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Message ID: 3122     Entry time: Fri Jun 25 20:32:30 2010
Author: kiwamu 
Type: Update 
Category: Green Locking 
Subject: green power on the PSL table 

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]  ~ E1EE1 E2*,

                     ~ 2 ( PP2)½ cos (phi), 

 where  E1 and Erepresent the complex fileds,  Pand Prepresent their powers and phi is a phase difference.

This equation tells us that the strength of the signal is proportional to  ( PP2)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] ~ ( PP2)½.

 According to the equations above, SNR is expressed by

        SNR = [signal] / [noise] ~ ( PP2)½  / ( PP2)½.

If we assume Pis 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 P increases. There are two kinds of the growing phase.

    (1) When PP1 , SNR is efficiently improved with the speed of  P2½.

    (2) But  when P>   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 PP 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.

ITM transmissivity @ 532nm  Ti 1.5 %
ETM transmissivity @ 532nm Te 4.5 %
Transmissivity of the arm cavity @ 532nm T_cav 74.4 %
Transmissivity of the BS @ 532nm T_BS 97 %
Transmissivity of  PR1 and SR1 @ 532nm T_PR 90%
Transmissivity of the PMC @ 1064 nm T_pmc 65 %
The power of the green beam at the end station P_end 1 mW
The power of the PSL  P_psl 2 W
Conversion efficiency of the PPKTP eta 3 %/W

         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.


Attachment 1: optical_power.png  147 kB  Uploaded Fri Jun 25 21:50:02 2010  | Hide | Hide all
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