How do the LIGO team arrive at the number of round trips in the laser arm etalon?
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According to the LIGO technical document the LIGO optical cavities are designed to have a finess of 450, where the finesse is defined as:
F=2π1−ρ" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-style: normal; font-variant: inherit; font-weight: normal; font-stretch: inherit; line-height: normal; font-family: inherit; font-size: 15px; vertical-align: baseline; display: inline; text-indent: 0px; text-align: center; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">F=2π1−ρF=2π1−ρ
where ρ" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-style: normal; font-variant: inherit; font-weight: normal; font-stretch: inherit; line-height: normal; font-family: inherit; font-size: 15px; vertical-align: baseline; display: inline; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">ρρ is the fractional loss per round trip. A finesse of 450 corresponds to a loss of about 1.4% per round trip, so after 280 round trips the beam is reduced to about 2% of its original intensity.
The discussion of why a finesse of 450 was chosen is a little opaque. The document says only that it was chosen as a tradeoff between laser power and thermal noise.
F=2π1−ρ" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-style: normal; font-variant: inherit; font-weight: normal; font-stretch: inherit; line-height: normal; font-family: inherit; font-size: 15px; vertical-align: baseline; display: inline; text-indent: 0px; text-align: center; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">F=2π1−ρF=2π1−ρ
where ρ" role="presentation" style="box-sizing: inherit; margin: 0px; padding: 0px; border: 0px; font-style: normal; font-variant: inherit; font-weight: normal; font-stretch: inherit; line-height: normal; font-family: inherit; font-size: 15px; vertical-align: baseline; display: inline; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">ρρ is the fractional loss per round trip. A finesse of 450 corresponds to a loss of about 1.4% per round trip, so after 280 round trips the beam is reduced to about 2% of its original intensity.
The discussion of why a finesse of 450 was chosen is a little opaque. The document says only that it was chosen as a tradeoff between laser power and thermal noise.
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