Calculate the transmitted power and transmission percentage of a laser beam through an aperture.
When considering a circular Gaussian laser beam, each waveplane it produces (theoretically) has a certain energy value anywhere in the universe. Therefore, if the laser beam passes through the aperture, no matter how large the aperture actually is, there will be a certain amount of incident laser beam energy that does not pass through the aperture. Knowing the diameter of 1/e² of the laser beam, the power passing through the aperture can be calculated. Predictably, the larger the aperture, the more insignificant the proportion of power being blocked. This is important when using detectors, mainly because an inappropriate aperture size can lead to inaccurate power or energy measurements. The same is true when considering the optical design of new technologies. Finally, depending on the measurement accuracy requirements (and the centering position of the beam on the detector), as a rule of thumb, the aperture should be twice the beam size at 1/e². At this point, more than 99.9% of the incident beam power has passed through the aperture (if fully centered).
These formulas describe the behavior of a perfectly circular Gaussian laser beam. As such, they represent an approximation of the values obtained under real-world conditions. The diameter value used for the beam refers to the 1/e² parameter. We also assume that the laser beam is perfectly centered in the aperture, making the beam and aperture two concentric circles. Also, we should also know that the diameter of a Gaussian beam is a function of z. Therefore, different measuring points have different values. This involves more complex physical concepts about the propagation of Gaussian beams in space, which are not discussed here.
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