Low-pass rugate spatial filters for beam smoothing Zhaoming Luo a,b , Shuangchun Wen a, ⁎, Zhixiang Tang a , Hailu Luo a , Yuanjiang Xiang a , Dongmo Song a a Key Laboratory for Micro/Nano Optoelectronic Devices of Ministry of Education, School of Computer and Communication, Hunan University, Changsha 410082, China b College of Information and Telecommunications Engineering, Hunan Institute of Science and Technology, Yueyang 414004, China abstract article info Article history: Received 18 September 2009 Received in revised form 24 January 2010 Accepted 22 February 2010 Keywords: Rugate structure Spatial filter Beam smoothing A new application of rugate structures is proposed as low-pass spatial filters for beam smoothing. By using the transfer matrix method to analyze the spatial properties of the bandgap of rugate structures, the low- pass rugate spatial filters with both an almost ideal flat bandpass and a rather steep switching between pass- and stop-bands are designed. The angle-domain bandwidth of the spatial filters can be adjusted by changing the parameters of rugate structures for a given light frequency. The near-field simulations carried out by using the finite-difference time-domain technique confirm the possibility of an efficient light smoothing. © 2010 Elsevier B.V. All rights reserved. 1. Introduction Many applications in optics require the use of beams of a good spatial quality characterized by a smooth envelope and, respectively, a narrow spatial spectrum. The “clean” beams diverge less in propaga- tion, and they can be focused more tightly and robust against nonlinear filamentation than the “dirty” ones. In laser science, the beam smoothing is usually achieved by using low-pass spatial filters. A simple and conventional low-pass spatial filter is implemented by the use of a telescope consisting of two focusing lenses in a confocal arrangement and an appropriate pinhole in the focus plane [1–3]. The pinhole lets the passing of the low angle-domain components and the blocking of the undesired high ones (related to the “noisy” part of the beam); therefore the beam after passing through the low-pass spatial filter is smoothed. The system, although widely used, has several deficiencies as a relatively large size (at least four focal lengths long), high sensitivity to alignment (since the focused beam must past exactly through the middle of the pinhole) or the absence of efficient focusing lenses in infrared and in ultraviolet frequencies [3,4]. The spatial filters may also be applied to image enhancement and information processing in several regions of the electromagnetic spectrum, such as spatial spectrum analysis, matched filtering, radar data processing, aerial imaging industrial quality control, and biomedical applications. Currently, some slab spatial filters are performed for the purpose of overcoming the disadvantages of conventional spatial filters [3–12]. The possibilities for the realization of the low-pass, high-pass, and bandpass spatial filters have been demonstrated, whereas the slab filters based on the resonant grating systems [5,6], multilayer stacks combined with a prism [7] and two-dimensional photonic crystals [4,8–10] are only used as one-dimensional spatial filters. However, beam smoothing in fact demands two-dimensional spatial filtering. The spatial filters including metamaterials [3,11,12] can realize two- dimensional spatial filtering, but the fabrication of metamaterials is more difficult than that of multilayer stacks or photonic crystals since the structure unit of metamaterials is much less than the wavelength of light transmitting inside them. As a result, the way to realize two- dimensional spatial filtering for beam smoothing by using metama- terials is limited in practice. Thus it is necessary to do further work on the easily realizable spatial filters for beam smoothing. Rugate structures are optical thin film with graded refractive- index profiles. Compared with conventional multilayer stacks, they have some advantages including low internal stress, suppression of sidelobes, and continuous index matching for broadband antireflec- tion coatings [13–19]. Hence the performance of some devices such as frequency filters can be greatly improved, and spatial and spatial– frequency filtering using one-dimensional graded-index lattices with defects is proposed [20]. In this paper, we utilize the the spatial properties of the bandgap of rugate structures to design the low-pass spatial filters with both an almost ideal flat bandpass and a rather steep switching between pass- and stop-bands. The effects caused by the spatial filters on two-dimensional beam smoothing are demon- strated by using the finite-difference time-domain simulations. 2. Structure model and numerical simulation In order to obtain a strongly pronounced frequency property of very smooth high transmittance regions on both sides of the stop- band, we consider the 51-layer Gaussian half-apodized rugate Optics Communications 283 (2010) 2665–2668 ⁎ Corresponding author. Fax: + 86 731 8823474. E-mail address: scwen@vip.sina.com (S. Wen). 0030-4018/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2010.02.047 Contents lists available at ScienceDirect Optics Communications journal homepage: www.elsevier.com/locate/optcom