Optik 124 (2013) 2713–2715 Contents lists available at SciVerse ScienceDirect Optik jou rn al homepage: www.elsevier.de/ijleo Tunable one-dimensional photonic crystals based on magnetic fluids Guojun Yu, Shengli Pu ∗ , Xiang Wang, Hongzhu Ji College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China a r t i c l e i n f o Article history: Received 21 April 2012 Accepted 3 August 2012 Keywords: Magnetic fluids Photonic crystals Tunable a b s t r a c t One-dimensional tunable photonic crystals based on MnFe 2 O 4 magnetic fluids are investigated theoret- ically. The band structures of the photonic crystals are calculated. Simulation results indicate that the mid frequencies of the first, second and third band gaps can be tuned by the external magnetic field. The widths of the first and second band gaps decrease with the external magnetic field strength gradually, but those of the third band gaps increase with the external magnetic field strength. © 2012 Elsevier GmbH. All rights reserved. 1. Introduction Photonic crystals (PCs), which are also known as photonic band gap materials, are attractive optical materials for confining and controlling the propagation of electromagnetic waves within the specific directions [1–4]. The pioneering ideas of PCs were firstly put forward by Yablonovitch and John in 1987 [5,6]. In the past decades, PCs have attracted a great deal of attention in both the- oretical and experimental side due to their potential applications. Comparing with two- or three-dimensional PCs, one-dimensional PCs (1D-PCs) are sometimes desirable because of their easy design, low-cost fabrication and high-yield production. Therefore, much effort has been put into exploring 1D-PCs since the invention of PCs. The feasibility of developing photonic devices such as resonator [7], optical reflectors [8] and wavelength demultiplexer [9] utiliz- ing 1D-PCs has been demonstrated. Although the significance and usefulness of 1D-PCs are clear, most 1D-PCs lack the on-line and real-time tunability, which may limit their applications. In recent years, there are great efforts to obtain tunable forbidden bands and then suitable forbidden bands can be achieved. The means for realizing tunable forbidden bands are generally summarized into two categories. The first one is based on changing concentra- tions or ingredients of the constitutive materials of the PCs [10,11]. The second one is based on controlling the refractive indices of the materials with external fields, such as electric [12], magnetic [13], thermal [14,15] and optical fields [7,16]. Apparently, the lat- ter precedes the former one due to its more practical and dexterous tunability. Magnetic fluids are particular magnetic functional materials, which are colloidal suspensions of magnetic nanoparticles [17] and ∗ Corresponding author. Tel.: +86 21 65666454; fax: +86 21 65667144. E-mail addresses: shenglipu@gmail.com, shlpu@usst.edu.cn (S. Pu). widely applied to engineering and technology areas. They have become increasingly important in magneto-optics because of their unique nature and latent applications [18–21]. When a magnetic field is applied to the magnetic fluids, the magnetic nanoparticles will self-assemble into ordered columns/chains structure within the magnetic fluids [22,23]. And then the refractive indices of mag- netic fluids are altered by the magnetic field. So, magnetic fluids may be the candidate materials for realizing the band-gap-tunable PCs. To the best of our knowledge, all the present work about mag- netic fluids PCs are based on self-assembled periodic structures. The requirements are usually very rigorous to obtain these structures. So it is difficult to form the periodic structures with high degree of order and the corresponding PCs effect will be weakened. To overcome this, the model of magnetic fluids PCs based on the solid substrate (or referred as solid-fluid PCs) is proposed. The period of this kind of magnetic fluids PCs is fixed by the substrate. Their for- bidden bands can be tuned by externally magnetic fields, which are based on the magnetic-field-dependent refractive indices of mag- netic fluids. To exemplify this model, we theoretically calculate the band structures, viz. dispersion relationship of the PCs. 2. Model and methods Under externally magnetic fields, the magnetic nanoparticles will self-assemble into ordered columns or chains structure along the field direction within the magnetic fluids. The dielectric con- stant of the magnetic fluids (liquid phase) ε liq will be changed by the externally magnetic fields, which is given by [24] ε liq - ε h ˛ε liq + (3 - ˛)ε h = P ε p - ε h ε p + 2ε h (1) where ε h and ε p are the dielectric constant of the carrier liquid (ε h = 1.77 for water) and the magnetic nanoparticles (ε p = 13.9876 for MnFe 2 O 4 ), respectively. P is the volume fraction of the magnetic 0030-4026/$ – see front matter © 2012 Elsevier GmbH. All rights reserved. http://dx.doi.org/10.1016/j.ijleo.2012.08.086