I want to collimate the light of a laser diode – how do I find the right aspheric lens?
Is the numerical aperture sufficient?
The numerical aperture (NA) is crucial when selecting an aspheric lens because it directly impacts the lens's performance in terms of light-gathering ability, resolution and its suitability for specific applications requiring precise control over light. Numerical aperture is a dimensionless number that combines the lens's refractive index and the half-angle of the maximum cone of light that can enter or exit the lens.
It is important that the lens captures as much of the diverging laser beam as possible. To do this, it must have a numerical aperture that is larger than the aperture of the more divergent axis (fast axis) of the laser beam. Otherwise clipping will occur and part of the laser beam will be lost for geometry reasons.
Often, however, you will not find the numerical aperture of the laser diode directly in the data sheet, but e.g. the parallel and perpendicular divergence of the beam. In this case, you can approximate the numerical aperture for air as the optical medium quite well by halving the larger of the two aperture angles of the beam ellipse and calculating the sine of the resulting angle: NA = sin (fast axis divergence / 2).
FWHM or 1/e²?
Matching the aspheric lens to the laser diode's beam width is essential for achieving the desired outcomes as it influences the performance of the optical system, including collimation, focusing, efficiency and aberration correction. It is important to know how the divergence or beam width of the laser diode is defined in the data sheet. For some applications, the part of the laser beam covered by the 50% or FWHM value (Full Width, Half Maximum) for the divergence is not sufficient; in this case you must refer to the 87% or 1/e² value. If this value cannot be found in the data sheet, you can approximate it for a Gaussian beam profile with 1/e² ~≈ FWHM x 1.7. If you really want to capture the entire beam diameter (i.e. 99% of the contained power) in your application, you must multiply the FWHM value by a factor of 2.576.
And what about the focal length?
The effective focal length is important when selecting an aspheric lens as it reflects the unique ability of the lens to correct aberrations and control the behavior of light, leading to improved optical performance. Now that we have calculated the minimum value for the numerical aperture (NA) of the aspheric lens, its effective focal length (EFL, f) is a second value important for the actual beam diameter. This beam diameter Ø can be approximated with the formula Ø ≈ 2 x NA x EFL. Use this formula to determine the required focal length of the lens from the desired diameter of the collimated beam. Remember that the resulting beam is elliptical – the beam diameter is larger in the "fast axis"!
Does the aspheric lens match the laser’s wavelength (visible, infrared, ultraviolet)?
In the data sheet of a molded aspheric lens you will usually find a "design wavelength" – with the optical performance of the lens optimized for this wavelength. This does not mean that you cannot use the lens for other wavelengths, but if you do so, its values for the effective focal length (EFL) will change, as well as for other parameters such as the back focal length (BFL) or the wavefront error (WFE). Here you can roughly assume that with a smaller wavelength compared to the design wavelength value, the focal lengths become shorter, while the focal length values increase when the actual wavelength is above the value of the design wavelength. How a different wavelength affects the wavefront error of the aspheric lens is best simulated with one of the common optical simulation programs such as Zemax, Oslo, etc.
Search, get set, go!
With the calculated values for the numerical aperture and the focal length, you can now browse through the lens manufacturer’s aspheric lens product portfolio. Suitable for your application are aspheric lenses whose numerical aperture is larger than your calculation result and whose effective focal length EFL is as close as possible to the calculated value. The design wavelength must match the laser light’s wavelength as well as possible.
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