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We demonstrate direct production of a high power Laguerre–Gaussian mode from a diode-pumped Nd:YVO4 1.3-μm bounce amplifier with an asymmetric cavity configuration. A maximum LG output of 7.7 W is obtained.
©2007 Optical Society of America
1. Introduction
The Laguerre–Gaussian (LG) beam is an eigen mode of the paraxial propagation electromagnetic equation and has received attention recently for possible use in various applications including optical manipulation and material processing, because of its orbital angular momentum arising from an on-axial phase singularity (optical vortex) [1–3]. An LG beam, having an annular spatial form in the far-field, can also be useful for super-resolution microscopes based on stimulated emission and up-conversion fluorescence depletion [4–6]. A hologram or spatial light modulator (SLM) is typically used to produce an LG beam [7]. However, these methods involve significant wastage of beam power, since only about 30% of the energy of the incident Gaussian beam is converted into the LG beam. The output power is also limited by the low damage threshold of holograms and SLMs. Direct production of LG modes has been demonstrated using a laser cavity by placing phase elements or special mirrors inside the resonator [8, 9]. However, the output power achieved is mostly limited, because insertion of additional elements inside the resonator causes severe internal loss in the laser cavity. Recently, Chen et al. have demonstrated a direct generation of LG output from an end-diode-pumped Nd:YVO4 laser by using a doughnut shaped pumping [10,11]. They did not mention quantitatively the laser performances including the output power and optical efficiency, and neither they did address 1.3-μm laser action.
Side-pumped bounce amplifiers, in which a very high inversion population density is produced near the pump face, have generated high power output at 1.06 μm and 1.3 μm [12–14]. These amplifiers can also be used to generate high quality output using an asymmetric resonator approach based on the power dependence of the thermal lens [15].
In this paper, we present the first demonstration, to the best of our knowledge, of the direct production of a high power (> 7 W) 1.3-μm LG mode from a diode-pumped Nd:YVO4 bounce amplifier with an asymmetric cavity configuration. This system does not require any additional phase elements, such as a hologram or a phase plate, to produce LG modes. It is based on the formation of a limiting aperture for the desired LG mode in the gain medium by utilizing power-dependent thermal lensing of the laser material. High power 1.3-μm LG lasers will open up new applications in optical manipulation due to their low absorption and scattering loss in water.
2. Experiment
Figure 1 shows a schematic diagram of a laser cavity. The amplifier used in the current study was a 1-at.% Nd-doped a-cut YVO4 slab with dimensions 2 mm × 5 mm × 20 mm. The pump diode was a 55-W CW diode bar array. The output of the diode was focused by a cylindrical lens to be a line with dimensions 0.2 mm × 18 mm on the pump face. The cavity was formed by a high reflection flat mirror and an 85% reflective flat output coupler, to give a wavelength of 1.3 μm. To achieve good spatial overlap between the pumped region and laser mode, two cylindrical lenses (f = 50 mm) were placed inside the cavity. The internal bounce angle with respect to the pump surface of the amplifier was ∼ 10°.
Fig. 1. Experimental setup of a laser system with a symmetric cavity. EM, and OC are a high-reflection flat mirror and a 85 % reflection output coupler, respectively. VCLs are vertical cylindrical lenses.
The cavity was compact and symmetric with respect to the position of the Nd:YVO4 amplifier, making the cavity stable at all pump levels. Its length was 160 mm (L1 = L2 = 80 mm). The output exhibited a typical multi-mode profile, as shown in Fig. 2(a), and its power reached 11.2 W at maximum pump level (Fig. 2(b)).
Fig. 2. (a) Spatial form of the output from the symmetric cavity. (b) Experimental plots of output power as a function of pump power.
To improve the beam quality, the cavity was lengthened on both sides to be slightly asymmetric with respect to the position of the Nd:YVO4 amplifier, as shown in Fig. 3. The total cavity length was 380 mm with L1 = 180 mm and L2 = 200 mm. Below a pump power of 40 W, the cavity was stable and the laser output showed a mixed-mode (a mixture of Hermite–Gaussian HG00 and HG01 modes) profile in the far-field. Above this pump level, the laser started to produce the HG01 mode (Fig. 4(a)). We carefully re-adjusted the cylindrical lens pair and cavity mirrors, after which the laser operated in a ‘doughnut’ mode with an annular intensity profile, as shown in Fig. 4(b).
To confirm that the laser output beam contains a phase singularity, we analyzed the wavefront of the output by interferometric fringes. Figure 4(c) shows fringes formed by the laser output beam and a copy of itself. The laser output exhibits an on-axial phase singularity. Fringes formed by the laser output and a spherical reference beam have a single-arm spiral, as shown in Fig. 4(d). These results indicate that the laser operates in the LG01 mode. Figure 5 shows experimental plots of the LG01 output power as a function of the pump power. A maximum output power of 7.7 W was obtained at a pump power of 54 W. A corresponding optical efficiency of 14 % was achieved.
Fig. 4. Spatial forms of (a) HG01 and (b) LG beams. (c) Observed fringes formed by the LG beam and a copy of itself. (d) Fringes formed by the LG and spherical reference beams.
3. Discussion
3.1 HG01 mode discrimination due to thermal lensing in a diode-side-pumped bounce laser
Asymmetric non-uniform pumping in a side-pumped bounce amplifier produces an astigmatic thermal lens in the crystal. The phase distribution along z-axis (vertical direction), which exhibits a parabolic curved temperature distribution, involves a pronounced thermal lens easily compensated by a cylindrical lens pair inside the cavity. The phase distribution along y-axis (horizontal direction), which exhibits an exponential temperature distribution, includes higher order terms related to effective aberrations than the second order (thermal lensing) term. Thus, the horizontal thermal lens power depends significantly on the transverse mode size, as shown in Fig. 6. In comparison with the HG01 mode, the HG00 mode with a minimum spot inside the cavity experiences a stronger horizontal thermal lens.
Fig. 6. Numerical simulation of phase distribution in an amplifier with 1342-nm lasing at 40-W pumping. The red and blue parabolic curves show the thermal lensing experienced in the amplifier for the HG00 and HG01 modes.
We numerically simulated the horizontal thermal lens powers by using the conventional heat diffusion equation [16] and the heat loading formula in 1.3-μm lasers proposed previously by our group [17,18]. At a pump power of 40 W, the HG00 mode experiences a 5.2-m-1 horizontal thermal lens, estimated from a parabolic fit curve to the simulated phase distribution within an effective HG00 mode size (2.4 mm) in the amplifier. When the cavity length is extended to L2 = 200 mm and made asymmetric with respect to the position of the slab amplifier, the horizontal thermal lens makes the cavity unstable and suppresses the HG00 mode operation. Meanwhile the HG01 mode experiences a horizontal thermal lens with a power of 3.8–4.0 m-1 within a pump power range of 40–50 W, and the laser can maintain the HG01 mode (Fig. 5). These simulations demonstrate that the horizontal thermal lens showing transverse-mode-dependence contributes mainly to the unexpected HG01 mode operation.
3.2 Mode conversion from HG modes to LG modes in a diode-side-pumped bounce laser
Although the physics of HG–LG mode conversion in a bounce laser is not fully understood, we believe that a bounce laser cavity can be used to create an HG–LG mode converter by utilizing the thermal lens in the amplifier and a cylindrical lens pair inside the cavity. A schematic model of a bounce cavity is shown in Fig. 7.
In the vertical plane, a con-focal cylindrical lens pair placed inside the cavity cancels the vertical thermal lens and causes a 2π Gouy phase shift in the cavity HG10 mode traveling from the EM to the OC. In the horizontal plane, where there is no cylindrical lens pair, a Gouy phase of the cavity mode is determined by the horizontal thermal lens. A wavefront of the HG01 mode experiences a Gouy phase shift of π while traveling from the EM to the OC. Consequently, there is a Gouy phase difference of π/2 between the vertical and horizontal modes while traveling from the amplifier to the OC (a half-way trip of the cavity). When the HG01 and HG10 modes are allowed to oscillate, the cavity operates in the LG01 mode.
4. Conclusion
We have demonstrated direct production of a high power 1.3-μm LG mode from a diode-pumped Nd:YVO4 bounce amplifier with an asymmetrically extended cavity. A maximum output power of 7.7 W was obtained for a pump power of 54 W. High power 1.3-μm LG lasers, exhibiting low absorption and scattering loss for propagation in water, have potential uses in various applications, such as in optical manipulation. The laser presented in this paper can be extended to generate highly intense pulses by Q-switching as well as mode-locking techniques and offers the possibility of the production of high power optical vortexes in the visible and ultra-violet regimes.
Acknowledgments
The authors acknowledge support from a scientific research grant-in-aid from the Ministry of Education, Science and Culture of Japan and the Japan Society for the Promotion of Science.
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