Creating a two lens system of tunable focal length

[quackyneudle]

Hello,
I would like to reduce the beam size of a laser by a factor of 10, with the purpose of replacing a long (750 mm) lens with a more compact design.

Ideally I'd make a Galilean lens pair where the ratio of the focal lengths are 10:1 to produce a small collimated beam. However, I think I could achieve my desired result (small beam just over some length) by using e.g. a 2:1 lens pair and moving the diverging lens "too close" to the converging lens, achieving a gentle focus and long confocal length.

Questions: How would one calculate the Gaussian beam parameters (waist, Rayleigh length, etc.) given the combined focal length 1/f= 1/f1 + 1/f2 -d/(f1*f2)? Would I use it "straight" in those formulas?

Thank you!

 

[eljose79]

Hello there,

Thank you for your question. I can understand your interest in reducing the beam size of a laser for a more compact design. Let me try to answer your questions about calculating the Gaussian beam parameters.

Firstly, to calculate the Gaussian beam parameters, you will need to know the wavelength of the laser, the beam diameter, and the focal length of the lens being used. In this case, you will need to know the focal length of both the converging and diverging lenses in the lens pair.

To calculate the combined focal length, you can use the formula you mentioned: 1/f= 1/f1 + 1/f2 -d/(f1*f2). In this formula, f1 and f2 are the focal lengths of the two lenses, and d is the distance between them. Once you have calculated the combined focal length, you can use it in the formulas for Gaussian beam parameters.

For example, to calculate the waist size of the beam, you can use the formula w0 = λ*f/π*D, where λ is the wavelength, f is the combined focal length, and D is the beam diameter. Similarly, the Rayleigh length can be calculated using the formula z0 = π*w0^2/λ.

I would recommend using these formulas as a starting point, but keep in mind that they are theoretical calculations and may not exactly match the actual beam parameters. It is always a good idea to test and adjust the setup to achieve the desired result.

I hope this helps answer your questions. Best of luck with your project!