Principle of Beam Expander Structure
Beam expanders are used to increase the diameter of a collimated beam of light, such as a laser beam, while preserving its collimation. It is commonly used in laser optics and other applications where modifying the size or divergence of a beam is necessary.
In a typical beam expander, the input beam is a collimated laser, or light beam enters the first optical element. When the beam is getting expansion, the first optical element changes the divergence of the incoming beam, and the second optical element re-collimates the beam, resulting in a larger diameter. The beam expansion ratio M is determined by the focal lengths of the two lenses or mirrors:
Where f1 and f2 are the focal lengths of the first and second optical element.
Beam Expander in Zemax Sequential Mode
When creating a beam expander model in Zemax OpticStudio, mostly in sequential mode, it typically involves setting up lenses or mirrors that expand a collimated beam of light. Sequential mode is ideal for lens-based beam expander design. Below is an example. With defining the system wavelength (550 um) and entrance pupil diameter (10 mm) to the initial beam diameter in the system explorer, the two lenses are to be defined. The beam is defined as a Gaussian Apodization, with factor of 2. Since the output of the beam expander is collimated beam, the “Afocal Image Space” should be selected.
The lens data of the beam expander is listed below. Two lenses made of N-BK7 are applied, with all four radii of both single lenses set as variable. The distance between two lenses, set as 200 mm here, geometrically relates to the expansion of the beam from input.
Resulted beam expander structure is shown below with 45 rays in ring shape.
Some operands of merit function are applied here to limit and optimize this beam expander structure. REAY reads local real ray y-coordinate in lens units at the surface No.6, the image plane. This operand directly defines output beam width as 15 mm, 3X of that of input beam, 5 mm. MNCA and MXCA restrain the distance, i.e. the air center thickness of the overall lens (from surface 1 to 5), into the range of 0.5 mm to 1 m. The minimum edge thickness of air between second lens to image plane is set as 0.5 mm by MNEA. The center thickness of both lenses is limited by operands MNCG and MXCG, with limits of 2 mm to 15 mm. Edge of both components are limited to be thicker than 2 mm, by MNEG.
All commands above lead a merit function of 0.0003 after optimization. Limits and requirements are reasonable and executable.
Prescription Data and Image Interference
After optimization, both focal lengths in object and image spaces are towards infinite, indicating a successful optimization of an afocal system.
For manufacturing purposes, volume and mass of the both lens elements are estimated in the format below. Density number is in g/cc, which is exported from library of materials.
As the input is a coherent light, i.e. single wavelength, the image plane will come with interference if there is a tilt light incidence. The interferogram is shown below with exit pupil shape at y-tilt of 2.5 degrees, suggesting the beam expander inducing interference from a thin light beam.
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