Towards focusing using photonic crystal flat lens N. FABRE * , S. FASQUEL, C. LEGRAND, X. MÉLIQUE, M. MULLER, M. FRANÇOIS, O. VANBÉSIEN, and D. LIPPENS Institut d’Electronique de Microélectronique et de Nanotechnologie, UMR CNRS 8520 Université de Lille 1, Avenue Poincaré, BP 60069, 59652 Villeneuve d’Ascq Cedex, France We report on the numerical simulation and fabrication of a two-dimensional flat lens based on negative refraction in photonic crystals. The slab acting as a lens is made of an hole array (operating at the wavelength of 1.5 μm) etched in a InP/InGaAsP/InP semiconductor layer. We first study the key issues for the achievement of a negative refractive index taking advantage of folding of dispersion branches with main emphasis in dispersion properties rather than the opening of forbid- den gaps. The diffraction and refraction regimes are analysed according to the comparison of the wave-vector with respect to the relevant dimensions of the hole array. In the second stage, we illustrate technological challenges in terms of e-beam li- thography on a sub-micron scale and deep reactive ion etching for an indium phosphide based technology. Keywords: negative refraction, optical wavelengths, photonic crystals fabrication. 1. Introduction Photonic crystals have received a tremendous interest [1] with the prospect to use them to confine light or more gen- erally electromagnetic waves notably in 1.3–1.5 μm win- dow of telecommunication systems. It is well known that the periodical arrangement of dielectric inclusions, notably of dielectric rods or hole array opens forbidden gaps in Brillouin zone (BZ). Notably, high quality factor cavities and planar waveguides have been thus fabricated using de- fected arrays paving the way of compact nanophotonics [2]. Recently, a number of studies have also addressed the transmission properties of photonic crystals whose electro- magnetic properties can be tailored according to a proper choice of geometrical parameters and dielectric constants [3]. This includes ultra refraction, channelling effect, and negative refraction [4–5]. In this paper, we address the latter issue with the goal to fabricate a flat focusing lens. Such a lens was primarily proposed by Veselago in 1968 [6] on the basis of the as- sumption of a negative refraction index material (NRIM) which composes the lens. Also recently, Pendry showed that NRIM allows the amplification of evanescent waves within the lens with the prospect to image a point source below the diffraction limit [7–8]. Basically, two routes can be followed in order to fabricate artificial NRIM’s, metallic and dielectric, respectively. For the former, the term metamaterial or double negative media is often used. For the latter, this corresponds mainly to the use of photonic crystal even if high-k dielectrics have been proposed for negative permeability materials [9]. For dielectric struc- tures, special care has to be paid to the recognition of nega- tive refraction effect. In fact, diffraction effects can modify the direction of transmitted wave at an interface between the PC and embedding medium with the appearance of a negative refraction. In other words, the angle of transmitted wave can be on the same half plane than the angle of inci- dence one due to diffraction and not to a real negative re- fraction. One criterion which can be used in order to guar- antee that a true refraction is observed is the insensitivity of the corresponding refractive index to the angle of incident wave according to Snell-Descartes law. In BZ, this means that equal-energy plots are isotropic. It will be shown that this condition is met close to the centre of BZ namely at the vicinity of G point. In addition, for the ground dispersion branch, the curva- ture is such that group and phase velocities have the same sign. The propagation is forward and the refractive index is positive. In contrast, in the second band, the curvature is re- verse. It is thus possible to envisage the achievement of a negative refractive index with the concomitant effect of backward propagation in such media. Because of the rever- sal of phase velocity forming an indirect triplet with E (electric field) and H (magnetic field), NRIM’s are also termed left handed materials (LHM). Several studies have already addressed theoretically and experimentally negative refraction in a flat lens. Nota- bly by taking advantage of the invariance of electromag- netic concepts as a function of frequencies, scaled models operating at microwave frequencies were assessed [10–11] which demonstrate the possibility of focusing electro-ma- gnetic waves. In optics, and more particularly at wave- lengths around 1.5 μm, only a few experimental works can be found in the literature owing mainly to the difficulty of Opto-Electron. Rev., 14, no. 3, 2006 N. Fabre OPTO-ELECTRONICS REVIEW 14(3), 225–232 DOI: 10.2478/s11772-006-0030-0 * e-mail: Nathalie.Fabre@iem.univ-lille1.fr Unauthenticated Download Date | 7/28/18 12:42 AM