Minimum Beam Waist of 655nm Gaussian Laser Beam

In summary, the given 655nm gaussian laser beam has a waist of 15mm at a lens with focal length of 12 cm. The minimum beam waist and its location can be calculated using the equation w = w0 * sqrt(1-(z/zr)^2), where w0 is the minimum beam waist, z is the distance, and zr is the Rayleigh range. The initial distance along the wave front of the beam and the focused spot size can also be calculated using the equations f = (1/R1)-(1/R2) and f*lambda/(\pi w_i), respectively. However, it is important to note that the Rayleigh range is much larger than the focal length of the lens.
  • #1
blorpinbloo
4
0

Homework Statement


A 655nm gaussian laser beam has a waist of 15mm located at a lens with focal length of 12 cm. What is the minimum beam waist and where is it located?


Homework Equations


Beam radius w = w0*sqrt(1-(z/zr)^2)
w0 = min beam waist; z = distance, zr = Rayleigh range


The Attempt at a Solution


I'm attempting to find the distance from where w0 is located to the focal point, so I'd be able to calculate the distance R1 to the lens. Then perhaps calculate R2 from (1/R1)-(1/R2)=(1/f), where I assume the minimum w0 is located. Problem is I have no idea how to find this initial distance along the wave front of the beam.
 
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  • #2
It sounds like the beam is collimated at the lens, so the source distance would be at infinity.
 
  • #3
It looks like you Rayleigh range is much larger than the focal length of the lens. In this case, your focused spot size will be given by f \lambda/(\pi w_i), where w_i is the initial waist size. You should find the derivation in any book on lasers (e.g. Yariv or Siegman)
 
  • #4
dnquark said:
It looks like you Rayleigh range is much larger than the focal length of the lens.
That's weird, I have calculated a much shorter Rayleigh range.
 
  • #5


To calculate the minimum beam waist, we can use the formula w0 = w * sqrt(1 - (z/zr)^2), where w is the waist of the beam at a distance z from the waist and zr is the Rayleigh range. Since we know the waist of the beam at a distance of 15mm from the lens, we can plug in these values to solve for zr.

w0 = 15mm, z = 12cm = 120mm

15mm = 120mm * sqrt(1 - (z/zr)^2)

Solving for zr, we get zr = 120mm * 0.875 = 105mm.

The minimum beam waist, w0, is located at the Rayleigh range, zr, which is 105mm from the lens. Therefore, the minimum beam waist is located at a distance of 105mm from the lens.
 

1. What is the minimum beam waist of a 655nm Gaussian laser beam?

The minimum beam waist of a 655nm Gaussian laser beam refers to the smallest diameter of the laser beam at its narrowest point. It is typically measured in millimeters and is an important parameter in determining the quality and focusability of the laser beam.

2. How is the minimum beam waist of a 655nm Gaussian laser beam determined?

The minimum beam waist of a 655nm Gaussian laser beam is determined by the beam's divergence and its wavelength. It can be calculated using the formula w0 = λ/(π*θ), where w0 is the minimum beam waist, λ is the wavelength, and θ is the beam's divergence angle.

3. Why is the minimum beam waist of a 655nm Gaussian laser beam important?

The minimum beam waist of a 655nm Gaussian laser beam is important because it affects the beam's focusability and intensity. A smaller beam waist means a more tightly focused beam, which can be useful for precision cutting or drilling applications. It also affects the beam's power density, which is important for material processing and laser-matter interactions.

4. Can the minimum beam waist of a 655nm Gaussian laser beam be adjusted?

Yes, the minimum beam waist of a 655nm Gaussian laser beam can be adjusted by changing the beam's divergence angle. This can be done by using optical components such as lenses or mirrors to manipulate the beam's shape and size.

5. How does the minimum beam waist of a 655nm Gaussian laser beam compare to other laser beams?

The minimum beam waist of a 655nm Gaussian laser beam can vary depending on the laser's power and other parameters. However, in general, it is smaller than other laser beams with longer wavelengths, such as 1064nm infrared lasers. This is because shorter wavelengths have a higher diffraction limit, allowing for tighter focus and smaller beam waists.

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