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[email protected].ac.cn. Abstract: We present a direct-method solution toward the general problem of plasmonic wavefront manipulation and shaping to realize ...
Holographic plasmonic lenses for surface plasmons with complex wavefront profile Yu-Hui Chen,1 Mingqian Zhang,2 Lin Gan,1 Xiaoyu Wu,2 Lin Sun,2 Ju Liu,1 Jia Wang,2 and Zhi-Yuan Li1,* 2

1 Laboratory of Optical Physics, Institute of Physics, Chinese Academy of Sciences,Beijing 100190, China State Key Laboratory of Precision Measurement Technology and Instruments, Department of Precision Instruments, Tsinghua University, Beijing 100084, China * [email protected]

Abstract: We present a direct-method solution toward the general problem of plasmonic wavefront manipulation and shaping to realize pre-designated functionalities based on the surface-wave holography (SWH) method. We demonstrate theoretically and experimentally the design and fabrication of holographic plasmonic lenses over surface plasmons with complex wavefront profiles. We show that visible light at 632.8 nm transmitting through a high-aspect-ratio slit or a micro-rectangle hole in a silver film can be focused to a preset three-dimensional point spot in free space via appropriately manipulating the interaction of excited surface plasmons with the nanoscale groove pattern of the holographic lens. The experiment results of scanning near-field optical microscopy for measuring the threedimensional optical field distribution agree well both with designs and with numerical simulations, and this strongly supports the effectiveness and efficiency of the SWH method in the design of plasmonic devices that can fulfill manipulation and transformation of complicated-profile surface plasmons. ©2013 Optical Society of America OCIS codes: (090.1760) Computer holography; (220.4241) Nanostructure fabrication; (240.3990) Micro-optical devices; (240.6680) Surface plasmons; (240.6690) Surface waves.

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Received 20 Jun 2013; revised 8 Jul 2013; accepted 8 Jul 2013; published 15 Jul 2013 29 July 2013 | Vol. 21, No. 15 | DOI:10.1364/OE.21.017558 | OPTICS EXPRESS 17558

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1. Introduction Surface plasmon polaritons (SPPs) are propagating waves confined at the metal-dielectric interface [1–4]. Plasmonic nanostructures can manipulate the in-plane transport and scattering of SPPs in a controllable means. Thus they provide a promising route to construct ultracompact integrated micro/nano optical devices and systems [5,6]. In addition, plasmonic nanostructures can also be exploited to fulfill and model conventional optical transport control functionalities, but with a much smaller size scale. Patterning metallic surfaces to utilize the scattering of SPPs to realize conventional optical functionalities has attracted much attention in recent years [7–17]. The advantage is that these structured components have a subwavelength scale and the total structures can be fabricated in a small area on a flat metallic surface [18]. Therefore, plasmonic structures provide an ultracompact integration solution to the exploitation of micro-size and nano-size optical devices. For example, light collimators [7–13], plasmonic wave plates [14], lenses [9, 15, 16], and focusing [17] have been designed to manipulate light waves above the metallic surface in the Fresnel region. To fully realize device and system functionalities in the conventional optics, plasmonic devices must have the capability to address various complicated conditions and situations for both the input wave and the output wave. However, so far these plasmonic devices were designed with special skills, such as simulated annealing method, where complicated and time-consuming iteration algorithms and computations are requested to solve inverse electromagnetic problems [17] to obtain pre-designated devices and functionalities. Fairly speaking, these design methodologies are not universal enough to deal with very general systems and functionalities. Recently a novel methodology called surface wave holography (SWH) [19, 20] was proposed as a universal method to manipulate light waves scattered by appropriately patterned grooves milled on the surface of a metallic plate. For a given light wave transportation, SWH allows one to directly determine the geometric morphology of the grooves without the need of complicated and time-consuming iterative computation to obtain inverse-problem solutions in the conventional wisdoms. In this regard, SWH belongs to the direct-method category of device and system design. It has been shown that complex output

#192242 - $15.00 USD (C) 2013 OSA

Received 20 Jun 2013; revised 8 Jul 2013; accepted 8 Jul 2013; published 15 Jul 2013 29 July 2013 | Vol. 21, No. 15 | DOI:10.1364/OE.21.017558 | OPTICS EXPRESS 17559

functionalities of light transmitting through a subwavelength circular hole perforated in an opaque metal screen could be achieved through the SWH method. These functionalities include focusing light waves to an arbitrary point in three dimensions [19], collimating light waves to an arbitrary solid angle [19], and shaping light waves to an “L” pattern and an “O” pattern at a given plane in the Fresnel zone after the metallic screen [20]. As a counterpart of its powerful capability on shaping the output wavefront, we will show that the SWH method also has the equal powerful capability to allow the input plasmonic wave to take a complex profile pattern. The capability to manipulate both the input and output freedom of a plasmonic structure will significantly improve the design of plasmonic devices for application to modern optical devices and systems. In this paper, we specify the output functionality as the focusing of light to demonstrate our idea. We build a plasmonic lens that can focus light transmitting through an aperture of complicated geometric shape (other than a simple circular subwavelength aperture) in an opaque metal screen. It is well known for some years that milling grooves on the outgoing surface of a metal film can focus and collimate light emerging from a subwavelength hole [7– 13]. As an application, Capasso’s group integrated these structures on the output surface of semiconductor lasers and greatly reduced the light-emitting angular divergence [11,12]. The prospect of integrating plasmonic structures to shape the output beams of semiconductor lasers was therefore expected and demonstrated in Refs [11,12]. However, by now these researches are limited to apertures of the simplest shape, i.e., a narrow slit which was treated as a line, and a tiny hole which was treated as a point. For the case of a slit, the structure was usually taken as a two-dimensional (2D) case and only the light confinement along the short axis could be realized. In this paper, we show that the light from a slit, which is usually treated as a 2D structure, can also be confined in three dimensions. In other words, we can use a specially designed plasmonic lens to achieve three-dimensional (3D) focusing of light transmitting through such a slit on a spot. With this exotic lens placed at the exit plane of semiconductor lasers, the ordinary output slit beam can be shaped into a 3D focusing spot in the Fresnel zone. In our experimental demonstration, we build these plasmonic samples with their surface morphology of grooves perforated on a silver thin film directly determined according to the SWH method, and the 632.8 nm light emerging from a slit (11 × 0.12 μm2) or a micro rectangular hole (3 × 0.12 μm2) can be focused to a point located at 7 μm above the silver surface by these plasmonic lenses. We perform the finite-difference time-domain (FDTD) simulations and the scanning near-field optical microscopy (SNOM) experiments to evaluate the performance of these exotic plasmonic lenses. Good agreement between both numerical and experimental results with the pre-designated functionality strongly supports the feasibility of our idea and also further confirms the efficiency of the SWH method in shaping complicated input wavefront of surface plasmons into a given optical functionality. 2. Principal steps of SWH to design holographic plasmonic lens As has been discussed in Refs [19, 20], the SWH has borrowed the concept from the conventional optical holography and also involves the writing and reading processes of the object wave with the aid of the reference wave. But different from the conventional optical holography, the reference wave is now a confined plasmonic wave excited by illumination of the aperture and propagating outwards away from the aperture, instead of the usual plane wave. Figure 1 illustrates the three principal steps involved in the determination of the morphology of the perforated grooves for a complex input plasmonic wave emanating from the slit. As detailed in the literatures [19, 20], we need the information of the object wave and the reference wave to determine the plasmonic holographic structure. As what we are concerned is the 3D focusing effect at a preset position, i.e., 7 μm above the metallic surface, so the object wave is the outgoing propagating wave of a point source located at z = 7 μm. Notice that for 2D focusing functionality, the source would be a line source. The field pattern of this object wave at the metal surface is determined by rigorous FDTD calculations. In our FDTD simulation, an x-polarized (the coordinates is defined

#192242 - $15.00 USD (C) 2013 OSA

Received 20 Jun 2013; revised 8 Jul 2013; accepted 8 Jul 2013; published 15 Jul 2013 29 July 2013 | Vol. 21, No. 15 | DOI:10.1364/OE.21.017558 | OPTICS EXPRESS 17560

according to the fabricated sample, as shown in Section 3) point source is placed at z = 7 μm and the field distribution of the x component of the electric field at z = 0 μm (the outgoing surface of metal plate) is stored as U0, as shown in Fig. 1(a). Then, we extract the phase distribution of U0 and denoted it as φ0(x,y). As for the reference wave, we use a light beam to illuminate a hole of complex shape (now a slit or a line aperture) to get the complex-pattern surface waves. Some structure details of such a hole must have the subwavelength scale in order to efficiently excite the surface waves.

Fig. 1. The three steps of the surface-wave-holography method. (a) The wavefront of the objective wave U0. Place a point source with x polarization at (0, 0, 7) μm, calculate its propagation and store the field distribution at z = 0 μm as U0. (b) The wavefront of the reference wave Ur. An x-polarized incident light is shined to an aperture in a 240-nm-thick silver film. The field distribution immediately above the surface of the silver film is stored as Ur. (c) The designed sample. Grooves are fabricated at positions where the phase of U0Ur equals 2mπ.

In our FDTD simulation, we use a plane wave to shine the hole on a silver film and the field distribution (also the x component of electric field) immediately above the metallic surface is stored as the reference wave Ur, whose phase term is φr(x,y). In our numerical studies, the optical permittivity data of silver are taken from Ref [21]. and input into the FDTD simulations. According to the SWH method, we pattern grooves at positions where φ0(x,y) + φr(x,y)-2mπ = 0 (m is an integer). In practice we divided the sample plane into 20 × 20 nm2 pixels and used the criterion | φ0 + φr-2mπ