What is the formal definition of Coupling efficiency

Generally, an efficiency is going to be the ratio of power or energy successfully delivered or used to the power input to the system

$$eta =frac{P_{out}}{P_{in}}$$

In the case of coupling efficiency, $P_{out}$ is the power coupled into the desired output mode or modes, or to a photdector or some other device, and $P_{in}$ is the power provided at the input of the coupling mechanism.