This is version 2 of the
last note on this subject.
Example 1: Given an input Gaussian beam of waist radius W01, a lens of focal length f, what is the output beam's waist radius W02 and waist location z2?
To quickly calculate the paraxial result, a simple Zemax model can be created as follows. In this example, W01 = 0.5 mm, z1 = 10 mm, f = 50 mm and wavelength = 640 nm.
The aperture and field settings are irrelevant to Gaussian calculation; they are set for making the optical layout look good:
Pressing [Ctrl]+[b] opens the Paraxial Gaussian Beam Data window. Right-click mouse opens the setting window:
So the waist radius (1/e^2 value) is set to 0.5 mm at the surface 1. Press OK the paraxial Gaussian beam results are given:
Notice that the image plane, the geometrical focus, is not exactly at the Gaussian beam waist. So a simple Merit Function can be used to move the image plane to the waist:
Optimize it and the image plane is adjusted to be at the waist. As the result, the Gaussian beam focus is about 66 um in front of the geometrical focus:
Example 2: We still have the same input Gaussian beam W01 = 0.5 mm and the lens f = 50 mm, but we want the focused beam waist radius to be 5 um. To do this, another lens is needed to expand the input beam first; say we have a f = -10 mm lens in hand. Where does this lens need to be? (d = ?)
To solve this, simply insert the lens f1 = -10 mm into the Zemax model:
Add in a GBPW operand into the Merit Function to calculate Gaussian waist. The target value is 5 um:
After optimization, Zemax gives the correct thickness of lens 1 to be 80.74 mm and the Paraxial Gaussian result shows that the beam is focused to 5 um radius:
Note that these are the first-order, paraxial calculations. Real lenses have aberrations and usually cannot give exactly the same results and will usually yield strong side-lobes. The next step should be to replace with the real lens models and use POP for actual beam evaluation.
