1. Introduction

Coherent optical sources in the mid-infrared (mid-IR) have become of increasing interest over the past years for a variety of scientific and technological applications due to the presence of rich spectroscopic signatures and strong absorption fingerprints of numerous molecules, harmful gases, and biological tissues [1]. To date, the vast majority of applications of mid-IR sources have been based on exploiting their spectral and temporal output characteristics in Gaussian beam profile, and over time, efforts have been made to improve such properties by harnessing advances in laser technology and material science [1]. At the same time, spatially structured beams, in particular optical vortices [2], have been studied as promising tools for a variety of new applications [3], owing to the presence of an extra degree of freedom in terms of orbital angular momentum (OAM) and doughnut-shaped intensity distribution. Because of helical transverse phase variation in the complex electric field of an optical vortex, represented by exp(ilϕ), where l is the order (topological charge), a complete destructive interference occurs along the propagation axis, resulting in a dark core at the center of the beam. The optical vortex of order, l, carries OAM of l${\hbar}$ per photon, which can be several times larger than the spin angular momentum [2]. Since the OAM forms infinite-dimensional Hilbert spaces, optical vortices are widely used for the generation of multi-dimensional entanglement, quantum and classical communication [4]. Similarly, the doughnut-shaped intensity distribution and vortex beams are useful for material processing [5], lithography [6], and particle trapping [7]. While optical vortices have found numerous applications over time, efforts continue to generate such beams across the electromagnetic spectrum, including UV [8,9], visible [10], near-IR [11], mid-IR [12], and the THz region [13], to enable new applications. Conventionally, an optical vortex beam is generated through spatial mode conversion of a Gaussian beam using various commercially available mode converters, including cylindrical lens [14], spiral phase plate (SPP) [15], or computer-generated hologram using spatial light modulator (SLM) [16]. Although most of these mode converters are very effective for the generation of vortex beams in the visible and near- IR wavelength range, they are based on materials that are not transparent over most of the electromagnetic spectrum. Given the potential scope of applications in the mid-IR, the generation of higher-order vortex beams in this spectral region can open up new avenues towards, for example, non-destructive super-resolution spectroscopy of molecules [17], free-space optical networking and OAM multiplexing [18], and controlled fabrication of chiral organic materials [19]. Therefore, it is imperative to devise alternative techniques for the generation of higher-order optical vortices in the mid-IR.

In recent years, nonlinear frequency conversion techniques have evolved as the most practical and direct route for generating optical vortices in different spectral regions. Based on OAM conservation, nonlinear frequency conversion processes [9,11] can transfer the OAM of an input pump beam at a given wavelength to a new spectral range. For example, frequency up-conversion techniques such as second-harmonic-generation (SHG), sum-frequency-generation (SFG), and high-harmonic-generation (HHG) have been used to transfer the pump OAM to discrete shorter wavelengths [8,20]. On the other hand, frequency down-conversion in an optical parametric oscillator (OPO) [20,21] or optical parametric generation (OPG) process [22] transfer the OAM of the pump beam at a fixed wavelength in the visible and near-IR to a broad range of wavelengths in the near-IR and mid-IR spectral regions. However, due to the intrinsically low nonlinear gain in the single-pass OPG process, the exploitation of vortex pump beams in such schemes for the transfer of OAM to parametric beams in the mid-IR can be achieved only with ultrafast lasers providing high peak pulse intensites, but even in this case with limited conversion efficiency and output power [22]. As a result, resonant schemes based on OPOs have evolved as the most viable alternative approach for the generation of high-power and higher-order optical vortices in new wavelength regions. To provide a general perspective on the progress in this field, Table 1 contains a summary of near-IR and mid-IR vortex sources based on nonlinear frequency conversion processes demonstrated to date. As evident from the table, higher-order mid-IR ultrafast vortex sources have not so far been explored using the OPO approach.

Table 1. A review of high-order vortex generated from mid-IR OPOs in various time-scales. l_p, l_s, l_i are the vortex order of the pump, signal, and idler, respectively [11,21,26,27].

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It is now widely established that OPOs are capable of generating coherent radiation over wide spectral regions and in all temporal domains from continuous-wave (cw) to ultrafast picosecond and femtosecond time-scale. In the cw domain, the shorter cavity lengths enable the generation of optical vortices in the mid-IR spectral region. However, in the ultrafast regime, the short pulses restrict the use of longer crystal length and demand cavity length synchronization to the repition rate of the pump laser. As a result, the generation of vortex beams with high output power in mid-IR has not been explored so far. Specifically, the mid-IR molecular fingerprint region in combination with the ultrafast optical vortices could lead to the study and advancement of light-induced chiral structure formation in organic molecules [19] and THz spectroscopy [23]. For the generation of optical vortices in the mid-IR spectral range, OPOs based on MgO-doped periodically poled LiNbO₃ (MgO:PPLN) offer the most viable and practical potential approach. The exploitation of MgO:PPLN in such OPOs enables the use of long interaction lengths, resulting in high nonlinear gain, providing mid-IR radiation up to ∼4 µm at high efficiency when pumped at 1.064 µm [24]. In this work, we demonstrate the direct generation of ultrafast optical vortices with maximum vortex order, l = 5, in the mid-IR using a picosecond OPO based on MgO:PPLN. We demonstrate an average idler output power of up to 2.2 W at 2423 nm in vortex spatial profile of vortex order, l_i = 1, and the generation of optical vortices for all orders up to l_i = 5 with a spectral coverage spanning over 1503 nm (1615 nm for l_i = 1).

2. Experimental setup

The schematic of the experimental setup to generate high-order ultrafast optical vortices in the mid-IR is shown in Fig. 1. As the pump source, we use a picosecond Yb-fiber laser at 1064 nm with a spectral bandwidth of 1.4 nm, delivering pulses of ∼20 ps duration at 80 MHz repetition rate, with a maximum average power of 20 W in TEM₀₀ spatial profile. The laser power is controlled using a combination of the half-wave plate (λ/2) and a polarizing beam splitter cube (PBS). The same PBS in combination with a quarter-wave plate (λ/4), mirror (M), and a spiral phase plate (SPP) act as a vortex doubler setup [10] to modulate the Gaussian pump beam into optical vortices of order twice the phase winding of the SPP. Using two SPPs of phase winding corresponding to vortex order, l = 1 and 2, combined with the vortex doubler setup, we can generate pump vortex of order, l_p= 1-6. However, the successful operation of the picosecond vortex pumped OPO is limited to l_p= 1-5 due to the significant reduction in the parametric gain and increase in OPO threshold beyond l_p= 5. A second λ/2 plate is used to adjust the polarization of the pump beam with respect to the poling direction of the nonlinear crystal for optimum phase-matching for parametric generation. The beam is focused at the center of the nonlinear crystal using a plano-convex lens of focal length, f = 150 mm, corresponding to a Gaussian pump beam waist radius of w₀∼40 µm. The singly-resonant oscillator (SRO) design for the OPO comprises a four-mirror X-cavity, with two concave mirrors (M1-M2) of a radius of curvature, r = 150 mm, and two plane mirrors (M3-M4). All mirrors (M1-M4) have high reflectivity (R> 99.5%) for the signal across 1450-2100 nm and high transmission (T > 90%) for the pump at 1064 nm and idler across 2200-4000 nm. The OPO is synchronously pumped at the second harmonic of the pump laser repetition rate with a total cavity length of 938 mm, generating output signal pulses at 160 MHz and idler pulses at 80 MHz. The nonlinear crystal for the vortex-pumped picosecond OPO is multi-grating MgO:PPLN, 50-mm-long, 8.1-mm-wide, and 1-mm-thick, with grating periods varying from Λ=29.05 to Λ=31.5 µm. The crystal end faces are antireflection-coated (R < 0.5) over the signal wavelength range of 1450-2100 nm. The crystal is housed in an oven adjustable up to 200 °C with temperature stability of ±0.1 °C. The idler output is extracted from the undepleted pump and leakage signal using the wavelength separator (S) and subsequently imaged using a lens (L2) and a camera. The spatial profile of the leakage signal through the high reflecting mirror (M4) is recorded using a pyroelectric camera. An intracavity aperture is used to operate the OPO in fundamental cavity mode by eliminating the higher-order resonant modes.

 

Fig. 1. Schematic of the experimental setup. SPP, spiral phase plate; PBS, polarizing beam splitter; λ/2, half-wave plate; λ/4, quarter-wave plate; L1, focusing lens; C, MgO:PPLN nonlinear crystal; M1-M4, OPO mirrors; S, wavelength separator; L2, idler collimating lens.

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3. Results and discussion

3.1 Transfer of high-order near-IR vortex to mid-IR using an OPO

To verify the generation of higher-order vortices in the mid-IR, we initially fixed the crystal temperature at 50 °C and used a grating period of Λ=29.03 µm, resulting in a signal and idler wavelength of 1445 nm and 4035 nm, respectively. Keeping the pump power constant at 5 W, well above the OPO threshold, we varied the order of the pump vortex and measured the spatial profile of the signal and idler beams, with the results shown in Fig. 2. As evident from the first column, (a-c), of Fig. 2, the pump beam has doughnut-shaped intensity distribution with increasing dark core size for higher vortex orders. To determine the order and sign of the optical vortices throughout the experiments, we used the tilted lens technique, where an optical vortex of order, l, on propagation through a tilted lens, splits into |l|+1 lobes at the focal plane of the lens [25]. As evident from the tilted lens images shown in the second column, (d-f), of Fig. 2, recorded at the back focal plane of the lens using a CCD camera with a pixel size of 4.4 × 4.4 µm², the pump vortices have orders of l_p= 1, 4, 5. As reported previously [12,26], due to the low parametric gain in the cw regime, in addition to the vortex profile of the pump beam, the OAM of the pump beam in a SRO is directly transferred to the idler while the resonant signal beam maintains fundamental cavity mode (Gaussian), ensuring optimum spatial overlap among the interacting beams and OAM conservation in the parametric process. Moreover, in such cases, the OAM transfer mechanism is not observed for lower-order (l≤2) pump vortices [26]. However, the higher parametric gain when using ultrashort pump pulses can also lead to OAM exchange in a SRO for different combinations of vortex orders for signal and idler satisfying OAM conservation with a high value of spatial overlap integral among the interacting beams. To avoid such OAM exchanges and restrict the pump OAM transfer to the mid-IR, we incorporated an aperture within the OPO cavity to limit the higher-order cavity modes for the resonant signal.

 

Fig. 2. Far-field intensity distribution of (a-c) pump beam for l_p= 1, 4, 5, (d-f) tilted lens images of the pump beam, (g-i) corresponding idler beam profile, and (j-l) tilted lens images of idler beam, (m-o) signal beam profile.

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As evident from the third column, (g-i), of Fig. 2, the idler beam recorded using a pyroelectric camera with a pixel size of 85 × 85 µm² has a doughnut-shaped intensity profile with increasing dark core size and decreasing ring width for higher pump vortex order. The tilted lens images as shown in the fourth column, (j-l), of Fig. 2, confirm the order of the idler vortex to be l_i= 1, 4, and 5, same as that of the pump vortex order, l_p. Similarly, the corresponding signal beam as shown in the fifth column, (m-o), of Fig. 2, carries Gaussian beam (l_s= 0) intensity profile for all pump vortex orders, l_p, confirming the OAM conservation, l_p= l_i+l_s, even for the high-gain ultrafast SRO. Unlike the symmetric intensity distribution of the tilted lens images of the pump beam, the asymmetry in the tilted lens images of the idler can be attributed to the asymmetric intensity distribution of the idler vortex, especially for higher-order vortices. Such asymmetric intensity distribution of the idler vortex arises due to the increase in beam divergence for higher vortex orders, influencing the spatial overlap of the interacting beams along the length of the nonlinear crystal. Contrary to previous reports [26], here, the high nonlinear gain due to the presence of picosecond pulses and long interaction length of the nonlinear crystal enables direct transfer of higher-order pump OAM mode to the idler beam in a SRO, enabling the generation of higher-order optical vortices over wide wavelength range in the mid-IR.

3.2 Generation of high-order vortices in the mid-IR

Given the transfer of pump OAM to the idler beam in a SRO, with the signal maintaining the Gaussian spatial profile, we studied the generation of higher-order optical vortices across the mid-IR wavelength range. Using multiple gratings of the MgO:PPLN crystal from Λ=29.03 to 31.5 µm and varying the crystal temperature from 50°C to 180°C, we characterized the spatial profile of idler beam across 2424-4035 nm. The results are shown in Fig. 3. Although we recorded the idler beam profile across the entire tuning range, here, we present the results at three arbitrary wavelengths of 2493, 2844, and 3866 nm, and for pump vortices of orders, l_p= 1, 4, and 5. As evident from the first column, (a-c), of Fig. 3, the idler beam for pump vortex order, l_p= 1, has a symmetric doughnut-shaped intensity profile across the tuning range with expected large annular width. The order of the idler vortex is confirmed to be l_i= 1 using the tilted lens images, as shown in the second column, (d-f), of Fig. 3. As expected, the tilted lens images have a symmetric lobe structure due to the symmetric intensity distribution of the idler vortex beam of order, l_i= 1. Similarly, the idler beam for pump vortex order, l_p= 4, has a doughnut-shaped intensity profile with a large dark core and narrow annular ring, as shown in the third column, (g-i), of Fig. 3, which is further confirmed to have vortex order, l_i= 4, using the tilted lens images, as shown in the fourth column, (j-l), of Fig. 3. On the other hand, as evident from the fifth column, (m-o), of Fig. 3, the idler vortex across the tuning range has a doughnut-shaped intensity profile with a large dark core and narrow annular ring for pump vortex order, l_p= 5, and confirmed to carry vortex order of l_i= 5 using the tilted lens image, as shown in the column, (p-r), of Fig. 3. However, as expected, the idler beam has asymmetric intensity distribution and corresponding asymmetric lobe structure in the tilted lens images across the tuning range. We can also conclude that going away from the degeneracy leads to a increase in dark core, as evident from from Fig. 3. It is to be noted that the signal beam across the tuning range (not shown here) carries Gaussian spatial distribution, l_s= 0, confirming OAM conservation, l_p= l_i+l_s. These experimental results prove the possibility of generating higher-order optical vortices tunable across 2424 nm to 4035 nm through direct transfer of the pump OAM mode to the non-resonant idler radiation using a SRO.

 

Fig. 3. (a-c) Idler beam intensity profile and corresponding (d-f) tilted lens images profile for pump vortex order, l_p= 1. (g-i) Idler beam intensity profile and corresponding (j-l) tilted lens images profile for pump vortex order, l_p= 4. (m-o) Idler beam profile for pump vortex order, l_p= 5, (p-r) corresponding tilted lens images.

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3.3 Output power of high-order vortices across the mid-IR

We also measured the output power of the higher-order idler vortices across the mid-IR tuning range. For a comparative study of the idler power variation for different idler vortex orders, we pumped the SRO with a constant power of 8 W and pump vortex orders of l_p= 1-3 and recorded the idler vortex power, with the results shown in Fig. 4. As seen in Fig. 4(a), the output power in the idler vortex of order, l_i= 1, varies from 1.6 W to 658 mW for a wavelength variation from 2538 nm to 4035 nm. However, it is to be noted that the SRO produces an idler vortex beam with >1 W of output power over >60% of the full tuning range. Similarly, as seen from Fig. 4(b) and Fig. 4(c), the output power in idler vortex of order, l_i= 2, varies from 1130 mW to 546 mW across 2845-3924 nm, and for the vortex of order, l_i= 3, varies from 547 mW to 422 mW across 2820-3862 nm with maximum output power of 583 mW at 2982 nm. It should similarly be noted that the SRO produces >800 mW of output power across 65% of tuning range in idler vortex of order, l_i= 2, and >400 mW of power over the entire tuning range in idler vortex of order, l_i= 3, making the vortex source useful for a variety of applications in the mid-IR. From the results of Fig. 4, it is evident that the overall idler power decreases with the increase in pump vortex order, and for a given vortex order, the idler power decreases towards longer wavelengths in the mid-IR away from degeneracy. We also measured the power variation of 324-166 mW across the tuning range of 2816 to 3852 nm for vortex order, l_i= 4 (not shown here). While the decrease of the idler power with the increase of pump vortex order at constant pump power can be attributed to the reduction in parametric gain with the increase in pump beam size and divergence for higher vortex orders, the drop in idler vortex power at longer wavelengths can be attributed to reduced parametric gain away from degeneracy, as commonly observed in OPOs [28].

 

Fig. 4. Power variation across the mid-IR wavelength range for idler vortex order, (a) l_i= 1, (b) l_i= 2, and (c) l_i= 3.

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3.4 Output power of high-order vortices in the mid-IR

We further studied the output power characteristics of the high-order vortex source in the mid-IR. Pumping the SRO with vortex orders, l_p= 1-5, we measured the idler vortex output power as a function of input power at two different wavelengths of 2493 nm and 4035 nm, with the results shown in Fig. 5(a) and Fig. 5(b), respectively. As evident from Fig. 5(a), the idler vortex power at 2493 nm increases linearly with the input pump power for all vortex orders, but with decreasing slope efficiency of 23%, 21%, 19%, 11%, and 12% for increasing pump vortex order of l_p= 1-5. At the highest input pump power of 10 W, the SRO produces a maximum idler output power of 2.2 W, 1.9 W, 1.53 W, 0.78 W, and 0.63 W for pump vortex order of l_p= 1, 2, 3, 4, and 5, respectively. Similarly, the idler vortex power at the mid-IR wavelength of 4035 nm, as shown in Fig. 5(b), rises linearly with the pump power, again with decreasing slope efficiency of 9%, 7%, 6.5%, 4%, and 3.3% for increasing vortex order of l_p= 1-5. For the highest input pump power of 10 W, the SRO generates maximum idler vortex power of 0.8 W, 0.54 W, 0.3 W, 0.21 W, and 0.16 W for pump vortex order of l_p= 1, 2, 3, 4, and 5, respectively. It is interesting to note that the idler power for all orders does not show any sign of saturation or roll-off, even at 10 W of pump power, indicating the possibility of further scaling of the idler vortex power across the tuning range with the increase in pump power. However, possible crystal damage at elevated power with an ultrafast pump laser can be a limiting factor for the maximum attainable idler power in the present setup. Therefore, during these experiments, we restricted the operation of the OPO to 10 W of input pump power. As also evident from Fig. 5(a) and Fig. 5(b), the threshold of the OPO increases with the pump vortex orders and operation away from degeneracy, as expected. To gain further insight, we measured the OPO threshold at 4035 nm for different pump vortex orders, with the results shown in Fig. 5(c). As expected, the OPO has the lowest power threshold of 1.1 W for pump vortex order, l_p= 1, and increases linearly with the pump vortex order to 2.1 W, 3.8 W, 4.8 W, and 6.2 W for l_p= 2, 3, 4, and 5, respectively. It is to be noted that the higher pumping intensities necessary to overcome threshold at higher vortex orders are the critical factor restricting the successful generation of higher-order vortices (l > 2) in cw OPOs. We also characterized the power stability of the idler vortices at 2493 nm by keeping the pump power fixed at 8 W and recording the output power for idler vortex orders of l_i= 1-3 over 1 hour. The results are shown in Fig. 5(d), where power fluctuation of 34 mW, 29 mW, and 16 mW over the mean output power of 1.6 W, 1.42 W, and 1.15 W are recorded over 1 hour for idler vortex orders, l_i= 1, 2, and 3, respectively. These values correspond to power stability of 4.4%, 4.1%, and 2.8% rms over 1 hour for idler vortex orders, l_i= 1, 2, and 3, respectively. Such output power stability is of the same order as that commonly observed in OPOs pumped by conventional Gaussian beams. Hence there is no major impact on the overall power stability of OPOs under vortex pumping.

 

Fig. 5. Idler output power scaling at (a) 2493 nm with idler beam profile at 4 W, 6W and 9W and (b) 4035 nm, with input pump power for pump vortex order, l_p= 1-5. (c) OPO threshold variation with pump vortex order, l_p= 1-5. (d) Power stability of idler output power for vortex order, l_i= 1 to 3.

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4. Conclusions

In conclusion, we have demonstrated the successful generation of high-power and higher-order optical vortices over a broad spectral coverage in the mid-IR by direct transfer of the pump vortices to the non-resonant idler beam in an Yb-fiber-pumped picosecond ultrafast OPO in SRO configuration. The OPO source produces vortex beams of orders l_i= 1-5 with tunability across the 2493 nm to 4035 nm spectral range, and delivers idler ouptut beam with maximum power ∼2.2 W in vortex order, l_i= 1, near degeneracy, and maximum output power of >1 W in vortex beam up to order, l_i= 3. This current scheme demonstrates, for the first time, generation of tunable optical vortices in this wavelength region in the ultrafast picosecond time-scale. Combined with the Yb-fiber pump laser technology, the demonstrated source provides a robust and practical approach for the generation of widely tunable, high-power, high-order optical vortices in the mid-IR with the potential to benefit many applications.