An Axicon-Based Annular Pump Acousto-Optic Q-Switched Nd:GdVO₄ Self-Raman Vortex Laser

Abstract

We report, for the first time, the generation of a 1173 nm acousto-optic Q-switched self-Raman vortex laser with an axicon-based annular pump system. A 20 mm long Nd:GdVO₄ crystal was used as the self-Raman crystal. Both the fundamental field and the first-Stokes field were investigated using the respective output couplers. In comparison with both vortex fields, a noticeable beam cleaning-up effect and pulse compression were observed from the 1063 nm fundamental field to the 1173 nm first-Stokes field. A Stokes field carrying a unitary topological charge was achieved. Finally, the average output power of the first-Stokes vortex emission reached 454 mW under an incident pump power of 19.5 W, corresponding to a pulse width of 45.7 ns. It was beneficial to apply a high peak power from the Q-switched laser and self-Raman conversion to expand the applications of the vortex laser beam.

1. Introduction

Carrying spiral wavefront and central phase singularity, optical vortices are known as a kind of beam with doughnut intensity distribution [1]. Given their unique structure, many applications have been found in fields such as optical tweezing, particle manipulation, optical communication, topological quantum simulation, ultra-resolution imaging, chiral processing and astronomy [2,3,4,5,6,7,8,9]. Currently, the methods used to generate optical vortices include extra-cavity tuning and intracavity direct generation. For extra-cavity tuning, extra components are utilized, such as a spiral phase plate [10], Q-plate [11], mode converter [12], forked diffraction grating [13] and meta-surfaces [14]. In comparison, intracavity methods are cost-effective and suitable for multi-wavelength vortex beam generation with a higher conversion efficiency and higher beam quality. Moreover, it is relatively easy to produce optical vortex beams with tunable handedness and a topological charge. Recent studies have revealed promising results [15,16].

Of the four intracavity optical vortex generation methods, namely, mode selection with a spheric lens, off-axis pumping, a defect mirror and an annular pump, the most promising method with extensive developments is the annular pump. The idea is to excite the Laguerre–Gaussian mode with an annular gain profile. Given its simple linear structure and flexibility, the annular pump can be used in many laser designs, making it an ideal choice for producing high-power optical vortices. An axicon is a better approach for realizing flexibility in the annular gain profile. In 2015, Zeng et al. [17] presented a theoretical analysis of an annular beam generated with an axicon–lens system based on interference theory; they found that a thin ring will be formed in the focal position. In 2016, Hu et al. [18] applied an axicon–lens system in a 1.0%at Nd:YVO₄ microchip laser for a 10 cm cavity. Under the absorbed power of 7 W, a pulsed LG₀₁ laser with an output power of approximately 570 mW and pulse width of 198 ns was obtained under the pulse repetition frequency of 65 kHz.

Nonlinear frequency conversion methods [19,20], such as stimulated Raman scattering, are a useful tool for achieving an easy frequency conversion, orbital angular momentum transfer and even topological charge doubling. In 2013, Andrew et al. [21] from Macquarie University used a 20 mm long Nd:GdVO₄ as a Raman and lasing medium, which as a first-Stokes emission produced an output power of 380 mW and a fundamental beam of 400 mW under the incident pump power of 6.8 W. The LG₀₁ mode was preserved for the fundamental and the Stokes fields, respectively, which showed that the orbital angular momentum in the fundamental fields was transferred to the Stokes field. In 2020, Ma et al. [22] applied an annular pump beam to power a 5 mm Nd:GdVO₄ crystal for stimulated Raman conversion. Under the pump power of 5.69 W, continuous-waves first-Stokes were emitted at the wavelengths of 1173 nm (corresponding to a Raman shift of 882 cm⁻¹) and 1108 nm (corresponding to a Raman shift of 382 cm⁻¹). The corresponding output power was 133.4 mW and 49.8 mW, respectively. They also observed that in the pump power region of 3.46~3.97 W, 1108 nm and 1173 nm Stokes emissions can both retain the annular intensity profile through a slight adjustment of the output coupler.

With regard to stimulated Raman scattering, an acousto-optic Q-switched pulse may prove more favorable against continuous waves, since Q-switched pulsed leads to a high peak power and efficient Raman conversion. Vanadate crystal has been used for stimulated Raman scattering owing to its rich Raman shifts [23,24]. In this paper, we report on an acousto-optic Q-switched self-Raman vortex laser operated based on a 20 mm long Nd: GdVO₄ crystal, which simultaneously achieved optical vortex generation and orbital angular momentum transfer from the fundamental field to the Stokes field. In this experiment, fundamental and self-Raman vortex laser operation were investigated. Comparing the obtained intensity and pulse profiles of the fundamental and the Stokes emissions, the beam cleaning-up effect and pulse compression could be clearly observed. A first-Stokes vortex field with an average output power of 454 mW and pulse width of 45.7 ns was obtained at the pump power of 19.5 W and the pulse repetition frequency of 40 kHz.

2. Materials and Methods

Nd³⁺-doped vanadate is widely used as a laser crystal for diode-pumped solid-state lasers. Being in the vanadate family, GdVO₄ crystal is a uniaxial crystal with $\overline{4}$2 m symmetry, where every Gd³⁺ is surrounded by eight oxygen atoms. [25] Since Gd³⁺ is larger in size than Y³⁺, the distance between adjacent atoms in GdVO₄ crystal is greater than that in YVO₄. The decrease of the interactions between adjacent atoms gives GdVO₄ an edge over YVO₄. For instance, the absorption coefficient of Nd:GdVO₄ at 808 nm and its stimulated emission cross-section are much greater than those of other neodymium-doped crystals at the same doping concentration. The primary transition is ⁴F_3/2→⁴I_11/2 with the emission wavelength of 1063 nm. The great natural birefringence of a-cut crystal results in a linearly polarized laser beam of the fundamental laser oscillation, which has an advantage in frequency conversion. For a-cut Nd:GdVO₄ crystal, the oscillation in the laser cavity without polarization-selective optics always produces a c-axis polarized laser. Compared with Nd:YVO₄, Nd:GdVO₄ has a higher thermal conductivity (11.7 W·m⁻¹·K⁻¹) and higher damage threshold, which means it is widely used for high-power lasers. Moreover, it has rich Raman shifts and a high Raman gain coefficient. The primary Raman shifts of Nd:GdVO₄ are the active vibration modes at 882 cm⁻¹ with a Raman gain coefficient of approximately 4.5 cm/GW excited by a ~1 μm laser [26]. Based on an 882 cm⁻¹ Raman shift, a first-Stokes emission at 1173 nm can be achieved with the fundamental wave at 1063 nm. Additionally, one can combine lasing and Raman conversion in a single crystal (a process called self-Raman conversion), which significantly reduces the cavity length.

In this experiment, an 808 nm fiber-coupled diode laser with a core diameter of 200 μm and numeric aperture of 0.22 was used as the pump source. A tailoring device for the pump beam was configured with a collimated lens (L1), an axicon (Thorlabs AX251-B, $\mathsf{\gamma } =1$°) and a focus lens (L2), as shown in Figure 1A,B. According to [27], a collimated beam will be reconfigured into a Bessel beam in a given region upon passing through an axicon. The maximum range of that region is called the maximum diffraction range $Z_{\max }$. Outside this range, an annular beam can be formed, but with multiple diffraction rings. L2 was used to refocus the beam in order to produce a better annular pump beam with fewer diffraction effects. The distance between the axicon and the lens $Z_0$ was a key element affecting the structure of the annular pump beam. The point where the annular gain appeared was called the appearance point. $z_1$ represents the distance between the appearance point and the lens L2. The point where the central intensity is resumed is called the disappearance point. $z_2$ represents the distance between the disappearance point and the lens L2. When the distance $Z_0$ was shorter than the focal length of the lens L2 ($0<Z_0<F$), a divergent annular beam was formed with $z_1$ being a function of F and $Z_0$ and $z_2$ being infinite. When the distance $Z_0$ was greater than the focal length of $F$ but smaller than the maximum diffraction range $Z_{\max }$ ($F<Z_0<Z_{\max }$), a localized annular beam (sometimes referred to as the optical bottle beam) was formed, with $z_1$ and $z_2$ both being a function of the distance $Z_0$ and the focal length of L2. In both cases, the focal radius of the annular pump beam satisfies $R=F\gamma \left(n-1\right)$ [17], where F, n and $\gamma$ are the focal length, the refractive index and the base angle of the axicon, respectively. Considering mode matching for a 20 mm long laser crystal, we decided to apply the second scenario, where the focal length of L2 was 80 mm and the distance $Z_0$ was 90 mm.

The linear cavity comprised a plane mirror (IM) and a concave mirror (OC). The total cavity length was approximately 90 mm. The IM had a high transmission coating at 808 nm (T > 95%) and a high reflection coating from 1.06 to 1.18 μm. The output coupler had a radius of curvature of 100 mm. It also had a high reflection coating at 1.0~1.1 μm (R > 99.9%) and a 4% transmission at 1173 nm. An a-cut 0.3 at.% Nd:GdVO₄ with the dimensions of 3 × 3 × 20 mm³ was wrapped with indium foil and placed in a water-cooled copper block for heat dissipation. The temperature was set to 20 °C. The two-facet crystal was polished and had an anti-reflection coating of 808 nm and 1.06 μm (R < 0.2%). An acousto-optic module (AOM, Gooch & Housego Co. (Ilminster, UK)) with anti-reflection coating of 1.06 μm was placed next to it for the Q-switching operation.

The parameters of the output beam were measured with the respective devices. To measure the topological charge, a home-made Mach–Zehnder interferometer was devised with two reflection mirrors and two beam splitters, as shown in Figure 1C. The intensity profile and self-referenced interference fringes of the vortex beam were recorded using a CCD-based laser profiler (Model: BeamOn U3, Thorlabs Inc. (Newton, NJ, USA)). The spectrum of the self-Raman vertex laser emission was obtained using a grating monochromator (Model: Omni-λ500, ZOLIX (Beijing, China)). The temporal pulse profiles of the laser output were detected with an InGaAs free-space photo detector (5 GHz, Thorlabs Inc.) and displayed on a 500 MHz oscilloscope (Model DPO3052B). The average output power was measured with a thermal sensor power meter (Model: PM310D, Thorlabs Inc.).

3. Results and Discussion

3.1. Acousto-Optic Q-Switched 1063 nm Fundamental Vortex Laser

According to the experimental configuration in Figure 1, the output coupler was first replaced with a concave mirror with a radius of curvature of 100 mm and a transmission of 5% at 1.06 μm. The average output power of the acousto-optic Q-switched 1063 nm fundamental vortex laser is depicted in Figure 2. The output power increased linearly with the increase in the incident pump power. At the incident pump power of 9.38 W, the maximum output was 855 mW at the pulse repetition frequency of 20 kHz. The conversion efficiency was 9.1%. Increasing the pulse repetition frequency to 30 kHz, the output power reached 1.02 W with a corresponding conversion efficiency up to 10.9%. The fitted slope efficiency for the output power with respect to the incident pump power was 10.2% at the pulse repetition frequency of 20 kHz, as shown in Figure 2. When the pulse repetition frequency increased to 30 kHz, the fitted slope efficiency rose to 12.7%.

Then, a CCD-based laser profiler (Beamon U3, Thorlabs Inc.) was used to record the intensity profile. As shown in Figure 2a–c, the intensity pattern changed as the pump power increased from the threshold to the maximum pump power of 9.38 W. The intensity at the center increased with the increase in the pump power. Although only the intensity profile under the pulse repetition frequency of 30 kHz is given in Figure 2, we would like to point out that this phenomenon was also observed in the fundamental field under the pulse repetition frequency of 20 kHz. This phenomenon could be explained by the superposition of the fundamental mode LG₀₀ and first-order LG₀₁ beam. A theoretical simulation of the results was performed, as shown in Figure 3. As can be observed, the center intensity increased as the intensity ratio of the LG₀₀ and LG₀₁ components increased. The ratio m is defined as the intensity of the LG₀₀ component divided by the total intensity. The intensity of the LG₀₀ component will increase as the ratio increases. Near the threshold, the loss for the LG₀₀ mode was greater than the loss for the LG₀₁ mode. As a result, the LG₀₀ component was weak, which resulted in a relatively weak central intensity and a clear doughnut structure (see Figure 3a,d). With the increase in the pump power, the gain condition changed, allowing for the intensity of the LG₀₀ component to grow. According to the simulation, the LG₀₁ mode was still a dominant component when the decrease in the depth of the central dip became noticeable (see Figure 3b,e, when m was merely 0.1; Figure 3c,f, when the ratio m was 0.2). In this case, the vortex feature of the fundamental field could also be observed and verified based on the spiral interference fringes.

Considering their highly degenerate cavity condition, the LG₀₀ and LG₀₁ components could not be separated. This may cause concerns regarding mode purity. The long laser crystal used for efficient self-Raman conversion could be responsible for this problem, causing the mismatch between the pump beam and the laser mode in the Nd:GdVO₄ crystal.

The temporal characteristics of the LG₀₁ vortex pulse were investigated. Figure 4a,c shows the pulse train and the pulse profile at a pulse repetition frequency of 20 kHz. In Figure 4b,d, the pulse train and the pule profile for the 1063 nm fundamental field under the pulse repetition frequency of 30 kHz are depicted. When the pulse repetition frequency decreased from 30 kHz to 20 kHz, the pulse width shrank from 146 ns to 115.7 ns. At a low pulse repetition frequency, the peak power was higher. Compared with the LG₀₀ pulse, the pulse width of the LG₀₁ vortex beam was significantly broadened owing to spatial effects.

3.2. Acousto-Optic Q-Switched Self-Raman Vortex Laser

Next, the acousto-optic Q-switched self-Raman vortex laser’s operation was investigated using an output coupler with 4% transmission for a first-Stokes emission at 1173 nm. Under the pulse repetition frequency of 20 kHz, the first-Stokes emission appeared as the pump power increased to 10.2 W. With the increase in the pump power, the average output power also increased, though nonlinearly. The turn-over power for 1173 nm under the pulse repetition frequency of 20 kHz was 17.5 W, where the maximum output power was 314 mW and the conversion efficiency was only 1.8%. As the pulse repetition frequency increased to 30 kHz, the threshold pump power increased to 11.9 W, while the maximum output power rose to 421 mW. When the pulse repetition frequency was increased to 40 kHz, the maximum average output power and the conversion efficiency reached 454 mW and 2.3% under the incident pump power of 19.5 W. In Figure 5, the intensity profile of the Stokes field retains a well-defined doughnut pattern, as shown by the inset in Figure 5a–c. The mode purity, as compared with that of the fundamental field, was greatly improved due to the Raman beam cleaning-up effect.

The spectrum of the self-Raman vortex laser emission is shown in Figure 6. The central wavelength was measured to be 1172.9 nm, corresponding to the Raman shift of 882 cm⁻¹. The polarization state of the Stokes field was measured with a Glan laser prism. Rotating the prism, the extinction appeared, which suggested that the Stokes field was also linearly polarized, just the same as the fundamental wave. Moreover, the polarization state of the first Stokes field was along the c-axis of the Nd:GdVO₄ crystal. The vortex beam carries orbital angular momentum, which is signified by spiral interference patterns and a topological charge $l$. The topological charge was measured with a home-made Mach-Zehnder interferometer. The self-reference interference fringes at pulse repetition frequencies of 20 kHz, 30 kHz and 40 kHz were recorded with a CCD-based laser profiler, as shown in Figure 7a–c. In all three images, spiral interference fringes with a unitary arm and clockwise heading can be observed. We also created simulated interference fringes for an optical vortex carrying unitary orbital angular momentum. It is well-known that an optical vortex carries a Hilbert factor $E_l\propto \exp \left(il\mathsf{\theta }\right)$. Considering a paraxial spherical wave as a reference wave, a spherical phase term $E_r\propto \exp \left(ik\sqrt{x^2+y^2}\right)$ contributes the formation of the spiral interference fringes. The intensity of the interference fringes can be written as $I\propto {\left|{\mathrm{E}}_{\mathrm{l}}+{\mathrm{E}}_{\mathrm{r}}\right|}^2\propto \cos \left(l\theta -k\sqrt{x^2+y^2}\right)$. The interference is a spiral pattern where the number of the spiral arm signifies the absolute value of the topological charge, while the heading of the spiral signifies the sign of the topological charge and the handedness. For instance, $l=1$ corresponds to an optical vortex with left handedness and a clockwise heading. Meanwhile, $l=-1$ corresponds to an optical vortex with right handedness and an anti-clockwise heading. The simulation conforms to the images recorded with the CCD laser profiler. It proves that the Stokes field carried a unitary topological charge, i.e., $l$= 1.

The temporal characteristics of the Stokes pulse were measured at different pulse repetition frequencies, as shown in Figure 8. In Figure 8a,b, the pulse profiles of the Stokes emission at pulse repetition frequencies of 20 kHz and 30 kHz are depicted. In Figure 8c,d, the pulse profile and the pulse train of the Stokes emission under the pulse repetition frequency of 40 kHz can be observed. As the pulse repetition frequency decreased, the average power also decreased. Meanwhile, the peak power increased with the decrease in the pulse repetition frequency. The peak power for the Stokes emission at the pulse repetition frequencies of 40 kHz, 30 kHz and 20 kHz were 0.33 kW, 0.78 kW and 1.11 kW, respectively. In addition, the pulse width became narrower as the pulse repetition frequency decreased. The pulse width for the Stokes emission under the pulse repetition frequencies of 40 kHz, 30 kHz and 20 kHz were 45.7 ns, 39.8 ns and 28 ns, respectively. As compared to the pulse width of the fundamental pulse, the pulse width of the Stokes field was shortened due to Raman pulse width compression.

4. Conclusions

In summary, we reported the generation of an acousto-optic Q-switched self-Raman optical vortex beam with an annular pump design. According to our knowledge, this is the first report of acousto-optic Q-switching applied to a 1173 nm Raman vortex beam’s generation. An annular pump beam was obtained with an γ = 1° axicon and a focus lens. Firstly, a 1063 nm LG₀₁ vortex beam was obtained in a plano-concave cavity. Under the pulse repetition frequency of 30 kHz, the maximum power reached 1.02 W under the pump power of 9.38 W. Driven by the acousto-optic Q-switched fundamental field, a 1173 nm Stokes emission was realized based on self-Raman conversion in the Nd: GdVO₄ crystal. The average output power of the Stokes fields reached 454 mW under the pulse repetition frequency of 40 kHz, corresponding to the pulse width of 45.7 ns. The results revealed that acousto-optic Q-switching can further increase the average output power of the vortex Stokes emission. The laser peak power can be increased through Q-switching, while stimulated Raman conversion helps to expand the wavelength of the vortex beam. All of these findings can be applied to further the applications of vortex lasers.