## Question:

While injecting a signal into the Michelson’s arms do we need to use fsig for the thickness of the lens and other lengths in and the X and Y arm.

1. Sean Leavey says:

Hi Harley,

If I understand your question correctly, you are worried about whether you must compensate your mode matching lenses to keep perfect mode matching while you change the length of the arms using fsig. The answer is no, because of the way Finesse works internally it computes the steady-state solution to the interferometer using the case without fsig applied to any component values, then performs a so-called “small-signal analysis” using fsig around this operating point. This essentially means that fsig‘s effect is purely mathematical and does not change your interferometer’s mode matching, or any other dynamic property. Incidentally, this small-signal analysis is one reason why fsig‘s results cannot be trusted for large tunings since in reality such tunings would considerably change the interferometer’s operating point.

(Note: if you use xaxis to vary a parameter directly, such as a cavity length, instead of using it to vary an fsig, then this will change the interferometer’s operating point and thus influence mode matching etc.)

Please let me know if this was not what you were asking!

1. Harley Suchiang says:

Thats a useful information and we were thinking about it but I was asking if when we generate a signal in the two arms do we need to modulate all lengths using fsig involved in the two arms together. For example in the x arm we have lx1, LX. So do we use fsig for lx1 too?

1. Sean Leavey says:

Only LX is inside the arm cavity (the two high-reflectivity mirror surfaces), right? Then modulating this length will tell you the effect of arm cavity motion. Modulating lx1 on the other hand will tell you the effect of moving the arm of the “inner Michelson”. It all depends on which degree of freedom of the interferometer you are interested in.

1. Harley Suchiang says:

But aren’t we trying to mimic a GW signal by injecting such a signal using the fsig command?
And if we are trying to do that won’t that mean we have to modulate every length along X out of phase wrt the lengths along Y in the cavity.

1. Philip Jones says:

In reality yes, a GW signal would modulate every length in the interferometer that’s in the right plane. The detector however is much, much more sensitive to DARM (LX & LY in antiphase) than MICH (lx1 & ly1 in antiphase), so you can treat a GW signal as just modulating LX & LY. You can try this for yourself – take a look at the power at the dark port of the detector when you sweep DARM vs MICH.