Commun. Comput. Phys., Notice: Undefined index: year in /var/www/html/issue/abstract/readabs.php on line 20 Notice: Undefined index: ppage in /var/www/html/issue/abstract/readabs.php on line 21 Notice: Undefined index: issue in /var/www/html/issue/abstract/readabs.php on line 23 Volume 4. Computational Modeling of Optical Response from Excitons in a Nano Optical Medium Yuanchang Sun 1*, Hiroshi Ajiki 2, Gang Bao 11 Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA. 2 Graduate School of Engineering Science, Osaka University, 1-3 Machikaneyama, Toyonaka 560-8531, Japan. Received 4 January 2008; Accepted (in revised version) 26 May 2008 Available online 16 July 2008 Abstract Consider a time-harmonic electromagnetic plane wave incident on a microscopic semiconductor. Inside the medium, at any given frequency $\omega$, more than one polariton mode can arise with the same frequency but different wavenumbers due to the presence of excitons. Besides Maxwell's boundary conditions, additional boundary conditions are required to handle the multi-mode polariton. In order to model the confinement effect of excitons in the microscopic semiconductor, Maxwell's equations and the Schrodinger equation are coupled to characterize the polarization in terms of the quantum description. In the weak confinement regime, we derive a perturbed dispersive dielectric constant by taking the exciton effect into account. We also analyze and compute the optical linear response of the exciton in both one-dimensional and two-dimensional confinements. For the one-dimensional case, the existence and uniqueness of the analytical solution are established in the resonance region. A finite difference method is developed to compute the two dimensional confinement. AMS subject classifications: 78A45, 78M20, 81V10 Notice: Undefined variable: pac in /var/www/html/issue/abstract/readabs.php on line 164 Key words: Nano optics, exciton, modeling. *Corresponding author. Email: sunyuanc@msu.edu (Y. Sun), ajiki@mp.es.osaka-u.ac.jp (H. Ajiki), bao@math.msu.edu (G. Bao)