We introduce new concepts for increasing the efficiency of solid state lasers by using gratings deposited on laser slabs or disks. The gratings improve efficiency in two ways: (1) by coupling out of the slab deleterious amplified spontaneous emission (ASE) and (2) by increasing the absorption efficiency of pump light. The gratings also serve as antireflective coatings for the extracting laser beam. To evaluate the potential for such coatings to improve laser performance, we calculated optical properties of a 2500 groove/mm, tantala-silica grating on a 1cm x 4cm x 8cm titanium-doped sapphire slab and performed ray-trace calculations for ASE and pump light. Our calculations show substantial improvements in efficiency due to grating ASE-coupling properties. For example, the gratings reduce pump energy required to produce a 0.6/cm gain coefficient by 9%, 20% and 35% for pump pulse durations of 0.5 {micro}s, 1{micro}s and 3{micro}s, respectively. Gratings also increase 532-nm pump-light absorption efficiency, particularly when the product slab overall absorption is small. For example, when the single-pass absorption is 1 neper, absorption efficiency increases from 66%, without gratings, to 86%, when gratings are used.