Please cite this article in press as: H. Kaviani, A. Asgari, Investigation of self-focusing effects in wurtzite InGaN/GaN quantum dots, Optik - Int. J. Light Electron Opt. (2012), doi:10.1016/j.ijleo.2012.01.012 ARTICLE IN PRESS G Model IJLEO-52105; No. of Pages 6 Optik xxx (2012) xxx–xxx Contents lists available at SciVerse ScienceDirect Optik jo ur n al homepage: www.elsevier.de/ijleo Investigation of self-focusing effects in wurtzite InGaN/GaN quantum dots H. Kaviani a , A. Asgari a,b,∗ a Research Institute for Applied Physics, University of Tabriz, Tabriz 51665-163, Iran b School of Electrical, Electronic and Computer Engineering, The University of Western Australia, Crawley, WA 6009, Australia a r t i c l e i n f o Article history: Received 5 September 2011 Accepted 11 January 2012 Keywords: Nonlinear optic InGaN QDs Self-focusing effects a b s t r a c t The third-order nonlinear optical properties in wurtzite InGaN/GaN pyramid and truncated-pyramid quantum dots are studied, and the oscillator strength, third-order nonlinear optical susceptibility and self-focusing effects are analyzed theoretically taken into account the strong built-in electric field effect due to the piezoelectric and spontaneous polarization in nitride materials. The numerical results clearly show that the quantum dot (QD) size of InGaN/GaN have a significant influence on the nonlinear optical properties of wurtzite InGaN/GaN quantum dots. Furthermore, the self-focusing effect increases with decrease in size of QDs. © 2012 Elsevier GmbH. All rights reserved. 1. Introduction In recent years, III-nitride alloys have been the wide research subjects due to practical applications in the field of optoelectronic devices, high thermal conductivity, high electron-saturated drift velocity and small dielectric constant [1,2]. These materials have direct wide band gaps from 0.7 eV to 3.42 eV at room temperature, therefore, they are so useful in blue light emitting diodes industrial [3–5]. III–V nitride materials are founded in two different type struc- tures: (i) wurtzite (WZ) [6] and, (ii) zinc-blend (ZB) [7]. In wurtzite structures, electronic states and optical properties are highly affected by the built-in electric field due to spontaneous (P s ) and piezoelectric (P z ) polarizations. The magnitude of the built-in elec- tric field is estimated to be in the order of MV/cm. These properties do not exist in ZB structures, because they have high crystal sym- metry [8–10]. Among III-nitride quantum dots (QDs) are already acknowledged as quantum nanostructures with high potentials in optoelectronic field; for instance, in light emitting diodes (LEDs), laser diodes (LDs), optical memories and single electron transistors [11–13]. In this nanometer scale semiconductors, the charge carriers (electrons and holes) are confined in all three dimensions [14,15] and due to the modification in the density of states, these quantum nanostructures are expected to exhibit enhanced optical non- linearities and enhanced electro-optic effects. Indeed many of these optical nonlinear properties associated with intersubband transitions those due to large dipole transition and very large oscil- ∗ Corresponding author at: Research Institute for Applied Physics, University of Tabriz, Tabriz 51665-163, Iran. Tel.: +98 411 339 3005; fax: +98 411 334 7050. E-mail address: asgari@tabrizu.ac.ir (A. Asgari). lator strength, these optical intraband nonlinear are large too. As the intrasubband dipole length extend over the QDs which are in nanometer ranges [16,17]. Compare to bulk semiconductors, QD semiconductors have larger third-order nonlinear susceptibility [18,19]. One of the most interesting effect associated with third order susceptibility ( 3 ) is the self-focusing. It is typical type of nonlinear wave propagation that depends critically on the transverse profile of the beam. Self-focusing of the light is the process in which an intense beam of light modifies the optical properties of a material medium in such a manner that the beam is caused to come to a focus within or outside the material [20]. In this paper in order to understand the optical nonlinearity in QDs and its application as self-focusing effects, first we assume two different shapes of wurtzite In x Ga 1-x N QDs (pyramid and truncated pyramid), then we calculated the Schrödinger equation in presence of the built-in polarization electric field in the framework of the envelope function, and the effective mass theory. The third-order nonlinear susceptibility of the taken QDs as function of DQ’s size is investigated. Finally, the effects of QD size and shape on self- focusing effects have been analyzed. 2. Theoretical model To model the device, two pyramid and truncated-pyramid shaped InGaN wurtzite QDs embedded in GaN material are assumed. The proposed structure has been shown in Fig. 1. In order to study the electronic structures, different methods have been experienced [21–24]. The single band method is used 0030-4026/$ – see front matter © 2012 Elsevier GmbH. All rights reserved. doi:10.1016/j.ijleo.2012.01.012