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Light loss when passing a Gaussian beam through a circular aperture

Consider the light loss when a Gaussian beam passes through a circular aperture as shown in the figure below.

Amount of light passing through the aperture of a Gaussian beam_001.PNG

The intensity at a distance r from the central axis of a Gaussian beam is expressed as follows:

Amount of light passing through the aperture of a Gaussian beam_002.PNG

Here, w is the beam waist radius and i 0 =i(0).

The amount of light V(α) after leaving an aperture of radius α can be calculated using the "shell integration method" as follows:

Amount of light passing through the aperture of a Gaussian beam_003.PNG

In addition, the amount of light V0 before it leaves the aperture is equal to the result of changing α →∞ in the above equation, and is given by:

Amount of light passing through the aperture of a Gaussian beam_004.PNG

Therefore, the ratio of the amount of light before and after passing through the aperture is expressed as follows:

Amount of light passing through the aperture of a Gaussian beam_005.PNG

In particular, when α = w, the value is:

Amount of light passing through the aperture of a Gaussian beam_007.png

In this way, when the aperture is determined based on the beam waist radius, approximately 13.5 % of the light amount is lost.

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