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# Questions about Gaussian Beam Propagation

#### MrCool

##### New member
I hope it's the right forum for this topic. I'm new to lasers and I'm trying to understand the physics behind, yesterday I read about Gaussian beams.
I read the first 7 paragraph of above article (and a bunch of other docs about Gaussian beams) and tried to apply the formulas to a real life laser, I chose this one:
The data sheet part says that the beam diameter at the aperture is min. 1.3mm, the beam divergence is around 2mRad and the wavelength is 532nm.
If the beam diameter is 1.3mm at the aperture (I assume it's the narrowest point) then the w0 value is 0.65mm. The Rayleigh length with these values: (pi * (6.3e-4)^2) / 5.32e-7, The google gave me 2.34m as result. For the beam divergence: (2 * 5.32e-7) / (pi * 6.3e-4) (the 2 multiplier is there because I want the full angle instead of the half) the result is 0.5mRad, it is clearly not around 2mRad. I read about the M^2 value, which shows how close my beam to the ideal Gaussian beam and I have to include this M^2 value in the formula for the beam divergence as a multiplier. Since I know that the real beam divergence is somewhere around 2mRad and the calculated is 0.5mRad the M^2 value of this laser should be around 4. I tried to apply these formulas to other lasers, but I got smaller beam divergence around 0.2mRad and ~9 as M^2 which seemed impossible to me, since I read somewhere that the better lasers have M^2 values between 1 and 2. I watched some youtube videos, the guy used the same formulas, and got the same crazy results with 0.1mRad divergence. So, my question is where do I go wrong?

Thanks in advance

#### Encap

##### Well-known member
What do you want to know or do? lol
What JetLasers spec says is ----beam size at aperture is 1.3mm, divergence is 2mRad ---that means the beam spot size will increase 2mm per meter---so at 10 meters spot size will be 21.3mm , at 100 meters away the spot size is 201.3 mm am so on.

• Alaskan

#### Alaskan

##### Well-known member
Two in a row, on a roll.

#### MrCool

##### New member
What do you want to know or do? lol
What JetLasers spec says is ----beam size at aperture is 1.3mm, divergence is 2mRad ---that means the beam spot size will increase 2mm per meter---so at 10 meters spot size will be 21.3mm , at 100 meters away the spot size is 201.3 mm am so on.
Yes, I know that. My question is about gaussian beam parameters and how can I calculate those values. I want to describe a real life laser with them but if I apply the formulas the results are too extreme to be true. I want to know that why my calculated beam divergence is so small compared to the real beam divergence (0.2-0.5mRad instead of 2-3mRad). I want to know if I use the wrong formula/values or my theory of the concept is wrong.