1. Introduction

Optical vortices featured with spatially structured intensity distribution and spiral phase front, possess a well-defined orbital angular momentum (OAM) [1], thus manifesting various novel physical phenomena in light-matter interaction and finding widespread applications in optical manipulation [2], quantum communications [3], and so forth. In addition, pulsed vortex lasers in the infrared (IR) region enable extending the applications in the fields of structuring the three-dimensional organic materials [4], hard or soft tissue ablation [5], super-resolution molecular spectroscopy [6], and as pump or seed sources to produce mid- or far-IR optical vortices through optical parametric oscillation / amplification (OPO / OPA) [7]. The new applications stimulate the development of various techniques for generation of pulsed optical vortices in the mid-IR region. Common methods are based on transformation of a pre-existing mid-IR TEM$_{00}$ mode through external phase modulation elements, such as conventional spiral phase plates (SPP) [8] and metamaterials [9,10]. For SPP this is inevitably accompanied by high wavelength sensitivity [11] which is generally not suitable for wideband operation. The metamaterials can overcome such wavelength limitation by special structure design but normally suffer from lower conversion efficiency [10]. In comparison, nonlinear frequency down conversion, OPO or OPA, pumped by a vortex laser in the near-IR region, seems to be an efficient way to produce high-power and wavelength-tunable mid-IR vortex lasers [12–14]. The principle is based on the transformation of OAM from the fundamental wave to the signal or idler waves according to the angular-momentum conservation law [12,13]. Therefore, OAM transforming to signal or idler light is somewhat random, and the total topological charge of the output beam is limited by that of the pump laser [14].

In recent years, direct generation of optical vortices from a robust laser cavity using a spatially structured pump beam, is attracting attention owing to its power scaling capability, high beam quality, wide spectral tuning range [15–17], and the rich dynamic behavior [18]. Up to date, 107 W output power of first-order Laguerre–Gaussian (LG$_{0,1}$) beam in a vector form has been produced from an Yb:YAG thin-disk laser, giving a theoretically limited $M^2$-factor of around 2, and, most importantly, the temperature increase of the crystal was 21% lower compared to standard homogeneous pumping, which means that further power scaling the LG$_{0,1}$ mode shall be still possible just through a suitable cavity design [15]. In combination with a reflective volume Bragg grating (VBG), wavelength tuning of optical vortices of different topological charges ($l$) can be realized from a compact $Z$-shaped cavity without any phase dislocation [16]. However, in the mid-IR region and in particular in the 3-$\mathrm{\mu }$m spectral range, also known as the "molecular fingerprint region" which suffers from large propagation loss in air due to the strong water vapor absorption, direct vortex beam generation has been scarcely reported and the first demonstration was in 2019 using an Er$^{3+}$-doped sesquioxide ceramic laser [17]. To conserve the high purity of the vortex beam, additional insertion and asymmetric cavity losses were required, leading to a much lower output laser power (less than 125 mW [17]). By slightly stretching the cavity, a sharp power roll-off was observed due to the serious thermal-lens effect and the increased propagation losses, which complicates further extensions to Q-switched operation, both in the active form where a long cavity is generally required, and for the passive method which normally leads to large insertion losses. Nevertheless, direct generation of mid-IR vortex beams in the 3-$\mathrm{\mu }$m spectral range can be expected by optimizing the mode-matching and employing a high-optical-quality saturable absorber (SA). In addition, the passive Q-switch SA can introduce additional transverse mode discrimination owing to the intensity-dependent absorption, thus serving as a dynamic spatial filter to clean the optical vortices [19].

In the present work, by employing polycstalline Fe:ZnSe as a SA and using a modified theoretical model for transverse-mode selection, a pulsed vortex laser in the mid-IR spectral region is experimentally demonstrated from a passively Q-switched Er:YAP solid-state laser. The directly generated 2.7-$\mathrm{\mu }$m scalar LG$_{0,l}$ ($l = 0,\;{\pm }1$) beams are emitted in the nanosecond regime within a stable pulse train, and exhibit clear beam patterns with well-defined handedness. This work, as a proof of principle study, paves the way for direct generation of pulsed vortex beams in the mid-IR region.

2. Theoretical analysis and cavity design

In the present work, the annular pumping technique was employed to generate optical vortices based on transverse-mode selection at the early stage of oscillation establishment [20], i.e., based on laser threshold condition, $P_{th,min} = min[P_{th}(LG_{0,l})]$. By assuming a single-transverse-mode operation of the laser oscillator, the threshold for each mode is mainly dependent on the mode size of the pump and laser through an overlap integral $J_{l}$ [21]:

Here $\omega _{0}$ is the waist radius of the fundamental mode in the cavity, and $l_{c}$ represents the length of the laser crystal. For the pump which is a ring-shaped beam with multi-mode structure the expression is more complicated. By assuming a constant inner and outer radius along $z$-axis, the normalized pump rate, $r_0(x,y,z)$, has been previously described as a step function with top-hat intensity distribution in the radial range of $r_{a} < r < r_{b}$ [21]. However, this assumption is not justified for our case because both the inner and outer radii obviously vary along the propagation direction, see Fig. 1(a). To better describe the propagation features and thus to obtain a more accurate $J_{l}$ value, the step function for the pump beam has to be modified following the actually measured data. Since a Gaussian laser mode follows a hyperbolic dependence along the $z$-axis, the outer radius $r_{b}$ was fitted using the following modified propagation function where $A_{0}$ and $B_{0}$ are fitting parameters.

 

Fig. 1. Measured and fitted propagation of the ring-shaped and fiber-coupled Gaussian-like ($M^2$ $\sim$ 37) pump beam (a), and (b) the calculated $V_{eff}$ for LG$_{0,l}$ modes with $l =$ 0, 1, and 2.

Download Full Size | PDF

Here $\omega _{p}$ is the minimum beam radius of the reshaped pump light at $z \approx$ −0.1 mm in Fig. 1(a), i.e., slightly ahead of the crystal. However, for the inner radius $r_{a}(z)$ the situation is more complex because it evolves along the $z$-axis from zero to a maximum, and thereafter gradually diminishes again. To better describe such a dependence, a second order polynomial fitting was employed in combination with the least square deviation method. As shown in Fig. 1(a), the best fit gives the following curve function:

Here, $A_{2}$, $B_{2}$, $C_{2}$, $D_{2}$, and $E_{2}$ are constants. Note that the pump density in other regions ($r < r_{a}$ or $r > r_{b}$) is defined as zero. Substituting Eqs. (3) and (6) into Eq. (2), and thereafter integrating over the entire cavity, $J_{l}$ can be derived and finally gives an effective pump beam volume for the LG$_{0,l}$ mode:

Figure 1(b) shows the calculated $V_{eff}$ for the LG$_{0,l}$ modes with $l = 0, 1$, and $2$, with respect to the different cavity design, i.e., different beam waist ($\omega _{0}$) of the fundamental mode. For $\omega _{0} > {\sim }$ 160 $\mathrm{\mu }$m, a TEM$_{00}$ mode will be excited. Decreasing the beam waist to the range of 116 $\mathrm{\mu }$m $< \omega _{0} <$ 160 $\mathrm{\mu }$m, the LG$_{0,1}$ mode will be preferentially excited due to the lowest lasing threshold. A higher order LG$_{0,l}$ mode can be produced by further reducing the mode size, but this will normally lead to a lower output power because of the weaker overlap with the pump beam and a larger propagation loss [16,23]. Therefore, emission of the high-order LG$_{0,l}$ modes with $l \geq 2$ was not investigated in this work.

3. Setup and vortex laser in the CW regime

Using the ABCD matrix analysis, the cavity mode was designed to satisfy the above mentioned excitation condition for the LG$_{01}$ mode. Figure 2(a) shows the schematic of the 2.7-$\mathrm{\mu }$m Er:YAP vortex laser pumped by a ring-shaped beam at 976 nm. The pump beam emitted from a fiber-coupled laser diode (105-$\mathrm{\mu }$m fiber core and 0.22 NA), was reshaped to a "doughnut" profile in the near field. As can be seen the inset of Fig. 2(a), the beam pattern maintained a ring-shaped profile along the entire crystal from $z$ = 0 to 5 mm, which can also be recognized from the radial beam evolution along the $z$-axis in Fig. 1(a). A plane input mirror (IM, anti-reflective coated at 976 nm and high-reflective coated at 2650–2950 nm) and a concave output coupler (OC) with a radius of curvature (R${\rm _{oc}}$) of – 50 mm and a transmission of 5%, were employed to form the laser cavity. The 5-mm-thick, 10 at.%, high-optical-quality Er:YAP crystal was cut along the crystallographic $b$-axis ($Pbnm$ space group), and both of its end faces (2 $\times$ 2 mm$^2$) were polished but uncoated. To mitigate the thermal load, the sample was tightly mounted in a copper holder and water cooled to 13 $^{\circ }\textrm {C}$. The output beam profiles and the corresponding intensity interference patterns were recorded by using an infrared CCD camera (Xeneth-Tigris-64) and a home-made Mach-Zehnder interferometer.

 

Fig. 2. Schematic of the 2.7-$\mathrm{\mu }$m Er:YAP vortex laser (a), CW laser performance of TEM$_{00}$ and LG$_{0,1}$ modes (b), and the optical spectrum of LG$_{0,+1}$ mode (c). Insets in (a): pump and laser beam profiles, and the intensity dependence along $X$- and $Y$-axis for the pump beam at $z$ = 1.9 mm. Inset in (b): optical spectra of TEM$_{00}$ mode with and without YAG Brewster plate. Insets in (c): beam profile, interference pattern and polarization measurement of the LG$_{0,+1}$ mode.

Download Full Size | PDF

At first, the laser was operated in TEM$_{00}$ mode pumped with a Gaussian-like beam. As shown by the inset of Fig. 2(b), dual-wavelength operation at 2711 and 2731 nm was observed. By using a Glan-Taylor polarizer, the output at 2711 nm was found to be vertically-polarized along the crystalline $c$-axis, however, the 2731-nm output was horizontally-polarized along $a$-axis. So, a 1 mm-thick YAG plate was placed in the cavity at Brewster’s angle to determine a horizontal linear polarization (i.e., $E//a$) and thus suppressing the unwanted dual-wavelength emission. As can be seen in Fig. 2(b), a maximum CW laser power of $\sim$ 0.52 W was achieved, corresponding to a slope efficiency of 13.2%. Further power scaling was limited by the cavity instability induced by the thermal lens.

Slightly stretching the cavity to a length of 20 mm ($\omega _{0}$ = 140 $\mathrm{\mu }$ m) and pumping with the ring-shaped beam, an optical vortex was readily produced. Near the lasing threshold, the output beam pattern exhibited a petal-like profile with two lobes. This is attributed to the coherent superposition of the LG$_{01}$ modes with opposite handedness while identical spatial intensity distribution [17]. By further increasing the pump power and slightly misaligning the cavity, the LG$_{0,+1}$ or LG$_{0,-1}$ mode was successfully selected owing to the asymmetric-loss-induced frequency-locking [18]. As shown in Fig. 2(b), powers of 0.41 W for the LG$_{0,+1}$ and 0.42 W for the LG$_{0,-1}$ mode were achieved, corresponding to a slop efficiency of 13.0% and 13.6%, respectively. The similar efficiency compared to that of the TEM$_{00}$ mode can be explained by the optimized mode-matching between the ring-shaped pump beam and the LG$_{0,1}$ mode, which confirms the high accuracy of our modified theoretical model. As can be seen from the insets of Fig. 2(c), the recorded beam profile of the LG$_{0,+1}$ mode and the corresponding intensity interference pattern at maximum output power, as well as the clean doughnut profile and clear spiral interference fringes are indication of the high-purity of the produced LG$_{0,+1}$ mode. The polarization extinction ratio (PER) of the 2.7-$\mathrm{\mu }$m scalar vortex laser was measured to be $\sim$ 20 dB.

4. Pulsed laser operation of 2.7-$\mathrm{\mu }$m optical vortex

4.1 Pulsed laser operation of TEM$_{00}$ mode

As shown in the inset of Fig. 3(a), a 1-mm-thick polycrystalline Fe:ZnSe prepared using thermal diffusion method served as a SA for passive Q-switching. A stable pulse train was obtained as the absorbed pump power reached $\sim$ 2.35 W, corresponding to an average output power of 83 mW. The average output power with respect to the absorbed pump power is shown in Fig. 3(a). A maximum power of 0.26 W was obtained, yielding a lower slop efficiency of 9.5% compared to that in the CW regime due to the additional insertion loss. The average intracavity pulse fluence on the SA was estimated to be $\sim$ 50 mJ/cm$^{2}$ (saturation fluence of 40 mJ/cm$^{2}$ [24]), corresponding to an on-axis intracavity intensity of $\sim$ 830 kW/cm$^{2}$. The time-domain behavior of the passively Q-switched Er:YAP laser was characterized by using a high-speed photodiode detector and a 1-GHz digital oscilloscope. As shown in Fig. 3(b), the pulse width decreased to 120 ns and the pulse repetition frequency (PRF) increased to 300.6 kHz at the highest pump power. In this case, the single-pulse energy was measured to be 0.86 $\mathrm{\mu }$J and the PER amounted to $\sim$ 23 dB. Figure 3(c) depicts a typical temporal trace of the 120-ns pulse; no satellites before or after the main pulse are observed. The corresponding pulse train recorded on a time interval of 300 $\mathrm{\mu }$s is shown in Fig. 3(d). The uniform pulse train with low energy fluctuation is a further indication of the stability of the Q-switching. In comparison with the performance of previously reported 2.7-$\mathrm{\mu }$m bulk Er-lasers passively Q-switched by using of conventional SESAM or novel low-dimensional materials [25], the pulse duration achieved in the present work was substantially shorter.

 

Fig. 3. Average output power of TEM$_{00}$ mode (a), and the corresponding pulse width and PRF (b) versus absorbed pump power. Temporal trace of a 120-ns single-pulse (c) and the corresponding pulse train on a time scale of 300 $\mathrm{\mu }$s (d). Insets in (a): Photograph of the 1-mm-thick polycrystalline Fe:ZnSe and the beam profile of the TEM$_{00}$ mode at the highest average power.

Download Full Size | PDF

4.2 Pulsed scalar vortex laser at 2.7 $\mathrm{\mu }$m

By inserting the polycrystalline Fe:ZnSe SA in the vortex-laser cavity as shown in Fig. 2(a), pulsed vortex laser operated in the LG$_{0,+1}$ or LG$_{0,-1}$ mode, depending on the introduced asymmetric losses, was achieved. Figure 4(a) shows the average output power for the two modes with respect to the absorbed pump power. It should be emphasized that stable Q-switching could be obtained only if the absorbed pump power was higher than 3 W. Pulsed LG$_{0,+1}$ mode with a highest power of 0.25 W, and LG$_{0,-1}$ mode with 0.26 W, were generated, corresponding to a slope efficiency of 6.8% and 7.6%, respectively. Further increasing the pump power, the laser mode was no longer a clear LG$_{0,1}$ eigenmode but a "mixed" mode with undefined spiral interference fringes and a roll-off in the power dependence. We attribute this to the mode-matching with higher-order transverse modes and instability of the resonator caused by the thermal lens effect. Optical spectra of the LG$_{0,+1}$ and LG$_{0,-1}$ modes with a central wavelength of 2731 and 2732 nm are shown in Figs. 4(b) and 4(c), respectively. Single-wavelength laser operation without any satellites should be helpful for the stability of the pulsed vortex laser [17]. The insets in Figs. 4(b) and 4(c) show the beam profiles and the intensity interferogram of both modes at the highest average power. The clean doughnut profile with even clearer spiral interference fringes compared to the CW regime can be explained by the "spatial filter" effect of the Fe:ZnSe SA on other transverse modes [19]. In addition, the good mode-matching with the ring-shaped pump beam, as well as the high PER of the pulsed vortex laser, e.g., $\sim$ 20 dB for the LG$_{0,-1}$ mode as shown in the inset of Fig. 4(a), should also facilitate high-purity optical vortex generation [17,23].

 

Fig. 4. Average output power (a) and optical spectra (b, c) of the passively Q-switched Er:YAP laser operating in LG$_{0,\pm 1}$ modes. The hollow symbols in (a) represent the unstable Q-switching operation. (d) depicts a single-pulse temporal trace of the LG$_{0,-1}$ mode at the highest output power and the corresponding pulse train on a time scale of 300 $\mathrm{\mu }$s. Inset in (a): polarization measurement of the pulsed vortex laser operating in the LG$_{0,-1}$ mode. Insets in (b) and (c): beam profiles of the LG$_{0,\pm 1}$ modes and the corresponding intensity self-interference patterns.

Download Full Size | PDF

The temporal behavior of the pulsed Er:YAP vortex laser was similar to that of the TEM$_{00}$ mode. By increasing the pump power, the PRF increased to 203 kHz and the pulse width dropped to 251 ns for the LG$_{0,-1}$ mode, with a single pulse energy of 1.29 $\mathrm{\mu }$J. For the LG$_{0,+1}$ mode, there parameters were 275 ns, 181 kHz and 1.39 $\mathrm{\mu }$J at the highest power level. In comparison with the fundamental mode, the lower PRF and thus the higher pulse energy at the same absorbed pump power, were related to the lower laser intensity on the Fe:ZnSe SA due to the larger beam size and the annular spatial profile of the LG$_{0,1}$ mode. Figure 4(d) shows a typical temporal trace of the 251-ns single pulse whereas the corresponding pulse train is shown in the inset. From the pulse train the energy fluctuation is slightly larger than that of the TEM$_{00}$ mode; again the lower intensity on the SA should be the primary mechanism responsible for this. Nevertheless, the clear beam pattern with well-defined handedness and the clean single-pulse operation in the time domain indicate that polycrystalline Fe:ZnSe is a promising candidate for Q-switching of vortex lasers in the 2.7-$\mathrm{\mu }$m spectral range.

5. Conclusion

In conclusion, we have experimentally demonstrated the direct generation of stable CW and pulsed LG$_{0,l}$ beams ($l = 0,\;{\pm }1$) in the 3-$\mathrm{\mu }$m spectral range. By considering the propagation features of the reshaped annular pump beam, a modified theoretical model was derived to select the desired vortex beam through mode-matching. 0.41 W output power for LG$_{0,+1}$ and 0.42 W for LG$_{0,-1}$ mode was achieved in the CW regime, corresponding to a slope efficiency of 13% and 13.6%, respectively. This is similar to the 13.2% reached for the fundamental mode ($l =$ 0) pumped with a fiber-coupled Gaussian-like beam, indicating a high accuracy of the modified theoretical model. Thereafter, a home-made polycrystalline Fe:ZnSe was employed for Q-switching of the 2.7 $\mathrm{\mu }$m Er:YAP laser. The shortest pulse of 120 ns was obtained for the fundamental mode. Due to the lower intracavity fluence on the SA, longer pulse duration of 251 ns for the LG$_{0,-1}$ and 275 ns for the LG$_{0,+1}$ modes were obtained, respectively. Nevertheless, the LG$_{0,\pm 1}$ modes with larger beam size exhibited higher single pulse energy. The optical vortices with clear self-interference spiral fringes and clean temporal profile, benifited from the good mode-matching, high PER and the "spatial filter" effect of the SA, and this confirms the unique capability of polycrystalline Fe:ZnSe for production of stable pulses of different transverse modes in the 2.7-$\mathrm{\mu }$m spectral range. Further power scaling of pulsed LG$_{0,l}$ beams was limited by the thermal lens effect, so the future work will focus on better thermal management through special design of the cooling system and optimization of the size or geometry structure of the laser gain medium.