Selection of Single Longitudinal Modes

In single-mode operation with internal mode selection we can expect output powers that reach the fraction Ai g of the multimode power, 

In the argon-ion laser the width of the gain profile is about 8 GHz. With a free spectral range of Au = c/(2nt) = 10 GHz of the intracavity etalon, single-mode operation can be achieved. This implies with n = 1.5 a thickness t = 1 cm. 

The finesse F of the etalon has to be sufficiently high to ensure for the modes adjacent to the selected mode losses that overcome their gain (Fig.5.37). Fortunately, in many cases their gain is already reduced by the oscillating mode due to gain competition. This allows the less stringent demand that the losses of the etalon must only exceed the saturated gain at a distance away from the transmission peak. 

Often a Michelson interferometer is used for mode selection, coupled by a beam splitter BS to the laser resonator (Fig.5.38). The free spectral 

In a more detailed discussion the absorption losses of the beam splitter BS cannot be neglected, since they cause the maximum reflectance R of the Fox-Smith cavity to be less than 1. Similar to the derivation of (4.73), the reflectance of the Fox-Smith selector, which acts as a wavelength-selecting laser reflector, can be calculated to be [5.52] 

5v = ic/(L2 + L3) of this Fox-Smith cavity [5.51] again has to be broader than the width of the gain profile. With a piezoelement PE, the mirror M3 can be translated by a few microns to achieve resonance between the two coupled resonators. For the resonance condition 

The two prisms narrow the spectral width of the gain profile above threshold to about 100 GHz. If the free spectral range of the thin etalon 1 is 100 GHz (= AA 1 nm at A = 600 nm) and that of the thick etalon 2 is 10 GHz, single-mode operation of the cw dye laser can be achieved. This demands t =0.1 cm and 2 = 1 cm for 2 = 1.5. 

From the discussion in Sect. 5.3 it should have become clear that simultaneous oscillation on several longitudinal modes is possible when the inhomogeneous width Avg of the gain profile exceeds the mode spacing c/d (Fig. 5.22). A simple way to 

This is the reason why virtually all single-mode lasers use internal mode selection. We now discuss some experimental possibilities that allow stable single-mode operation of lasers with internal mode selection. As pointed out in the previous section, all methods for achieving single-mode operation are based on mode sup- 

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Ihnable laser oscillator A laser resonator, or cavity, integrating intracavity frequency selective elements such as gratings, etalons, or prisms, or a combination of these. Usually this definition applies to laser devices capable of narrow-hnewidth, or single-longitudinal mode, emission. 

In the previous sections we have seen that without specific manipulation a laser generally oscillates in many modes, for which the gain exceeds the total losses. In order to select a single wanted mode, one has to suppress all others by increasing their losses to such an amount that they do not reach the oscillation threshold. The suppression of higher-order transverse TEM modes demands actions other than the selection of a single longitudinal mode out of many other TEMqq modes. 

Fig.13.9. Laser cavity using Fox-Smith interferometer for selection of a single longitudinal mode.

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... 

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