controlled surface plasmon holography - Wiley Online Library

Laser Photonics Rev., 1–9 (2016) / DOI 10.1002/lpor.201600212

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ORIGINAL PAPER

Abstract The ability of generating arbitrary surface plasmon (SP) profiles in a controllable manner is of particular interest in designing plasmonic imaging, lithography and forcing devices. During the past decades, holography has gained enormous interest and achievements in free-space three-dimensional displays. Here, by applying a two-dimensional version of holography, we experimentally demonstrate a generic method to control the SP profiles. Through controlling the orientation angles of two separated slits under circular polarization incidence, the amplitude and phase of the excited SPs can be freely manipulated, which allows direct generation of the desired SP profiles. A series of controllable SP holography schemes are theoretically and experimentally demonstrated, where the holographic SP profiles with high imaging quality can be dynamically modulated by varying the circular polarization handedness or orientation angle of linear polarization. The universality and simplicity of the proposed design strategies would offer promising opportunities for practical plasmonic applications.

Polarization-controlled surface plasmon holography Quan Xu1,2 , Xueqian Zhang1,2,∗ , Yuehong Xu1,2 , Chunmei Ouyang1,2 , Zhen Tian1,2 , Jianqiang Gu1,2 , Jensen Li3 , Shuang Zhang3 , Jiaguang Han1,2,∗ , and Weili Zhang1,2,4,∗

1. Introduction Surface plasmons (SPs) are a special form of electromagnetic waves confined and propagate at the metal/dielectric interface [1]. The most attractive feature of SPs is their capability of manipulating the electromagnetic fields on the subwavelength scale at a two-dimensional (2D) platform. Over the past few years, control over SPs by use of artificially structured surfaces (metasurfaces) has attracted a lot of attention [2–4], which opens up the possibility for many cutting-edge applications, such as subdiffractional lithography [5, 6], holography [7, 8], optical polarization and orbital angular momentum manipulation [9, 10], as well as SP propagation engineering [11]. Among these, a number of spin-controlled SP applications were also demonstrated, including SP metalenses [12,13], SP vortices [14,15], unidirectional launchers [16, 17], and SP wavefront engineering [18, 19], which are directly related to the spin Hall effect of light [20, 21]. However, the above works only focused on realizing simple SP profiles. In many applications, it is quite desirable to generate more complex and externally controllable SP profiles, which is promising in surface displays and tunable plasmonic force. The holography principle has emerged as a viable tool in designing novel plasmonic interfaces to excite either SP or

free-space beams with desirable field distributions [22]. Recently, in the free-space regime, metasurfaces that control the amplitude [23], phase [24–27], and polarization [28,29] of electromagnetic waves have shown intriguing ability to realize computer-generated holography [30], where the phase and amplitude profiles of the hologram interface were numerically calculated and subsequently coded into specific surface patterns [31–36]. Among those, phase-only holography is widely employed since the arbitrary phase distribution of the target image provides an additional degree of freedom to optimize the uniformity of the intensity of the hologram by using an iterative algorithm [33–36]. In plasmonics, however, SPs emitted from each pixel of the target SP profile are propagating at the same 2D platform [37–40]. Therefore, in order to ensure the clarity of the SP profile itself, its phase distribution cannot be arbitrary and should be designed coherently to reduce the undesired wave interference. As such, the above phase optimization is no longer applicable for SPs. Recently, polarization-controllable complex SP holography was demonstrated based on a geometric phase concept [41]. Though only a phase control hologram was applied, it is different from the free-space phaseonly holography where the required amplitude information was ignored. As a result, multiple rings of structures with proper distance were typically required so as to enhance the

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Center for Terahertz Waves, College of Precision Instrument and Optoelectronics Engineering, and the Key Laboratory of Optoelectronics Information and Technology (Ministry of Education), Tianjin University, Tianjin 300072, China 2 Cooperative Innovation Center of Terahertz Science, Chengdu 610054, China 3 School of Physics and Astronomy, University of Birmingham, Birmingham B15 2TT, UK 4 School of Electrical and Computer Engineering, Oklahoma State University, Stillwater, Oklahoma 74078, USA ∗ Corresponding authors: e-mail: [email protected]; [email protected]; [email protected] C 2016 by WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

LASER & PHOTONICS REVIEWS 2

Q. Xu et al.: Polarization-controlled surface plasmon holography

Figure 1 Schematic views of the basic hologram unit and the hologram ring, as well as the corresponding calculated results for amplitude and phase manipulation. (a) Schematic view of the slit-pair resonators used to deduce the SP field at point M. (b) Schematic view of a ringshaped hologram, the inward propagating SPs will rebuild the desired SP profiles. (c, d) Calculated normalized amplitude and phase distributions of the SPs excited by the slit-pair resonators at various θ 1 and θ 2 (here, LCP incidence was taken as an example).

contrast of the rebuilt target profiles. To make the SP hologram more straightforward and increase the imaging quality at the same time, it is very desirable to introduce the SP amplitude control simultaneously. Recently, it was reported that by properly designing the position and number of metal gratings or diffraction units, such simultaneous control of phase and amplitude were achieved, which allows generation of special holographic SP beams [42, 43]. However, more flexible controlling strategy is still lacking. In this paper, we present a detailed study on realizing simultaneous control of the phase and amplitude of the excited SPs by using slit-pair resonators. Then, we apply such a control strategy to directly generate complex SP holographic profiles. Taking advantages of the spin-dependent feature of the geometric phase, spin-switchable SP profiles are achieved. More interestingly, by specially designing the interference between the SPs excited by different circular polarizations, the proposed method also allows continuous control of the SP profiles using linear polarizations, including tuning the SP profiles from maximum intensity to off state, and gradually tuning two independent SP profiles from one to another. The simplicity and versatility of the proposed designing strategy would offer promising opportunities for realistic plasmonic applications.

demonstrated in [18] that if such slit-pair resonators are separated with a distance S = λSP /2 and arranged perpendicular to each other, under circular polarization normal incidence, the phase of the excited SPs can be tuned in the whole 2π range with nearly constant amplitude (λsp is the wavelength of the designated SPs). Here, we take a more general derivation, where the excitation condition and distance S are conserved, while the relation of the orientation angles θ 1 and θ 2 are no longer fixed (θ 1 and θ 2 represent the angles of E1 and E2 with respect to the x-axis, respectively). In this case, the SP field at point M (|l| >> S/2) can be calculated as (see Supplementary Note 1)

2. Design of the basic holography unit

2 k02 − kSP and k0 being the vacuum wave number. According to Eq. (1), it is clear that the phase of the excited SPs can be freely controlled by the summation of angles θ 1 and θ 2 with the sign determined by the incident spin

Figure 1a illustrates the proposed basic SP excitation unit structure that contains a pair of slit resonators. It has been C 2016 by WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

√ EM = i 2 2Csign (l) eikSP |l| eiσ (θ1 +θ2 +π /2) |l|, × sin(θ1 − θ2 )aˆ

(1)

where C is the conversion efficiency of the excited SPs √ from the incident circularly polarized light Ein = 2/2(1, σ i) with σ ∈ {+, −} representing the left-handed circular polarization (LCP) and righthanded circular polarization (RCP), respectively; kSP = 2π/λSP is the SP wave number; aˆ is a unit vector given by −[−ik z , 0, kSP sign(l)]/ |k z |2 + |kSP |2 with k z =

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ORIGINAL PAPER Laser Photonics Rev. (2016)

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Figure 2 SP hologram designing scheme and holographic results of an exemplary single-point SP profile. (a–c) Schematic views of the SP hologram designing scheme for both hologram generating (a,b) and target SP profile rebuilding (b,c). (d–f) Calculated, simulated and experimental SP intensity profiles (|Ez |2 ) rebuilt under LCP incidence, respectively. The inset arrow at the bottom-left corner of each rebuilding figure represents the corresponding incident polarization state, similarly hereinafter. The hologram ring contains 80 slitpair resonators, and the ring radius is 4.5λsp .

direction, while the amplitude follows a sinusoidal relation to the difference between the orientation angles (θ1 − θ2 ). Obviously, arbitrary excited SP amplitude and phase can be simultaneously realized by properly designing the orientation angles θ 1 and θ 2 . Figures 1c and d plot the relation of the normalized SP amplitude and phase distribution as a function of θ 1 and θ 2 under LCP incidence, respectively. It can be seen that there are actually more than one group of angles that could satisfy such a manipulation. Similar results could also be obtained under RCP incidence.

3. Designing scheme of the proposed SP holography In simplicity, the basic principle of holography is the reversibility of the light path. To achieve better SP holography quality, we use the above slit-pair resonators to form a hologram ring to record the scattered field from the enclosed target SP profiles as much as possible, as illustrated in Fig. 1b. Actually, an arbitrary close-loop-shaped hologram that contains the target SP profile can work very well, since it records all the scattered field information from the inside. Before determining the orientation angles of each slit resonator, it is necessary to find an effective way to generate a high-quality target SP profile first. Considering the target profile is consisted of a series of SP point sources Sn = An eiγn inside the hologram ring, as shown in Fig. 2a, where An and γ n represent the amplitude and phase of the nth point source, respectively. Because of the 2D feature, the SPs excited by such sources will ripple around the whole imaging range and interfere with each other. Therefore, in order to improve the imaging quality, such interferences should be optimized by organizing the point sources with a proper phase gradient. Here, we simply apply a propagating phase gradient along the SP profiles in the SP holography design. Meanwhile, if the density of the point sources is large enough (i.e. the distance between the neighboring point sources is smaller than λsp /8), the target SP profile becomes continuous propagating profile rather than www.lpr-journal.org

a discontinuous standing-wave profile (see Supplementary Note 2), which would in turn significantly improve the rebuilt results. Next, the complex scattering SP field from the target SP profiles at each slit-pair position can be calculated by using the 2D Huygens–Fresnel principle [44, 45]: Hm = An ei(γn +kSP |rnm |) / | rnm |, where rnm is the vector from the n

nth point source of the target profile to the center of the mth slit-pair resonators, as illustrated in Fig. 2a. Thus, according to Eq. (1) and taking the LCP incidence as an instance, the phase and amplitude information of the mth hologram unit can be represented by a slit-pair with angles

θ1 m = arg (Hm ) + asin (|Hm | / max |H |) 2 − αm /2 − π/2 + ϕ0 , θ2

m

= θ1

m

− asin (|Hm | / max |H |) ,

(2)

where θ 1_m and θ 2_m are the orientation angles of the outer and inner slit of the mth slit-pair, respectively; α m is an extra phase compensation that arisen from the geometric phase, which is equal to the location angle of the mth slit-pair (see Supplementary Note 3), as illustrated in Fig. 2b; ϕ 0 is a phase constant that represents the initial phase of all the slits. Here, we choose ϕ0 = 0 for all the designs. Once the orientation angles of all the slits are arranged according to Eq. (2), the target SP profile will be rebuilt. To theoretically calculate the rebuilt result, we can consider each slit resonator as an inplane SP dipole source and superpose all the emitted SP fields from these sources at every position in the plane [16, 44]. As shown in Fig. 2c, the superposed SP field at an arbitrary point l under Ein incidence can be calculated as:

| rml |, (3) C Ein · tˆm eik S P |rml | cos θml El = m

where tˆm is the unit vector perpendicular to the mth slit resonator; rml is the vector from the mth slit resonator to the point l; θ ml is the angle between the vectors rml and tˆm . C 2016 by WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim



Figure 3 Holography results of squareshaped and circle-shaped nonuniform SP profiles. (a–c) Calculated, simulated and experimental square-shaped SP intensity profiles (|Ez |2 ) that rebuilt under LCP incidence, respectively. The hologram is constituted by 4 hologram rings. Each hologram ring contains 120 slitpair resonators. The radius of the innermost hologram ring is 7λsp , and the radius difference between neighboring hologram rings is 5λsp /6. (d–f) Calculated, simulated and measured nonuniform circle-shaped SP intensity profiles (|Ez |2 ) that rebuilt under LCP incidence, respectively. The hologram is constituted by 4 hologram rings. Each hologram ring contains 80 slit-pair resonators. The radius of the innermost ring is 4λsp , and the radius difference between neighboring hologram rings is 5λsp /6. (g–i) Calculated, simulated and measured normalized nonuniform circle-shaped SP field profiles (real-part Ez ) that rebuilt under LCP incidence, respectively.

In order to elaborate the above designing and rebuilding scheme, we take a single-point SP holography as an example. Figure 2b illustrates the designed hologram ring using the slit-pair resonator according to the above 2D Huygens– Fresnel principle and Eq. (2), where the point SP source is supposed at the ring center. Figure 2d illustrates the calculated result using the hologram ring according to Eq. (3), where a clear point SP profile is rebuilt as expected. Furthermore, to demonstrate our approach, we also carry out numerical simulations and experiments in the terahertz regime. The simulations were carried out using a commercial software package CST Microwave Studio, and the experiments were implemented by use of a near-field scanning terahertz microscope system (see Supplementary Note 4). The hologram ring is made from 200-nm thick aluminum structures patterned on a 2-mm thick quartz substrate. The length and width of the slit are 120 μm and 10 μm, respectively. The resonance frequency of the slit is 0.75 THz, at which the intensity of the excited SPs is the strongest, corresponding to a SP wavelength of λsp = 400 μm. In order to enhance the confinement of the SPs at the metal surface, the whole structures were spin coated with a 20-μm thick dielectric layer. Figures 2e and f illustrate the simulated and near-field measured results of the single-point SP holography, both of which are well consistent with the theoretical result, proving the validity of our approach. In contrast to a single-point SP profile, where only the phase control is sufficient, for rebuilding complex SP profiles, introducing amplitude control would greatly simplify the SP holography and improve the holography performance. Such a holography approach could rebuild the desired SP profile very well with only a single hologram

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ring, which is in strong contrast to the phase-only SP holography where the complex SP profiles can hardly be rebuilt by a single hologram ring (see Supplementary Note 5). However, in the following design, multiple hologram rings are also applied, which will help increase the overall intensity of the rebuilt SP profiles and meanwhile eliminate the conjugate SP profile. It should be noted that each single hologram ring here can rebuild the target SP profiles individually under certain polarization incidence. All the hologram rings are designed with a same initial phase ϕ 0 to ensure the rebuilt profiles constructively interfere with each other. Figures 3a–c show the calculated, simulated and experimental results of a SP holography that was designed to rebuild a square-shaped SP intensity profiles under LCP incidence, respectively. A clear square-shaped SP profile can be seen that further confirms the proposed holography strategy very well. Although there are interference fringes at the corners, the intensity contrast between the rebuilt SP profiles and the dark background are quite obvious. The appearance of the fringes can be attributed to the fact that the SPs excited from each slit resonator to the final squareshaped SP profile would pass through the corners and interfere with each other. Figures 3d–f show the intensity results of rebuilding a circle-shaped nonuniform SP profile whose intensity distribution is described by Iδ = δ/2π , where δ represents the location angle, as illustrated in Fig. 3d. Meanwhile, the corresponding SP field profiles are also presented, as shown in Figs. 3g–i. The calculated, simulated and experimental results are again well consistent with each other, further indicating the validity of our approach and also the ability to generate gray-scale SP profiles.

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Figure 4 Spin-switchable SP holography. (a, c, e) Calculated, simulated and measured V-shaped SP intensity profiles (|Ez |2 ) that rebuilt under LCP incidence, respectively. (b, d, f) Calculated, simulated and measured N-shaped SP intensity profiles (|Ez |2 ) that rebuilt under RCP incidence, respectively. The hologram is constituted by 4 hologram rings. Each hologram ring contains 120 slit-pair resonators. The radius of the innermost hologram ring is 7λsp , and the radius difference between neighboring hologram rings is 5λsp /6.

4. Arbitrary spin-switchable SP holography The above designs are only for SP holography under certain incident spin states. In this section, we show that the proposed structure could also be applied in realizing spin-switchable SP holography. According to Eq. (1), for same set of hologram rings, when the incident spin direction changes, the excited SP field H σ would turn to its conjugate version −(H σ )∗ . Therefore, if a hologram ring is designed as H + = HA + (HB )∗ , the rebuilt SP profiles under LCP incidence would be a normal A profile and a conjugate B profile. In contrast, the rebuilt SP profiles would become a conjugate A profile and a normal B profile under RCP incidence H − = −(HA )∗ − HB . In this case, if the conjugate profiles are different from the normal profiles, the imaging quality will be greatly reduced due to the crosstalk. Thus, the conjugate profiles should be

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diminished in order to achieve spin-switchable SP holography. This can be done by carefully choosing the difference between the neighboring radius of the hologram rings rH (see the inset in Fig. 4a). We compared several results of holograms that consisted of 4 hologram rings with different

rH , and found that rH played a crucial role in diminishing the conjugate profiles and meanwhile had nearly no effect on the normal profiles (see Supplementary Note 6). Considering the overall holographic performance, here, we choose rH = 5λSP /6. Figure 4 illustrates the calculated, simulated and experimental results of a spin-switchable SP holography design for rebuilding the V- and N-shaped SP profiles. Under LCP incidence, a clear V-shaped profile was rebuilt, as shown in Figs. 4a, c and e. Under RCP incidence, a clear N-shaped profile was rebuilt, as shown in Figs. 4b, d and f. All these rebuilt profiles show high imaging quality, clear contrast




Figure 5 Linear polarization tunable SP holography. (a–i) Calculated, simulated and measured -shaped SP intensity profiles (|Ez |2 ) that rebuilt under 90°, 45° and 0° linear polarization incidences, respectively. (j–l) Ideal phase distribution, ideal amplitude distribution and 5-level matched amplitude distribution along the innermost hologram ring, respectively. Here, a 5-level matched amplitude distribution is selected. The hologram is constituted by 4 hologram rings. Each hologram ring contains 120 slit-pair resonators. The radius of the innermost hologram ring is 7λsp , and the radius difference between the neighboring hologram rings is 5λsp /6.

and less crosstalk, indicating the robustness of the proposed design strategy. Such a feature could offer promising opportunities for applications in doubling the data storage, since two sets of holograms are simultaneously stored in a same set of slit-pair resonators, meanwhile, the stored information can be independently read-out by different spins.

5. Tunable SP holography by linear polarization With the ability of generating spin-switchable SP holography, the proposed design could also be applied in realizing intensity-tunable SP holography by designing the interference between the SP profiles excited by LCP and RCP. This is particularly suitable for SP holography, since the LCP and RCP are degenerated into the same SP polarization which guarantees the possibility of full interference instead of changing to a new polarization state as that in the free-space case. Here, we applied such a feature in tuning the overall intensity of the rebuilt SP profiles from on to off by use of linear-polarization excitation. It is known that a linear polarization can be seen as a superposition of LCP and RCP and its polarization angle ξ (with respect to the x-axis) is determined by the phase difference β between LCP and RCP as ξ = β/2. If the hologram rings are designed as H = HA + (HA )∗ eiβ0 , it means that the rebuilt SP profiles excited by the LCP and RCP incidences are the same A profiles but with a different initial phase π − β 0 . C 2016 by WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

When the hologram rings are excited by linear polarization, the A profiles rebuilt by the RCP and LCP components will interfere with each other. In this case, by rotating the polarization angle ξ from (β0 − π )/2 to (β0 − π )/2 ± π/2, the interference could be gradually tuned from constructive to destructive. Figures 5a–i show the holography results of the above design with β 0 = 0 for rebuilding -shaped SP profile at 90°, 45° and 0° linear polarization incidences, respectively. The -shaped SP profiles can be clearly seen, and the intensity gradually decreases from maximum to the off state, further proving the versatile abilities of our approach. Such tunability is particularly attractive in designing SP force to manipulate the motion of nanoparticles, which can be trapped or released by the intensity tunable closed-loop SP profiles. Actually, the above linear polarization tunable holography design only needs to control the real part of the excited SP field since H = 2real(H ). In this case, the phase control is reduced to only 2 levels with π phase difference and the amplitude control become more important. Figure 5j illustrates the corresponding phase distribution along the innermost hologram ring, where only 0 and π were included. Figures 5k and l show the ideal and 5-level amplitude distribution, respectively, in which the 5-level amplitude could rebuild the ideal amplitude distribution very well. In order to clarify the uniqueness and necessity of the amplitude control in this SP holography design, the rebuilt results of 1-level (phase-only) and random amplitude holography design was investigated in Supplementary Note

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Figure 6 Linear polarization switchable SP holography. (a–i) Calculated, simulated and measured SP intensity profiles (|Ez |2 ) that rebuilt under 90°, 45° and 0° linear polarization incidences, respectively. The hologram is constituted by 4 hologram rings. Each hologram ring contains 120 slit-pair resonators. The radius of the innermost hologram ring is 7λsp , and the radius difference between the neighboring hologram rings is 5λsp /6.

7. Though the results also show similar tunablility, the imaging quality becomes worse. Such results indicate that the phase distribution ensures the linear polarization tunability, while the amplitude distribution ensures the imaging quality. On the other hand, such phenomena once more prove the importance of controlling the SP phase and amplitude simultaneously. Another freedom of this design strategy is that different linear polarization tunable SP profiles can be predesignated with an initial phase difference and simultaneously stored in the same set of hologram rings. Such a property can be used to generate linear polarization switchable SP holography by combining the designing schemes of the spin-switchable and linear polarization tunable SP holography. For instance, the hologram rings can be designed as H = HA + (HA )∗ + HB + (HB )∗ eiπ to rebuild A and B profiles under different linear polarization incidences. Due to the phase difference π , the rebuilt SP profiles would be tuned from A profile to coexistence of both A and B profiles, then to B profile as the polarization angle ξ rotates from 90° to 0°. Figure 6 illustrates the calculated, simulated and experimental results of a design for realizing

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switchable SP profiles between a -shaped profile and a V-shaped profile under 90°, 45° and 0° linear polarization incidences, respectively, where the results agree well with the prediction.

6. Conclusions We proposed a generic method to simultaneously manipulate the excitation phase and amplitude of the SPs using slit-pair resonators. Various controllable SP holograms were designed that exhibit enhanced imaging quality than that generated by the phase-only hologram. We show that the SP profiles can be freely controlled not only by the spin direction of circular polarization, but also linear polarization of different angles. By using the near-field scanning terahertz microscopy system, we directly mapped the field information of the rebuilt SP profiles, which verify the calculations and simulations very well. The present design strategy is general and can be extended to the infrared and visible regimes. Meanwhile, the functinalities C 2016 by WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim



we demonstrate here are very promising in future applications of surface display, data storage, polaization analysis and plasmonic force engineering.

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Supporting Information Additional supporting information may be found in the online version of this article at the publisher’s website. Acknowledgements. This work was supported by the National Key Basic Research Program of China (Grant No. 2014CB339800), the National Science Foundation of China (Grant Nos. 61138001, 61422509, 61605143, and 61420106006), the Program for Changjiang Scholars and Innovative Research Team in University (Grant No. IRT13033), the Major National Development Project of Scientific Instruments and Equipment (Grant No. 2011YQ150021), the Specialized Research Fund for the Doctoral Program of Higher Education (Grand No. 20110032120058), and the U.S. National Science Foundation (Grand No. ECCS-1232081). Received: 11 August 2016, Revised: 12 October 2016, Accepted: 16 November 2016 Published online: 13 December 2016 Key words: Surface plasmons, controllable holography, metasurface, terahertz, near-field.

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