Final answer:
The saturation intensity is the point at which the gain of a homogeneously broadened optical amplifier no longer increases linearly with input intensity. to calculate the exact value for saturation intensity, we would need additional information about the amplifier's characteristics and saturation behavior.
Step-by-step explanation:
The question asks for the saturation intensity of a homogeneously broadened optical amplifier operating as an ideal four-level system. Given a small-signal gain of 13 dB and input and output intensities (Iᵢₙ and Iₒᵤₜ) of 5 W/cm² and 30 W/cm² respectively the amplifier has likely reached its saturation point where the gain is no more linearly dependent on the input intensity. To calculate the saturation intensity, we would typically use the input-output relationship for the amplifier under the assumption that the gain has reduced due to saturation. however, without the explicit equations that relate to the saturation intensity for a four-level laser system, it is not possible to provide an accurate number.
To find the saturation intensity in general you would refer to laser physics principles and associated formulae related to the specific type of laser amplifier being used. Unfortunately, the information provided is insufficient to calculate the exact value of the saturation intensity without additional details about the amplifier's characteristics and the relationship between input intensity and gain near saturation.