2013)1304-1307. 16. M.B. Pu, P. Chen, Y.Q. Wang, Z.Y. Zhao, C. Huang, C.T. Wang, X.L. Ma, X.G. Luo, Anisotropic meta-mirror for achromatic electromagnetic polarization manipulation, Appl. Phys. Lett. 102(13)(2013) 131906. 17. P.B. Johnson, R.W. Christy, Optical constants of the noble metals, Phys. Rev. B 6(12)(1972) 4370-4379. 18. M. Kang, T. Feng, H. Wang, J. Li, Wave front engineering from an array of thin aperture antennas, Opt. Express 20(14)(2012) 15882-90.
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