Spin-selected focusing and imaging based on metasurface lens

Sen Wang; Xinke Wang; Qiang Kan; Jiasheng Ye; Shengfei Feng; Wenfeng Sun; Peng Han; Shiliang Qu; Yan Zhang

doi:10.1364/OE.23.026434

1. Introduction

Polarization (spin), one of the basic freedoms of electromagnetic waves, has vital applications in various fields including radio communications, 3D display, spectroscopy, etc [1–3 ]. In the nature, insects utilize the polarization to navigate, prey and even mate [4–6 ]. However, human eyes as well as most optoelectronic detectors are insensitive to the polarization of light. Thus, it remains to be a challenge to directly distinguish the polarization states of light and further manipulate photons with different spin states.

Resembling the spin Hall effect (SHE) in the electronics [7], photonic SHE which results from the spin and orbit (trajectory) interaction of photons can separate the photons with different spin states [8–10 ]. Specifically, for light incident on the interface between homogeneous media or propagating in materials with inhomogeneous index of refraction, the spin and orbital angular momentum of the photons will couple and interact to conserve the total angular momentum, leading to the transverse shift of light. However, the transverse shift resulting from photonic SHE is extremely small due to the lack of natural materials with a large gradient of index of refraction, thus it is difficult to observe the photonic SHE. Multiple reflections [9] or ultrasensitive quantum weak measurements with additional selections of the spin states [10, 11 ] are commonly required to magnify the shift and observe the photonic SHE, which is demanding and challenging for practical applications.

Consisted of sub-wavelength metallic antennas, metasurface has been shown to exhibit some special electromagnetic responses that mainly depend on the structure of antennas rather than its constituent material [12]. The counterparts of traditional optical devices such as lens [13, 14 ], wave plates [15] and holograms [16] have been realized with the metasurfaces. Considering that the phase profile in the metasurface can be arbitrarily engineered, a strong phase gradient can be designed and thus the photonic SHE can be easily achieved [17–19 ]. A giant photonic SHE has been observed with a metasurface consisted of V-shaped antennas [20]. Moreover, the polarization state of light can also be manipulated by the metasurface, which is closely related to the Pancharatnam-Berry (PB) phase [21–24 ]. A spin-dependent shift in the k-space can be induced by the PB phase and thus a giant photonic SHE in the real space can be obtained [25]. However, most spin-based metasurface devices have been restricted to the separation of photons with different spin states [17–25 ], without further manipulating photons based on the corresponding spin states. In [14] and [26], only either left circularly polarized (LCP) light or right circularly polarized (RCP) light can be focused, but both the LCP and RCP lights propagate in the same direction and are not separated.

Here, we propose and demonstrate a spin-selected metasurface lens in the terahertz (THz) frequency range. The spin-selected lens cannot only achieve a giant transverse shift but also focus the photons with different spin states to two separated focal spots in a broadband frequency range. More interestingly, this lens can also perform the spin-selected imaging. The versatile spin-based lens is a powerful tool to exploit the spin states of light and can inspire more designs and applications of spin-based devices.

2. Design and experimental setup

The designed metasurface lens is consisted of rectangular slit antennas with spatial variant orientation angles $φ (x, y)$ , as shown in the inset of Fig. 1(a) . The working principle of the lens is based on the shift of wave vector resulting from the geometric PB phase. Briefly, when left circularly polarized (LCP) or right circularly polarized (RCP) light, corresponding to the $σ_{-}$ or $σ_{+}$ spin state of a photon, is incident on the slit antenna, light with opposite helicity (RCP or LCP) is excited and imprinted with a PB phase. The geometric PB phase is related to the orientation angle of the antenna by $Φ (x, y) = 2 σ_{\pm} φ (x, y)$ , where $σ_{\pm} = \pm 1$ is determined by the helicity of the incident and excited light [14]. Such the shift of wave vector in the k-space is induced by a spatial variant PB phase [25]:

Δ k (x, y) = \nabla Φ (x, y) = \frac{\partial Φ}{\partial x} \hat{x} + \frac{\partial Φ}{\partial y} \hat{y},

where

\hat{x}

and

\hat{y}

are the unit vector in the x and y direction, respectively. The shift of wave vector in the momentum space corresponds to a real space shift of light. Thus, the propagation of the excited light can be controlled by appropriately designing the PB phase distribution. Moreover, considering that the amplitude of the excited light is independent of orientation angle, spin-selected optical function can be realized by properly engineering the orientation angles of the slit antennas.

Fig. 1 Photograph of the fabricated metasurface lens (a) and the procedure of spin-selected focusing (b). The metasurface consists of subwavelength slits antennas with spatially varied orientations. With the illumination of LCP/RCP light, the excited RCP/LCP light will be focused to the left/right side of the focal plane, respectively.

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To realize the spin-selected focusing function of the metasurface lens, the wave vector shifts in both x and y directions are required and the orientation angle distribution of the antennas can be determined as follows:

φ (x, y) = {(- 1)}^{(m + n)} k_{0} (\sqrt{f^{2} + {[x + {(- 1)}^{(m + n)} x_{0}]}^{2} + y^{2}} - | f |) / 2,

where

(x, y)

is the location of the antenna,

m = x / d

and

n = y / d

,

d

is the period of the antenna,

k_{0} = 2 π / λ

is the free-space wave vector of incident light,

f

is the focal length and

x_{0}

is the distance of the transverse shift for the focal spots. Such an orientation angle distribution will generate a PB phase profile which can act as two spherical lenses with focal spots located in

(x_{0}, f)

and

(- x_{0}, f)

, respectively. Figure 1(b) schematically illustrates the procedure of spin-selected focusing. For the LCP incident light, the antennas located in positions where

(m + n)

is even will converge the wave vector of the excited RCP light and focus the light to the left side

(- x_{0}, f)

. While with the illumination of RCP light, the antennas located in positions where

(m + n)

is odd will converge the wave vector of the excited LCP light and focus the light to the right side

(x_{0}, f)

. Similarly, the spin-selected imaging can also be achieved in the imaging plane.

As a proof of concept, a spin-selected metasurface lens working in the THz frequency range is designed and fabricated with micro photolithography. The photograph of the part of the fabricated metasurface lens is shown in Fig. 1(a). The antennas are rectangular slits with a width of 50 μm and a length of 150 μm on a 100 nm thick gold film and the substrate is a high resistance Si wafer with a thickness of 1mm. The antennas are evenly distributed with a period of 200 μm in both x and y directions. For the THz radiation with a frequency of 0.75 THz, the focal length $f$ is designed to be 4 mm and the distance between the two focal spots is 2.2 mm.

The fabricated metasurface lens is characterized with a THz focal plane imaging system which is schematically shown in Fig. 2 . The THz focal plane imaging system can selectively detect the horizontally or vertically polarized THz radiation by changing the polarization of the probe beam [27]. Considering that the circularly polarized THz radiation is the superposition of two orthogonal linearly polarized THz radiations, the spin-selected metasurface lens can be investigated by detecting two orthogonal linearly polarized THz radiations and a subsequent simple calculation. Specifically, the horizontally polarized THz radiation generated by a <110> ZnTe crystal can be switched to either horizontally (E_x) or vertically polarized (E_y) by rotating the THz half wave plate (THWP). The E_x / E_y THz radiation is incident on the metasurface lens and the THz radiation with orthogonal polarization E_y / E_x is excited and detected. The excited E_y / E_x THz radiation can be selectively detected by modulating the polarization of the probe beam with a polarizer (P) and a half wave plate (HWP). The detected THz radiations are then used to synthesize the LCP/RCP THz radiations by $E_{L (R)} = E_{x} \pm i E_{y} .$ The detection ZnTe crystal is mounted on a moving stage and can be scanned along the z-axis with a step of 0.25 mm. Thus, the spin-selected focusing and imaging can be investigated with the imaging system.

Fig. 2 Schematic diagram of THz focal plane imaging system. The polarization direction of the incident THz radiation can be tuned with a THWP. After passing the metasurface lens, the THz radiation is detected by a <110> ZnTe crystal and the probe beam. The probe beam is then incident into the imaging module consisting of a 4f system (L1, L2), a quarter wave plate (QWP), a Wollaston prism (WP) and a CCD for differential detection.

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3. Results and discussions

The spin-selected focusing property of the lens is simulated with commercial software FDTD Solutions. In the simulation, the parameters of the antenna are the same as those used in the experiment. The boundary conditions in the x, y and z directions are all set as perfect match layer (PML). The incident source is set as a plane THz wave with a frequency of 0.75 THz. The normalized simulation intensity distributions in the focal plane and the propagation plane are presented in Figs. 3(a)-3(c) for the RCP, LCP and linearly polarized (LP) THz radiations, which are indicated by the clockwise circle, counterclockwise circle and linear arrow, respectively. For the RCP THz radiation, a focal plane 4 mm away from the lens surface can be clearly seen and the focal spot is on the right side. If the polarization of the incident THz radiation is switched from RCP to LCP, the THz radiation will be focused in the same focal plane but the focal spot is on the left side. With the illumination of LP THz radiation which can be regarded as the combination of the LCP and RCP THz radiation, two focal spots are clearly shown in the focal plane. The separation between the two focal spots is 2.2 mm, which is the same as the designed value. The simulation shows that the designed lens can focus the THz radiation to two separate focal spots according to the polarization of incident THz radiation, which resembles the photonic SHE. The spin-selected metasurface lens is experimentally characterized with the THz focal plane imaging system. The normalized experimental intensity profiles in the focal plane and propagation plane are shown in Figs. 3(d)-3(f), which are similar to the simulation results. In the focal plane 4 mm away from the lens, the focal spots with a transverse shift of 1.05 mm for the RCP and LCP THz radiations and double focal spots for the LP THz radiation are experimentally achieved, which further verify the spin-selected focusing function of the lens.

Fig. 3 Simulation and experimental demonstrations of spin-selected focusing. Simulated intensity distribution in the focal plane and propagation plane for RCP (a), LCP (b) and LP (c) THz radiations, indicated by the arrows. (d), (e) and (f) are the corresponding experimental results. Transverse shifts of the focal spots and the split of the focal spots are observed for the circularly polarized and LP THz radiations, respectively.

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Taking advantage of the generated broadband THz radiation, the dispersion of the spin-selected lens is analyzed with the illumination of the LP THz radiation. The normalized intensity distributions in the propagation plane and the corresponding Stokes parameter S₃ are shown in Figs. 4(a)-4(c) for 0.65 THz, 0.75 THz and 0.94 THz radiations, respectively. It can be seen that THz radiations with different frequencies are all focused to two focal spots but the focal lengths are different. The Stokes parameters S₃ are utilized to describe the degree of circular polarization and confirms that the splitting is spin-dependent [25]. The transversal and longitudinal intensity distributions for 0.65 THz, 0.75 THz and 0.94 THz are quantitatively compared in Figs. 4(d) and 4(e). The distances between the two focal spots remain almost the same (2.1 mm) for different frequencies. However, the focal length is longer for THz radiation with a larger frequency. The focal lengths are about 2.9 mm, 3.9 mm, and 5.0 mm for 0.65 THz, 0.75 THz and 0.94 THz, respectively. The dispersion of the spin-selected lens is similar to the dispersion of a traditional lens based on the topography and refractive index. Although the focal length varies with the frequency, the spin-selected focusing is not affected, which means the designed lens can work in a broadband frequency range (300 GHz).

Fig. 4 Dispersion analyses of the spin-selected lens. Focusing profile for 0.65 THz (a) and 0.94 THz (b) with the LP incident THz radiation and the corresponding Stokes parameter S₃. Comparison of transversal (d) and longitudinal (e) intensity distributions for three different frequencies.

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The spin-selected imaging function of the metasurface lens is experimentally demonstrated by imaging three letter patterns 'C', 'N' and 'U' milled on a stainless steel sheet, see Fig. 5(a) . The size of each pattern is $4 \times 5$ mm² and the patterns are put 12 mm away from the lens. Based on the simple object-image relationship, an imaging plane with a magnification of 0.5 at 6 mm away from the lenses is expected for the lens with a focal length of 4 mm. The images of the patterns obtained with the illumination of RCP, LCP and LP THz radiations are shown in Figs. 5(b)-5(d), which are similar to the spin-selected focusing distribution. For the RCP and LCP THz radiations, the letter patterns are imaged on the right and left side of the imaging plane, respectively, meanwhile, two images of the patterns are observed with the illumination of LP THz radiation.

Fig. 5 Experimental investigation of spin-selected imaging. (a) Three letter patterns 'C', 'N' and 'U'. For the RCP (b) and LCP (c) incident THz radiation, the letter patterns (C, N and U) are imaged to the right and left respectively. Two images of the letter patterns are observed with LP THz radiation (d) illumination.

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Conversion efficiency is a key problem for optical devices based on metasurface. For the designed spin-selected metasurface lens, the conversion efficiency between two circularly polarized states is estimated to be approximately 6%, which can be further improved by increasing the density and optimizing the parameters of the antennas. Furthermore, the efficiency could be significantly improved by enabling the lens to work in the reflecting mode [28–30 ] or replacing the metal antennas with dielectric antennas [22]. Recently, metasurface hologram working in the reflecting mode and reaching 80% efficiency has been demonstrated [29]. Thus, in principle, the efficiency of the spin-selected lens can be readily improved to the level of practical applications.

Furthermore, the versatility of the spin-selected metasurface lens can provide more freedoms for practical applications. The LCP and RCP THz radiations are not only separated with a giant transverse shift reaching 2.1 mm but are also focused to two distinct points, which can enable the direct detection of the polarization of light with a higher efficiency. This feature may enable the metasurface lens to be used for circular polarization analyzer [31] and polarization beam splitting. The lens may also find applications in the measurement of the circular dichroism [32] which has been widely used in the structural studies of proteins and DNA [33]. And the separation between the two focal spots can be arbitrarily designed and further enlarged by setting a larger $x_{0}$ in Eq. (2). The PB phase modulation induced by the slit antenna is independent of wavelength. Thus, the working frequency of the spin-selected lens is broadband and is mainly limited by the working frequency of the quarter wave plates used in the experiment. The broadband feature implies that the proposed scheme can be extended to other wavebands (visible, infrared and microwave) by scaling the slit antenna. Moreover, the spin-selected imaging is more flexible than holograms based on polarization [34, 35 ] and can be used for spin-based information processing and communication [1].

4. Conclusions

In summary, we proposed a spin-selected metasurface lens and experimentally verified its focusing and imaging functions in the THz frequency range. The design of the lens is based on the modulation of wave vector shift induced by the PB phase. Focal spot can be transversely shifted to the left or right side of the focal plane by switching the helicity of the incident circularly polarized THz wave and double focal spots are observed for the LP THz radiation. Moreover, spin-selected imaging is achieved with the metasurface lens. With the flexibility of manipulating photons with different spin states, the spin-selected lens is a substantial step in the field of spin-based photonics devices, which can further inspire more designs of such devices as counterparts of spintronics devices and thus promote polarization-related applications in sensing, nano-optics and quantum information processing.

Acknowledgments

This work was supported by the 973 Program of China (No. 2013CBA01702), the National Natural Science Foundation of China (Nos. 11204188, 11474206, 61205097, 91233202, 11374216, and 11174211), the National High Technology Research and Development Program of China (No. 2012AA101608-6), the Beijing Natural Science Foundation (No. 1132011), the Program for New Century Excellent Talents in University (NCET-12-0607), the CAEP THz Science and Technology Foundation (CAEPTHZ201306), the Scientific Research Project of Beijing Education Commission (KM201310028005), the Specialized Research Fund for the Doctoral Program of Higher Education (20121108120009) and the Scientific Research Base Development Program of the Beijing Municipal Commission of Education.

References and links

1. M. R. Andrews, P. P. Mitra, and R. deCarvalho, “Tripling the capacity of wireless communications using electromagnetic polarization,” Nature 409(6818), 316–318 (2001). [CrossRef] [PubMed]

2. S. G. Park, S. Yoon, J. Yeom, H. Baek, S. W. Min, and B. Lee, “Lamina 3D display: projection-type depth-fused display using polarization-encoded depth information,” Opt. Express 22(21), 26162–26172 (2014). [CrossRef] [PubMed]

3. P. H. Vaccaro, “Spectroscopy: Handedness in quick time,” Nature 458(7236), 289–290 (2009). [CrossRef] [PubMed]

4. S. Heinze and U. Homberg, “Maplike representation of celestial E-vector orientations in the brain of an insect,” Science 315(5814), 995–997 (2007). [CrossRef] [PubMed]

5. N. Shashar, R. T. Hanlon, and A. D. Petz, “Polarization vision helps detect transparent prey,” Nature 393(6682), 222–223 (1998). [CrossRef] [PubMed]

6. A. Sweeney, C. Jiggins, and S. Johnsen, “Insect communication: Polarized light as a butterfly mating signal,” Nature 423(6935), 31–32 (2003). [CrossRef] [PubMed]

7. J. E. Hirsch, “Spin Hall effect,” Phys. Rev. Lett. 83(9), 1834–1837 (1999). [CrossRef]

8. M. Onoda, S. Murakami, and N. Nagaosa, “Hall effect of light,” Phys. Rev. Lett. 93(8), 083901 (2004). [CrossRef] [PubMed]

9. K. Y. Bliokh, A. Niv, V. Kleiner, and E. Hasman, “Geometrodynamics of spinning light,” Nat. Photonics 2(12), 748–753 (2008). [CrossRef]

10. O. Hosten and P. Kwiat, “Observation of the spin hall effect of light via weak measurements,” Science 319(5864), 787–790 (2008). [CrossRef] [PubMed]

11. Y. Gorodetski, K. Y. Bliokh, B. Stein, C. Genet, N. Shitrit, V. Kleiner, E. Hasman, and T. W. Ebbesen, “Weak measurements of light chirality with a plasmonic slit,” Phys. Rev. Lett. 109(1), 013901 (2012). [CrossRef] [PubMed]

12. A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Planar photonics with metasurfaces,” Science 339(6125), 1232009 (2013). [CrossRef] [PubMed]

13. D. Hu, X. Wang, S. Feng, J. Ye, W. Sun, Q. Kan, P. J. Klar, and Y. Zhang, “Ultrathin terahertz planar elements,” Adv. Opt. Mater. 1(2), 186–191 (2013). [CrossRef]

14. X. Chen, L. Huang, H. Mühlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, C. W. Qiu, S. Zhang, and T. Zentgraf, “Dual-polarity plasmonic metalens for visible light,” Nat. Commun. 3, 1198 (2012). [CrossRef] [PubMed]

15. N. Yu, F. Aieta, P. Genevet, M. A. Kats, Z. Gaburro, and F. Capasso, “A broadband, background-free quarter-wave plate based on plasmonic metasurfaces,” Nano Lett. 12(12), 6328–6333 (2012). [CrossRef] [PubMed]

16. L. L. Huang, X. Z. Chen, H. Muhlenbernd, H. Zhang, S. M. Chen, B. F. Bai, Q. F. Tan, G. F. Jin, K. W. Cheah, C. W. Qiu, J. S. Li, T. Zentgraf, and S. Zhang, “Three-dimensional optical holography using a plasmonic metasurface,” Nat. Commun. 4, 2808 (2013). [CrossRef]

17. N. Shitrit, I. Bretner, Y. Gorodetski, V. Kleiner, and E. Hasman, “Optical spin Hall effects in plasmonic chains,” Nano Lett. 11(5), 2038–2042 (2011). [CrossRef] [PubMed]

18. G. Li, M. Kang, S. Chen, S. Zhang, E. Y. Pun, K. W. Cheah, and J. Li, “Spin-enabled plasmonic metasurfaces for manipulating orbital angular momentum of light,” Nano Lett. 13(9), 4148–4151 (2013). [CrossRef] [PubMed]

19. N. Shitrit, I. Yulevich, E. Maguid, D. Ozeri, D. Veksler, V. Kleiner, and E. Hasman, “Spin-optical metamaterial route to spin-controlled photonics,” Science 340(6133), 724–726 (2013). [CrossRef] [PubMed]

20. X. Yin, Z. Ye, J. Rho, Y. Wang, and X. Zhang, “Photonic spin Hall effect at metasurfaces,” Science 339(6126), 1405–1407 (2013). [CrossRef] [PubMed]

21. M. V. Berry, “The adiabatic phase and Pancharatnam’s phase for polarized light,” J. Mod. Opt. 34(11), 1401–1407 (1987). [CrossRef]

22. D. Lin, P. Fan, E. Hasman, and M. L. Brongersma, “Dielectric gradient metasurface optical elements,” Science 345(6194), 298–302 (2014). [CrossRef] [PubMed]

23. L. Huang, X. Chen, H. Mühlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, T. Zentgraf, and S. Zhang, “Dispersionless phase discontinuities for controlling light propagation,” Nano Lett. 12(11), 5750–5755 (2012). [CrossRef] [PubMed]

24. X. Ling, X. Zhou, W. Shu, H. Luo, and S. Wen, “Realization of tunable photonic spin Hall effect by tailoring the Pancharatnam-berry phase,” Sci. Rep. 4, 5557 (2014). [CrossRef] [PubMed]

25. X. Ling, X. Zhou, X. Yi, W. Shu, Y. Liu, S. Chen, H. Luo, S. Wen, and D. Fan, “Giant photonic spin Hall effect in momentum space in a structured metamaterial with spatially varying birefringence,” Light Sci. Appl. 4(5), e290 (2015). [CrossRef]

26. E. Hasman, V. Kleiner, G. Biener, and A. Niv, “Polarization dependent focusing lens by use of quantized Pancharatnam–Berry phase diffractive optics,” Appl. Phys. Lett. 82(3), 328 (2003). [CrossRef]

27. X. Wang, Y. Cui, W. Sun, J. Ye, and Y. Zhang, “Terahertz polarization real-time imaging based on balanced electro-optic detection,” J. Opt. Soc. Am. A 27(11), 2387–2393 (2010). [CrossRef] [PubMed]

28. N. K. Grady, J. E. Heyes, D. R. Chowdhury, Y. Zeng, M. T. Reiten, A. K. Azad, A. J. Taylor, D. A. Dalvit, and H. T. Chen, “Terahertz metamaterials for linear polarization conversion and anomalous refraction,” Science 340(6138), 1304–1307 (2013). [CrossRef] [PubMed]

29. G. Zheng, H. Mühlenbernd, M. Kenney, G. Li, T. Zentgraf, and S. Zhang, “Metasurface holograms reaching 80% efficiency,” Nat. Nanotechnol. 10(4), 308–312 (2015). [CrossRef] [PubMed]

30. W. Luo, S. Xiao, Q. He, S. Sun, and L. Zhou, “Photonic spin Hall effect with nearly 100% efficiency,” Adv. Opt. Mater., in press (2015).

31. W. Chen, D. C. Abeysinghe, R. L. Nelson, and Q. Zhan, “Experimental confirmation of miniature spiral plasmonic lens as a circular polarization analyzer,” Nano Lett. 10(6), 2075–2079 (2010). [CrossRef] [PubMed]

32. D. R. Bobbitt, “Instrumentation for the measurement of circular dichroism: past, present and future developments,” in Analytical Applications of Circular Dichroism, N. Purdie and H.G.Brittain, ed. (Elsevier, 1994).

33. I. Mukerji and A. P. Williams, “UV resonance Raman and circular dichroism studies of a DNA duplex containing an A(3)T(3) tract: evidence for a premelting transition and three-centered H-bonds,” Biochemistry 41(1), 69–77 (2002). [CrossRef] [PubMed]

34. 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(1), 225–230 (2014). [CrossRef] [PubMed]

35. Y. Montelongo, J. O. Tenorio-Pearl, W. I. Milne, and T. D. Wilkinson, “Polarization switchable diffraction based on subwavelength plasmonic nanoantennas,” Nano Lett. 14(1), 294–298 (2014). [CrossRef] [PubMed]

Spin-selected focusing and imaging based on metasurface lens

Abstract

1. Introduction

2. Design and experimental setup

3. Results and discussions

4. Conclusions

Acknowledgments

References and links

Cited By

Figures (5)

Equations (2)

Optics Express