Spatial Domain. ≈ In the spatial domain, the highest HG-mode that participates in the coupling can be found in two ways. First of all, it can be deduced from the spatial structure in the mode profile shown in Fig. 3.3b. The highest spatial frequency can be attributed to the highest-order mode involved. Xxxxxxx [12] states that the spatial period Λm of mode number m and the mode number m are related via Λm 4w/√m, with w the waist of the fundamental mode. An ≈ intersection of the intensity profile shows that the lowest spatial period is Λ 31 µm, which corresponds to a mode number of m = 480 for a waist of w = 170 µm. Taking into account the 4-fold frequency-degeneracy, which means that at resonance only one out of four modes is excited, we estimate for the total number of coupled modes ∼ 480/4 = 120. As an alternative method to determine the highest-order coupled mode, we insert an on- axis diaphragm inside the resonator. The opening of the diaphragm is increased until the intensity profile on the mirror does not change anymore. For this setting, all modes pass ≈ apparently the diaphragm. The diameter of the diaphragm 2a is a direct measure for the mode size. The corresponding mode m number is found from m (a/w)2 [12]. Experimentally, we find that for a diameter of the diaphragm of 6 mm (and higher) the spatial period remains constant. Combined with w = 170 × 10−4 µm, the highest-order mode has a mode number m ∼ 310. This is roughly in agreement with the measurement based on the spatial period.
Spatial Domain
