What Can TEMPROFILE Do?
TEMPROFILE calculates the distribution of temperature in a multilayer stack illuminated by a normally-incident, monochromatic beam of light. The stack (deposited on a flat substrate) may consist of any number of metal and dielectric layers up to a maximum of 99. The incident beam, which can illuminate the stack either from the top surface or through the substrate, must have circular symmetry but is otherwise arbitrary (see the figure below). Due to the linearity of the problem, the program first computes the response to a rectangular "impulse" having a fixed power and a short duration t. This "impulse-response" is then stored in a disk file, which may be retrieved subsequently for calculating thermal profiles by superposition.
The Compute Impulse Response option of the main menu of TEMPROFILE allows the user to specify the multilayer stack, mode of illumination, distribution of light intensity, and the required mesh parameters.
In the Generate Temperature Profile mode, a data-file containing a previously computed impulse-response is read into the program. The program then prompts the user for the temporal profile P(t) of the light pulse, and the velocity V of the beam relative to the multilayer stack. At this point the user may request one of several possible temperature profiles, namely, T(x), T(y), T(z), T(t), as well as various isotherms at fixed z. (Note: The stacks layers are parallel to the XY-plane, the Z-axis is the direction of the surface-normal along which the beam propagates, t is the time, and T stands for temperature above ambient.) The specified profiles are saved to the hard disk within the working subdirectory, and the user is returned to the main menu, where he/she can invoke the PLOT option to view the computed profiles.
TEMPROFILE assumes that the profile of the incident beam within the XY-plane is circularly symmetric, and that the various layers of the stack are isotropic (both optically and thermally). The natural coordinate system for this problem, therefore, is a cylindrical system in which Z is the axis of symmetry as well as the optical axis of the light beam (i.e., the axis along which the beam propagates), R is the radial distance from Z, and f is the azimuthal angle in the XY-plane of the stack.
Multilayer stack consisting of N layers, coated on a semi-infinite substrate. The surface of the last layer is at Z = 0, while the interface between the substrate and layer 1 is at Z = z1 + z2 + ... + zN , where zi is the thickness of the i th layer. The incident beam has circular symmetry, and moves with constant velocity V along the positive X-axis. The program allows the user to choose the direction of incidence; thus the beam may enter through the substrate, or be incident on the top surface of the multilayer stack, as indicated.
Notation and the System of Units:
The physical quantities encountered in TEMPROFILE, their respective symbols, and their corresponding dimensional units are listed in the Table below. The refractive index and the absorption coefficient are usually combined together to form the complex refractive index (n, k). Each layer has a specific heat C and a thermal conductivity K. The ratio K/C is known as the thermal diffusivity D. The parameter g denotes the effective heat-loss-factor from the top surface of the stack.
Units of the physical quantities
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