Investigation of the Impact of the Pumping Beam Waist Size and Position on the Efficiency of YVO4/Nd : YVO4/YVO4 Laser Generation

This article presents the results of the investigation of the generation eﬃciency for diﬀerent sizes and positions of the pumping beam waist inside the active medium of the YVO 4 /Nd :YVO 4 /YVO 4 lasers. The measurements were carried out for a ﬁxed resonator length of 36.1mm, a constant pumping power of 1.16W, and four output couplers with diﬀerent radii of curvature. According to the knowledge of the authors, such an extended experimental approach is presented for the ﬁrst time.


Introduction
Lasers based on the Nd : YVO4 active medium are an essential group of diode laser end-pumped solid-state lasers (DEPSSLs) due to their well-developed applications. Work on lasers with this active medium has been carried out for many years. is can be evidenced by numerous publications on this subject; however, in most cases, they relate to a specific laser configuration for a specific size and location of the pumping beam waist, which are usually close to the optimal values [1][2][3][4][5][6][7][8][9][10][11]. is article presents the results of the measurements of the generated beam power for different sizes and positions of the pumping beam waist for a constant resonator length of 36.1 mm, a constant pumping power of 1.16 W, and four output couplers with different radii of curvature. is may be a kind of complement to the work carried out so far. e measurement results were presented without theoretical analysis involving the matching of the pumping beam to the radiation distribution generated inside the resonator. Such an in-depth mathematical analysis may be the subject of further investigation on this type of lasers. However, this article can be successfully used as a reference by laser investigators and designers.

Materials and Methods
In the experiments, an active medium made by diffusion bonding of a neodymium-doped yttrium vanadate (Nd : YVO 4 ) crystal of 10 mm length with undoped yttrium vanadate (YVO 4 ) of 2 mm length was used, as shown in Figure 1. e entire manufacturing and diffusion bonding process was carried out by Claser Photonics. e use of the undoped part of the medium at the ends of the laser rod significantly reduces the harmful effect of thermal phenomena, which, under unfavourable conditions, may lead to the resonator destabilization and, consequently, interruption of the laser action. Moreover, such a structure of the active medium protects it from thermal damage through better heat dissipation.
On one side of the active medium, a dichroic input mirror was deposited, which allowed for the introduction of the pumping beam into the optical cavity with minimal losses. e mirror was characterized by a high reflectivity of the generated radiation (1064 nm) and high transmission of the pumping radiation (808 nm). On the other side of the active medium, antireflective layers at the wavelength of 1064 nm were deposited to minimize the losses of the generated radiation. e transmission of the active medium was measured using a Perkin Elmer Lambda 900 spectrometer in the range from 780 nm to 830 nm. Based on the measured transmission, the absorption coefficient for the wavelength of 808 nm was determined in accordance with the formula k � (1/d)ln(1/T), where d � 10 mm and T � 6.8%. Determined in this way, the absorption coefficient of 2.7 cm −1 corresponds to an absorption length of 0.37 cm. On the basis of the absorption coefficient and the absorption cross section for a wavelength of 808 nm equal to σ � 6 · 10 − 19 cm 2 [12], the concentration of neodymium ions was determined according to the formula N � k/σ and was equal to N � 4.5 · 10 18 cm −3 .
e source of the pumping radiation was composed of a fibre coupled LIMO 25-F100 diode laser characterized by a 100 µm core diameter and a 0.22 numerical aperture and a beam forming optic characterized by a 14 mm focal length. e spatial parameters of the pumping beam such as the waist, the distance of the waist from the optics, the divergence, and the Rayleigh range were changed by changing the distance of the fibre from the optics. e parameters of the pumping beam for a few distances of the fibre from the optics are presented in Table 1. Figure 2 shows the experimental setup used to investigate the impact of the pumping beam waist size and position on the laser generation efficiency. For the experiments, the constant power of the pumping beam equal to 1.16 W (after passing through the optics) and the constant length of the resonator equal to 36.1 mm were applied. Four output couplers with different radii of curvature were used. e parameters of the output couplers are presented in Table 2.
During the experiments, the active medium was air-cooled.
To measure the power of the generated beam, it was necessary to use an appropriate filter separating the generated radiation (1064 nm) from the unabsorbed radiation of the pump (808 nm). For this purpose, an auxiliary dichroic mirror with high reflectance at 1064 nm and high transmission at 808 nm was used. e mirror was set so that the   angle of incidence of the radiation was minimal and did not exceed a few degrees.

Results and Discussion
e measurements of the dependence of the generated beam power on the pumping beam waist size and position for four different output couplers were carried out. Figures 3-6 show the generated beam power as a function of the pumping beam waist position at five different beam waists equal to w � 96 µm, w � 118 µm, w � 161 µm, w � 252 µm, and w � 345 µm for output couplers with a radius of curvature equal to R � 50 mm, R � 103 mm, R � 150 mm, and R � ∞ mm, respectively.
In each case, the biggest changes in the output power as a function of the position of the beam waist were observed for the beam waist size equal to 96 µm. e bigger the waist, the smaller the changes of the power of the generated beam as a function of the waist position were measured. e highest power of the generated beam was recorded for a   Distance of the beam waist from the input side of the active medium (mm) Power of the generated beam (mW)  Table 3.
Taking into account all sizes of the pumping beam waist, it can be stated that the most effective position of the waist, in terms of generation, is approximately 2 mm from the input side of the active medium. is is the length of the undoped YVO 4 crystal, so the beam waist is located at the input face of the neodymium-doped Nd : YVO 4 crystal. For each of the four tested laser configurations, the pumping beam characterized by the waist of 252 µm turned out to be the most effective with the highest power of the generated beam.
e Rayleigh range of this pumping beam was 1.4 mm. is means that, at a distance of 1.4 mm from the waist, the beam diameter was equal to 355 µm. e diameter of the active medium was 4 mm; hence, it can be assumed that all pump radiations were absorbed by the active medium.
e pumping beams with waists smaller than 252 µm were characterized by a greater divergence angle and a shorter Rayleigh range. As a result, a significant part of the pumping radiation could escape beyond the active medium and did not participate in generation. In the case of the waist greater than 252 µm, the decrease in the generated power could be caused by too low power density in the active medium.
e presented effect can be explained by analysing the overlapping efficiency between the space characteristics of Power of the generated beam (mW) Figure 5: Power of the generated beam as a function of the distance of the beam waist from the input side of the active medium for the output coupler with the radius of R � 150 mm.

Conclusions
e selection of the optimal spatial parameters of the pumping beam has a large impact on the generated power. During the investigation, it was found that, for the tested lasers based on the active medium YVO 4 /Nd : YVO 4 / YVO 4 , the most effective position of the waist, in terms of generation, was approximately 2 mm from the input side of the active medium. is is the length of the undoped YVO 4 crystal, so the beam waist is located at the input face of the neodymium-doped Nd : YVO 4 crystal. e most efficient pumping beam was characterized by the waist of 252 µm.

Data Availability
No data were generated or analysed in the presented research.