The Open Optics Journal, 2008, 2, 67-74 67 1874-3285/08 2008 Bentham Open Open Access Thermal Modeling of Optical Power Absorption in Moving Multilayer Thin Films W.A. Challener * and A. Itagi Seagate Technology, Pittsburgh, PA 15222, USA Abstract: A technique for computing the thermal profile in a multilayer moving medium is described. This technique is particularly suitable for studying the near field optical/thermal interplay in hybrid optical/magnetic recording because the boundaries of the computation space are effectively removed from the optical source. It is shown that a three layer me- dium can be designed with a thermal time constant which is suitable for high recording data rates and that minimizes the thermal bloom from motion of the medium with respect to the optical spot. However, the thermal spot is much larger than the optical spot which leads to a reduced storage density. INTRODUCTION Numerical techniques for efficiently computing the tem- perature rise [1-3] in a multilayer thin film stack [4-6] due to a focused laser beam have been developed for a variety of applications such as recordable optical data storage. The focused optical spot size for current optical storage products ranges from ~0.88 μm for CD’s at a wavelength of 780 nm to 0.24 μm for Blu-Ray disks at a wavelength of 405 nm. When the optical spot is much larger than or comparable to the thickness of the thin film stack, the heat sink/reflector layer in the disk ensures that the dominant direction for heat flow is perpendicular to the thin films. As a result, the ther- mal boundary conditions in the lateral direction are not diffi- cult to handle with simple approximations, such as a quad- ratic temperature dependence at the boundary [4]. Future optical data storage products may require near field optics to achieve larger storage densities. Magnetic hard discs may also incorporate a hybrid optical/magnetic tech- nology called “heat assisted magnetic recording” (HAMR) using near field optics to transfer the optical energy into the recording medium in a highly localized spot smaller than the total thickness of the film stack [7,8]. In such a case, the lat- eral heat flow can become as important as the perpendicular heat flow and thermal boundary conditions must be carefully applied. The advantages of the alternate direction implicit (ADI) technique for thermal modeling of optical data storage media have been described by Mansuripur et al. [4,5] They devel- oped the ADI equations for a cylindrical coordinate system and a circularly symmetric optical spot in both the stationary and moving frame of reference. The ADI equations were subsequently applied by Peng et al. [6] to a stationary 3D Cartesian coordinate system to investigate the amorphization and crystallization dynamics of optical phase change media. *Address correspondence to this author at the Seagate Technology, 1251 Waterfront Place, Pittsburgh, PA 15222, USA; Tel. 412-918-7197; Fax: 412-918-7010; E-mail: william.a.challener@seagate.com Itagi [9] extended the ADI equations to include variable layer thicknesses, thereby enabling a substantial decrease in com- putation time for film stacks with thick layers. He also de- rived the ADI equations for the moving frame in a cylindri- cal coordinate system [10]. In this paper we present the ADI equations for a Cartesian coordinate system in the moving frame of reference and a method for accurately handling the lateral thermal boundary conditions in a multilayer film stack, and then apply these results to a HAMR recording medium. BASIC THEORY The Fourier heat conduction equation is C  r, t ( 29  t T  r, t ( 29 =   k  r, t ( 29 T  r, t ( 29     + g  r, t ( 29 (1) where C is the heat capacity,  k is the thermal conductivity tensor, g is the input power, t is the time, and T is the tem- perature. Eq. (1) can be implemented numerically by subdi- viding the region of interest into many smaller cells to ap- proximate the spatial gradients, and stepping the time in dis- crete increments. In the explicit method, the temperature at a specific point in the cell space at time t = n+1 is completely determined by the temperatures within the cell space for the previous time step, t = n. C T n + 1  T n ( 29 t =   k T n ( 29 + g . (2) There is only one unknown variable, T n+1 (i,j,k), at each point in the cell space and time step. However, there is a constraint on the size of the time step to ensure numerical stability of the calculation. It is generally necessary to choose very small time steps, and as a result, the simple ex- plicit technique is not suitable for many problems of practi- cal interest. The simplest implicit method for solving the heat con- duction equation rewrites Eq. (1) as C T n + 1  T n ( 29 t =   k T n + 1 ( 29 + g . (3)