1. Introduction

Coherent optical radiation is the backbone of various applications in science and technology. The laser represents the primary source of coherent radiation, with a spatial beam of Gaussian intensity profile. However, in recent years, various applications have found laser beams of different spatial structures to be more advantageous over the Gaussian beams. For example, optical vortices having doughnut-shaped intensity distribution, due to the presence of azimuthal phase variation represented by exp(ilθ), where l is the order or the quantized orbital angular momentum (OAM) [1], are indispensable for various applications including quantum information and communication [2,3], material lithography [4], micro-particle manipulation [5], and the increase of channel capacity in communication systems [6]. On the other hand, as compared to Gaussian beams, Airy beams having peculiar properties such as non-diffraction [7], self-healing, and self-acceleration [8,9] are widely used for plasma guiding [10], light-sheet microscopy [11], and particle manipulation [12]. However, vortex-Airy beams have all the peculiar properties of Airy beams such as acceleration, non-divergence and self-healing, but the central lobe of the beam has doughnut-shaped intensity profile and carries OAM.

Conventionally, structured optical beams are generated through spatial mode conversion of a Gaussian laser beam using holographic techniques based on liquid crystal spatial light modulators (SLMs) [13], cylindrical mode converters [14,15], q-plate [16], and spiral phase plates (SPPs) [17]. Due to the dynamic phase modulation and control, SLMs are also used to generate structured beams of any spatial features including the Airy beams. However, Airy beams are generated through the cubic phase modulation using a cubic phase mask [8,9] of the Gaussian beam and subsequent Fourier transformation. Despite the huge demand for various structured beams of different characteristics, none of the above mentioned mode convertors can produce structured beams with high output power over an extended wavelength range. To address such acute need, efforts have been made to produce structured beams at different wavelengths through nonlinear frequency conversion [9,18] of structured beams generated by a specific spatial mode converter. At the same time, given the potential of optical parametric oscillators (OPOs) to generate high-power, high-energy coherent radiation over a broad wavelength range from a single source [19], efforts have been made to generate various spatial structured beams directly from the OPO [20,21]. However, to date, all previous reports on structured-beam OPOs have shown the generation of a specific type of structured beam from a particular device according to the intended requirement and design. For example, an OPO designed for the generation of vortex beam [22] or the vector vortex beam [23], does not produce an Airy beam and vice versa. As a result, one needs to deploy a different input pump source and change the overall OPO system design to produce a particular desired structured beam. Such limitations have restricted the realization of a versatile coherent source capable of providing of different types of structured beams from a single OPO source. To overcome such limitations and address the generation of multiple spatial structures from a single system, here, we report a novel experimental scheme for the simultaneous generation of various types of structured beams from a single OPO source. Using a picosecond OPO in singly-resonant oscillator (SRO) configuration, synchronously-pumped by a vortex beam, and by controlling the intracavity mode with a simple mechanical aperture, we have generated Gaussian, vortex, Airy, and vortex Airy beams through different output ports of the device, with extended wavelength tunability in the near-IR and mid-IR, and output power in excess of 1 W.

2. Experimental setup

The schematic of the experimental setup is shown in Fig. 1. A mode-locked Yb-fiber laser at 1064 nm with a spectral width of 1.4 nm producing output pulse width of 20 ps at a repetition rate of 80 MHz in Gaussian spatial intensity profile (M²<1.1) is used as the pump source. For optimum performance, we operate the laser at its maximum average output power of 14 W and subsequently control the input power to the experiment using a half-wave plate (λ/2) and a polarizing beam-splitter (PBS) cube. A second λ/2 plate controls the polarization of the beam. The spiral phase plate (SPP) of phase winding corresponding to vortex order, l=2, is used to convert the Gaussian pump beam into an optical vortex. The input pump beam is focused at the center of the crystal using a lens, L1, of focal length, f=150 mm, resulting in a beam waist radius of w₀=40 µm for the Gaussian pump beam. A 50-mm-long, 8-mm-wide, 1-mm-thick MgO-doped periodically-poled LiNbO₃ (MgO:PPLN) crystal with multiple gratings varying in period from Λ=29.05 µm to Λ=31.05 µm in steps of 0.25 µm, is used as the nonlinear gain crystal for the OPO. To control wavelength tuning of the OPO, the crystal is housed in an oven allowing its temperature variation up to 200°C with the stability of ±0.1°C. The OPO is configured as a SRO in a four-mirror standing-wave X-cavity formed by two concave mirrors, M1 and M2 (with 200 mm separation), of a radius of curvature r=150 mm, and two plane mirrors, M3 and M4/OC. The mirrors, M1-M3, have high reflectivity (R>99%) for signal wavelengths across 1400-2100 nm and high transmission (T>90%) for idler across 2100-4400 nm and the pump at 1064 nm. To extract the resonant signal power, we use mirror M4 as an output coupler (OC) with a transmission of 5% across 1400-1600 nm. To record and study the idler beam profile, we use a CaF² lens of focal length, f=150 mm, after separating the beam from the undepleted pump and leaked signal power using the wavelength separator, S. For Airy beam generation, we employ a cubic phase mask (CPM) in the form of a binary diffraction grating [21]. The CPM is optimized to have 5% diffraction efficiency in the first diffraction orders to outcouple the resonant signal beam in the form of a cubic phase-modulated beam (as shown in 3-D intensity pattern in Fig. 1), which is subsequently Fourier transformed using a lens, L3, of focal length, f=300 mm. However, to control the spatial mode and corresponding OAM of the resonant beam, an aperture is used before M4. The OPO cavity is synchronized to the second harmonic of the pump repetition rate with a total physical cavity length of 981 mm.

 

Fig. 1. Schematic of the experimental setup. λ/2, half-wave plate; PBS, polarizing beam splitter cube; L1-3, plano-convex lenses of different focal lengths; SPP: spiral phase plate, M1-4: OPO mirrors; OC, output coupler; C, MgO: PPLN crystal; CPM, cubic phase mask. Also shown is the 3-D intensity pattern of the Airy beam.

Download Full Size | PDF

3. Results and discussion

To study the generation of multiple structured beams from single source, we configured the SRO in a compact four-mirror standing-wave cavity, as shown in Fig. 1, and fixed the crystal temperature at 115°C with the grating period of Λ=29.3 µm, corresponding to signal and idler wavelengths of 1482 nm and 3772 nm, respectively. We then pumped the OPO with vortex beam of order, l_p=2. Since OAM cannot be a fraction, we purposefully selected the higher-order pump OAM (l_p>1) to control the OAM exchange of the pump beam with the signal and idler beams [24] in the SRO. According to the OAM conservation in an OPO, the signal and idler beams can carry the OAM mode combination of (l_s,l_i)=(1,1), (0,2) and (2,0) for pump OAM mode of l_p=2. However, as reported previously [25,26], the beam overlap integral, Λ_p,s,i, between the spatial modes of pump, signal, idler, and the cavity loss mechanism, decide the OAM exchange in the SRO [25]. Using the theoretical formula [25,26], we calculate the value of Λ_p,s,i to be 0.7 for the signal and idler OAM mode combination, (l_s,l_i)=(1,1), and Λ_p,s,i to be 0.5 for both (l_s,l_i)=(0,2) and (2,0) for the pump OAM mode of l_p=2. Among all these three possible combinations of signal and idler OAM modes, the mode combination, (l_s,l_i)= (2, 0), has a very high OPO threshold [24]. Therefore, at a moderate level of pump power, one can expect the OPO to produce OAM mode combination, (l_s,l_i)=(1,1) or (0,2), depending on the cavity loss. Since the (l_s,l_i)=(1,1) require the intracavity signal to resonate in a higher-order cavity mode, we control the selection of the OAM mode combination of the cavity for a fixed pump power using an intracavity aperture. The presence of the aperture inside the cavity eliminates the higher-order cavity modes and forces the resonant signal to oscillate in the fundamental cavity mode. In the same cavity we have observed OPO operation threshold of 800 mW for (l_s,l_i)=(1,1) and 1.5 W for (l_s,l_i)=(0,2). For the fixed pump OAM mode of l_p=2 and power of 1.5 W, and in the presence of the intracavity aperture, we recorded the spatial intensity profile of all interacting beams, with the results shown in Figs. 2(a)–(f). To study the spatial profile and topological charge of the pump beam, we recorded the intensity distribution and the tilted lens image (a vortex beam of topological charge |l| after passing through a tilted lens splits into the |l|+1 number of characteristic lobes at the Fourier plane of the lens [27]) using a CCD-based camera, with the results shown in Fig. 2(a) and Fig. 2(b), respectively. As expected, the pump beam has a doughnut-shaped intensity profile (Fig. 2(a)) resembling an optical vortex, and the tilted lens image (Fig. 2(b)) having three characteristic lobes confirms the order of the pump vortex to be l_p=2. Using a camera (Spiricon Pyrocam III HR) with a pixel size of 85 × 85 µm², we recorded the spatial profile of the idler and signal beams. As evident from Fig. 2(c), the idler beam at 3380 nm has a doughnut-shaped intensity profile and the tilted lens image (Fig. 2(d)) having three lobes confirms the order of the idler vortex to be l_i=2, similar to the pump vortex. Therefore, according to OAM conservation, the signal should have a Gaussian spatial distribution. As evident from Fig. 2(e), the recorded profile of the signal beam at 1552 nm extracted through the output coupler, M4/OC, indeed displays a Gaussian mode. However, the output-coupled signal beam in the first diffraction order of the CPM and subsequent Fourier transformation, as shown in Fig. 2(f), shows an intensity pattern resembling an Airy beam. Therefore, due to the presence of the intracavity aperture, the vortex-beam-pumped OPO produces an idler beam in a vortex spatial profile with the same OAM content as the pump, and the signal beam in both Gaussian and Airy spatial profiles. Further, we removed the intracavity aperture and recorded the spatial intensity profile of the beams, with the results shown in Figs. 2(g)–(l). As evident from Fig. 2(g), the idler beam has a doughnut-shaped intensity profile, but the dark core size of the beam is smaller than in Fig. 2(c), indicating the generation of a lower-order vortex beam. However, using the tilted lens image, as shown in Fig. 2(h), we confirm the order of the idler vortex to be l_i=1. Similarly, the signal beam extracted from M4/OC, as shown in Fig. 2(i), has a doughnut-shaped intensity profile and the tilted lens image, as recorded in Fig. 2(j), confirms the order of the signal vortex to be l_s=1, satisfying the OAM conservation, l_p=l_i+l_s. On the other hand, the diffracted beam of CPM, as shown in Fig. 2(k), has an Airy intensity profile with a dark core at the central lobe. To find the topological charge in dark core area, we interfered the vortex beam with itself [25] using a Mach-Zehnder interferometer after the CPM. The interference of the Airy beam with itself, as shown in Fig. 2(l), results in two fork patterns in opposite direction and confirms the presence of vortex of order, l_s=1, at the central lobe of the Airy beam. From the results shown in Fig. 2, it is confirmed that by controlling the intracavity mode of the vortex-pumped OPO and introducing the cubic phase modulation to the resonant beam, one can generate optical beams of different spatial structures, including Gaussian, vortex, Airy, and vortex Airy beams from a single source. All spatial structures except Airy and vortex Airy beam profile (program plotted ascii files) are taken in the camera in RGB profile with corresponding color scale, as shown in Fig. 2.

 

Fig. 2. (a) Intensity and (b) lobe structure of the pump. Idler (c) intensity and (d) lobe structure, and (e) Gaussian and (f) Airy profile of the signal generated in presence of aperture. Idler (g) intensity and (h) lobe structure, vortex signal (i) intensity and (j) lobe structure, vortex Airy signal (k) intensity profile, and (l) interference pattern generated in absence of aperture. (inset) Magnified image with black lines to show the presence of fork pattern in the self-interference of the vortex-Airy beam.

Download Full Size | PDF

To confirm the generation of the Airy beam and vortex Airy beams, we studied self-acceleration, non-diffraction, and self-healing, with the results shown in Fig. 3. We recorded the intensity profile of both beams, see Fig. 2(f) and Fig. 2(k), considering Fourier plane of the lens as z=0 in regular intervals of 10 cm over a propagation distance of 1.4 m, and measured the position of the central lobe of the beam. The results are shown in Fig. 3(a). As evident, both Airy (solid circles) and vortex Airy (open circles) beam move away from the rectilinear path of the beam propagation with a shift of y_d=1.02 mm for z=130 cm and y_d=1.13 mm for z=110 cm, respectively. To find the ballistic dynamics of the beams [9,21], we measured the launching angle, θ, and characteristic length, y_o, by fitting (solid lines) the quadratic equation, y_d=dz²+θz, where the deflection coefficient, d = √2λ²/16π²y_o³, to the experimental data with a correlation coefficient of the fitting, r²=0.99, to be θ=1 mrad and y_o=586 µm for Airy beam, and θ=4 mrad and y_o=484 µm for vortex Airy beam. Further, we measured the width of the central lobe of the Airy beam and the dark core size of the vortex Airy beam along beam propagation, as shown in Fig. 3(b). As evident, the central lobe size (solid circles) of the Airy beam and the dark core size (open circles) of the vortex Airy beam varies from 644 µm to 709 µm and 680 µm to 725 µm, respectively, well below the pixel size (85 µm) of the camera over a beam propagation of 1 m, confirming the non-divergence property of both beams. Finally, to verify the self-healing property, we blocked one of the secondary lobes next to the central lobe using a knife-edge placed at the Fourier plane and recorded the beam intensity profile along beam propagation axis. While we recorded the beam at regular intervals of 10 cm, we present here the spatial profiles only for propagation distances of z=10, 50, 90, and 110 cm. As evident from Figs. 3(c)–(f) for Airy beam, and Figs. 3(g)–(j) for vortex Airy beam, the beams do not have one of the side lobes at z=10 cm. However, there is a sign of reappearance of the missing side lobe at z=50 cm, and complete reappearance of the beam at propagation distance of z=90 cm. The beam maintains its profile with further propagation to z=110 cm, confirming the self-healing property of the beam. It is also interesting to note that the dark core of the vortex Airy beam remains in the central lobe of the beam even after the beam propagation of 110 cm.

 

Fig. 3. (a): Experimental (circles) trajectory of the 2D Airy beam and vortex Airy beam along with theoretical fit (solid lines). (b) Width of the central lobe of the beam along propagation distance. Intensity profile of the Airy beam (c-f) and vortex Airy beam (g-j) along beam propagation.

Download Full Size | PDF

After confirming the generation of the multi-structured beam from the single OPO source, we studied the generation of such beams across the tuning range of the device. Pumping the OPO with vortex beam of order, l_p=2, at a constant average power of 4 W, we recorded the intensity profile of the generated beams with and without the intracavity aperture, while varying the crystal temperature and grating period to produce signal and idler beams tunable across 1457-1680 nm and 2902-3944 nm, respectively. The results are shown in Fig. 4. As evident from the first column, (a-c), of Fig. 4, the signal beam extracted from mirror M4/OC has a Gaussian intensity distribution, l_s=0, and the Fourier transform of the signal diffracted off the CPM, as shown in the second column, (d-f), of Fig. 4, has Airy intensity pattern across the wavelength range of 1480-1645 nm. However, the corresponding idler beam across 3785-3012 nm has doughnut-shaped intensity profile resembling a vortex beam, as shown in the third column, (g-i), of Fig. 4, further confirming it to carry optical vortex of order, l_i=2 (same as the pump vortex order, l_p=2, satisfying the OAM conservation, l_p=l_s+l_i), verified from the tilted lens images recorded in the fourth column, (j-l), of Fig. 4. On the other hand, in absence of any intracavity aperture, the signal beam, as shown in the fifth column, (m-o), of Fig. 4, has doughnut-shaped intensity profile and carries vortex or order, l_s=1, as confirmed by the tilted lens images presented in sixth column, (p-r), of Fig. 4. However, the Fourier transform of the cubic phase modulated signal beam off the CPM across the tuning range has Airy intensity distribution with a dark core in the main lobe of the beam, as observed in the images shown in the seventh column, (s-u), of Fig. 4, resembling a vortex Airy beam. On the other hand, the corresponding idler beam, as shown in the eighth column, (v-x), of Fig. 4, has doughnut-shaped intensity profile and found to carry optical vortex of order, l_i=1, confirmed by the tilted lens images shown in the ninth column, (y-a), of Fig. 4, satisfying OAM conservation, l_p=l_s+l_i, across the OPO tuning range.

 

Fig. 4. Intensity profile of the Gaussian signal (a-c), Airy signal (d-f), vortex idler (g-i), and corresponding lobe structure (j-l) generated in presence of aperture. Intensity profile of the vortex signal (m-o), lobe structure (p-r), vortex Airy (s-u), and corresponding vortex idler (v-x) and lobe structure (y-a1) generated in absence of the aperture.

Download Full Size | PDF

We also measured the output power and power scaling of the multi-structured beam OPO across the wavelength tuning range, with the results shown in Fig. 5. Pumping the OPO with vortex beam of order, l_p=2, at a constant average power of 8 W, we recorded the output power of all the beams across the tuning range in the presence of the intracavity aperture. As evident from Fig. 5(a), the output power varies from 162 mW to 132 mW with maximum power >200 mW in the Airy beam (open circles), and from 340 mW to 1275 mW for the Gaussian beam (solid circles) across the tuning range of 1457-1680 nm. Similarly, the corresponding vortex idler power (solid square) varies from 435 mW to 1059 mW across the tuning range of 3945-2902 nm. Operating the OPO at a signal (idler) wavelength of 1477 nm (3805 nm), we performed the power scaling of the source. As shown in Fig. 5(b), the average output power in the signal beam of Gaussian and Airy spatial profile increases linearly with pump power, providing up to 547 mW and 243 mW for the maximum vortex pump power of 10 W at a slope efficiency of 6.7% and 3%, respectively. Similarly, the vortex idler average power increases linearly with vortex pump power, producing a maximum of 800 mW for 10 W of pump power at a slope efficiency of 9.5%. We then repeated the power scaling measurement across the tuning range of the OPO without the aperture inside the cavity. As evident from Fig. 5(c), in this case, the output power of the vortex signal (solid circles) and the vortex Airy signal (open circles) vary from 408 mW to 1388 mW and 208 mW to 179 mW, respectively, across the tuning range of 1457-1680 nm. Similarly, the vortex idler power varies from 506 mW to 1273 mW across the tuning range of 2902-3945 nm. The output power of the vortex signal, vortex Airy signal, and vortex idler beams also increase linearly with pump power at slope efficiency of 7.8%, 4% and 10.8%, providing maximum power of 704 mW, 359 mW and 984 mW, respectively, for a pump power of 10 W. The overall increase in output power and slope efficiency of the generated beams in the absence of aperture can be attributed to the enhancement of the overall parametric gain arising from the higher mode overlap integral (Λ_2,1,1 = 0.7) of the signal and idler vortices, with unit charge (l_s=l_i=1), with the pump vortex, l_p=2. Further, we measured the temporal duration and spectral width of the output signal at 1551 nm to be Δτ∼15 ps and Δλ∼0.6 nm, respectively, resulting in a time-bandwidth product of ΔτΔυ=1.12, well above the transform-limit due to the non-ideal pump laser characteristics.

 

Fig. 5. (a) Output power across the tuning range, and (b) the power scaling characteristics of Gaussian signal, Airy signal and vortex idler. (c) variation of output power across the tuning range and (d) the power scaling of vortex signal, vortex Airy signal and vortex idler.

Download Full Size | PDF

4. Conclusion

In conclusion, we have demonstrated the generation of multiple structured beams tunable across a wide wavelength range from a single source, for the first time to out knowledge. Using a picosecond OPO in SRO scheme synchronously pumped by a vortex beam, and manipulating spatial mode of the intracavity resonant beam using a simple mechanical aperture, we have generated optical beams with Gaussian, vortex, Airy and vortex Airy spatial profile from the device. The generated beams are tunable across the wavelength range of 1457-1680 nm and 2902-3945 nm with practical average powers of as much as 1.38 W at 80 MHz pulse repetition rate. The current scheme can be further utilized for higher-order vortex pump beam, where by controlling OAM exchange between signal and idler one can generate higher-order vortex Airy beam. The described approach is generic and can be deployed to access other regions of the optical spectrum through proper selection of pump laser and the nonlinear crystal and in all temporal domains from continuous-wave and nanosecond pulsed to ultrafast femtosecond time-scale.