Effect of many apertures in laser resonators on modes and its losses

We have studied the CO2 laser resonator (consists of a plane and a concave mirrors) in two cases. The first case delt with a resonator containing one circular aperture, and the second case two apertures, whose diameters were equal. The finite difference method has been used in order to solve Fresnel's integral equation, which describes the electric field deflection at the edges of both resonators mirrors. We have obtained the fundamental mode TEM00, which was generated inside the resonator, and we have studied its losses as a function of the position and radius of the apertures. It was found, in the first case that: TEM00 mode loss as a function of the aperture position is minimum at the vinicity of either mirrors. In addition, the loss is bigger if the aperture is located closer to the concave mirror than to the plane mirror. The loss is inversely proportional to the aperture radius. The aperture existence inside the cavity causes the TEM00 mode shape to suffer deformations due to the electric field disturbance at the edge of the aperture. In the case of two apertures within the laser resonator, it was found that: If one of the apertures coincides with either mirrors, the problem is then reduced to a laser resonator with one aperture only. The loss is inversely proportional to the apertures radii. The apertures existence inside the cavity causes the TEM00 mode shape to suffer deformations due to the electric field disturbance at the edge of the aperture. (author)