by Din » Fri Jan 06, 2023 10:07 am
John Howard wrote: ↑Fri Jan 06, 2023 9:43 am
That leads to another related question: Is there an easy way to measure coherence length of a laser? Thanks again.
Yes. You set up a Michelson interferometer, and vary the path difference. I've drawn up a diagram. The beams splitter sends the beam along both path a and path b (black lines). On reflection from the mirrors, the beams combine at the output of the splitter (green lines). The combined beams go to a screen. If the paths are equal, ie a = b, you get a strong interference pattern at the screen and a high fringe contrast. As you vary the path difference, a - b, the fringe structure in the interference pattern gets weaker, ie there's less contrast between fringe and not-fringe. So, moving either mirror away from the beam splitter will lower contrast. At some point, the contrast will be too weak to notice. At this point, the coherence length is the path difference between mirrors, a - b (or b - a, depending on which mirror you move). Note, though, you don't want to make a hologram with a path difference between the two beams at the limit of the coherence length. The greater the path length difference approaches the coherence length, the weaker the hologram.
If you want to think of it in this way, a hologram is a photograph of the pattern you see on the screen of a Michelson, albeit on a much smaller scale. The efficiency of a hologram is dependent on the fringe contrast (also known as 'modulation'), so as you get to a path difference of the hologram on the edge of the coherence length, the modulation decreases, and hence the hologram gets weaker.
- Michelson20230106_06531341.jpg (176.97 KiB) Viewed 6968 times
[quote="John Howard" post_id=72769 time=1673016194 user_id=5340]
That leads to another related question: Is there an easy way to measure coherence length of a laser? Thanks again.
[/quote]
Yes. You set up a Michelson interferometer, and vary the path difference. I've drawn up a diagram. The beams splitter sends the beam along both path a and path b (black lines). On reflection from the mirrors, the beams combine at the output of the splitter (green lines). The combined beams go to a screen. If the paths are equal, ie a = b, you get a strong interference pattern at the screen and a high fringe contrast. As you vary the path difference, a - b, the fringe structure in the interference pattern gets weaker, ie there's less contrast between fringe and not-fringe. So, moving either mirror away from the beam splitter will lower contrast. At some point, the contrast will be too weak to notice. At this point, the coherence length is the path difference between mirrors, a - b (or b - a, depending on which mirror you move). Note, though, you don't want to make a hologram with a path difference between the two beams at the limit of the coherence length. The greater the path length difference approaches the coherence length, the weaker the hologram.
If you want to think of it in this way, a hologram is a photograph of the pattern you see on the screen of a Michelson, albeit on a much smaller scale. The efficiency of a hologram is dependent on the fringe contrast (also known as 'modulation'), so as you get to a path difference of the hologram on the edge of the coherence length, the modulation decreases, and hence the hologram gets weaker.
[attachment=0]Michelson20230106_06531341.jpg[/attachment]