Manipulating photoinduced voltage in metasurface with circularly polarized light Qiang Bai∗ Department of Physics, Tohoku University, Sendai 980-8578, Japan *[email protected]
Abstract: Recently, the concept of metasurface has provided one an unprecedented opportunity and ability to control the light in the deep subwavelength scale. However, so far most efforts are devoted to exploiting the novel scattering properties and applications of metasurface in optics. Here, I theoretically and numerically demonstrate that longitudinal and transverse photoinduced voltages can be simultaneously realized in the proposed metasurface utilizing the magnetic resonance under the normal incidence of circularly polarized light, which may extend the concept and functionality of metasurface into the electronics and may provide a potential scheme to realize a nanoscale tunable voltage source through a nanophotonic roadmap. The signs of longitudinal and transverse photoinduced voltages can be manipulated by tuning the resonant frequency and the handedness of circularly polarized light, respectively. Analytical formulae of photoinduced voltage are presented based on the theory of symmetry of field. This work may bridge nanophotonics and electronics, expands the capability of metasurface and has many potential applications. © 2015 Optical Society of America OCIS codes: (160.3918) Metamaterials; (260.5740) Resonance; (260.3910) Metal optics; (260.5430) Polarization.
References and links 1. H. M. Barlow, “The Hall effect and its application to microwave power measurement,” Proc. IRE 46, 1411–1413 (1958). 2. A. F. Gibson, M. F. Kimmitt, and A. C. Walker, “Photon drag in germanium,” Appl. Phys. Lett. 17, 75–77 (1970). 3. T. S. Moss, “Photon pressure effects in semiconductors,” Phys. Status Solidi A 8, 223–232 (1971). 4. G. Ribakovs and A. A. Gundjian, “Photon drag and other emfs induced in tellurium by a TEA CO2 laser,” Appl. Phys. Lett. 24, 377–379 (1974). 5. V. L. Gurevich, R. Laiho, and A. V. Lashkul, “Photomagnetism of metals,” Phys. Rev. Lett. 69, 180–183 (1992). 6. V. L. Gurevich and R. Laiho, “Photomagnetism of metals: microscopic theory of the photoinduced surface current,” Phys. Rev. B 48, 8307–8316 (1993). 7. V. M. Shalaev, C. Douketis, J. T. Stuckless, and M. Moskovits, “Light-induced kinetic effects in solids,” Phys. Rev. B 53, 11388–11402 (1996). 8. J. E. Goff and W. L. Schaich, “Hydrodynamic theory of photon drag,” Phys. Rev. B 56, 15421–15430 (1997). 9. J. E. Goff and W. L. Schaich, “Theory of the photon-drag effect in simple metals,” Phys. Rev. B 61, 10471–10477 (2000). 10. A. S. Vengurlekar and T. Ishihara, “Surface plasmon enhanced photon drag in metal films,” Appl. Phys. Lett. 87, 091118 (2005). 11. M. Durach, A. Rusina, and M. I. Stockman, “Giant surface-plasmon-induced drag effect in metal nanowires,” Phys. Rev. Lett. 103, 186801 (2009).
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Received 5 Jan 2015; revised 31 Jan 2015; accepted 10 Feb 2015; published 20 Feb 2015 23 Feb 2015 | Vol. 23, No. 4 | DOI:10.1364/OE.23.005348 | OPTICS EXPRESS 5348
12. T. Hatano, T. Ishihara, S. G. Tikhodeev, and N. A. Gippius, “Transverse photovoltage induced by circularly polarized light,” Phys. Rev. Lett. 103, 103906 (2009). 13. A. English, C.-W. Cheng, L. Lowe II, M.-H. Shih, and W. Kuang, “Hydrodynamic modeling of surface plasmon enhanced photon induced current in a gold grating,” Appl. Phys. Lett. 98, 191113 (2011). 14. N. Noginova, A. V. Yakim, J. Soimo, L. Gu, and M. A. Noginov, “Light-to-current and current-to-light coupling in plasmonic systems,” Phys. Rev. B 84, 035447 (2011). 15. H. Kurosawa, T. Ishihara, N. Ikeda, D. Tsuya, M. Ochiai, and Y. Sugimoto, “Optical rectification effect due to surface plasmon polaritons at normal incidence in a nondiffraction regime,” Opt. Lett. 37, 2793–2795 (2012). 16. H. Kurosawa and T. Ishihara, “Surface plasmon drag effect in a dielectrically modulated metallic thin film,” Opt. Express 20, 1561–1574 (2012). 17. N. Noginova, V. Rono, F. J. Bezares, and J. D. Caldwell, “Plasmon drag effect in metal nanostructures,” New J. Phys. 15, 113061 (2013). 18. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000). 19. R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77–79 (2001). 20. D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic clock at microwave frequencies,” Science 314, 977–980 (2006). 21. Z. Jacob, L. V. Alekseyev, and E. Narimanov, “Optical hyperlens: far-field imaging beyond the diffraction limit,” Opt. Express 14, 8247–8256 (2006). 22. N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. 100, 207402 (2008). 23. S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101, 047401 (2008). 24. J. Shin, J.-T. Shen, and S. Fan, “Three-dimensional metamaterials with an ultrahigh effective refractive index over a broad bandwidth,” Phys. Rev. Lett. 102, 093903 (2009). 25. Q. Bai, J. Chen, C. Liu, J. Xu, C. Cheng, N.-H. Shen, and H.-T. Wang, “Polarization splitter of surface polaritons,” Phys. Rev. B 79, 155401 (2009). 26. T. Kaelberer, V. A. Fedotov, N. Papasimakis, D. P. Tsai, and N. I. Zheludev, “Toroidal dipolar response in a metamaterial,” Science 330, 1510–1512 (2010). 27. Q. Bai, J. Chen, N.-H. Shen, C. Cheng, and H.-T. Wang, “Controllable optical black hole in left-handed materials,” Opt. Express 18, 2106–2115 (2010). 28. P. B. Catrysse and S. Fan, “Transverse electromagnetic modes in aperture waveguides containing a metamaterial with extreme anisotropy,” Phys. Rev. Lett. 106, 223902 (2011). 29. R. Maas, J. Parsons, N. Engheta, and A. Polman, “Experimental realization of an epsilon-near-zero metamaterial at visible wavelengths,” Nat. Photonics 7, 907–912 (2013). 30. N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334, 333–337 (2011). 31. X. Ni, N. K. Emani, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Broadband light bending with plasmonic nanoantennas,” Science 335, 427 (2012). 32. S. Sun, K.-Y. Yang, C.-M. Wang, T.-K. Juan, W. T. Chen, C. Y. Liao, Q. He, S. Xiao, W.-T. Kung, G.-Y. Guo, L. Zhou, and D. P. Tsai, “High-efficiency broadband anomalous reflection by gradient metasurfaces,” Nano Lett. 12, 6223–6229 (2012). 33. D. Lin, P. Fan, E. Hasman, and M. L. Brongersma, “Dielectric gradient metasurface optical elements,” Science 345, 298–302 (2014). 34. P. Genevet, N. Yu, F. Aieta, J. Lin, M. A. Kats, R. Blanchard, M. O. Scully, Z. Gaburro, and F. Capasso, “Ultrathin plasmonic optical vortex plate based on phase discontinuities,” Appl. Phys. Lett. 100, 013101 (2012). 35. X. Yin, Z. Ye, J. Rho, Y. Wang, and X. Zhang, “Photonic spin Hall effect at metasurfaces,” Science 339, 1405– 1407 (2013). 36. X. Ni, A. V. Kildishev, and V. M. Shalaev, “Metasurface holograms for visible light,” Nat. Commun. 4, 2807 (2013). 37. L. Huang, X. Chen, H. Mhlenbernd, H. Zhang, S. Chen, B. Bai, Q. Tan, G. Jin, K.-W. Cheah, C.-W. Qiu, J. Li, T. Zentgraf, and S. Zhang, “Three-dimensional optical holography using a plasmonic metasurface,” Nat. Commun. 4, 2808 (2013). 38. W. T. Chen, K.-Y. Yang, C.-M. Wang, Y.-W. Huang, G. Sun, I-D. Chiang, C. Y. Liao, W.-L. Hsu, H. T. Lin, S. Sun, L. Zhou, A. Q. Liu, and D. P. Tsai, “High-efficiency broadband meta-hologram with polarization-controlled dual images,” Nano Lett. 14, 225–230 (2014). 39. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972). 40. J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1962).
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Received 5 Jan 2015; revised 31 Jan 2015; accepted 10 Feb 2015; published 20 Feb 2015 23 Feb 2015 | Vol. 23, No. 4 | DOI:10.1364/OE.23.005348 | OPTICS EXPRESS 5349
1.
Introduction
When the light impinges on the conductive material, the free carriers in the material will be redistributed due to the optical force exerted on free carriers and the optical force will be balanced by the electrostatic force, which manifests itself as an observable photoinduced voltage (PIV). This phenomenon is known as the photon drag effect (PDE) [1–7]. Goff and Schaich have theoretically studied the PDE in simple metal [8, 9]. In bulk metals, the PDE is very weak [5, 6]. Surface plasmon enhanced PDE have been theoretically and experimentally investigated in plasmonic structures [10–17]. However, magnetic resonance enhanced PDE has not been studied theoretically or experimentally. Furthermore, most of PIVs in plasmonic structures vanish under normal incidence of light and strong diffracted light occurs, which limit their performances in some applications. Metamaterials (MMs), as a new kind of artificially structured materials with subwavelength building blocks, have attracted considerable interest in past decade, due to their exotic optical properties and applications [18–29]. As a reduced dimensional counterpart of bulk MMs, metasurfaces are two-dimensional MMs with subwavelength thickness and can provide the possibility of constructing magnetic resonances in subwavelength scale. Magnetic resonances can greatly enhance electric and magnetic fields, may perfectly absorb lights and benefit the PDE. Thus far a large number of unprecedented properties and phenomena based on various metasurfaces have been demonstrated, for example, phase discontinuity [30, 31], gradient metasurfaces [32, 33], orbital angular momenta [34], photonic spin Hall effect [35], and optical holography [36–38]. However, most efforts are devoted to exploiting the scattering properties of metasurface in optics. There is little work on exploiting the possible property and application of metasurface in electronics, which may bridge nanophotonics and electronics, has the significance in integrated nanophotonic and electronic circuits and deserves an investigation. Here, a novel metasurface is proposed to simultaneously realize longitudinal and transverse PIVs utilizing the magnetic resonance when circularly polarized light (CPL) is normally incident, which may provide a potential scheme to realize a nanoscale tunable voltage source through a nanophotonic roadmap and may extend the metasurface into the electronics. Furthermore, the signs of longitudinal and transverse PIVs can be tuned by changing the resonant frequency and the handedness of CPL, respectively. Numerical results are well explained with analytical formulae of PIVs based on the theory of symmetry of field. This work can find many important and potential applications in nanophotonics, electronics, molecule detection and light harvesting. 2.
Structure of the proposed metasurface
The structure of the proposed metasurface consists of a layer of triangular metal particles (TMPs) with the thickness of tt = 30 nm, the base side of b = 180 nm and the height of h = 180 nm and a layer of homogeneous metal film (HMF) with the thickness of t f = 30 nm and the side of d = 300 nm separated by a dielectric interlayer with the thickness of td = 30 nm. The geometry of its unit cell is sketched in Fig. 1, and the metasurface is put on the top of a dielectric substrate. As an example, the metal is chosen to be gold which is described as a dispersive medium with a complex relative permittivity taken from the experimental data by Johnson and Christy [39]. The dielectric is quartz with the relative permittivity of 2.25. 3.
Longitudinal photoinduced voltage
When the CPL is normally incident on the proposed metasurface, voltage can be induced across the HMF due to the force acting on the free electrons in the HMF. The PIV can be estimated
#231871 - $15.00 USD © 2015 OSA
Received 5 Jan 2015; revised 31 Jan 2015; accepted 10 Feb 2015; published 20 Feb 2015 23 Feb 2015 | Vol. 23, No. 4 | DOI:10.1364/OE.23.005348 | OPTICS EXPRESS 5350
td tf
tt
y
z x
b Au Quartz
(a)
d
h
(b)
Fig. 1. Schematic of geometric structure (a) and parameters (b) of the proposed metasurface.
using [15, 16] Vi =
LFi , qρ Ω
(1)
where the subscript i denotes the x, y or z component of the corresponding quantity, Vi is the PIV across the length of L, L is the total length of metasurface along the i-direction, q is the charge of free electron, ρ is the concentration of free electrons in the HMF, Ω is the volume of the HMF, and Fi is the total time-averaged force acting on free electrons in the HMF, which can be obtained by [40] " Fi =
Ti j n j dS,
(2)
S
in which the subscript j stands for the x, y or z component of the corresponding quantity, n j is the unit normal vector in j-direction, and Ti j is the time-averaged Maxwell stress tensor which is defined by 1 1 1 (3) Ti j = Re ε Ei E ∗j − δi j E 2 + μ Hi H ∗j − δi j H 2 , 2 2 2 where δi j is the Kronecker delta, ε and μ are the permittivity and permeability of the dielectric. The force is obtained by integrating Eq. (2) over the closed surface of the homogeneous metal film layer. Numerical calculations are performed with the commercial software (CST Microwave Studio). Here Vx and Vy are defined as longitudinal and transverse PIVs, respectively. p and s polarized plane waves denote the ones with electric fields along x and y directions, respectively. The change of longitudinal PIV (LPIV) with the frequency of normally incident CPL is shown in Fig. 2. The blue (red) solid curve with square (circle) shows the numerical results of LPIV for right-handed CPL (RCPL) and left-handed CPL (LCPL), respectively. The LPIV is of the order of 3 μ V for 1 × 1010 W/m2 and 556 unit cells. It can be seen that the LPIV cannot distinguish the handedness of CPL, since both voltages are the same for different handedness. As the frequency increases, there exist two peaks of LPIV at the frequencies of 306.8 and 345 THz, respectively, one is negative-valued and the other is positive-valued. This feature enables one to alter the sign of LPIV by switching the operation frequency and is very significant in practical applications, such as active and tunable nanophotonics and integrated photonics and electronics. To understand the two-peak phenomenon of the spectrum of LPIV for both LCPL and RCPL, the spectra of LPIV of the proposed metasurface for both normally incident p and s polarized plane waves are illustrated in Fig. 3. For p and s polarized plane waves, there is a peak of LPIV at the frequency of 315 and 340 THz, respectively, and both peaks have opposite signs, which #231871 - $15.00 USD © 2015 OSA
Received 5 Jan 2015; revised 31 Jan 2015; accepted 10 Feb 2015; published 20 Feb 2015 23 Feb 2015 | Vol. 23, No. 4 | DOI:10.1364/OE.23.005348 | OPTICS EXPRESS 5351
4
Vx (V)
2
RCP LCP
0
-2 -4 210
240
270 300 330 Frequency (THz)
360
390
Fig. 2. Longitudinal photoinduced voltage as a function of frequency for normally incident right- and left-handed circularly polarized lights, respectively. RCP and LCP represent the right- and left-handed circular polarizations, respectively.
shows that two electromagnetic (EM) resonant modes are excited by p and s polarizations, respectively. The spectrum of Va = (Vxp +Vxs )/2 has the same values and positions of peaks as that of LPIV for both LCPL and RCPL. Therefore the p and s components of both LCPL and RCPL dominate two peaks of LPIV for both LCPL and RCPL, respectively.
12
Vx (V)
8 4
Vp x Vs x Va
0 -4 -8 210
240
270 300 330 Frequency (THz)
360
390
Fig. 3. Longitudinal photoinduced voltage as a function of frequency for normally incident p p and s polarized plane waves, respectively. Vx and Vxs represent the longitudinal photoinp duced voltage for p and s polarized plane wave, respectively. Va = (Vx +Vxs )/2.
In order to gain a deep insight into the underlying physics behind the peaks of LPIV for p and s polarized plane waves, the EM responses of the proposed metasurface under the normal incidence of both p and s polarized plane waves are numerically simulated. Figure 4 shows the distributions of magnetic fields and currents on the x-z and y-z planes and electric field patterns on the x-y middle planes of gold particles at the peaks of 315 and 340 THz for p and s polarized plane waves, respectively. We can see that both peaks correspond to two magnetic resonances, respectively, and the magnetic fields are greatly enhanced due to the anti-parallel currents circulating between the top gold particles and bottom gold film. Furthermore, the electric field #231871 - $15.00 USD © 2015 OSA
Received 5 Jan 2015; revised 31 Jan 2015; accepted 10 Feb 2015; published 20 Feb 2015 23 Feb 2015 | Vol. 23, No. 4 | DOI:10.1364/OE.23.005348 | OPTICS EXPRESS 5352
patterns are different at both peaks. Therefore, the peaks of LPIV for p and s polarized plane waves respectively stem from the magnetic resonance of the proposed metasurface. The x components of the total time-averaged forces generated by these two magnetic resonances possess the opposite directions, which results in the opposite polarities of LPIV at two peaks of p and s polarized plane waves. The p components of both LCPL and RCPL mainly excite the magnetic resonance which is responsible for the first peak of LPIV for both LCPL and RCPL in the negative-valued regime and s components mainly excite the other magnetic resonance which dominates the second peak of LPIV for both LCPL and RCPL in the positive-valued regime. Hy
Current
E
(b)
Max
(c)
Max
P
(a)
Max
0
Hx
0
Current Max
(e)
Max
(f)
Max
S
(d)
0
E
0
0
0
Fig. 4. Distributions of the magnetic fields on the x-z (a) and y-z (d) planes and current on the x-z (b) and y-z (e) planes and electric field patterns on the x-y (c and f) middle planes of gold particles at the peaks of 315 and 340 THz for normally incident p and s polarized plane waves, respectively. P and S denote the p and s polarized plane waves, respectively.
4.
Transverse photoinduced voltage
Figure 5 shows the change of transverse PIV (TPIV) with the frequency of normally incident LCPL and RCPL. Blue (red) solid curve with square (circle) corresponds to the numerical results of TPIV for RCPL and LCPL, respectively. The TPIV is of the order of 7 μ V for 1×1010 W/m2 and 556 unit cells. It can be found that at the same frequency the TPIV has the identical values but the opposite signs. Therefore the TPIV can distinguish the different handedness of CPL. For both RCPL and LCPL, when increasing the frequency, there is only a peak of TPIV at the frequency of 330 THz. Thus the signs of TPIV can be manipulated by changing the handedness of CPL. This feature can find very important applications in active and tunable nanophotonics and integrated photonics and electronics. Comparing with the results of LPIV for both LCPL and RCPL, the TPIV only has one peak for both LCPL and RCPL. To understand this one-peak phenomenon of TPIV, Fig. 6 depicts the change of | Vxp × Vxs | with the frequency. The spectrum of | Vxp × Vxs | has a peak at the frequency of 330 THz, which has a similar lineshape with that of TPIV and may imply that two magnetic resonances mentioned above all contribute to the peak of TPIV. To reveal the underlying physics behind the peaks of TPIV for both RCPL and LCPL, Fig. 7 shows the electric field patterns and distributions of the magnetic fields on the x-y middle planes of both gold particles (top row) and dielectric interlayer (bottom row), respectively, for normally incident RCPL and LCPL at the frequency of 330 THz. For the frequency of 330 THz, the electric field patterns are different for RCPL and LCPL, and the magnetic fields are also large
#231871 - $15.00 USD © 2015 OSA
Received 5 Jan 2015; revised 31 Jan 2015; accepted 10 Feb 2015; published 20 Feb 2015 23 Feb 2015 | Vol. 23, No. 4 | DOI:10.1364/OE.23.005348 | OPTICS EXPRESS 5353
8 6
RCP LCP
Vy (V)
4 2 0
-2 -4 -6 -8 210
240
270 300 330 Frequency (THz)
360
390
5 4 3
s
2 1
p
-11
Vx Vx(10 arb. units)
Fig. 5. Transverse photoinduced voltage as a function of frequency for normally incident right- and left-handed circularly polarized lights, respectively.
0 210
240
270 300 330 Frequency (THz)
360
390
p
Fig. 6. The change of | Vx ×Vxs | with frequency.
between the top gold particles and bottom gold film. 5.
Discussion
These intriguing results discussed above can be also understood with the theory of symmetry of field in the proposed metasurface [12]. For the metasurface illustrated in Fig. 1, its structure possesses the mirror symmetry with respect to the x-z plane, but the mirror symmetries of its structure for both the y-z and x-y planes are all broken. This retained mirror symmetry of the structure with respect to the x-z plane can be utilized to characterize the EM field in the proposed metasurface. For both RCPL and LCPL, their electric fields can be expressed as s , E = √1 E p ± iE 2
(4)
where p and s denote two orthogonally linear polarizations. When CPL is normally incident on the proposed metasurface, the total electric and magnetic fields in metasurface can be viewed as the superposition of the electric and magnetic fields produced by the s and p components of
#231871 - $15.00 USD © 2015 OSA
Received 5 Jan 2015; revised 31 Jan 2015; accepted 10 Feb 2015; published 20 Feb 2015 23 Feb 2015 | Vol. 23, No. 4 | DOI:10.1364/OE.23.005348 | OPTICS EXPRESS 5354
LCP
Max
E
RCP
H
0 Max
0 Fig. 7. Electric field patterns and distributions of the magnetic fields on x-y middle planes of both gold particles (top row) and dielectric interlayer (bottom row), respectively, at the frequency of 330 THz for normally incident right- and left-handed circularly polarized lights, respectively.
CPL, respectively. According to the reflection operation with respect to the retained x-z mirror plane, for the p component, E px , E pz and Hpy are even; E py , H px and Hpz are odd. For the s component, Esx , Esz and Hsy are odd; Esy , Hsx and Hsz are even. Here Ei j and Hi j (i=p or s and j=x, y or z) denotes the j component of the electric and magnetic fields produced by the i component of CPL. Based on the above parity of electric and magnetic fields, the LPIV with the remained terms are expressed as ¨ ¨ L ∗ ∗ Re( ε E px E pz dSu − ε E px E pz dSl Vx = 4qρ Ω Su
Sl
¨ ¨ ¨ ∗ ∗ ∗ + μ Hpx Hpz dSu − μ Hpx Hpz dSl + ε Esx Esz dSu Su
Sl
Su
¨ ¨ ¨ ∗ − ε Esx Esz dSl + μ Hsx Hsz∗ dSu − μ Hsx Hsz∗ dSl ), Sl
Su
(5)
Sl
where subscript u and l stand for the upper and lower surfaces of HMF along the z direction, respectively. It can be seen that for each term of Eq. (5), it only has one of + and − signs. Thus the sign of LPIV for CPL does not depend on the handedness of CPL. Furthermore, all of terms in the right side of Eq. (5) can be divided into two sets according to their origins of p and s components: one set only originates from the p component and the other set only originates from the s component. These two sets of terms are responsible for two peaks observed in the spectrum of LPIV for both RCPL and LCPL, respectively. Similarly, the TPIV with the
#231871 - $15.00 USD © 2015 OSA
Received 5 Jan 2015; revised 31 Jan 2015; accepted 10 Feb 2015; published 20 Feb 2015 23 Feb 2015 | Vol. 23, No. 4 | DOI:10.1364/OE.23.005348 | OPTICS EXPRESS 5355
remained terms are written as Vy =
L Re(∓i 4qρ Ω ¨ ∓i
¨
¨
ε E py Esz∗ dSu ±i
Su
¨
∗ μ Hsy Hpz dSu ±i
Su
¨ ∓i Sl
ε E py Esz∗ dSl
Sl
¨
∗ μ Hsy Hpz dSl ±i
Sl
¨
∗ ε Esy E pz dSl ±i
Su
∗ ε Esy E pz dSu
Su
¨
μ Hpy Hsz∗ dSu ∓i
μ Hpy Hsz∗ dSl ).
(6)
Sl
Each term of Eq. (6) has both signs of + and −. Therefore the sign of TPIV for CPL depends on the handedness of CPL. All of terms in the right side of Eq. (6) cannot be classified into two sets, since each term of them simultaneously originates from both p and s components. Thus two magnetic resonances respectively excited by the s and p components of CPL all contribute to the peak of TPIV for both RCPL and LCPL. Under the condition of normal incidence, the z components of electric and magnetic fields generated by the proposed metasurface are crucial for achieving both LPIV and TPIV. These results based on the theory of symmetry of field have an excellent agreement with the ones obtain with the full-vector numerical calculations. 6.
Conclusion
In conclusion, I have proposed a scheme to simultaneously realize LPIV and TPIV in the metasurface utilizing the magnetic resonance when the CPL is normally impinging, which may realize a nanoscale tunable voltage source through a nanophotonic roadmap and may extend the concept and functionality of metasurface into the electronics. The signs of both LPIV and TPIV can be manipulated by use of the resonant frequency and the handedness of CPL, respectively. Analytical formulae of both LPIV and TPIV are presented based on the theory of symmetry of field, which perfectly explain the numerical results. Furthermore, this phenomenon that the sign of TPIV is changed with the handedness of CPL is analogous to the photonic spin Hall effect [35] and may be used to measure the weak shift of light beam depending on the spin angular momentum of light. By rotating the orientation of TMP and/or changing the geometric parameters of the proposed metasurface, the voltage can be flexibly manipulated. This work may bridge nanophotonics and electronics, and has many significant and potential applications in detecting chiral molecules, light harvesting, integrated photonics and electronics, and spindependent optoelectronics and so on. Acknowledgments This work is supported by the Grant-in-Aid for Scientific Research on Innovative Areas No. 22109005 (Electromagnetic Metamaterials) from the Ministry of Education, Culture, Sports, Science, and Technology (MEXT), Japan.
#231871 - $15.00 USD © 2015 OSA
Received 5 Jan 2015; revised 31 Jan 2015; accepted 10 Feb 2015; published 20 Feb 2015 23 Feb 2015 | Vol. 23, No. 4 | DOI:10.1364/OE.23.005348 | OPTICS EXPRESS 5356
Abstract: Recently, the concept of metasurface has provided one an unprecedented opportunity and ability to control the light in the deep subwavelength scale. However, so far most efforts are devoted to exploiting the novel scattering properties and applications of metasurface in optics. Here, I theoretically and numerically demonstrate that longitudinal and transverse photoinduced voltages can be simultaneously realized in the proposed metasurface utilizing the magnetic resonance under the normal incidence of circularly polarized light, which may extend the concept and functionality of metasurface into the electronics and may provide a potential scheme to realize a nanoscale tunable voltage source through a nanophotonic roadmap. The signs of longitudinal and transverse photoinduced voltages can be manipulated by tuning the resonant frequency and the handedness of circularly polarized light, respectively. Analytical formulae of photoinduced voltage are presented based on the theory of symmetry of field. This work may bridge nanophotonics and electronics, expands the capability of metasurface and has many potential applications. © 2015 Optical Society of America OCIS codes: (160.3918) Metamaterials; (260.5740) Resonance; (260.3910) Metal optics; (260.5430) Polarization.
References and links 1. H. M. Barlow, “The Hall effect and its application to microwave power measurement,” Proc. IRE 46, 1411–1413 (1958). 2. A. F. Gibson, M. F. Kimmitt, and A. C. Walker, “Photon drag in germanium,” Appl. Phys. Lett. 17, 75–77 (1970). 3. T. S. Moss, “Photon pressure effects in semiconductors,” Phys. Status Solidi A 8, 223–232 (1971). 4. G. Ribakovs and A. A. Gundjian, “Photon drag and other emfs induced in tellurium by a TEA CO2 laser,” Appl. Phys. Lett. 24, 377–379 (1974). 5. V. L. Gurevich, R. Laiho, and A. V. Lashkul, “Photomagnetism of metals,” Phys. Rev. Lett. 69, 180–183 (1992). 6. V. L. Gurevich and R. Laiho, “Photomagnetism of metals: microscopic theory of the photoinduced surface current,” Phys. Rev. B 48, 8307–8316 (1993). 7. V. M. Shalaev, C. Douketis, J. T. Stuckless, and M. Moskovits, “Light-induced kinetic effects in solids,” Phys. Rev. B 53, 11388–11402 (1996). 8. J. E. Goff and W. L. Schaich, “Hydrodynamic theory of photon drag,” Phys. Rev. B 56, 15421–15430 (1997). 9. J. E. Goff and W. L. Schaich, “Theory of the photon-drag effect in simple metals,” Phys. Rev. B 61, 10471–10477 (2000). 10. A. S. Vengurlekar and T. Ishihara, “Surface plasmon enhanced photon drag in metal films,” Appl. Phys. Lett. 87, 091118 (2005). 11. M. Durach, A. Rusina, and M. I. Stockman, “Giant surface-plasmon-induced drag effect in metal nanowires,” Phys. Rev. Lett. 103, 186801 (2009).
#231871 - $15.00 USD © 2015 OSA
Received 5 Jan 2015; revised 31 Jan 2015; accepted 10 Feb 2015; published 20 Feb 2015 23 Feb 2015 | Vol. 23, No. 4 | DOI:10.1364/OE.23.005348 | OPTICS EXPRESS 5348
12. T. Hatano, T. Ishihara, S. G. Tikhodeev, and N. A. Gippius, “Transverse photovoltage induced by circularly polarized light,” Phys. Rev. Lett. 103, 103906 (2009). 13. A. English, C.-W. Cheng, L. Lowe II, M.-H. Shih, and W. Kuang, “Hydrodynamic modeling of surface plasmon enhanced photon induced current in a gold grating,” Appl. Phys. Lett. 98, 191113 (2011). 14. N. Noginova, A. V. Yakim, J. Soimo, L. Gu, and M. A. Noginov, “Light-to-current and current-to-light coupling in plasmonic systems,” Phys. Rev. B 84, 035447 (2011). 15. H. Kurosawa, T. Ishihara, N. Ikeda, D. Tsuya, M. Ochiai, and Y. Sugimoto, “Optical rectification effect due to surface plasmon polaritons at normal incidence in a nondiffraction regime,” Opt. Lett. 37, 2793–2795 (2012). 16. H. Kurosawa and T. Ishihara, “Surface plasmon drag effect in a dielectrically modulated metallic thin film,” Opt. Express 20, 1561–1574 (2012). 17. N. Noginova, V. Rono, F. J. Bezares, and J. D. Caldwell, “Plasmon drag effect in metal nanostructures,” New J. Phys. 15, 113061 (2013). 18. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000). 19. R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77–79 (2001). 20. D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic clock at microwave frequencies,” Science 314, 977–980 (2006). 21. Z. Jacob, L. V. Alekseyev, and E. Narimanov, “Optical hyperlens: far-field imaging beyond the diffraction limit,” Opt. Express 14, 8247–8256 (2006). 22. N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. 100, 207402 (2008). 23. S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101, 047401 (2008). 24. J. Shin, J.-T. Shen, and S. Fan, “Three-dimensional metamaterials with an ultrahigh effective refractive index over a broad bandwidth,” Phys. Rev. Lett. 102, 093903 (2009). 25. Q. Bai, J. Chen, C. Liu, J. Xu, C. Cheng, N.-H. Shen, and H.-T. Wang, “Polarization splitter of surface polaritons,” Phys. Rev. B 79, 155401 (2009). 26. T. Kaelberer, V. A. Fedotov, N. Papasimakis, D. P. Tsai, and N. I. Zheludev, “Toroidal dipolar response in a metamaterial,” Science 330, 1510–1512 (2010). 27. Q. Bai, J. Chen, N.-H. Shen, C. Cheng, and H.-T. Wang, “Controllable optical black hole in left-handed materials,” Opt. Express 18, 2106–2115 (2010). 28. P. B. Catrysse and S. Fan, “Transverse electromagnetic modes in aperture waveguides containing a metamaterial with extreme anisotropy,” Phys. Rev. Lett. 106, 223902 (2011). 29. R. Maas, J. Parsons, N. Engheta, and A. Polman, “Experimental realization of an epsilon-near-zero metamaterial at visible wavelengths,” Nat. Photonics 7, 907–912 (2013). 30. N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334, 333–337 (2011). 31. X. Ni, N. K. Emani, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Broadband light bending with plasmonic nanoantennas,” Science 335, 427 (2012). 32. S. Sun, K.-Y. Yang, C.-M. Wang, T.-K. Juan, W. T. Chen, C. Y. Liao, Q. He, S. Xiao, W.-T. Kung, G.-Y. Guo, L. Zhou, and D. P. Tsai, “High-efficiency broadband anomalous reflection by gradient metasurfaces,” Nano Lett. 12, 6223–6229 (2012). 33. D. Lin, P. Fan, E. Hasman, and M. L. Brongersma, “Dielectric gradient metasurface optical elements,” Science 345, 298–302 (2014). 34. P. Genevet, N. Yu, F. Aieta, J. Lin, M. A. Kats, R. Blanchard, M. O. Scully, Z. Gaburro, and F. Capasso, “Ultrathin plasmonic optical vortex plate based on phase discontinuities,” Appl. Phys. Lett. 100, 013101 (2012). 35. X. Yin, Z. Ye, J. Rho, Y. Wang, and X. Zhang, “Photonic spin Hall effect at metasurfaces,” Science 339, 1405– 1407 (2013). 36. X. Ni, A. V. Kildishev, and V. M. Shalaev, “Metasurface holograms for visible light,” Nat. Commun. 4, 2807 (2013). 37. L. Huang, X. Chen, H. Mhlenbernd, H. Zhang, S. Chen, B. Bai, Q. Tan, G. Jin, K.-W. Cheah, C.-W. Qiu, J. Li, T. Zentgraf, and S. Zhang, “Three-dimensional optical holography using a plasmonic metasurface,” Nat. Commun. 4, 2808 (2013). 38. W. T. Chen, K.-Y. Yang, C.-M. Wang, Y.-W. Huang, G. Sun, I-D. Chiang, C. Y. Liao, W.-L. Hsu, H. T. Lin, S. Sun, L. Zhou, A. Q. Liu, and D. P. Tsai, “High-efficiency broadband meta-hologram with polarization-controlled dual images,” Nano Lett. 14, 225–230 (2014). 39. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972). 40. J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1962).
#231871 - $15.00 USD © 2015 OSA
Received 5 Jan 2015; revised 31 Jan 2015; accepted 10 Feb 2015; published 20 Feb 2015 23 Feb 2015 | Vol. 23, No. 4 | DOI:10.1364/OE.23.005348 | OPTICS EXPRESS 5349
1.
Introduction
When the light impinges on the conductive material, the free carriers in the material will be redistributed due to the optical force exerted on free carriers and the optical force will be balanced by the electrostatic force, which manifests itself as an observable photoinduced voltage (PIV). This phenomenon is known as the photon drag effect (PDE) [1–7]. Goff and Schaich have theoretically studied the PDE in simple metal [8, 9]. In bulk metals, the PDE is very weak [5, 6]. Surface plasmon enhanced PDE have been theoretically and experimentally investigated in plasmonic structures [10–17]. However, magnetic resonance enhanced PDE has not been studied theoretically or experimentally. Furthermore, most of PIVs in plasmonic structures vanish under normal incidence of light and strong diffracted light occurs, which limit their performances in some applications. Metamaterials (MMs), as a new kind of artificially structured materials with subwavelength building blocks, have attracted considerable interest in past decade, due to their exotic optical properties and applications [18–29]. As a reduced dimensional counterpart of bulk MMs, metasurfaces are two-dimensional MMs with subwavelength thickness and can provide the possibility of constructing magnetic resonances in subwavelength scale. Magnetic resonances can greatly enhance electric and magnetic fields, may perfectly absorb lights and benefit the PDE. Thus far a large number of unprecedented properties and phenomena based on various metasurfaces have been demonstrated, for example, phase discontinuity [30, 31], gradient metasurfaces [32, 33], orbital angular momenta [34], photonic spin Hall effect [35], and optical holography [36–38]. However, most efforts are devoted to exploiting the scattering properties of metasurface in optics. There is little work on exploiting the possible property and application of metasurface in electronics, which may bridge nanophotonics and electronics, has the significance in integrated nanophotonic and electronic circuits and deserves an investigation. Here, a novel metasurface is proposed to simultaneously realize longitudinal and transverse PIVs utilizing the magnetic resonance when circularly polarized light (CPL) is normally incident, which may provide a potential scheme to realize a nanoscale tunable voltage source through a nanophotonic roadmap and may extend the metasurface into the electronics. Furthermore, the signs of longitudinal and transverse PIVs can be tuned by changing the resonant frequency and the handedness of CPL, respectively. Numerical results are well explained with analytical formulae of PIVs based on the theory of symmetry of field. This work can find many important and potential applications in nanophotonics, electronics, molecule detection and light harvesting. 2.
Structure of the proposed metasurface
The structure of the proposed metasurface consists of a layer of triangular metal particles (TMPs) with the thickness of tt = 30 nm, the base side of b = 180 nm and the height of h = 180 nm and a layer of homogeneous metal film (HMF) with the thickness of t f = 30 nm and the side of d = 300 nm separated by a dielectric interlayer with the thickness of td = 30 nm. The geometry of its unit cell is sketched in Fig. 1, and the metasurface is put on the top of a dielectric substrate. As an example, the metal is chosen to be gold which is described as a dispersive medium with a complex relative permittivity taken from the experimental data by Johnson and Christy [39]. The dielectric is quartz with the relative permittivity of 2.25. 3.
Longitudinal photoinduced voltage
When the CPL is normally incident on the proposed metasurface, voltage can be induced across the HMF due to the force acting on the free electrons in the HMF. The PIV can be estimated
#231871 - $15.00 USD © 2015 OSA
Received 5 Jan 2015; revised 31 Jan 2015; accepted 10 Feb 2015; published 20 Feb 2015 23 Feb 2015 | Vol. 23, No. 4 | DOI:10.1364/OE.23.005348 | OPTICS EXPRESS 5350
td tf
tt
y
z x
b Au Quartz
(a)
d
h
(b)
Fig. 1. Schematic of geometric structure (a) and parameters (b) of the proposed metasurface.
using [15, 16] Vi =
LFi , qρ Ω
(1)
where the subscript i denotes the x, y or z component of the corresponding quantity, Vi is the PIV across the length of L, L is the total length of metasurface along the i-direction, q is the charge of free electron, ρ is the concentration of free electrons in the HMF, Ω is the volume of the HMF, and Fi is the total time-averaged force acting on free electrons in the HMF, which can be obtained by [40] " Fi =
Ti j n j dS,
(2)
S
in which the subscript j stands for the x, y or z component of the corresponding quantity, n j is the unit normal vector in j-direction, and Ti j is the time-averaged Maxwell stress tensor which is defined by 1 1 1 (3) Ti j = Re ε Ei E ∗j − δi j E 2 + μ Hi H ∗j − δi j H 2 , 2 2 2 where δi j is the Kronecker delta, ε and μ are the permittivity and permeability of the dielectric. The force is obtained by integrating Eq. (2) over the closed surface of the homogeneous metal film layer. Numerical calculations are performed with the commercial software (CST Microwave Studio). Here Vx and Vy are defined as longitudinal and transverse PIVs, respectively. p and s polarized plane waves denote the ones with electric fields along x and y directions, respectively. The change of longitudinal PIV (LPIV) with the frequency of normally incident CPL is shown in Fig. 2. The blue (red) solid curve with square (circle) shows the numerical results of LPIV for right-handed CPL (RCPL) and left-handed CPL (LCPL), respectively. The LPIV is of the order of 3 μ V for 1 × 1010 W/m2 and 556 unit cells. It can be seen that the LPIV cannot distinguish the handedness of CPL, since both voltages are the same for different handedness. As the frequency increases, there exist two peaks of LPIV at the frequencies of 306.8 and 345 THz, respectively, one is negative-valued and the other is positive-valued. This feature enables one to alter the sign of LPIV by switching the operation frequency and is very significant in practical applications, such as active and tunable nanophotonics and integrated photonics and electronics. To understand the two-peak phenomenon of the spectrum of LPIV for both LCPL and RCPL, the spectra of LPIV of the proposed metasurface for both normally incident p and s polarized plane waves are illustrated in Fig. 3. For p and s polarized plane waves, there is a peak of LPIV at the frequency of 315 and 340 THz, respectively, and both peaks have opposite signs, which #231871 - $15.00 USD © 2015 OSA
Received 5 Jan 2015; revised 31 Jan 2015; accepted 10 Feb 2015; published 20 Feb 2015 23 Feb 2015 | Vol. 23, No. 4 | DOI:10.1364/OE.23.005348 | OPTICS EXPRESS 5351
4
Vx (V)
2
RCP LCP
0
-2 -4 210
240
270 300 330 Frequency (THz)
360
390
Fig. 2. Longitudinal photoinduced voltage as a function of frequency for normally incident right- and left-handed circularly polarized lights, respectively. RCP and LCP represent the right- and left-handed circular polarizations, respectively.
shows that two electromagnetic (EM) resonant modes are excited by p and s polarizations, respectively. The spectrum of Va = (Vxp +Vxs )/2 has the same values and positions of peaks as that of LPIV for both LCPL and RCPL. Therefore the p and s components of both LCPL and RCPL dominate two peaks of LPIV for both LCPL and RCPL, respectively.
12
Vx (V)
8 4
Vp x Vs x Va
0 -4 -8 210
240
270 300 330 Frequency (THz)
360
390
Fig. 3. Longitudinal photoinduced voltage as a function of frequency for normally incident p p and s polarized plane waves, respectively. Vx and Vxs represent the longitudinal photoinp duced voltage for p and s polarized plane wave, respectively. Va = (Vx +Vxs )/2.
In order to gain a deep insight into the underlying physics behind the peaks of LPIV for p and s polarized plane waves, the EM responses of the proposed metasurface under the normal incidence of both p and s polarized plane waves are numerically simulated. Figure 4 shows the distributions of magnetic fields and currents on the x-z and y-z planes and electric field patterns on the x-y middle planes of gold particles at the peaks of 315 and 340 THz for p and s polarized plane waves, respectively. We can see that both peaks correspond to two magnetic resonances, respectively, and the magnetic fields are greatly enhanced due to the anti-parallel currents circulating between the top gold particles and bottom gold film. Furthermore, the electric field #231871 - $15.00 USD © 2015 OSA
Received 5 Jan 2015; revised 31 Jan 2015; accepted 10 Feb 2015; published 20 Feb 2015 23 Feb 2015 | Vol. 23, No. 4 | DOI:10.1364/OE.23.005348 | OPTICS EXPRESS 5352
patterns are different at both peaks. Therefore, the peaks of LPIV for p and s polarized plane waves respectively stem from the magnetic resonance of the proposed metasurface. The x components of the total time-averaged forces generated by these two magnetic resonances possess the opposite directions, which results in the opposite polarities of LPIV at two peaks of p and s polarized plane waves. The p components of both LCPL and RCPL mainly excite the magnetic resonance which is responsible for the first peak of LPIV for both LCPL and RCPL in the negative-valued regime and s components mainly excite the other magnetic resonance which dominates the second peak of LPIV for both LCPL and RCPL in the positive-valued regime. Hy
Current
E
(b)
Max
(c)
Max
P
(a)
Max
0
Hx
0
Current Max
(e)
Max
(f)
Max
S
(d)
0
E
0
0
0
Fig. 4. Distributions of the magnetic fields on the x-z (a) and y-z (d) planes and current on the x-z (b) and y-z (e) planes and electric field patterns on the x-y (c and f) middle planes of gold particles at the peaks of 315 and 340 THz for normally incident p and s polarized plane waves, respectively. P and S denote the p and s polarized plane waves, respectively.
4.
Transverse photoinduced voltage
Figure 5 shows the change of transverse PIV (TPIV) with the frequency of normally incident LCPL and RCPL. Blue (red) solid curve with square (circle) corresponds to the numerical results of TPIV for RCPL and LCPL, respectively. The TPIV is of the order of 7 μ V for 1×1010 W/m2 and 556 unit cells. It can be found that at the same frequency the TPIV has the identical values but the opposite signs. Therefore the TPIV can distinguish the different handedness of CPL. For both RCPL and LCPL, when increasing the frequency, there is only a peak of TPIV at the frequency of 330 THz. Thus the signs of TPIV can be manipulated by changing the handedness of CPL. This feature can find very important applications in active and tunable nanophotonics and integrated photonics and electronics. Comparing with the results of LPIV for both LCPL and RCPL, the TPIV only has one peak for both LCPL and RCPL. To understand this one-peak phenomenon of TPIV, Fig. 6 depicts the change of | Vxp × Vxs | with the frequency. The spectrum of | Vxp × Vxs | has a peak at the frequency of 330 THz, which has a similar lineshape with that of TPIV and may imply that two magnetic resonances mentioned above all contribute to the peak of TPIV. To reveal the underlying physics behind the peaks of TPIV for both RCPL and LCPL, Fig. 7 shows the electric field patterns and distributions of the magnetic fields on the x-y middle planes of both gold particles (top row) and dielectric interlayer (bottom row), respectively, for normally incident RCPL and LCPL at the frequency of 330 THz. For the frequency of 330 THz, the electric field patterns are different for RCPL and LCPL, and the magnetic fields are also large
#231871 - $15.00 USD © 2015 OSA
Received 5 Jan 2015; revised 31 Jan 2015; accepted 10 Feb 2015; published 20 Feb 2015 23 Feb 2015 | Vol. 23, No. 4 | DOI:10.1364/OE.23.005348 | OPTICS EXPRESS 5353
8 6
RCP LCP
Vy (V)
4 2 0
-2 -4 -6 -8 210
240
270 300 330 Frequency (THz)
360
390
5 4 3
s
2 1
p
-11
Vx Vx(10 arb. units)
Fig. 5. Transverse photoinduced voltage as a function of frequency for normally incident right- and left-handed circularly polarized lights, respectively.
0 210
240
270 300 330 Frequency (THz)
360
390
p
Fig. 6. The change of | Vx ×Vxs | with frequency.
between the top gold particles and bottom gold film. 5.
Discussion
These intriguing results discussed above can be also understood with the theory of symmetry of field in the proposed metasurface [12]. For the metasurface illustrated in Fig. 1, its structure possesses the mirror symmetry with respect to the x-z plane, but the mirror symmetries of its structure for both the y-z and x-y planes are all broken. This retained mirror symmetry of the structure with respect to the x-z plane can be utilized to characterize the EM field in the proposed metasurface. For both RCPL and LCPL, their electric fields can be expressed as s , E = √1 E p ± iE 2
(4)
where p and s denote two orthogonally linear polarizations. When CPL is normally incident on the proposed metasurface, the total electric and magnetic fields in metasurface can be viewed as the superposition of the electric and magnetic fields produced by the s and p components of
#231871 - $15.00 USD © 2015 OSA
Received 5 Jan 2015; revised 31 Jan 2015; accepted 10 Feb 2015; published 20 Feb 2015 23 Feb 2015 | Vol. 23, No. 4 | DOI:10.1364/OE.23.005348 | OPTICS EXPRESS 5354
LCP
Max
E
RCP
H
0 Max
0 Fig. 7. Electric field patterns and distributions of the magnetic fields on x-y middle planes of both gold particles (top row) and dielectric interlayer (bottom row), respectively, at the frequency of 330 THz for normally incident right- and left-handed circularly polarized lights, respectively.
CPL, respectively. According to the reflection operation with respect to the retained x-z mirror plane, for the p component, E px , E pz and Hpy are even; E py , H px and Hpz are odd. For the s component, Esx , Esz and Hsy are odd; Esy , Hsx and Hsz are even. Here Ei j and Hi j (i=p or s and j=x, y or z) denotes the j component of the electric and magnetic fields produced by the i component of CPL. Based on the above parity of electric and magnetic fields, the LPIV with the remained terms are expressed as ¨ ¨ L ∗ ∗ Re( ε E px E pz dSu − ε E px E pz dSl Vx = 4qρ Ω Su
Sl
¨ ¨ ¨ ∗ ∗ ∗ + μ Hpx Hpz dSu − μ Hpx Hpz dSl + ε Esx Esz dSu Su
Sl
Su
¨ ¨ ¨ ∗ − ε Esx Esz dSl + μ Hsx Hsz∗ dSu − μ Hsx Hsz∗ dSl ), Sl
Su
(5)
Sl
where subscript u and l stand for the upper and lower surfaces of HMF along the z direction, respectively. It can be seen that for each term of Eq. (5), it only has one of + and − signs. Thus the sign of LPIV for CPL does not depend on the handedness of CPL. Furthermore, all of terms in the right side of Eq. (5) can be divided into two sets according to their origins of p and s components: one set only originates from the p component and the other set only originates from the s component. These two sets of terms are responsible for two peaks observed in the spectrum of LPIV for both RCPL and LCPL, respectively. Similarly, the TPIV with the
#231871 - $15.00 USD © 2015 OSA
Received 5 Jan 2015; revised 31 Jan 2015; accepted 10 Feb 2015; published 20 Feb 2015 23 Feb 2015 | Vol. 23, No. 4 | DOI:10.1364/OE.23.005348 | OPTICS EXPRESS 5355
remained terms are written as Vy =
L Re(∓i 4qρ Ω ¨ ∓i
¨
¨
ε E py Esz∗ dSu ±i
Su
¨
∗ μ Hsy Hpz dSu ±i
Su
¨ ∓i Sl
ε E py Esz∗ dSl
Sl
¨
∗ μ Hsy Hpz dSl ±i
Sl
¨
∗ ε Esy E pz dSl ±i
Su
∗ ε Esy E pz dSu
Su
¨
μ Hpy Hsz∗ dSu ∓i
μ Hpy Hsz∗ dSl ).
(6)
Sl
Each term of Eq. (6) has both signs of + and −. Therefore the sign of TPIV for CPL depends on the handedness of CPL. All of terms in the right side of Eq. (6) cannot be classified into two sets, since each term of them simultaneously originates from both p and s components. Thus two magnetic resonances respectively excited by the s and p components of CPL all contribute to the peak of TPIV for both RCPL and LCPL. Under the condition of normal incidence, the z components of electric and magnetic fields generated by the proposed metasurface are crucial for achieving both LPIV and TPIV. These results based on the theory of symmetry of field have an excellent agreement with the ones obtain with the full-vector numerical calculations. 6.
Conclusion
In conclusion, I have proposed a scheme to simultaneously realize LPIV and TPIV in the metasurface utilizing the magnetic resonance when the CPL is normally impinging, which may realize a nanoscale tunable voltage source through a nanophotonic roadmap and may extend the concept and functionality of metasurface into the electronics. The signs of both LPIV and TPIV can be manipulated by use of the resonant frequency and the handedness of CPL, respectively. Analytical formulae of both LPIV and TPIV are presented based on the theory of symmetry of field, which perfectly explain the numerical results. Furthermore, this phenomenon that the sign of TPIV is changed with the handedness of CPL is analogous to the photonic spin Hall effect [35] and may be used to measure the weak shift of light beam depending on the spin angular momentum of light. By rotating the orientation of TMP and/or changing the geometric parameters of the proposed metasurface, the voltage can be flexibly manipulated. This work may bridge nanophotonics and electronics, and has many significant and potential applications in detecting chiral molecules, light harvesting, integrated photonics and electronics, and spindependent optoelectronics and so on. Acknowledgments This work is supported by the Grant-in-Aid for Scientific Research on Innovative Areas No. 22109005 (Electromagnetic Metamaterials) from the Ministry of Education, Culture, Sports, Science, and Technology (MEXT), Japan.
#231871 - $15.00 USD © 2015 OSA
Received 5 Jan 2015; revised 31 Jan 2015; accepted 10 Feb 2015; published 20 Feb 2015 23 Feb 2015 | Vol. 23, No. 4 | DOI:10.1364/OE.23.005348 | OPTICS EXPRESS 5356
