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 Wed Jan 30 15:07:32 2019, awade, anchal, HowTo, FSS, Shot noise in FSS loops? Fri Feb 1 14:59:01 2019, awade, anchal, HowTo, FSS, Noise tallies Fri Feb 1 20:20:11 2019, awade, HowTo, FSS, Modifying North FSS EOM path Tue Feb 5 11:40:02 2019, awade, HowTo, FSS, Modifying South FSS boost Tue Feb 5 20:39:52 2019, anchal, Summary, FSS, Complete model of TTFSS box with TF and crossover analysis Wed Feb 6 19:13:06 2019, anchal, Summary, FSS, Complete model of TTFSS box with TF and crossover analysis Wed Feb 6 21:30:24 2019, awade, Summary, FSS, Complete model of TTFSS box with TF and crossover analysis Thu Feb 7 10:33:27 2019, anchal, Summary, FSS, Complete model of TTFSS box with TF and crossover analysis
Message ID: 2300     Entry time: Wed Jan 30 15:07:32 2019     Reply to this: 2301
 Author: awade, anchal Type: HowTo Category: FSS Subject: Shot noise in FSS loops?

The FSS at some point is going to be limited by shot noise. I understand that the apparent frequency noise should go as [1]:

$\dpi{100} S^\textrm{SH}_f = \frac{1}{8 L \mathcal F}\sqrt{\frac{hc^3}{P_0\lambda}}\quad [\textrm{Hz}/\textrm{rtHz}]$

where h is plank's constant (6.626e-34), c is the speed of light (3e8), L is cavity length (36.83 mm), F is finesse (~15000), lambda is wavelength (1064 nm) and P0 is incident power (order 1 mW right now).  The inherent frequency equivalent shot noise would then be $\inline \dpi{100} \small \delta f_\textrm{SN}=\sqrt{S_f^\textrm{SN}}$, which for our cavities would be 30 mHz/rtHz for each path for 1 mW of incident powerWhere does this leave the frequency noise of the transmitted light?  Within the cavity line width does it not just pass all the frequency/phase noise?

Obviously our SN value will be slightly worse than this because we don't have excellent mode matching.  But even in the ideal case do we have to use 100 mW of light to get to 10 mHz/rtHz where the brownian noise is at?

These may be stupid questions but I'm not sure how SN limited PDH frequency noise looks like on transmission from a reflection locked cavity.

So for 1 mW of power we should be getting 0.9 mHz/rtHz in the ideal case that MM to the cavity is perfect. So we are good on the ultimate SN limit of the FSS loops.

Edit awade Wed Jan 30 16:34:59 2019: Correction to original post the quoted spectum is and ASD not a PSD, I got the units wrong. Values are corrected above

### References

[1] Black, E. D. An introduction to Pound–Drever–Hall laser frequency stabilization. Am. J. Phys. 69, 79 (2001).

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