Which type of laser mode is characterized by average power being half of peak power?

The type of laser mode characterized by average power being half of peak power is gated laser operation. In gated laser systems, the output pulse duration and the duty cycle are managed such that the average power can be controlled relative to the peak power during the pulse. This typically results in average power being a fraction of the peak power value, and in many cases, such as the one posed in the question, that fraction can be one-half.

This mode is especially useful in applications where you need high peak power for short bursts but want to manage the thermal effects and overall average power delivered over time. It allows for effective energy delivery without excessive heating, which is crucial in many practical applications of lasers in industries like material processing or medical applications.

In contrast, continuous wave lasers continuously emit laser light without interruption, while free running pulsed lasers operate in a pulsed mode but can have more variable relationships between peak and average power. Pulsed continuous lasers, while sounding similar to gated, do not specifically adhere to the relation of average power being half of peak power. Thus, gated operation is the correct answer in this context.