978
OPTICS LETTERS / Vol. 40, No. 6 / March 15, 2015
Coupling between surface plasmon polaritons and transverse electric polarized light via L-shaped nano-apertures Jing Yang,1 Chuang Hu,1 Qiuling Wen,1 Chenglong Zhao,1,3 and Jiasen Zhang1,2,* 1
State Key Laboratory for Mesoscopic Physics and Department of Physics, Peking University, Beijing 100871, China 2
Collaborative Innovation Center of Quantum Matter, Beijing 100871, China 3
Currently a guest researcher in the Physical Measurement Laboratory, National Institute of Standards and Technology (NIST), Gaithersburg, Maryland 20899, USA *Corresponding author: [email protected] Received December 11, 2014; revised January 29, 2015; accepted January 29, 2015; posted February 4, 2015 (Doc. ID 229457); published March 10, 2015 Given that plasmonic fields are intrinsically transverse magnetic (TM), coupling surface plasmon polaritons (SPPs) and transverse electric (TE) polarized light, especially at nanoscale, remain challenging. We propose the use of L-shaped nano-apertures to overcome this fundamental limitation and enable coupling between SPPs and TE polarized light. Polarization conversion originates from the interference of two resonant modes excited in the nano-apertures and the nearly 180° phase retardation between them. The experiments show that both TE-toplasmon and plasmon-to-TE couplings can be implemented at the subwavelength scale. This discovery provides great freedom when manipulating light based on SPPs at the nanoscale and helps in using the energy of TE polarized light. © 2015 Optical Society of America OCIS codes: (240.6680) Surface plasmons; (310.6628) Subwavelength structures, nanostructures; (250.5403) Plasmonics; (260.5430) Polarization. http://dx.doi.org/10.1364/OL.40.000978
Surface plasmon polaritons (SPPs) are charge-density oscillations on metal surfaces that couple with incident light and generate strongly enhanced local optical fields [1,2]. Given the strongly enhanced and localized fields of SPPs, research on the topic has increased in the past decades and has important applications in many fields, such as biosensing [3], photovoltaics [4], spectroscopy [5], nonlinear optics [6], data storage [7], and passive and active devices [8–10]. SPP coupling is an important issue for most applications. Recently, different plasmonic structures have been proposed for SPP coupling and many novel and useful coupling properties, including unidirectional SPP coupling [11–17], polarization-controlled SPP coupling [18], and even spin-controlled SPP coupling [19–22], have been obtained. However, despite various coupling methods, SPP launching is strongly limited to transverse magnetic (TM) incidence because of the intrinsic TM polarization state of SPP fields. This polarization matching requirement results in significant setbacks when controlling light based on SPPs. Feng et al. [23] proposed a designer plasmonic metamaterial composed of gold stripes arranged in a deep subwavelength scale to realize pure transverse electric (TE) polarized incidence to SPP coupling. However, finding new ways to overcome the inherent limitation of the TM-polarization nature of the SPPs, especially at the nanoscale, remains challenging. In this work, we demonstrate coupling between pure TE polarized light and SPPs at the nanoscale using Lshaped nano-apertures. The polarization conversion originates from the interference of two orthogonal resonant modes in the L-shaped nano-apertures. SPPs can be launched in the direction orthogonal to the polarization direction of the incident field. Moreover, SPP radiation via L-shaped nano-apertures has been studied, and TE polarized radiation can be obtained. The coupling 0146-9592/15/060978-04$15.00/0
between pure TE-polarized light and TM-polarized SPPs provides great freedom when manipulating light field based on SPPs at the nanoscale and helps when using the energy of TE-polarized light. The L-shaped nano-aperture is schematically shown in Fig. 1(a). Two perpendicular rectangle holes are fabricated in a gold film on a silica substrate. The thickness of the gold film is labeled as h, which also represents the depth of the holes. The L-shaped aperture has the same arm lengths in the x and y directions and is labeled L. The arm width is labeled w. The origin is set at the outermost corner of the L-shaped aperture and lies at the air/gold interface. The direction of the symmetric axis of the structure (45° with respect to the x axis) and its orthogonal direction are labeled as m and k axes, respectively. For linearly polarized incidence, the polarization angle with respect to the x axis is labeled θ. The resonant properties of the L-shaped nanoapertures were investigated using the finite difference time-domain (FDTD) method (Lumerical FDTD solutions). The meshing cell size is 2 nm, and the perfectly
Fig. 1. (a) Schematic of an L-shaped nanoaperture. (b) Nearfield electric field amplitude jEy j at center point A (x 155 nm, y 35 nm, and z 0) of the x-arm in the L-shaped nanoaperture (L 310 nm, w 70 nm, and h 280 nm) versus the wavelength for different incident polarization angles θ. Inset: schematic of the position of point A. The red arrows indicate the peak wavelengths. © 2015 Optical Society of America
March 15, 2015 / Vol. 40, No. 6 / OPTICS LETTERS
matched layer adsorbing boundaries are used. The permittivity of gold was extracted from the data in [24]. The geometric parameters of the nano-apertures are L 310 nm, w 70 nm, and h 280 nm. The aperture is normally illuminated by a plane wave linearly polarized in the x or y directions from the bottom of the substrate along the z axis. The amplitude of the incident electric field is 1 V/m. The near-field electric field amplitude jEy j at point A (x 155 nm, y 35 nm, and z 0) [inset of Fig. 1(b)], which is the geometric center of the x arm of the L-shaped nanoaperture, is recorded for θ 45° and 135°. The results are shown in Fig. 1(b). For m-polarized (θ 45°) incident light, there are two resonant peaks at 1610 and 960 nm. The resonant mode at 1610 nm is the first-order plasmon resonance mode, and both the top and bottom surfaces of the aperture show a dipolar resonance. For the resonant mode at 960 nm, the aperture shows a single-surface first-order plasmon resonance (SFPR) mode, and only the top surface has a dipolar resonance, whereas the bottom surface has no plasmon resonance [22]. The SFPR mode is the plasmon resonance mode of the hole on the air/gold interface, and its resonance is related to the thickness of the metallic film [25]. In this work, the thickness of the gold film is 280 nm, which is thick enough to ensure that the SFPR mode is excited. For k-polarized (θ 135°) incident light, only one resonant peak is present at 720 nm, and the aperture exhibits a second-order plasmon resonance (SPR) mode on both surfaces. The electric fields on both two surfaces of the gold film are in the resonance for the SPR mode, which differs from those for the SFPR mode. For m- and k-polarized incident light, the near-field electric field Ey at point A (x 155 nm, y 35 nm, and z 0) are labeled Eym and Eyk , and their phases are labeled as φym and φyk , respectively. Because of the different resonant characteristics of the SPR mode and the SFPR mode, there is a phase retardation Δφmk φym − φyk between these two modes, which is used to implement polarization conversion in this work. The nearfield electric field amplitude ratio jEym j∕jEyk j and the phase retardation Δφmk are calculated with respect to the incident wavelength. The results are shown in Fig. 2. At 864 nm, jEym j∕jEyk j equals 0.99, and the phase retardation Δφmk reaches 176°. The electric field of the SFPR mode on the top surface of the gold film is symmetric with respect to the m axis, whereas that of the SPR mode is asymmetric. When the incident beam is linearly polarized along the x axis, the SFPR and SPR modes can be simultaneously excited and interfere with each other. The different symmetries of the two modes should
Fig. 2. Near-field electric field amplitude ratio jEym j∕jEyk j and phase retardation (Δφmk φym − φyk ) versus the wavelength for the L-shaped nanoaperture with L 310 nm, w 70 nm, and h 280 nm.
979
Fig. 3. Near-field electric field amplitude jEj distributions at the air/gold interface (z 0 plane) for incident polarization angles (a) θ 0° and (b) θ 90°. The incident wavelength is 864 nm. The incident polarization directions are shown at the right-top corners in (a) and (b).
induce a 180° phase retardation Δφmk sym in the x arm between the two modes. The total phase retardation between these two modes excited by the x-polarized incident beam is Δφmk total Δφmk Δφmk sym . For the above mentioned size and λ 864 nm, Δφmk total ≈ 0° and 180° in the x and y arms, respectively, which results in a constructive interference in the x arm and destructive interference in the y arm. The near-field electric field amplitude jEj distribution on the top surface of the gold film is shown in Fig. 3(a). The near-field electric field intensity at the middle point of the x arm is 107 times larger than that at the middle point of the y arm. The electric field in the x arm has y-polarization, which launches SPPs that propagate along the y directions. The result for a y-polarized incidence is shown in Fig. 3(b). The constructive interference of the SPR and SFPR modes induces a strong electric field in the y arm and excites the SPPs along the x directions. The pure TE-to-SPP coupling originates from the design of the interference of two orthogonal resonant modes in the L-shaped nano-apertures. The SPP excitation efficiency for an L-shaped nanoaperture at the air/gold interface was calculated using the method in [26], and the launched SPP energy on the top surface of the gold film is normalized to the incident energy illuminated on the L-shaped nano-aperture area (310 nm × 310 nm). The excitation efficiency reaches 15.8% at 864 nm. To demonstrate TE-to-SPP coupling experimentally, L-shaped nano-apertures were fabricated in a 280-nmthick gold film deposited on a 1.5-mm-thick silica substrate using focused ion beam milling. The scanning electron microscope (SEM) image of the sample is shown in Fig. 4(a). For the sake of an increased SPP intensity, the fabricated sample consists of 16 L-shaped nano-apertures, which are 4 × 4 squarely arranged. The distances between adjacent apertures in the x and y directions are both 815 20 nm. A magnified SEM image of the aperture array is shown in Fig. 4(b). The arm length and width of the fabricated nano-apertures are L 315 15 nm and w 70 10 nm. The launched SPPs are scattered by two gratings fabricated in the −x and −y directions. The periods and lengths of the two gratings are 820 nm and 30 μm, respectively. The distances between the gratings and the center of the aperture array are 22 μm. The SPPs launched in the x∕ y direction have nearly the same intensities as those launched in the −x∕ − y direction. In this work, only SPPs that propagate along the −x and −y directions were investigated, and their intensity ratio was measured.
980
OPTICS LETTERS / Vol. 40, No. 6 / March 15, 2015
Fig. 4. (a) SEM image of the fabricated sample. (b) Magnified SEM image of the L-shaped nanoaperture array. (c) Schematic of the experimental setup. (d) and (e) CCD images of the scattering gratings for the incident light with polarization angle θ 0° and 90°, respectively, at 930 nm. The incident polarization directions are shown at the right-top corners in (d) and (e). (f) and (g) Measured intensity ratios of SPPs that propagate in the x and y directions versus wavelength (θ 90°, y-polarized incident light) and incident angles θ (incident wavelength λ 930 nm), respectively.
A schematic of the experimental setup is shown in Fig. 4(c). The light source used in the experiment is a continuous wave Ti:sapphire laser, and the incident wavelength can be tuned from 780 to 930 nm. The polarization of the incident beam was controlled by a polarizer (P) and a half-wave plate (H). The sample (S) was normally illuminated from the substrate side with a linearly polarized laser beam, which was focused by a lens L1 and an objective O1 . SPPs on the air/gold interface were launched in the x and y directions and scattered by the two gratings. The scattering light was collected by another objective O2 and two lenses L2 and L3 and imaged onto a charge-coupled device (CCD) to measure the intensity ratio. A beam block (BB) was used to block the light transmitting through the nano-apertures directly. The CCD images of the two scattering gratings are shown in Figs. 4(d) and 4(e) for incident light polarized along the x and y axes, respectively, at λ 930 nm. For the x-polarized (θ 0°) incident light in Fig. 4(d), scattering light at the −y direction is much stronger than that at the −x direction. The intensity ratio is defined in dB as 10 logI x ∕I y , where I x and I y represent the intensities of the SPPs that propagate in the −x and −y directions, respectively. In Fig. 4(d) the intensity ratio is −5.8 dB. When the incident beam is y-polarized
(θ 90°), the scattering light at the −x direction is much stronger than that at the −y direction, and the intensity ratio reaches 7.1 dB. The SPPs were launched in a direction orthogonal to the polarization direction of the incident electric field. Therefore, pure TE-to-SPP coupling via L-shaped nano-apertures has been demonstrated experimentally. The change of the performance of the L-shaped nanoapertures in TE-to-SPP coupling with respect to the incident wavelength was investigated with a y-polarized (θ 90°) incident beam. The intensity ratio 10 logI x ∕I y was recorded, and the result is shown in Fig. 4(f). As the measured wavelength changes from 830 to 930 nm, the intensity ratio increases from 1.1 to 7.1 dB. As a result, the best working wavelength of the L-shaped nanoapertures in the experiment is 930 nm. Unfortunately, the light source used in this work has a maximum wavelength at 930 nm. Despite the limitation of the light source, an intensity ratio of 7.1 dB at 930 nm is sufficient to demonstrate the TE-to-SPP coupling of L-shaped nanoapertures experimentally. For the L-shaped nano-apertures with L 310 nm, w 70 nm, and h 280 nm, the best working wavelength appears at 864 nm, according to the FDTD calculation results. However, the best working wavelength is very sensitive to the geometric parameters of the nano-apertures. For example, the calculation results show that the best working wavelength redshifts to 920 nm for the nano-apertures with L 300 nm, w 60 nm, and h 280 nm. The discrepancy in the best working wavelengths obtained from the experiment and calculation originates from the imperfect fabrication of the sample. The change of the intensity ratio with respect to the incident polarization angles was studied, and the result is shown in Fig. 4(g). The incident wavelength is 930 nm. The minimum intensity ratio is −5.8 dB at θ 0°, whereas the maximum intensity ratio is 7.4 dB at θ 100°. However, the calculation result in Fig. 2 indicates that the maximum intensity ratio appears at θ 90°. The difference between the calculation and experimental results is likely due to the fabrication tolerances in the experiment. In addition to TE-to-SPP coupling, the reverse process, i.e., SPP-to-TE radiation, can be implemented via the L-shaped nano-apertures. For SPPs propagating at the air/gold surface, the L-shaped nano-aperture cuts off surface electron currents, and the two resonant mode, i.e., the SFPR mode and the SPR mode, are excited in the aperture, which interfere with each other. Light with different polarizations radiate along the −z direction. We investigate the radiation of SPPs that propagate in the x direction for a single nano-aperture (L 310 nm, w 70 nm, and h 280 nm). The radiation along the −z direction in the far-field is investigated, and the electric field at point F (x 0, y 0, and z −1 m) is recorded. The intensity ratio of the electric fields Ey and Ex at point F, which is defined as 10log (jEy j2 ∕jEx j2 ) in dB, is calculated as the incident wavelength changes. The result is shown in Fig. 5(a). At 875 nm, the intensity ratio has a maximum of 19.1 dB, which means the radiation field is mainly y-polarized, i.e., perpendicular to the propagation direction of the incident SPPs. Therefore,
March 15, 2015 / Vol. 40, No. 6 / OPTICS LETTERS
981
61377050) and the Research Fund for the Doctoral Program of Higher Education (grant no. 20130001110050).
Fig. 5. (a) Numerical result and (b) experimental result of the intensity ratio of the radiation light polarized in the y and x directions versus wavelength. Insets in (b) are CCD images of the radiation light polarized in the y (left inset) and x (right inset) directions at 930 nm.
SPP-to-TE radiation can be achieved via L-shaped nanoapertures. To experimentally demonstrate SPP-to-TE coupling, the samples in Figs. 4(a) and 4(b) were used. The grating at the −x direction was normally illuminated from the air side by a linearly x-polarized laser beam, and the launched SPPs propagating in the x direction can be radiated by the L-shaped apertures. The far-field radiation was collected at the substrate side and imaged on the CCD. The polarization state of the radiated electric field from the nano-apertures was analyzed by a broadband linear polarizer. The intensity ratio of the far-field electric field polarized along the y and x directions was measured at different incident wavelengths, and the result is shown in Fig. 5(b). At 930 nm, the far-field intensity ratio has a maximum of 6.4 dB, which shows that the farfield radiation is approximately linearly y-polarized. The CCD images of the radiation light polarized in the y and x directions at 930 nm are shown in the insets of Fig. 5(b), respectively. The intensity of the radiation light polarized in the y direction is much stronger than that polarized in the x direction. Thus, SPP-to-TE coupling is demonstrated experimentally. In conclusion, coupling between SPPs and pure TEpolarized light via L-shaped nano-apertures has been proposed and demonstrated experimentally at a nanoscale. The polarization conversion originates from the interference of the SFPR mode and the SPR mode excited in the L-shaped nano-apertures. Approximately 180° phase retardation between the two modes was obtained according to their different resonant properties. This method provides a new route for launching SPPs with TEpolarized incidence and SPP radiation to TE polarization. As a result, both TE- and TM-polarized light, which are two basic polarization states of photons, can couple with SPPs through optical nano-apertures. In recent years, researchers have been attempting to reduce the size of photonic devices to the nanoscale. The L-shaped nanoapertures, which have ultra-small footprints and can work in a single element, have significant advantages when applied in plasmonic and nanophotonic devices and circuits. This work was supported by the National Natural Science Foundation of China (grant nos. 11404012 and
References 1. S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2007). 2. W. L. Barnes, A. Dereux, and T. W. Ebbesen, Nature 424, 824 (2003). 3. O. Vazquez-Mena, T. Sannomiya, L. G. Villanueva, J. Voros, and J. Brugger, ACS Nano 5, 844 (2011). 4. L. Cao, J. S. White, J. S. Park, J. A. Schuller, B. M. Clemens, and M. L. Brongersma, Nat. Mater. 8, 643 (2009). 5. J. Kneipp, H. Kneipp, M. Mclaughlin, D. Brown, and K. Kneipp, Nano Lett. 6, 2225 (2006). 6. S. Kim, J. Jin, Y.-J. Kim, I.-Y. Park, Y. Kim, and S.-W. Kim, Nature 453, 757 (2008). 7. W. Srituravanich, L. Pan, Y. Wang, C. Sun, D. B. Bogy, and X. Zhang, Nat. Nanotechnol. 3, 733 (2008). 8. C. Zhao and J. Zhang, ACS Nano 4, 6433 (2010). 9. K. C. Y. Huang, M. K. Seo, T. Sarmiento, Y. Huo, J. S. Harris, and M. L. Brongersma, Nat. Photonics 8, 244 (2014). 10. R. F. Oulton, V. J. Sorger, T. Zentgraf, R. M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, Nature 461, 629 (2009). 11. F. Lopez-Tejeira, S. G. Rodrigo, L. Martin-Moreno, F. J. Garcia-Vidal, E. Devaux, T. W. Ebbesen, J. R. Krenn, I. P. Radko, S. I. Bozhevolnyi, M. U. Gonzalez, J. C. Weeber, and A. Dereux, Nat. Phys. 3, 324 (2007). 12. Y. Sonnefraud, S. Kerman, G. D. Martino, D. Y. Lei, and S. A. Maier, Opt. Express 20, 4893 (2012). 13. A. Baron, E. Devaux, J. C. Rodier, J. P. Hugonin, E. Rousseau, C. Genet, T. W. Ebbesen, and P. Lalanne, Nano Lett. 11, 4207 (2011). 14. Y. Liu, S. Palomba, Y. Park, T. Zentgraf, X. Yin, and X. Zhang, Nano Lett. 12, 4853 (2012). 15. L. Wang, T. Li, L. Li, W. Xia, X. G. Xu, and S. N. Zhu, Opt. Express 20, 8710 (2012). 16. J. Yang, X. Xiao, C. Hu, W. Zhang, S. Zhou, and J. Zhang, Nano Lett. 14, 704 (2014). 17. J. Chen, Z. Li, S. Yue, and Q. Gong, Appl. Phys. Lett. 97, 041113 (2010). 18. J. Lin, J. P. B. Mueller, Q. Wang, G. H. Yuan, N. Antoniou, X. C. Yuan, and F. Capasso, Science 340, 331 (2013). 19. B. B. Tsema, Y. B. Tsema, M. R. Shcherbakov, Y. Lin, D. Liu, V. V. Klimov, A. A. Fedyanin, and D. P. Tsai, Opt. Express 20, 10538 (2012). 20. S.-Y. Lee, I.-M. Lee, J. Park, S. Oh, W. Lee, K.-Y. Kim, and B. Lee, Phys. Rev. Lett. 108, 213907 (2012). 21. L. Huang, X. Chen, B. Bai, Q. Tan, G. Jin, T. Zentgraf, and S. Zhang, Light: Sci. Appl. 2, e70 (2013). 22. J. Yang, S. Zhou, C. Hu, W. Zhang, X. Xiao, and J. Zhang, Laser Photon. Rev. 8, 590 (2014). 23. L. Feng, A. Mizrahi, S. Zamek, Z. Liu, V. Lomakin, and Y. Fainmain, ACS Nano 5, 5100 (2011). 24. E. D. Palik, Handbook of Optical Constants of Solids II (Academic, 1985). 25. J. Yang and J. Zhang, Opt. Express 21, 7934 (2013). 26. A. L. Baudrion, F. D. L. Perez, O. Mahboub, A. Hohenau, H. Ditlbacher, F. J. Garcia-Vidal, J. Dintinger, T. W. Ebbesen, L. Martin-Morner, and J. R. Krenn, Opt. Express 16, 3420 (2008).
OPTICS LETTERS / Vol. 40, No. 6 / March 15, 2015
Coupling between surface plasmon polaritons and transverse electric polarized light via L-shaped nano-apertures Jing Yang,1 Chuang Hu,1 Qiuling Wen,1 Chenglong Zhao,1,3 and Jiasen Zhang1,2,* 1
State Key Laboratory for Mesoscopic Physics and Department of Physics, Peking University, Beijing 100871, China 2
Collaborative Innovation Center of Quantum Matter, Beijing 100871, China 3
Currently a guest researcher in the Physical Measurement Laboratory, National Institute of Standards and Technology (NIST), Gaithersburg, Maryland 20899, USA *Corresponding author: [email protected] Received December 11, 2014; revised January 29, 2015; accepted January 29, 2015; posted February 4, 2015 (Doc. ID 229457); published March 10, 2015 Given that plasmonic fields are intrinsically transverse magnetic (TM), coupling surface plasmon polaritons (SPPs) and transverse electric (TE) polarized light, especially at nanoscale, remain challenging. We propose the use of L-shaped nano-apertures to overcome this fundamental limitation and enable coupling between SPPs and TE polarized light. Polarization conversion originates from the interference of two resonant modes excited in the nano-apertures and the nearly 180° phase retardation between them. The experiments show that both TE-toplasmon and plasmon-to-TE couplings can be implemented at the subwavelength scale. This discovery provides great freedom when manipulating light based on SPPs at the nanoscale and helps in using the energy of TE polarized light. © 2015 Optical Society of America OCIS codes: (240.6680) Surface plasmons; (310.6628) Subwavelength structures, nanostructures; (250.5403) Plasmonics; (260.5430) Polarization. http://dx.doi.org/10.1364/OL.40.000978
Surface plasmon polaritons (SPPs) are charge-density oscillations on metal surfaces that couple with incident light and generate strongly enhanced local optical fields [1,2]. Given the strongly enhanced and localized fields of SPPs, research on the topic has increased in the past decades and has important applications in many fields, such as biosensing [3], photovoltaics [4], spectroscopy [5], nonlinear optics [6], data storage [7], and passive and active devices [8–10]. SPP coupling is an important issue for most applications. Recently, different plasmonic structures have been proposed for SPP coupling and many novel and useful coupling properties, including unidirectional SPP coupling [11–17], polarization-controlled SPP coupling [18], and even spin-controlled SPP coupling [19–22], have been obtained. However, despite various coupling methods, SPP launching is strongly limited to transverse magnetic (TM) incidence because of the intrinsic TM polarization state of SPP fields. This polarization matching requirement results in significant setbacks when controlling light based on SPPs. Feng et al. [23] proposed a designer plasmonic metamaterial composed of gold stripes arranged in a deep subwavelength scale to realize pure transverse electric (TE) polarized incidence to SPP coupling. However, finding new ways to overcome the inherent limitation of the TM-polarization nature of the SPPs, especially at the nanoscale, remains challenging. In this work, we demonstrate coupling between pure TE polarized light and SPPs at the nanoscale using Lshaped nano-apertures. The polarization conversion originates from the interference of two orthogonal resonant modes in the L-shaped nano-apertures. SPPs can be launched in the direction orthogonal to the polarization direction of the incident field. Moreover, SPP radiation via L-shaped nano-apertures has been studied, and TE polarized radiation can be obtained. The coupling 0146-9592/15/060978-04$15.00/0
between pure TE-polarized light and TM-polarized SPPs provides great freedom when manipulating light field based on SPPs at the nanoscale and helps when using the energy of TE-polarized light. The L-shaped nano-aperture is schematically shown in Fig. 1(a). Two perpendicular rectangle holes are fabricated in a gold film on a silica substrate. The thickness of the gold film is labeled as h, which also represents the depth of the holes. The L-shaped aperture has the same arm lengths in the x and y directions and is labeled L. The arm width is labeled w. The origin is set at the outermost corner of the L-shaped aperture and lies at the air/gold interface. The direction of the symmetric axis of the structure (45° with respect to the x axis) and its orthogonal direction are labeled as m and k axes, respectively. For linearly polarized incidence, the polarization angle with respect to the x axis is labeled θ. The resonant properties of the L-shaped nanoapertures were investigated using the finite difference time-domain (FDTD) method (Lumerical FDTD solutions). The meshing cell size is 2 nm, and the perfectly
Fig. 1. (a) Schematic of an L-shaped nanoaperture. (b) Nearfield electric field amplitude jEy j at center point A (x 155 nm, y 35 nm, and z 0) of the x-arm in the L-shaped nanoaperture (L 310 nm, w 70 nm, and h 280 nm) versus the wavelength for different incident polarization angles θ. Inset: schematic of the position of point A. The red arrows indicate the peak wavelengths. © 2015 Optical Society of America
March 15, 2015 / Vol. 40, No. 6 / OPTICS LETTERS
matched layer adsorbing boundaries are used. The permittivity of gold was extracted from the data in [24]. The geometric parameters of the nano-apertures are L 310 nm, w 70 nm, and h 280 nm. The aperture is normally illuminated by a plane wave linearly polarized in the x or y directions from the bottom of the substrate along the z axis. The amplitude of the incident electric field is 1 V/m. The near-field electric field amplitude jEy j at point A (x 155 nm, y 35 nm, and z 0) [inset of Fig. 1(b)], which is the geometric center of the x arm of the L-shaped nanoaperture, is recorded for θ 45° and 135°. The results are shown in Fig. 1(b). For m-polarized (θ 45°) incident light, there are two resonant peaks at 1610 and 960 nm. The resonant mode at 1610 nm is the first-order plasmon resonance mode, and both the top and bottom surfaces of the aperture show a dipolar resonance. For the resonant mode at 960 nm, the aperture shows a single-surface first-order plasmon resonance (SFPR) mode, and only the top surface has a dipolar resonance, whereas the bottom surface has no plasmon resonance [22]. The SFPR mode is the plasmon resonance mode of the hole on the air/gold interface, and its resonance is related to the thickness of the metallic film [25]. In this work, the thickness of the gold film is 280 nm, which is thick enough to ensure that the SFPR mode is excited. For k-polarized (θ 135°) incident light, only one resonant peak is present at 720 nm, and the aperture exhibits a second-order plasmon resonance (SPR) mode on both surfaces. The electric fields on both two surfaces of the gold film are in the resonance for the SPR mode, which differs from those for the SFPR mode. For m- and k-polarized incident light, the near-field electric field Ey at point A (x 155 nm, y 35 nm, and z 0) are labeled Eym and Eyk , and their phases are labeled as φym and φyk , respectively. Because of the different resonant characteristics of the SPR mode and the SFPR mode, there is a phase retardation Δφmk φym − φyk between these two modes, which is used to implement polarization conversion in this work. The nearfield electric field amplitude ratio jEym j∕jEyk j and the phase retardation Δφmk are calculated with respect to the incident wavelength. The results are shown in Fig. 2. At 864 nm, jEym j∕jEyk j equals 0.99, and the phase retardation Δφmk reaches 176°. The electric field of the SFPR mode on the top surface of the gold film is symmetric with respect to the m axis, whereas that of the SPR mode is asymmetric. When the incident beam is linearly polarized along the x axis, the SFPR and SPR modes can be simultaneously excited and interfere with each other. The different symmetries of the two modes should
Fig. 2. Near-field electric field amplitude ratio jEym j∕jEyk j and phase retardation (Δφmk φym − φyk ) versus the wavelength for the L-shaped nanoaperture with L 310 nm, w 70 nm, and h 280 nm.
979
Fig. 3. Near-field electric field amplitude jEj distributions at the air/gold interface (z 0 plane) for incident polarization angles (a) θ 0° and (b) θ 90°. The incident wavelength is 864 nm. The incident polarization directions are shown at the right-top corners in (a) and (b).
induce a 180° phase retardation Δφmk sym in the x arm between the two modes. The total phase retardation between these two modes excited by the x-polarized incident beam is Δφmk total Δφmk Δφmk sym . For the above mentioned size and λ 864 nm, Δφmk total ≈ 0° and 180° in the x and y arms, respectively, which results in a constructive interference in the x arm and destructive interference in the y arm. The near-field electric field amplitude jEj distribution on the top surface of the gold film is shown in Fig. 3(a). The near-field electric field intensity at the middle point of the x arm is 107 times larger than that at the middle point of the y arm. The electric field in the x arm has y-polarization, which launches SPPs that propagate along the y directions. The result for a y-polarized incidence is shown in Fig. 3(b). The constructive interference of the SPR and SFPR modes induces a strong electric field in the y arm and excites the SPPs along the x directions. The pure TE-to-SPP coupling originates from the design of the interference of two orthogonal resonant modes in the L-shaped nano-apertures. The SPP excitation efficiency for an L-shaped nanoaperture at the air/gold interface was calculated using the method in [26], and the launched SPP energy on the top surface of the gold film is normalized to the incident energy illuminated on the L-shaped nano-aperture area (310 nm × 310 nm). The excitation efficiency reaches 15.8% at 864 nm. To demonstrate TE-to-SPP coupling experimentally, L-shaped nano-apertures were fabricated in a 280-nmthick gold film deposited on a 1.5-mm-thick silica substrate using focused ion beam milling. The scanning electron microscope (SEM) image of the sample is shown in Fig. 4(a). For the sake of an increased SPP intensity, the fabricated sample consists of 16 L-shaped nano-apertures, which are 4 × 4 squarely arranged. The distances between adjacent apertures in the x and y directions are both 815 20 nm. A magnified SEM image of the aperture array is shown in Fig. 4(b). The arm length and width of the fabricated nano-apertures are L 315 15 nm and w 70 10 nm. The launched SPPs are scattered by two gratings fabricated in the −x and −y directions. The periods and lengths of the two gratings are 820 nm and 30 μm, respectively. The distances between the gratings and the center of the aperture array are 22 μm. The SPPs launched in the x∕ y direction have nearly the same intensities as those launched in the −x∕ − y direction. In this work, only SPPs that propagate along the −x and −y directions were investigated, and their intensity ratio was measured.
980
OPTICS LETTERS / Vol. 40, No. 6 / March 15, 2015
Fig. 4. (a) SEM image of the fabricated sample. (b) Magnified SEM image of the L-shaped nanoaperture array. (c) Schematic of the experimental setup. (d) and (e) CCD images of the scattering gratings for the incident light with polarization angle θ 0° and 90°, respectively, at 930 nm. The incident polarization directions are shown at the right-top corners in (d) and (e). (f) and (g) Measured intensity ratios of SPPs that propagate in the x and y directions versus wavelength (θ 90°, y-polarized incident light) and incident angles θ (incident wavelength λ 930 nm), respectively.
A schematic of the experimental setup is shown in Fig. 4(c). The light source used in the experiment is a continuous wave Ti:sapphire laser, and the incident wavelength can be tuned from 780 to 930 nm. The polarization of the incident beam was controlled by a polarizer (P) and a half-wave plate (H). The sample (S) was normally illuminated from the substrate side with a linearly polarized laser beam, which was focused by a lens L1 and an objective O1 . SPPs on the air/gold interface were launched in the x and y directions and scattered by the two gratings. The scattering light was collected by another objective O2 and two lenses L2 and L3 and imaged onto a charge-coupled device (CCD) to measure the intensity ratio. A beam block (BB) was used to block the light transmitting through the nano-apertures directly. The CCD images of the two scattering gratings are shown in Figs. 4(d) and 4(e) for incident light polarized along the x and y axes, respectively, at λ 930 nm. For the x-polarized (θ 0°) incident light in Fig. 4(d), scattering light at the −y direction is much stronger than that at the −x direction. The intensity ratio is defined in dB as 10 logI x ∕I y , where I x and I y represent the intensities of the SPPs that propagate in the −x and −y directions, respectively. In Fig. 4(d) the intensity ratio is −5.8 dB. When the incident beam is y-polarized
(θ 90°), the scattering light at the −x direction is much stronger than that at the −y direction, and the intensity ratio reaches 7.1 dB. The SPPs were launched in a direction orthogonal to the polarization direction of the incident electric field. Therefore, pure TE-to-SPP coupling via L-shaped nano-apertures has been demonstrated experimentally. The change of the performance of the L-shaped nanoapertures in TE-to-SPP coupling with respect to the incident wavelength was investigated with a y-polarized (θ 90°) incident beam. The intensity ratio 10 logI x ∕I y was recorded, and the result is shown in Fig. 4(f). As the measured wavelength changes from 830 to 930 nm, the intensity ratio increases from 1.1 to 7.1 dB. As a result, the best working wavelength of the L-shaped nanoapertures in the experiment is 930 nm. Unfortunately, the light source used in this work has a maximum wavelength at 930 nm. Despite the limitation of the light source, an intensity ratio of 7.1 dB at 930 nm is sufficient to demonstrate the TE-to-SPP coupling of L-shaped nanoapertures experimentally. For the L-shaped nano-apertures with L 310 nm, w 70 nm, and h 280 nm, the best working wavelength appears at 864 nm, according to the FDTD calculation results. However, the best working wavelength is very sensitive to the geometric parameters of the nano-apertures. For example, the calculation results show that the best working wavelength redshifts to 920 nm for the nano-apertures with L 300 nm, w 60 nm, and h 280 nm. The discrepancy in the best working wavelengths obtained from the experiment and calculation originates from the imperfect fabrication of the sample. The change of the intensity ratio with respect to the incident polarization angles was studied, and the result is shown in Fig. 4(g). The incident wavelength is 930 nm. The minimum intensity ratio is −5.8 dB at θ 0°, whereas the maximum intensity ratio is 7.4 dB at θ 100°. However, the calculation result in Fig. 2 indicates that the maximum intensity ratio appears at θ 90°. The difference between the calculation and experimental results is likely due to the fabrication tolerances in the experiment. In addition to TE-to-SPP coupling, the reverse process, i.e., SPP-to-TE radiation, can be implemented via the L-shaped nano-apertures. For SPPs propagating at the air/gold surface, the L-shaped nano-aperture cuts off surface electron currents, and the two resonant mode, i.e., the SFPR mode and the SPR mode, are excited in the aperture, which interfere with each other. Light with different polarizations radiate along the −z direction. We investigate the radiation of SPPs that propagate in the x direction for a single nano-aperture (L 310 nm, w 70 nm, and h 280 nm). The radiation along the −z direction in the far-field is investigated, and the electric field at point F (x 0, y 0, and z −1 m) is recorded. The intensity ratio of the electric fields Ey and Ex at point F, which is defined as 10log (jEy j2 ∕jEx j2 ) in dB, is calculated as the incident wavelength changes. The result is shown in Fig. 5(a). At 875 nm, the intensity ratio has a maximum of 19.1 dB, which means the radiation field is mainly y-polarized, i.e., perpendicular to the propagation direction of the incident SPPs. Therefore,
March 15, 2015 / Vol. 40, No. 6 / OPTICS LETTERS
981
61377050) and the Research Fund for the Doctoral Program of Higher Education (grant no. 20130001110050).
Fig. 5. (a) Numerical result and (b) experimental result of the intensity ratio of the radiation light polarized in the y and x directions versus wavelength. Insets in (b) are CCD images of the radiation light polarized in the y (left inset) and x (right inset) directions at 930 nm.
SPP-to-TE radiation can be achieved via L-shaped nanoapertures. To experimentally demonstrate SPP-to-TE coupling, the samples in Figs. 4(a) and 4(b) were used. The grating at the −x direction was normally illuminated from the air side by a linearly x-polarized laser beam, and the launched SPPs propagating in the x direction can be radiated by the L-shaped apertures. The far-field radiation was collected at the substrate side and imaged on the CCD. The polarization state of the radiated electric field from the nano-apertures was analyzed by a broadband linear polarizer. The intensity ratio of the far-field electric field polarized along the y and x directions was measured at different incident wavelengths, and the result is shown in Fig. 5(b). At 930 nm, the far-field intensity ratio has a maximum of 6.4 dB, which shows that the farfield radiation is approximately linearly y-polarized. The CCD images of the radiation light polarized in the y and x directions at 930 nm are shown in the insets of Fig. 5(b), respectively. The intensity of the radiation light polarized in the y direction is much stronger than that polarized in the x direction. Thus, SPP-to-TE coupling is demonstrated experimentally. In conclusion, coupling between SPPs and pure TEpolarized light via L-shaped nano-apertures has been proposed and demonstrated experimentally at a nanoscale. The polarization conversion originates from the interference of the SFPR mode and the SPR mode excited in the L-shaped nano-apertures. Approximately 180° phase retardation between the two modes was obtained according to their different resonant properties. This method provides a new route for launching SPPs with TEpolarized incidence and SPP radiation to TE polarization. As a result, both TE- and TM-polarized light, which are two basic polarization states of photons, can couple with SPPs through optical nano-apertures. In recent years, researchers have been attempting to reduce the size of photonic devices to the nanoscale. The L-shaped nanoapertures, which have ultra-small footprints and can work in a single element, have significant advantages when applied in plasmonic and nanophotonic devices and circuits. This work was supported by the National Natural Science Foundation of China (grant nos. 11404012 and
References 1. S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2007). 2. W. L. Barnes, A. Dereux, and T. W. Ebbesen, Nature 424, 824 (2003). 3. O. Vazquez-Mena, T. Sannomiya, L. G. Villanueva, J. Voros, and J. Brugger, ACS Nano 5, 844 (2011). 4. L. Cao, J. S. White, J. S. Park, J. A. Schuller, B. M. Clemens, and M. L. Brongersma, Nat. Mater. 8, 643 (2009). 5. J. Kneipp, H. Kneipp, M. Mclaughlin, D. Brown, and K. Kneipp, Nano Lett. 6, 2225 (2006). 6. S. Kim, J. Jin, Y.-J. Kim, I.-Y. Park, Y. Kim, and S.-W. Kim, Nature 453, 757 (2008). 7. W. Srituravanich, L. Pan, Y. Wang, C. Sun, D. B. Bogy, and X. Zhang, Nat. Nanotechnol. 3, 733 (2008). 8. C. Zhao and J. Zhang, ACS Nano 4, 6433 (2010). 9. K. C. Y. Huang, M. K. Seo, T. Sarmiento, Y. Huo, J. S. Harris, and M. L. Brongersma, Nat. Photonics 8, 244 (2014). 10. R. F. Oulton, V. J. Sorger, T. Zentgraf, R. M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, Nature 461, 629 (2009). 11. F. Lopez-Tejeira, S. G. Rodrigo, L. Martin-Moreno, F. J. Garcia-Vidal, E. Devaux, T. W. Ebbesen, J. R. Krenn, I. P. Radko, S. I. Bozhevolnyi, M. U. Gonzalez, J. C. Weeber, and A. Dereux, Nat. Phys. 3, 324 (2007). 12. Y. Sonnefraud, S. Kerman, G. D. Martino, D. Y. Lei, and S. A. Maier, Opt. Express 20, 4893 (2012). 13. A. Baron, E. Devaux, J. C. Rodier, J. P. Hugonin, E. Rousseau, C. Genet, T. W. Ebbesen, and P. Lalanne, Nano Lett. 11, 4207 (2011). 14. Y. Liu, S. Palomba, Y. Park, T. Zentgraf, X. Yin, and X. Zhang, Nano Lett. 12, 4853 (2012). 15. L. Wang, T. Li, L. Li, W. Xia, X. G. Xu, and S. N. Zhu, Opt. Express 20, 8710 (2012). 16. J. Yang, X. Xiao, C. Hu, W. Zhang, S. Zhou, and J. Zhang, Nano Lett. 14, 704 (2014). 17. J. Chen, Z. Li, S. Yue, and Q. Gong, Appl. Phys. Lett. 97, 041113 (2010). 18. J. Lin, J. P. B. Mueller, Q. Wang, G. H. Yuan, N. Antoniou, X. C. Yuan, and F. Capasso, Science 340, 331 (2013). 19. B. B. Tsema, Y. B. Tsema, M. R. Shcherbakov, Y. Lin, D. Liu, V. V. Klimov, A. A. Fedyanin, and D. P. Tsai, Opt. Express 20, 10538 (2012). 20. S.-Y. Lee, I.-M. Lee, J. Park, S. Oh, W. Lee, K.-Y. Kim, and B. Lee, Phys. Rev. Lett. 108, 213907 (2012). 21. L. Huang, X. Chen, B. Bai, Q. Tan, G. Jin, T. Zentgraf, and S. Zhang, Light: Sci. Appl. 2, e70 (2013). 22. J. Yang, S. Zhou, C. Hu, W. Zhang, X. Xiao, and J. Zhang, Laser Photon. Rev. 8, 590 (2014). 23. L. Feng, A. Mizrahi, S. Zamek, Z. Liu, V. Lomakin, and Y. Fainmain, ACS Nano 5, 5100 (2011). 24. E. D. Palik, Handbook of Optical Constants of Solids II (Academic, 1985). 25. J. Yang and J. Zhang, Opt. Express 21, 7934 (2013). 26. A. L. Baudrion, F. D. L. Perez, O. Mahboub, A. Hohenau, H. Ditlbacher, F. J. Garcia-Vidal, J. Dintinger, T. W. Ebbesen, L. Martin-Morner, and J. R. Krenn, Opt. Express 16, 3420 (2008).
