Thermal analysis of optical elements and arrays on thick substrates with convection cooling

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Abstract
By solving the heat equation for a Gaussian heating source on the surface of a thick substrate with forced cooling, the relative desirability of conductive and convective cooling strategies for removing heat from single elements and arrays has been investigated. Small sources or arrays are most efficiently cooled by diffusion into a thick heat sink and here temperature is not critically dependent on cooling strength. As the arrays get larger, however, the relative efficiency of conductive heat removal is less and it is desirable to maximize convective heat transfer instead. So large arrays require very thin substrates and strong convective cooling.

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