Minimum Beam Waist of 655nm Gaussian Laser Beam

Click For Summary

Homework Help Overview

The discussion centers around a problem involving a 655nm Gaussian laser beam with a specified waist and focal length of a lens. Participants are exploring the concept of minimum beam waist and its location in relation to the lens.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • The original poster attempts to determine the distance from the minimum beam waist to the focal point and how to calculate the radius of curvature. Some participants question the assumptions regarding the collimation of the beam and the implications of the Rayleigh range in relation to the lens focal length.

Discussion Status

Participants are actively discussing the relationships between beam parameters and the lens characteristics. Some guidance has been offered regarding the calculation of the focused spot size, while others express confusion about the Rayleigh range calculations, indicating a productive exploration of the topic.

Contextual Notes

There is a noted discrepancy in the calculations of the Rayleigh range, with some participants suggesting it is larger than expected, while others have calculated a shorter range. This indicates potential assumptions or definitions under discussion that may need clarification.

blorpinbloo
Messages
3
Reaction score
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.
 
Physics news on Phys.org
It sounds like the beam is collimated at the lens, so the source distance would be at infinity.
 
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)
 
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.
 

Similar threads

Laser Beam Diameter which Minimizes Volume?
  • · Replies 1 ·
Replies
1
Views
2K
Graduate ABCD matrix formalism for real laser
  • · Replies 0 ·
Replies
0
Views
3K
Interaction of Gaussian Beams with Optics
  • · Replies 1 ·
Replies
1
Views
1K
Graduate Mode matching to an optical cavity
  • · Replies 0 ·
Replies
0
Views
3K
How to Find the Waist of a Gaussian Beam at the Focus Using a Lens?
  • · Replies 2 ·
Replies
2
Views
9K
Undergrad Could a Gaussian beam be described as parallel at a large distance?
  • · Replies 3 ·
Replies
3
Views
1K
How Do You Calculate the System Matrix for a Lens After a Beam Waist?
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Grating Resolving Power of Laser Beams with Gaussian Distribution
  • · Replies 2 ·
Replies
2
Views
3K
Gaussian Beam in a Symmetric Confocal Resonator.
  • · Replies 1 ·
Replies
1
Views
4K
Graduate Gaussian Beam Focusing: Find A(0) at Beam Waist
  • · Replies 3 ·
Replies
3
Views
2K