The power of the green beam generated on the PSL table should be about 650uW in terms of the shot noise.

       One of the important parameters we should know is the power of the green beam on the PSL table because it determines the SNR.

The green beam finally goes to a photo detector together with another green beam coming from the arm cavity, and they make a beat signal and also shot noise.

So in order to obtain a good SNR toward the shot noise at the photo detector, we have to optimize the powers.

If we assume the green power from the arm is about 650uW,  a reasonable SNR can be achieved when these powers are at the same level. 

To get such power on the PSL table, a 90% partial reflector is needed for picking it off from the PSL as we expected.

  power dependency of SNR

      Suppose two lasers are going to a photo detector while they are beating (interfering).

The beat signal is roughly expressed by

      [signal]  ~ E_1^* E₂ + E₁ E_2^*,

                     ~ 2 ( P₁ P₂)^½ cos (phi), 

 where  E_{1 ^and} E₂ represent the complex fileds,  P₁ and P₂ represent their powers and phi is a phase difference.

This equation tells us that the strength of the signal is proportional to  ( P₁ P₂)^½  .

At the same time we will also have the shot noise whose noise level depends on the inverse square route of the total power;

          [noise] ~ ( P₁ + P₂)^½.

 According to the equations above, SNR is expressed by

        SNR = [signal] / [noise] ~ ( P₁ P₂)^½  / ( P₁ + P₂)^½.

If we assume P₁ is fixed,  the maximum SNR can be achieved when  P₂ goes to the infinity. But this is practically impossible.

Now let's see how the SNR grows up as the power P₂  increases. There are two kinds of the growing phase.

    (1) When P₂ <  P₁ , SNR is efficiently improved with the speed of  P₂^½.

    (2) But  when P₂ >   P₁ , the speed of growing up becomes very slow. In this regime increasing of  P₂ is highly inefficient for improvement of the SNR.

Thus practically P₁ ~ P₂  is a good condition for the SNR.

At this point the SNR already reaches about 0.7 times of the maximum, it's reasonably good.

 power estimation

         According to the fact above, we just adjust the green powers to have the same power levels on the PSL table.

 The table below shows some parameters I assume when calculating the powers.

         Attached figure shows a simplified schematic of the optical layout with some numbers. 

By using those parameters we can find that the green beam from the arm cavity is reduced to 650uW when it reaches the PSL table.

To create the green beam with the same power level on the table, the power of 1064 nm going to the doubling crystal should be about 150mW.

This amount of the power will be provided by putting a 90% partial reflector after the PMC.