Walk-off losses

A pair of low-reflectivity etalons (finesse of 1.8) reduces the BRF oscillating bandwidth to that of a single longitudinal cavity mode, the thin etalon of 7.5 cm FSR or -mm physical thickness, and the thick etalon of 0.33-cm FSR and 10-mm physical thickness. Two etalons of low finesse give less loss for the selected mode than a single high-finesse etalon, due to a more complete overlap of the interfering beams (less walk-off loss). In Fig. I la the thin-etalon transmission functions for the three central orders are shown as solid lines, and the products of the BRF and thin etalon functions (the composite filter) for several more orders are shown as dashed. The... 

BRF suppresses the thin-etalon orders adjacent to the selected one by adding an extra 4% loss at the frequency offset of these orders. In Fig. 1 lb, the frequency scale is expanded 300 times to show the selection of a thick-etalon mode by the selected mode of the thin etalon. Here the curvature of the thin-etalon function is just noticeable, and a central thick-etalon mode is selected by an extra 2.4% loss at adjacent orders. Finally, the thick etalon selects a single mode of the ring cavity to complete the Alter stack, by inserting an addihonal 0.4% loss at adjacent cavity modes split off from the central one by a c/P = 0.18 GHz frequency offset (P is the path length around the ring perimeter). The total absorpAon and scatter loss per round trip at the selected mode frequency for the whole Alter stack of Fig. 11, the a of Eq. (9), is 2.5%, with the walk-off loss of the thick etalon at 0.7% the largest component. 

A parallel light beam with the diameter D passing a plane-parallel plate with the angle of incidence a therefore suffers reflection losses in addition to the eventual absorption losses. The reflection losses increase with and are proportional to the ratio djU) of the etalon thickness d and the beam diameter D (walk-off losses). 

Besides these walk-off losses, reflection losses also cause a decrease of the energy stored in the resonator modes. With the reflectivities R[ and R2 of the resonator mirrors M and M2, the intensity of a wave in the passive resonator has decreased after a single round-trip to... 

Fig. 5.4. Walk-off losses of inclined rays and reflection losses in an open resonator...

For wider tuning ranges interferometers with a variable air gap can be used at a fixed tilting angle 0 (Fig. 5.42a). The thickness t of the interferometer and with it the transmitted wavelength = 2nt cos 9/m can be tuned with a piezocylinder. This keeps the walk-off losses small. However, the extra two surfaces have to be antireflection-coated in order to minimize the reflection losses. 

Unfortunately, the reflection losses of an etalon increase with increasing tilting angle d (Sect. 4.2 and [340, 387]). This is due to the finite beam radius w of the laser beam, which prevents a complete overlap of the partial beams reflected from the front and back surfaces of the etalon. These walk-off losses increases with the square of the tilting angle 0, see (4.64a), (4.64b) and Fig. 4.42. 

The thickness t of the etalon should be small in order to minimize walk-off losses by the tilted etalon. If we assume as a reasonable number t = 0.5 cm,... 

The walk-off losses limit the tuning range of tilted etalons within a laser resonator. With increasing angle 3 the losses may become intolerably large [4.24b]. 

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