Modeling High-Power Solid-State Lasers

Dr. Michael Bass, University of Central Florida, Center for Research and Education in Optics and Lasers

Unlike other contributors to the Super High Efficiency Diode Sources (SHEDS) program, we are not addressing the efficiency of semiconductor lasers in our laboratory at the University of Central Florida. Instead, we are mathematically modeling diode-pumped high-power solid-state lasers. Our work has two immediate goals. First, we hope to provide guidance to diode laser manufacturers regarding which characteristics are advantageous for the pumping of high-power solid-state lasers. Second, we hope to provide insights into the optimal design of the lasers themselves.

One important conclusion from our work so far is that a laser with a broad spectral bandwidth is preferable to one with a narrow bandwidth for pumping a high-power solid-state laser. This contradicts the general wisdom regarding linewidth, which is based on experience with low-power (i.e., micro) lasers, wherein a spectrally narrow pump source is demanded for efficient pumping.

In low-power lasers, the gain medium is very small, and the path available for absorption is correspondingly short, typically on the order of a millimeter. Hence, to achieve efficient pumping, the pump source must be matched very closely to the absorption line. Because a neodymium-doped crystalline laser, for example, has a quite narrow absorption line, the pump should be narrow so that the entire pump light can be absorbed.

However, in a high-power solid-state laser, an end-pumped rod laser or a laser medium in which the pump light can rattle around many times, the path available for absorption is much longer, typically a centimeter or more. Thus, absorption length is sufficient to fully absorb even weakly absorbed light. All of the light from a broad linewidth pump source can be used.

Our modeling of both Nd:YAG and Yb:YAG slab-shaped, edge-pumped high-power solid-state lasers shows that spectrally broad pump sources provide high-efficiency pumping with better uniformity than narrow sources. For example, our models reveal that a typical diode array having spectral bandwidth of approximately 3 nm and centered between 807 and 809 nm will be absorbed in a 16-mm-wide, edge-pumped slab of 0.3 percent Nd:YAG with efficiency of more than 90 percent. The uniformity of the absorbed pump power — the ratio of that absorbed near the center of the slab to that near the edge where pump light enters — exceeds 50 percent in such a case.

Similar results were obtained for Yb:YAG high-power solid-state lasers using broad-linewidth pumping near either 975 or 940 nm. Pumping the same Nd:YAG slab with a narrow-linewidth pump source at neodymium’s strong 808.5-nm absorption line can offer highly efficient pumping (100 percent), but the uniformity will be only approximately 0.01 percent.

We also found that the efficiency and uniformity of pumping depends strongly on the dopant concentration. High concentration results in high efficiency but low uniformity of pumping in an edge-pumped slab. We are exploring the possibility of improved pump uniformity in crystalline and ceramic laser media that may result from grading the dopant concentration from low at the edges to high in the center.

When edge-pumping either slab or disk lasers, the diode laser array usually is oriented with its fast axis in the plane of the slab or disk. Our models for edge-pumped disk lasers have shown that the typically high divergence of the pump beam in the fast axis should be reduced to less than 25° full width half maximum for optimum efficiency and uniformity. This may require external optics if the diode laser cannot be designed to display sufficiently low divergence. The divergence in the slow axis need not be corrected, and it is actually helpful in filling areas of the thin disk that otherwise would not be illuminated. Control over the divergence of the pump light is critical in all configurations of diode arrays and solid-state laser gain media.

Figure 1. In this calculated temperature distribution in an edge-pumped 1 × 16 × 80-mm Yb:YAG slab pumped with 9.8 kW and cooled with water at 10 °C, neither pumping nor cooling extended into the triangular-shaped (Brewster angle) ends of the slab.

We recently completed a full three-dimensional model of the edge-pumped slab laser, including end effects. Figure 1 shows the calculated temperature distribution in an edge-pumped 1 × 16 × 80-mm Yb:YAG slab using 9.8 kW of pump power with cooling water at 10 °C flowing across the top and bottom surfaces. The pump arrays were assumed to extend only along the rectangular part of the edges, and as a result, there is a decrease in absorbed pump power and, hence, in temperature near the end (from 35 to 31 °C). Because the cooling was assumed to end with the rectangular part, the Brewster angle end gets quite hot.

If we allow the cooling to extend to the apex of the Brewster end, the temperature distribution is as shown in Figure 2. Although the color scale differs from that in the previous figure, we see that the same temperature distribution is reached in the central region of the slab. In the Brewster end, in contrast, the temperature falls smoothly.

Figure 2. In this calculated temperature distribution in an edge-pumped 1 × 16 × 80-mm Yb:YAG slab pumped with 9.8 kW and cooled with water at 10 °C, pumping extended only to the rectangular regions of the pumped edges, but cooling extended to the apexes of the Brewster ends of the largest faces.

In practice, this temperature profile will produce significantly less stress-induced birefringence and lensing than the one in Figure 1. Our earlier 2-D models assumed that the whole slab looked like the central region and ignored the Brewster ends. By completing the 3-D model, we have shown that end effects can be very significant and should not be overlooked.

Our models are being developed using such commercially available software as ASAP by Breault Research Organization Inc. of Tucson, Ariz., Matlab by The MathWorks Inc. of Natick, Mass., and Femlab by Comsol AB of Stockholm, Sweden. We also are preparing a program in Matlab to compute the output power and beam properties of a high-power solid-state laser by solving Maxwell’s equations, including gain, losses, birefringence and thermal lensing. This program runs using a sparse matrix method and can analyze a laser resonator on a desktop computer in about two minutes. To make these programs more user-friendly, we also are preparing an “umbrella” program with a graphic user interface.

Meet the author

Michael Bass is professor emeritus at the College of Optics and Photonics at the University of Central Florida in Orlando; e-mail: bass@creol.ucf.edu.