In specifying the performance of an optical coupler, one usually indicates the percentage division of optical power between the output ports by means of the splitting ratio or coupling ratio.

1) Coupling ratio or splitting ratio

$$CR=\frac{Power \ \ from \ \ any \ \ single \ \ Output}{Total \ \ power \ \ out \ \ to \ \ all \ \ ports}.{\frac{P_t}{P_{T-{out}}}}$$

In dB for 2*2 Coupler

$$C.R.10log_{10}\Bigg(\frac{P_2}{P_1+P_2}\Bigg)$$

3-dB coupler: P1 = P2 = 0.5 $P_0$

2) Excess Loss

The excess loss is defined as the ratio of the input power to the total output power.

$$L_e\frac{Input \ \ Power \ \ P_i}{Total \ \ output \ \ \ power P_{T-out}}$$

$$L_e=10log_{10}\bigg(\frac{P_0}{P_1+P_2}\bigg)$$

3) Insertion Loss

The insertion loss refers to the loss for a particular port-to-port path. For example, for the path from input port i to output port j, we have, in decibels,

$$L_i=\frac{Power \ \ from \ \ any \ \ single \ \ output }{Power \ \ input}.\frac{P_t}{P_i}$$

4) Isolation Loss or Crosstalk or Directivity

Another performance parameter is crosstalk, which measures the degree of isolation between the input at one port and the optical power scattered or reflected back into the other input port.

$$L_{iso}\frac{Input \ \ power \ \ at \ \ one \ \ port}{Reflected \ \ power \ \ back \ \ into \ \ other \\ input \ \ port}$$

In dB

$$L_{iso} 10log_{10}\bigg(\frac{P_0}{P_3}\bigg)$$