Gain factor, gain, and decibel dB

In laser physics, gain factor, gain, and decibel dB refer to the same effects. But they differ in their definition. In general, the terms refer to a change of power due to amplification or loss. In this context, power refers to all forms of power, e.g. electrical power or optical power.

The gain factor G is defined as the ratio from output power to input power: $$G = \frac{Pout}{Pin}.$$ The unit of the gain factor is 1.
For values of G > 1, the power is increasing, and amplification takes place. For values of G < 1, the power is decreasing, and loss occurs.

The gain g is defined as $$g = ln\left(\frac{Pout}{Pin}\right).$$ where ln is the natural logarithm. The unit of the gain factor is 1.
Based on the definition of the gain, it is often referred to as exponential gain.

Another common way to express gain is in the form of decibel dB. It is defined as $$g_{dB} = 10 log_{10} \left(\frac{Pout}{Pin}\right).$$ The unit is decibel dB.
This definition is particularly useful for high losses or gains as the numbers stay small while giving a sense for the change. E.g., a gain of 1,000,000,000 or 1 billion equals 10⁹ and therefore 90 dB.