We present a three-dimensional code for the optimization of energy storage, heat deposition, and amplification in square-shaped laser slabs and multi-slab laser amplifiers. The influence of the slab dimensions, slab face and edge reflectivities, pump parameters, and operating temperature on amplified spontaneous emission and stored energy has been investigated. The multi-slab and single-slab configurations are compared, analyzing in detail the influence of the absorption cladding for the suppression of amplified spontaneous emission radiation.