Diffraction losses and mode structure of equivalent TEM_00 optical resonators

Abstract

A general description is given which allows one to determine the diffraction losses and mode structure (intensity and phase distribution) of any arbitrary TEM(00) laser resonator lying in the stable region of the stability diagram. By means of equivalence] relations and adaption of the aperture size to the size of the undisturbed Gaussian beam it is possible to reduce the number of characterizing parameters to two: the adapting factor s, the product (g(1) . g(2)). Numerical results are shown. The intensity pattern of the far field is discussed.

Grid-based simulation program for gravitational wave interferometers with realistically imperfect optics

“…First, however, we note that many tests of the simulation program have been performed [37] to ensure its validity as a realistic model of a LIGO interferometer. These tests include: comparisons with numerical simulation results in the literature [16,38], to verify basic operations like beam propagation and diffractive loss from finite mirrors; comparisons against modal analysis methods [9] for simple interferometer imperfections, such as mirror tilts; and comparisons against analytical methods [39] for computing the effects of Zernike polynomial [40] mirror surface deformations. We have implemented anti-aliasing and energy-conservation procedures (cf.…”

“…Grid-based simulations of intra-cavity laser fields have a long history (e.g., [16]), and have been applied previously (e.g., [17,18,19]) to the study of the interferometric GW detectors now being implemented. But simplifications are generally imposed, such as restricting the optical deformations that are studied (e.g., considering only geometric imperfections, like tilt and curvature mismatch [17,18]), and/or by modeling a relatively simple cavity system [19].…”

<title>High-power solid state lasers with improved beam quality</title>

“…For resonators with internal lenses an equivalent two-mirror resonator can be found which makes calculation of the fundamental mode straightforward.' The beani parameter product M2, expressed by time second moments of the near-and far field intensity distributions amid normalized to the beam parameter product of the fundamental mode is approximately given by2 I M2s( a 1 (1) Wü (Za)) where Za 5 the location of the limiting aperture of radius a and W0(Za) j5 the radius of the fundamental mode at the axial position Za• For a >> w0, equation (1) is quite accurate. Form this equation it is obvious that for a given size of the fundamental mode the cross section of the active medium should be kept small in order to achieve a low beam parameter product.…”

“…The neaning of equations (2) and (3) is now exchanged, w is the waist radius at the mirrors and w01 the mode radius in the rod. The beam Parameter Product as a function of the pumping power can easily be calculated using equations ( 1) and (3) if the power of the thermal lens is known. Neglecting birefringence, the power of the lens is:6…”

“…For a slab with a = 7 mm and b = 25 miii one obtains A/A0 = 0.72 and for a slab with a = 5 nm and b = 30 mm the ratio is A/A0 = 0.83. Of course, another reason to choose a thin slab is that the beam quality is improving according to equation (1). Since folding of the beam makes the system more complicated the beam should be folded only in the y-direction.…”