Thermal effects are still an important factor for beam quality and stability in high-power laser systems, and many methods have been adopted to decrease their influence^[1–3]. A telescopic thermally stable cavity is a typical scheme that has been used for a long time^[4–7]. However, lots of telescopic resonators are designed based on a single-wavelength 1064 nm laser, and the length is usually more than 100 m long. In some cases, two different wavelengths of lasers are necessary to produce sum-frequency laser beams, such as 589 and 355 nm lasers, especially there are no corresponding fundamental waves in all-solid-state lasers. Thus, both fundamental beams must operate in a stable zone in order for the whole system to work efficiently. A T-shaped composite cavity has been demonstrated as a good resonator for 589 nm sum-frequency generation because of the virtues of flexibility and temporal and space overlapping^[8].

In this Letter, according to the background mentioned above, on the basis of analyzing the influence of the distance between each of the two optical elements as well as the telescope’s focal distance and defocusing amount on the fundamental mode radius at the laser rod and the system stability in the longer 1064 nm linear cavity, a shorter system is presented and the parameters are also used for the 1319 nm L-shaped telescopic resonator design. It demonstrates that a new shorter composite telescopic system would be suitable for yellow laser generation by sum-frequency conversion based on a 1064 and 1319 nm laser that would operate in a wide stable zone and be of good beam quality.

As shown in Fig. 1, the system consists of 1064 nm linear (M1 and M3) and 1319 nm L-shaped (M2, M4, and M3) resonators. All of the mirrors are plane-plane ones. The two fundamental beams are coupled to a sum-frequency crystal by a 45° mirror, M4. Both surfaces of M4 should be coated with a high-transmittance coating at 1064 nm. In addition, high reflectivity at 1319 and 589 nm is added to the left surface. For telescope 1 and telescope 2, the negative lens focal lengths are f1 and f3, respectively, and the positive lens focal lengths are f2 and f4. The negative lenses are near the sum-frequency crystal. The gain mediums are both Nd:YAG rods with the same radius, which are close to the corresponding end reflective mirrors M1 and M2. Q-switched devices may be inserted between the laser rod and the telescope for pulsed operation. The output mirror M3 should be covered with an antireflective coating at 589 nm and a high-reflective coating at 1064 and 1319 nm.

Generally speaking, laser crystals could be regarded as thick lenses under high-power operation^[9]. The equivalent configuration is shown in Fig. 2.

The thermal focal length of laser rods Nd:YAG1 and Nd:YAG2 are fr1 and fr2, respectively. Therefore, f1, f2, and fr1 could be regarded as a whole thick lens with focal length F. H1 and H2 are the right and left principal planes to the surface, which are described in Ref. [10], H1=(ΔL3+L2f2)fr1Δ(f2+fr1−L3)−f22,(1)H2=f1[L2(fr1+f2)−L3(f1−Δ)]Δ(f2+fr1−L3)−f22,(2)F=f1f2fr1Δ(f2+fr1−L3)−f22,(3)Δ=f2+f1−L2,(4)where L1 is the distance from output mirror M3 to the negative lens f1 of the telescope systems. The distance between the two lenses, f1 and f2, in the telescope is L2. fr1 and fr2 are the equivalent thermal lenses of the rods. L3 is the length from f2 to fr1, which is geometric distance l3 plus l/2n; l is the length of the rod, n is the refractive index, and L4 is the geometric distance l4 plus l/2n. Likewise, the 1319 nm L-shaped cavity can be defined with the same parameters. Δ represents the defocusing amount.

Moreover, by means of the characteristics of the telescopic resonator, the fundamental beam radius on the gain medium should be almost equal to the radius of the laser rod. We assumed that the radii of the laser crystals are both about 2.5 mm. Because the laser medium is close to the end mirror, the size of the fundamental beam on the mirror could be represented as that on the rod. By calculation and simulation, the first set of parameters were selected to meet with the demand. When L1=70cm, L2=10.3cm, L3=40cm, and L4=16cm, a 1064 nm thermally insensitive telescopic resonator is presented with f1=4.08cm and f2=14.9cm. The total length is more than 130 cm, and the fundamental mode radius on mirrors M1 and M3 are simulated in Fig. 3. It is shown that the fundamental beam radius is near 2.5 mm when the thermal focal length changes from 3.5 to 4.8 m, while the beam on M3 varies obviously.

In general, with the increase of pumping power, the stable range would be changed and the laser rod’s thermal focal length would be shorter. It is necessary to analyze some influencing factors for both the 1064 and 1319 nm laser system to establish a reasonable composite telescopic resonator for sum-frequency generation.

First, defocusing amount plays an important role in this arrangement, in which change means L2 varied. Three values of L2 are chosen and applied to the simulation, as shown in Fig. 4. It can be seen that the defocusing amount does not influence the laser beam size on M1, but the stable zone would be moved to the shorter thermal focal length as L2 varies from 10.34 to 9.94 cm. Thus, with the increase of pumping power, the stability of the laser system could be controlled by adjusting the defocusing amount and the laser mode would not be changed.

From Figs. 1 and 2 it can be seen that, for a fixed telescope system under a certain pumping power, L1 and L4 are the variation, so we also simulated the beam radius on M1 when L1 and L4 changed. It illustrated that L4 did not affect the beam and the stability, while L1 influenced not only the beam size but also the range of stability, as shown in Fig. 5.

It is obvious that some parameters may be changed that would not affect the whole laser system operation but would shorten the cavity length and save the space. Therefore, an optimized 1064 nm resonator is presented as the value of L1, L2, L3, and L4 is set to 40, 4.5, 20, and 4 cm, and the focal lengths of the telescope lenses are 9.6 and 5 cm, respectively. The results (Fig. 6) are the following: the total resonator length is about 69 cm, which is almost half of the first one; the stable zone is wider and the system could operate on a higher pumping power.

For the 1319 nm laser cavity we also used the same parameters mentioned above, as can be seen in Fig. 6. It is of the same change law as with 1064 nm, but there is some difference in size from the 1064 nm beam on the end mirror. Therefore, it could be deduced that changing some parameters, such as L1 and the defocusing amount, could adjust the 1319 nm laser beam radius. Here, we only changed L1 to 32 cm, while the 1319 nm beam size is near that of the 1064 nm laser (in Fig. 6, a second 1319 nm). That is beneficial for the T-shaped system’s operating stability because the two lasers are both in a stable zone, so the whole system is stable, which is also helpful for sum-frequency generation.

In conclusion, by establishing the thick lens model and calculating and analyzing the influence of the defocusing amount and the distances L1 and L2 on the beam radius on the rod and stable zone, a shorter thermally insensitive telescopic resonator is presented. The parameters are not only suited for a 1064 nm resonator, but also can be applied to a 1319 nm cavity, so a shorter new T-shaped composite cavity is designed that can be available for yellow laser generation.