Traditional methods for generating a light carrying orbital angular momentum (OAM) include the use of holographic diffraction gratings, vortex phase plates and spatial light modulators. Here we report a new method for highly efficient second-harmonic generation (SHG) of a light with OAM. By properly aligning an external cavity that contains a quasi-phase matching nonlinear crystal and pumping it with a light carrying OAM, mode matching between the pump light and the cavity’s higher order Laguerre-Gaussian (LG) mode is achieved, SHG with a conversion efficiency of up to 10.3% is obtained. We have demonstrated for the first time that the cavity can stably operate at its higher order LG mode similar to that of a Gaussian mode. The second harmonic generated light has an OAM value that is double with respected to the OAM value of the pump light. The parameters that affect the beam quality and conversion efficiency are discussed in detail. Our work opens a brand new field in laser optics and makes the first step toward high efficiency processing using a light carrying OAM.
© 2014 Optical Society of America
A light carrying orbital angular momentum (OAM) has gained attention since it was first introduced by Allen . The singularity of the spatial structure of a light carrying OAM makes it suitable for optical trapping and manipulation [2–4]. There is no limit on the dimension of the OAM degree of freedom of a light and OAM carrying light beam is preferred for high capacity optical communications [5, 6], high precision optical measurements [7, 8] and quantum key distribution . Higher dimensional entangled photon pairs carrying OAM are applied in quantum information processing for demonstrating the basic principles of quantum mechanics [10–13].
Traditional methods for generating a light carrying OAM are using holographic diffraction gratings , vortex phase plates  and spatial light modulators . Directly generates OAM-carrying light beam via traditional methods in the UV and infrared regions is very difficult, but frequency conversion of OAM-carrying light beam using nonlinear crystals provides an effective solution to this problem. The frequency conversion of an OAM-carrying light beam in birefringence phase matching (BPM) [14–17] and quasi-phase matching (QPM) [18, 19] crystals in the single pass configuration were demonstrated. Previous demonstrations showed that frequency conversion of OAM-carrying light beam using nonlinear crystals is feasible, while only a small part of the pump beam can be converted because of the low conversion efficiency in the single pass configuration, such weak light will not suitable for many practical applications. One commonly used method to enhance the conversion efficiency is to put the nonlinear crystal inside an optical cavity. The function of the cavity is to build up circulating power that is many times of the input pump power, thus the frequency conversion efficiency is enhanced many times, theoretically the conversion efficiency can reach near 100% for large enough circulating power. For frequency conversion of Gaussian pump light beam either BPM or QPM crystals are suitable. However, for OAM-carrying light beam frequency conversion, QPM crystals have advantages such as high effective nonlinear coefficient and no walk-off effect. For all the light beams involve in the nonlinear interaction process propagate along the optical principal axes in QPM crystals, the frequency converted light beam and the pump beam will not separate after transmitted through the crystal, while in BPM crystals, the two interacting beams will be separated. The walk-off effect in BPM crystals distorts the spatial shape of the frequency converted light and prevents achieving a high quality beam.
Previous investigations on the frequency conversion of a light in an external cavity configuration were focused on using Gaussian modes [20–23]. The frequency conversion of higher order modes in an external cavity has not been reported so far. The OAM modes (or Laguerre-Gaussian modes) are also eigenmodes of a confocal cavity, therefore by properly aligning the cavity, the beam can be on resonance with an OAM mode. In this work, high conversion efficiency of a light beam that carries an OAM value ofin an external confocal cavity is achieved for the first time. We obtain 22.5 mW of second harmonic generated (SHG) light with an input pump power of 219 mW, a conversion efficiency of 10.3% is achieved. This efficiency is comparable with the conversion efficiency achieved using a Gaussian pump light. When the cavity is locked, the leakage of the pump beam and the SHG beam all had donut like shapes, but the OAM value of the SHG light beam is double of the pump light beam, which is demonstrated using interferometer method the same as showed in the literature .
2. Experimental setup
The experimental setup is shown in Fig. 1. The pump beam is from a Ti:sapphire laser (Coherent, MBR110), and was modulated by an electro-optical modulator (EOM) with a radio frequency of 11.9 MHz. An isolator is placed behind the EOM to block the back reflected light from the cavity. The light is then imprinted with an OAM of valueusing a vortex phase plate (VPP, RP photonics). The polarization of the OAM light is controlled using a half wave plate (HWP). The OAM carrying light with proper polarization is mode matched to the cavity using lenses. The confocal cavity used here consisted of two concave mirrors, CM1 and CM2. The input coupler, CM1, has a curvature of 51.85 mm and a transmittance of 4% and >95% at 795 nm and 397.5nm respectively. The output coupler, CM2, with a curvature of 60 mm, has a reflective coating with a reflectivity of >99.9% at 795 nm and a transmittance of > 95% at 397.5 nm. The total length of the cavity is 80 mm. The periodically poled KTP (PPKTP) crystal (Raicol Crystals) has dimensions of 1 mm × 2 mm × 10 mm and both end faces have an anti-reflective coating for 795 nm and 397.5 nm. The temperature of the crystal is controlled using a homemade temperature controller with a stability of ± 2 mK. A piezoelectric transducer (PZT) is attached to CM2 for scanning and locking the cavity. The leakage of the pump beam and the generated SHG beam are separated by a dichroic mirror (DM). The transmission spectrum of the cavity is detected using a fast photodiode (D). The signal from the detector is mixed with the modulation signal from the EOM and filtered using a low pass filter to generate error signal for locking the cavity. The error signal is processed using a homemade proportional-integral-derivative (PID) circuit and amplified using a high voltage amplifier to control the PZT.
3. Experimental results
The experimental results are shown in Fig. 2. When the cavity is on resonance with the pump beam carrying OAM, the transmission spectrum is detected by the photodiode and recorded using an oscilloscope, as shown in Fig. 2(d). The highest peak corresponds to the LG eigenmode of the cavity and the other small peaks are unrelated modes cause by the imperfect mode matching of the pump beam and the cavity. When the cavity is locked to the highest peak using the Pound-Drever-Hall method , the leakage of the pump beam from the output coupler has a donut shape as shown in Fig. 2(a). The SHG beam also has a donut spatial shape as shown in Fig. 2(b). The asymmetry and distortion of the shape are from defects in the cavity mirror and aberrations of the beam propagation inside the cavity. We should point out that to coupling OAM-carrying light beam to the cavity is much more difficult than Gaussian mode, we need to search special cavity status that can support the mode we want, which is time consuming and need great patient.
We have demonstrated in our previous work  that the OAM is conserved in the SHG process so that the SHG beam possesses an OAM value that is twice that of the OAM value carried by pump beam. To demonstrate the cavity can support OAM-carrying pump beam and the SHG beam is also an OAM-carrying light beam, we send the SHG beam into an interferometer in the same manner as demonstrated in the literature . The result is showed in Fig. 2(c), the interference pattern of the output SHG beam from the cavity has a flower like shape with 8 “petals”, so the OAM value of the SHG beam is. This is in consistent with our previous study. We also measure the SHG power as function of the pump power. The result is shown in Fig. 2(e). The SHG power increases by almost the square of the pump power, which is similar to SHG using a Gaussian mode. When the pump power is 219 mW, we obtain a SHG power of 22.5 mW, corresponding to single side efficiency of 10.3%. If the output at the other mirror is considered, the efficiency is 20.6%. This efficiency is comparable to external cavity SHG using a Gaussian mode. The SHG conversion efficiency can be further increased by increasing the pump power, because the variation slope is still very steep for 219mW pump power. In order not to damage our EOM, we don’t increasing the pump power further in our experiments.Equation (1) is also true for external cavity SHG pump by LG mode. The locking behavior of our cavity on resonance with a LG mode is the same as a Gaussian mode. Our cavity can be stably operated for hours.
4. Summary and discussion
In conclusion, we have realized high efficient SHG in an external cavity when pumping using a light carrying OAM for the first time. Both the leakage of the pump and the SHG beams have donut like shapes. The OAM value of the SHG beam is doubled with respected to the OAM value of the pump beam. In this report, the mode matching is not perfect and the quality of the beam is poor, also only a fixed transmittance input coupler is used. However, these problems can be solved using high quality mirrors and by purifying the spatial mode from the laser with a single mode fiber. The conversion efficiency can improved by choosing a proper input coupling coefficient and designing a cavity with a smaller beam waist. All these concerns will be investigated in the near future. In the future, we will also convert OAM carrying light beam based on sum frequency generation in an external cavity. In this configuration, the light with an arbitrary OAM value can be converted with high efficiency. The present work opens a new field in laser optics and makes the first step towards high efficiency OAM light processing. This will have applications in high capacity optical communications and quantum information processing based on light carrying OAM.
This work was supported by the National Fundamental Research Program of China (Grant No. 2011CBA00200), the National Natural Science Foundation of China (Grant Nos. 11174271, 61275115, 61435011) and the Innovation Fund from the Chinese Academy of Science.
References and links
1. L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992). [CrossRef] [PubMed]
2. M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, “Creation and manipulation of three-dimensional optically trapped structures,” Science 296(5570), 1101–1103 (2002). [CrossRef] [PubMed]
3. M. Padgett and R. Bowman, “Tweezers with a twist,” Nat. Photonics 5(6), 343–348 (2011). [CrossRef]
4. Z.-Y. Zhou, Y. Li, D.-S. Ding, Y.-K. Jiang, W. Zhang, S. Shi, B.-S. Shi, and G.-C. Guo, “Generation of light with controllable spatial patterns via the sum frequency in quasi-phase matching crystals,” Sci Rep 4, 5650 (2014). [PubMed]
5. J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012). [CrossRef]
6. N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-Scale Orbital Angular Momentum Mode Division Multiplexing in Fibers,” Science 340(6140), 1545–1548 (2013). [CrossRef] [PubMed]
7. V. D’Ambrosio, N. Spagnolo, L. Del Re, S. Sulssarenko, Y. Li, L. C. Kwek, L. Marrucci, S. P. Walborn, L. Aolita, and F. Sciarrinao, “Photonics polarization gears for ultra-sensitive angular measurements,” Nature Commun. 4, 2432 (2013).
8. Z.-Y. Zhou, Y. Li, D.-S. Ding, W. Zhang, S. Shi, and B.-S. Shi, “Optical vortex beam based optical fan for high-precision optical measurements and optical switching,” Opt. Lett. 39(17), 5098–5101 (2014). [CrossRef] [PubMed]
9. M. Mirhosseini, O. S. Magana-Loaiza, M. N. O’Sullivan, B. Rodenburg, M. Malik, D. J. Gauthier, and R. W. Boyd, “High-dimensional quantum cryptography with twisted light,” arXiv:1402.7113v1 [quant-ph].
11. A. C. Data, J. Leach, G. S. Buller, M. J. Padgett, and E. Andersson, “Experimental high- dimensional two-photon entanglement and violations of generalized Bell inequality,” Nat. Phys. 7(9), 677–680 (2011). [CrossRef]
12. J. T. Barreiro, T.-C. Wei, and P. G. Kwiat, “Beating the channel capacity limit for linear photonic superdense coding,” Nat. Phys. 4(4), 282–286 (2008). [CrossRef]
15. J. Courtial, K. Dholakia, L. Allen, and M. J. Padgett, “Second-harmonic-generation and the conservation of orbital angular momentum with high-order Laguerre-Gaussian modes,” Phys. Rev. A 56(5), 4193–4196 (1997). [CrossRef]
16. F. A. Bovino, M. Braccini, M. Giardina, and C. Sibilia, “Orbital angular momentum in noncollinear second-harmonic generation by off-axis vortex beams,” J. Opt. Soc. Am. B 28(11), 2806–2811 (2011). [CrossRef]
17. Y. C. Lin, K. F. Huang, and Y. F. Chen, “The formation of quasi-nondiffracting focused beams with second-harmonic generation of flower Laguerre–Gaussian modes,” Laser Phys. 23(11), 115405 (2013). [CrossRef]
18. G.-H. Shao, Z.-J. Wu, J.-H. Chen, F. Xu, and Y.-Q. Lu, “Nonlinear frequency conversion of fields with orbital angular momentum using quasi-phase matching,” Phys. Rev. A 88(6), 063827 (2013). [CrossRef]
19. Z.-Y. Zhou, D.-S. Ding, Y.-K. Jiang, Y. Li, S. Shi, X.-S. Wang, B.-S. Shi, and G.-C. Guo, “Orbital angular momentum light frequency conversion and interference with quasi-phase matching,” Opt. Express 22(17), 20298–20310 (2014). [CrossRef]
22. X. Deng, J. Zhang, Y. C. Zhang, G. Li, and T. C. Zhang, “Generation of blue light at 426 nm by frequency doubling with a monolithic periodically poled KTiOPO4,” Opt. Express 21(22), 25907–25911 (2013). [CrossRef] [PubMed]
23. S. Ast, R. M. Nia, A. Schönbeck, N. Lastzka, J. Steinlechner, T. Eberle, M. Mehmet, S. Steinlechner, and R. Schnabel, “High-efficiency frequency doubling of continuous-wave laser light,” Opt. Lett. 36(17), 3467–3469 (2011). [CrossRef] [PubMed]
24. R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using and optical resonator,” Appl. Phys. B 31(2), 97–105 (1983). [CrossRef]
25. A. Ashkin, G. D. Boyd, and J. M. Dziendzic, “Resonant optical second harmonic generation and mixing,” IEEE J. Quantum Electron. 2(6), 109–124 (1966). [CrossRef]