DESIGN OF A META-SCREEN FOR NEAR-ZONE FIELD FOCALIZATION AT OPTICAL FREQUENCIES Luca Scorrano, Filiberto Bilotti, and Lucio Vegni Department of Applied Electronics, University Roma Tre, via della Vasca Navale, 84 – 00146, Rome, Italy; Corresponding author: lscorrano@uniroma3.it Received 20 May 2009 ABSTRACT: In this letter, we propose the design of a nano-circuit reactive artificial screen for the synthesis of a given field pattern with sub-wavelength features at visible frequencies. The meta-screen consists of a discrete set of dielectric cells, behaving as lumped reactive ele- ments. The cells have been designed according to the recently proposed new concept of metactronics. The spatial distribution of the cells, and the inter-element electrically small spacing enables the focalization of a sub-wavelength spot beyond the diffraction limit at a prescribed focal distance. The design is supported by full-wave simulations, showing the actual focusing properties of the artificial screen proposed. © 2009 Wiley Periodicals, Inc. Microwave Opt Technol Lett 51: 2718 –2721, 2009; Published online in Wiley InterScience (www.interscience.wiley. com). DOI 10.1002/mop.24719 Key words: near-field pattern synthesis; nanocircuit; optical frequen- cies; metamaterials 1. INTRODUCTION The interest of the scientific community in artificial surfaces with an engineered electromagnetic response (meta-surfaces) has re- cently arisen, because of the successful experimental demonstra- tions at microwave frequencies of near field focusing plates [1, 2]. This kind of surfaces is capable of modifying the phase front of an impinging wave and reconstructing a desired near-field sub-wave- length pattern at a given distance. In the present work, the new metactronic-based nano-circuit concept presented in Refs. [3, 4] is applied to the design of a purely reactive surface enabling a near-field pattern synthesis in the visible. In particular, the final goal is to focus a sub-wavelength optical spot on a given reference plane, placed electrically close to the screen. Even though sub-wavelength focusing at optical frequencies has already been demonstrated through the use of Fresnel Zone plates with metallic coatings [5], what we propose here is a different design, based on the patterning of an opaque surface with a discrete set of dielectric cells, to create an inhomogeneous spatial distribution of the electric permittivity of the screen. In addition, the proposed approach suggests the possibility to achieve a sub- wavelength desired pattern at arbitrary distances. This more gen- eral result can be achieved in principle through the recent advance- ments in metamaterial technology, allowing the fabrication of extremely miniaturized cells exhibiting both high values of reac- tance and a tunable active behavior. The results of the full wave simulations here presented have been performed through the commercial software CST Studio Suite 2009, based on finite integration technique [6]. 2. REVIEW OF THE GENERAL FORMULATION AND OF PREVIOUSLY PROPOSED SETUPS According to Refs. [1, 2], given a desired field pattern and a source, it is possible to design a planar screen (i.e., placed in z = 0, see Fig. 1), whose surface impedance is a function of the spatial coordinates in the form  x,y, capable of focusing such pattern at a fixed distance z = d (typically d  ], as it will be clearly explained in the following). The interaction between the incident electric field E inc  x,y and the surface impedance distribution  x,y induces on the screen an electric current density that will produce the desired field distribution at the focal length z = d: J s  x , y  = z ˆ  E tot  x,y  x,y (1) where E tot  x,y is the total electric field on the screen, including the contributions of both the incident field and the field induced by J s  x,y. As already pointed out in Refs. [1, 2], a discrete set of sampled values of the surface impedance at given points on the screen may be derived from the solution of a second-kind Fred- holm integral equation, written on the plane z = 0 and having as unknown the surface impedance distribution of the screen [1, 2]. It is, then, found out that, if the focusing plane is electrically close to the screen and the cell separation is well below the operating wavelength, the real part of the impedance can be neglected in calculation. This enables the synthesis of the screen only relying on the imaginary part of  x,y, thus extremely simplifying its design. Moreover, under the previous assumptions, the imaginary part of  x,y results purely capacitive, allowing the use of a single kind of reactive lumped element. It is, then, possible to synthesize the spatial-dependent surface impedance of the screen if the incident field is known and once the desired field pattern at a certain plane along z is given. Even if the numerical determination of  x,y is a straightfor- ward task, the actual implementation is not trivial. The reactive impedance of the surface obtained from the numerical solution of the integral equation is, in fact, a continuous function of the spatial coordinates x and y. When dealing with a practical implementa- Figure 1 Layout of the planar screen characterized by a surface imped- ance distribution  x,y. In the present analysis, it is assumed to lie on the x-y plane in case of a impinging TE(z)-polarized field. [Color figure can be viewed in the online issue, which is available at www.interscience.wiley. com] 2718 MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 51, No. 11, November 2009 DOI 10.1002/mop