Now I've been reading up on this mode cleaner business, so I thought I'd share my (mis)understanding of it. Such as it is. :-)

We have a laser that produces photons in phase, due to the quantum mechanical aspect of photons being Bose particles. But as nothing is ever exact, per Heisenberg, then whatever exits the lasing cavity is going to have some spread in phase. Or put another way, the time of arrival at a given point of some chosen phase value will vary amongst the photons in the beam. An 'ideal' laser is one where the phase has a 'Gaussian profile', really it's the best/minimum variation that one can hope for ( given the quantum mechanical nature of light ). The laser output acts partly as a point source, in that with distance from it there is some lateral diffraction. So the wavefront ( a surface of constant phase ) is not a flat plane but sort of spherical.

[ There is talk of the Guoy/Gouy phase, which is the difference between our Gaussian pattern and that of a plane wave. This Guoy/Gouy phase will shift/vary with distance along the beam. I couldn't find a consistent spelling for this Guoy/Gouy guy, so I don't know which one is right! :-) ]

So if I go along the apparatus some distance that difference in phase amongst the photons in the beam translates to, ultimately, a probability of detection. Because phase differences between paths is the primary trick with the interferometers then we would like any phase variation amongst the photons to be due to the paths alone, as much as possible.

So the mode cleaner is to reduce a source of noise ( unwanted signal ) then. The 'mode' label is a bit deceptive, as we're not getting rid of modes. There is an input and an output mode cleaner these days. Here's a rather dated diagram from an early design document ( this is not the exact present arrangement ) :

In this instance the Input Mode Cleaner is the triangular cavity in the centre of the graphic. The photons go around this 'racetrack', with the length of one leg adjustable as indicated by the left-right grey arrow under the right-side mirror. The effect is that with a correct setting only those photons that arrive at the right-side mirror of the triangle in the proper phase will transmit to the other side and proceed to the interferometer proper. Imagine a NASCAR race where to win is not to be the fastest, but to have the most consistent lap time at some particular value.

However there is a curly bit. We don't just want a single frequency running through the arms, we want sidebands also - as these are used to control the feedback loops for mirror positions, hence locking and whatnot. In the dotted box to the left of the mode cleaner is where the sidebands are formed. If you take two sinusoidal signals of different frequencies and 'mix' them you get the sum and the difference of those frequencies. The gadgets marked as 'PM' are Pockel's cells.

Pockel's cells are named after a German guy who worked out an effect in ~ 1906 which is now named after him. Basically crystals of certain substances have the property that an electric field applied to them can alter how light transmits - the refractive index in fact. If you have an oscillating electric field across a Pockel's cell orientated in a certain way, and at some frequency, then you get the mixing as above. In the diagram there are three frequencies used ( f1, f2 and f3 ) to oscillate the Pockel's with. You'll note at the right end of the entire diagram these frequencies are recovered ( using the gadgets denoted by a diagonal cross in a circle ), the level of which becomes an input for the control of the mirrors to gain and maintain lock.

This whole sideband rigamarole is a cheat to get many frequencies in the same regions, to work with for different reasons. If you have been able to follow this then you may spot a problem. How can we talk of light resonating in the one single cavity when several frequencies are used? Surely what's the right length for one selected frequency may not suit another. After all frequency determines the time to return to a given phase, and with a certain velocity that means at a certain distance too. I guess the answer is that if one chooses the frequencies right, such that there is some ratio/relationship between them, then a particular resonant cavity can have photons of different frequencies returning to a given point with suitable phases.

So I reckon that means the mode cleaner 'works' for the selected frequencies ( base plus sidebands ) because of the way the geometry is designed. That is, the racetrack suits different categories of cars - a bit like the LeMans 24 hour circuit race.

Cheers, Mike.

( edit ) So what's running around in the IFO potentially is the base frequency of the laser +/- f1, +/- f2, +/- f3. I don't think they can all suit all the cavities though. I haven't worked the math, yet. By 'cavity' I mean some region bounded by mirrors that gives the opportunity for multiple reflections and thus resonance. A glance at the diagram shows there are many possible pairs ( triples even ) of mirrors ...

( edit ) And while we label a mirror as such, it's not all reflection. Each one has some degree of transmission ( by specific design ), hence photons can transit from cavity to cavity. So a mirror can also be a junction of cavities, with the exact positioning of the mirror determining which photons get to transit between resonant 'rooms'.

( edit ) Pardon me, that right-side mirror adjustment in the mode cleaner will affect two legs of the triangle.

I have made this letter longer than usual because I lack the time to make it shorter ...

... and my other CPU is a Ryzen 5950X :-) Blaise Pascal

## Now I've been reading up on

)

Now I've been reading up on this mode cleaner business, so I thought I'd share my (mis)understanding of it. Such as it is. :-)

We have a laser that produces photons in phase, due to the quantum mechanical aspect of photons being Bose particles. But as nothing is ever exact, per Heisenberg, then whatever exits the lasing cavity is going to have some spread in phase. Or put another way, the time of arrival at a given point of some chosen phase value will vary amongst the photons in the beam. An 'ideal' laser is one where the phase has a 'Gaussian profile', really it's the best/minimum variation that one can hope for ( given the quantum mechanical nature of light ). The laser output acts partly as a point source, in that with distance from it there is some lateral diffraction. So the wavefront ( a surface of constant phase ) is not a flat plane but sort of spherical.

[ There is talk of the Guoy/Gouy phase, which is the difference between our Gaussian pattern and that of a plane wave. This Guoy/Gouy phase will shift/vary with distance along the beam. I couldn't find a consistent spelling for this Guoy/Gouy guy, so I don't know which one is right! :-) ]

So if I go along the apparatus some distance that difference in phase amongst the photons in the beam translates to, ultimately, a probability of detection. Because phase differences between paths is the primary trick with the interferometers then we would like any phase variation amongst the photons to be due to the paths alone, as much as possible.

So the mode cleaner is to reduce a source of noise ( unwanted signal ) then. The 'mode' label is a bit deceptive, as we're not getting rid of modes. There is an input and an output mode cleaner these days. Here's a rather dated diagram from an early design document ( this is not the exact present arrangement ) :

In this instance the Input Mode Cleaner is the triangular cavity in the centre of the graphic. The photons go around this 'racetrack', with the length of one leg adjustable as indicated by the left-right grey arrow under the right-side mirror. The effect is that with a correct setting only those photons that arrive at the right-side mirror of the triangle in the proper phase will transmit to the other side and proceed to the interferometer proper. Imagine a NASCAR race where to win is not to be the fastest, but to have the most consistent lap time at some particular value.

However there is a curly bit. We don't just want a single frequency running through the arms, we want sidebands also - as these are used to control the feedback loops for mirror positions, hence locking and whatnot. In the dotted box to the left of the mode cleaner is where the sidebands are formed. If you take two sinusoidal signals of different frequencies and 'mix' them you get the sum and the difference of those frequencies. The gadgets marked as 'PM' are Pockel's cells.

Pockel's cells are named after a German guy who worked out an effect in ~ 1906 which is now named after him. Basically crystals of certain substances have the property that an electric field applied to them can alter how light transmits - the refractive index in fact. If you have an oscillating electric field across a Pockel's cell orientated in a certain way, and at some frequency, then you get the mixing as above. In the diagram there are three frequencies used ( f1, f2 and f3 ) to oscillate the Pockel's with. You'll note at the right end of the entire diagram these frequencies are recovered ( using the gadgets denoted by a diagonal cross in a circle ), the level of which becomes an input for the control of the mirrors to gain and maintain lock.

This whole sideband rigamarole is a cheat to get many frequencies in the same regions, to work with for different reasons. If you have been able to follow this then you may spot a problem. How can we talk of light resonating in the one single cavity when several frequencies are used? Surely what's the right length for one selected frequency may not suit another. After all frequency determines the time to return to a given phase, and with a certain velocity that means at a certain distance too. I guess the answer is that if one chooses the frequencies right, such that there is some ratio/relationship between them, then a particular resonant cavity can have photons of different frequencies returning to a given point with suitable phases.

So I reckon that means the mode cleaner 'works' for the selected frequencies ( base plus sidebands ) because of the way the geometry is designed. That is, the racetrack suits different categories of cars - a bit like the LeMans 24 hour circuit race.

Cheers, Mike.

( edit ) So what's running around in the IFO potentially is the base frequency of the laser +/- f1, +/- f2, +/- f3. I don't think they can all suit all the cavities though. I haven't worked the math, yet. By 'cavity' I mean some region bounded by mirrors that gives the opportunity for multiple reflections and thus resonance. A glance at the diagram shows there are many possible pairs ( triples even ) of mirrors ...

( edit ) And while we label a mirror as such, it's not all reflection. Each one has some degree of transmission ( by specific design ), hence photons can transit from cavity to cavity. So a mirror can also be a junction of cavities, with the exact positioning of the mirror determining which photons get to transit between resonant 'rooms'.

( edit ) Pardon me, that right-side mirror adjustment in the mode cleaner will affect two legs of the triangle.

I have made this letter longer than usual because I lack the time to make it shorter ...

... and my other CPU is a Ryzen 5950X :-) Blaise Pascal

## Right, we'll continue

)

Right, we'll continue discussion in this thread. Since I'm posting images this will keep the download size per web page down.

Cheers, Mike.

I have made this letter longer than usual because I lack the time to make it shorter ...

... and my other CPU is a Ryzen 5950X :-) Blaise Pascal

## Some good reading

)

Some good reading material.

On science and practical jokes ;)