The He-Ne Laser (Helium-Neon Laser) is a widely used gas laser source that emits light in the 632.8 nm wavelength, located in the red portion of the visible spectrum. In this example, we will discuss how to design a lens system to focus the laser beam at its minimum size at a distance of 30mm from the laser source. We will also evaluate when it is appropriate to use ray-based simulations and when the laser beam can be treated as a ray bundle.
He-Ne Laser Source Specifications
The He-Ne Laser operates with a mixture of helium and neon gases, generating light through a high-voltage discharge. The typical coherence length for a 632.8 nm He-Ne laser is approximately 30 cm. Here are the specifications for the He-Ne Laser used in this design:
- Wavelength: 632.8 nm
- Coherence Length: 30 cm
- Beam Divergence Angle: Derived from the beam waist
Design Task: Focus the Laser Beam at 30mm
The goal is to design a lens system that focuses the He-Ne laser beam to its minimum size at a distance of 30mm from the laser source. The beam’s waist and divergence angle are key factors in determining the focal length and beam characteristics.
Knowing the wavelength and the far field divergence angle, the beam waist is calculated to be 0.1184 mm, with a Rayleigh range of 69.7 mm. The distance of waist to measurement point is 122.77mm. We will focus the beam using a singlet lens as example.
Note: Geometrical optics is the modeling of optical systems by tracing rays. Rays are imaginary lines which represent normals to the surfaces of constant phase, or the wavefront. For a paraxial Gaussian beam, within the Rayleigh range, z < zR, the beam size changes very slowly.
In this case, beam can be modeled as collimated ray bundle. When far outside the Rayleigh range, z >> zR, beam size changes linearly with propagation distance, so the beam can be modeled as a point source.
As shown, when using rays to model Gaussian beam, we need to know if the propagation is within or beyond the Rayleigh range. This can help us decide if we should use a point source or a collimated ray bundle to model the beam. In this case, we know the beam waist location is inside of the Laser source housing. And we have calculated beam waist 0.118 mm and Rayleigh range 69.7mm, we can manually calculate the beam propagation distance z from its waist, around 122.78 mm, when the beam hits the measurement location. Since this propagation distance is not much larger than the beam Rayleigh range, z>>zR, we cannot model the beam using a point source. However, the propagation distance is also outside of Rayleigh range, we also cannot use the parallel beam.
We tentatively use ray-based method to design the system and validate our judgment above.
The design setting and layout as below.
Find the optimize beam size and location
Above we used pure ray-based approach to optimize the singlet lens so that the beam size is the smallest at 30 mm away from the Laser source output. As we know the Laser source beam diffracts as it propagates through the space, which cannot be modeled by ray-based approach. While we know that the focused spot size reported by the ray based calculation is not accurate in this case.
Here, we’ll only look at the Paraxial Gaussian Beam results using 1D Universal Plot. This plot shows the computed paraxial Gaussian beam size as a function of the image plane location.
In the plot, you can see the smallest Gaussian beam size occurs at a back focal distance around 26 mm, which turns out to be not very close to our current back focal distance 30mm. This suggests the image location found by ray-based optimization is not yielding the smallest geometrical spot size also does not result in the smallest Gaussian beam size computed by the Paraxial Gaussian Beam tool. In other words in this system the smallest spot location found by ray-based approach doesn’t agree well with the location of the smallest Gaussian beam size.
In this case, Paraxial Gaussian beam analysis and physical optics propagation are the best method to represent the laser source beam, and should be the best method to simulate the system.
Reference
- https://www.zemax.com/
- The design file used in this article is attached. How to apply and simulate a He-Ne 632 Laser application