No device can output more energy than it receives. However, the same is not true of power.
Work Step by Step
A device, such as a laser, can take in energy at a slow rate (low power) and store it. It can then emit the energy over a short time interval (high power). The law of conservation of energy is not violated. Here is a mechanical analogy. Sisyphus rolls an enormous boulder up a hill, which slowly gains potential energy. This is analogous to the laser silently storing up energy. In a sudden (and heartbreaking) turn of events, the boulder then quickly rolls down the hill, releasing the pent-up potential energy in a flash (this is analogous to the laser pulse). The amount of energy released by the system is the same as that put into the system; energy is conserved.