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The phase difference at the beam splitter of a LIGO-like interferometer is given by $$ \Delta \phi \simeq \frac{4\pi}{\lambda} h L\ , $$ where $h$ is the gravitational wave strain (assuming a polarisation aligned with the detector arms), $L$ is the effective arm length (increased by a large factor in the Fabry-Perot cavities) and $\lambda$ is the interferometer laser wavelength, and assuming the frequency is low enough to not be affected by the response roll-off of the Fabry-Perot cavities.

Why then does LIGO use an IR laser ($\lambda = 1064$ nm), rather than something with shorter wavelength that would produce a larger (and more detectable) phase difference?

I would think this probably has to do with how absorptive the optics are at different wavelengths, but cannot find definitive statements about this other than that the fused silica substrate of the mirrors is "transparent" at both visible and IR wavelengths.

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While looking at LIGO signal noise curves given gravitational wave frequency,

enter image description here

becomes clear that main challenge in LIGO setup is not to extract highest phase difference possible, but maximally increase signal-to-noise ratio, since there's a LOT of different and hardly-stabilizable noise sources.

Main LIGO interferometer mirrors, which "catch" gravitational signal,

enter image description here

are coated with such high-precision high-reflection coatings that fail to reflect just $1~\text{photon per 5 million!}$

And we excel at producing IR precision-coatings, that is why laser wavelength is chosen from infrared domain. Changing wavelengths to shorted ones, like UV, would make scattering and absorption of photons at LIGO mirrors to increase very considerably so that thermal noise would be elevated a lot. To make UV high reflection coatings is super-hard since by default most glasses absorption maximum at visible wavelength range is at about UV spectral part.

Lastly, to illustrate how hard-science is gravitational wave detection at LIGO, I'll mention that ligo interferometer in the form of "microseismic noise" detects :

ocean storms, dam operations, forest logging, trucks driving on a road 2 km away, single human walking within 5 m of the mirror

All these noise types must be eliminated technically or subtracted from the overall signal to extract useful gravitational wave input.

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    $\begingroup$ If the goal is to increase the SNR, that can be achieved either by increasing the numerator or reducing the denominator. Can you demonstrate or cite any work that shows that the silica glass used by LIGO is less absorbent at IR wavelengths than say red wavelengths or that coatings that reflect almost all light could not be made at red wavelengths? $\endgroup$ Commented 2 days ago
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    $\begingroup$ I can't see the point of you getting annoyed about me asking for clarification and reliable sources for the information you present. The numerator and denominator I refer to are the signal/noise ratio. Decreasing the laser wavelength increases the signal. If it increases the noise by more, then that would possibly answer my question. $\endgroup$ Commented 2 days ago
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    $\begingroup$ @ProfRob I'm not sure that the answer is that 1064 nm + fused silica is strictly optimal for absorption. I think it's more a multi-objective engineering problem (laser stabilization, coatings with low absorption AND thermal noise, photodiode efficiency, ...) and the technology for all the various components exists and is mature at around 1064 nm. I'm not sure if any one reference explores all the tradeoffs. Interestingly, for low frequency ET the plan is to use 1550 nm and silicon mirrors (einsteintelescope-emr.eu/wp-content/uploads/2024/05/…) $\endgroup$ Commented 2 days ago
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    $\begingroup$ One of the chief limitations of LIGO is the noise introduced by the glass in the mirrors. See this from the Berkeley physics department - Hellman Lab Races to Find Perfect Glass for LIGO For information on coatings, see the RP Photonics Encyclopedia article on Bragg Mirrors. $\endgroup$ Commented 2 days ago
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    $\begingroup$ In fact, 1064 nm is not optimal for attenutation, they don't use it for fiber communications for that reason. 1550 nm is universal for long-haul fiber; it's the lowest glass absorption and you can get fiber amplifiers. 1310 nm is a bit cheaper for transceivers and is almost as good in attenuation, but no fiber amplification (semiconductor optical amplifiers are starting to appear). 1064 nm's benefits are raw power: you can get very high power laser diodes, solid-state lasers, fiber amplifiers, and very good Si detectors work. Common applications for 1064 are welding, marking, and surgery. $\endgroup$ Commented yesterday
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Nd:YAG is the highest stability high power laser technology

LIGO uses a solid state Nd:YAG-based NPRO laser at about 200 W. Nd:YAG wavelength is typically 1064 nm, though there are other wavelengths in the 946-1440 nm range that are possible.

Wikipedia has a nice diagram of commercially available laser types. In the more than 100 W, less than 1000 nm category, the main options are argon-ion lasers and frequency doubled Nd:YAG lasers.

Frequency doubling has an efficiency of less than 50% (see e.g. 1). The frequency doubling crystal will also contribute to the laser phase and amplitude noise, but I couldn't find good information on how large of an effect it would be. But even this rough information is enough to determine that if you halve the wavelength, but also halve the power and increase the noise, the net signal-to-noise ratio will become worse.

Argon-ion lasers appear to start off with magnitudes worse noise levels compared to Nd:YAG. Stabilized Nd:YAG laser systems often have linewidth less than 1 kHz. The best result I could find for a stabilized Ar+ laser is 70 kHz (at 514 nm). The LIGO laser is reported to have linewidth of 1 Hz.

There is ongoing research into actually using a longer wavelength of 1550 nm for future gravitation wave detectors, as it would allow the use of silicon test masses. This article looks into the available laser options, which include erbium fiber lasers and ECDL diode lasers fed into a fiber laser amplifier. Fiber-based laser amplifiers generally operate at wavelengths of 1000-1700 nm.

In summary, it appears there are currently no laser systems that would offer similar or better stability and power at a significantly shorter wavelength. The gains from reducing the wavelength would be offset by the increased noise.

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