RAPID COMMUNICATIONS PHYSICAL REVIEW B 89, 201415(R) (2014) Role of quasicylindrical waves and surface plasmon polaritons on beam shaping with resonant nanogratings in the infrared C. H. Gan, 1 J. R. Pugh, 2 M. J. Cryan, 2 J. G. Rarity, 2 and G. R. Nash 1 1 College of Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter EX4 4QF, United Kingdom 2 Department of Electrical and Electronic Engineering, University of Bristol, Bristol BS8 1UB, United Kingdom (Received 2 April 2014; published 30 May 2014) The role of quasicylindrical waves and surface plasmon polaritons in beam shaping with resonant nanogratings is investigated. It is shown that the field on the grating surface can be strongly influenced by plasmons and quasicylindrical waves in the infrared. A method that combines far-field measurements with the fast Fourier transform to map the field amplitude at the grating surface is demonstrated. For samples with a small degree of geometric asymmetry, it is shown that the imaginary part of the transform (with null zeroth-order component) can better map the amplitude of the resonant surface waves than the full complex-valued transform. Our results will impact the study, design, and footprint of resonant nanogratings. DOI: 10.1103/PhysRevB.89.201415 PACS number(s): 42.25.Fx, 42.30.Va, 42.79.Dj, 68.47.De Advances in nanofabrication and optical near-field mea- surement techniques have triggered extensive studies of light-matter interactions on patterned nanostructures for ma- nipulating the diffraction of electromagnetic fields at metallic surfaces [1–6]. In particular, surface waves supported on metallic nanogratings give rise to numerous exotic optical phe- nomena such as the well-known Wood’s anomalies, extraor- dinary optical transmission (EOT), and beam shaping/steering of light radiated from subwavelength apertures [5–9]. At optical frequencies, the field scattered on metallic surfaces by subwavelength indentations is composed mainly of surface plasmon polaritons (SPPs) and a residual “direct contribution” now widely referred to as quasicylindrical waves (QCWs) [2–4,9–11]. For intermediate infrared (IR) wavelengths (0.8  λ  5 μm), the scattered SPP and QCW amplitudes in nanostructures are comparable [2], and it can be challenging to distinguish between their contributions. Recently, it has been shown experimentally that the QCW is responsible for half the total transmission in EOT achieved through hole arrays illuminated with near-IR light [9], highlighting the important role that QCWs can play in metallic nanogratings. Additionally, QCW properties such as the cross-conversion with the SPP [12], its relatively weak degree of spatial coherence [13], and the existence of a transient near-zone regime where its effective wavelength varies with propagation [14], have been revealed in previous investigations. In this paper, we investigate theoretically and experimentally the contribution of QCWs and SPPs to beam shaping in the infrared using resonant nanogratings, and show that beam shaping could be achieved with QCWs alone. Figure 1(a) shows beam shaping of light radiated from a narrow slit (width a) perforated in an optically thick metal plate (thickness t ). We focus on the transverse-magnetic (TM) polarization, for which surface waves can be resonantly excited by the nanogrooves when the grating equation k 0 sin θ = 2mπ/ − k s is satisfied [15], with k 0 = 2π/λ, θ the angle of the diffracted beam, m an integer,  the period of the grating, and k s the wave number of the surface wave. Without the grooves, the far-field radiation pattern I (0) resembles a broad lobe. Throughout this article, all field quantities pertaining to the case of the isolated slit are superscripted with (0). With suitably spaced nanogrooves (width w and depth h) around the slit, surface waves emerging from the slit (black thick arrows) are reflected to form standing waves that decay in amplitude along the metal surface (σ plane), and constructive interference between the scattered fields produce a directional beam I . We begin by addressing the questions: (i) Can beam shaping be achieved with QCWs alone, and (ii) is it the QCW or the SPP that contributes dominantly to the observed beaming in the IR? To answer the first question, we analyze a resonant grating structure where the SPP field is dominant and another that supports only the QCW. Such a scenario can be achieved with gold and tungsten films in the visible spectrum. At λ = 0.6 μm, SPPs can be excited efficiently on the gold film. However, the tungsten film (n W = 3.57 + i 2.86), which behaves as a strongly absorbing dielectric, only supports QCWs [11]. For all simulations, the refractive index is taken from the data of Palik [16], the number of grooves (if present) on each side of the slit is taken to be N = 10, the incident illumination is taken to be a plane wave with unity (modulus) Poynting vector, the thickness t is taken to be 1 μm unless otherwise specified, and the structures are simulated using a Green Tensor formalism [17]. The amplitude of the total magnetic field H along the σ plane of the nanograting (dashed curves), and the amplitude of the magnetic field components associated with the QCW (H (0) cw ) and SPP (H (0) sp ) scattered by the isolated slit (solid curves), are shown for the gold and tungsten film in Figs. 1(b) and 1(c). Clearly, standing waves with decaying amplitudes are sustained along the σ plane in both cases. However, their behavior differs in several aspects. For the gold film, |H | falls rapidly below |H (0) sp | after the first couple of grooves. Whereas for the tungsten film, |H | falls below |H (0) cw | only after several wavelengths in the vicinity of the fourth groove. The SPP is more strongly trapped due to its well-defined wave vector, in contrast to the mixture of wave vectors [4,14] that constitute the QCW. The lower amplitude of H compared to that of H (0) sp (H (0) cw ) indicates that part of the energy of the SPP (QCW) that emerges from the slit are trapped within the nanogrooves. The dominance of the SPP for the gold film can also be inferred from the steplike decay of |H | between the grooves, which is typical of the piecewise-constant SPP excitation strength along 1098-0121/2014/89(20)/201415(4) 201415-1 ©2014 American Physical Society