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OPTICS LETTERS / Vol. 39, No. 8 / April 15, 2014
Thermally driven continuous-wave and pulsed optical vortex Yitian Ding,1,2,† Miaomiao Xu,1,3,† Yongguang Zhao,1 Haohai Yu,1,* Huaijin Zhang,1 Zhengping Wang,1 and Jiyang Wang1 1
State Key Laboratory of Crystal Materials and Institute of Crystal Materials, Shandong University, Jinan 250100, China 2
Department of Physics, Shandong University, Jinan 250100, China 3 Taishan College, Shandong University, Jinan 250100, China *Corresponding author: [email protected]
Received November 21, 2013; revised March 16, 2014; accepted March 17, 2014; posted March 18, 2014 (Doc. ID 201751); published April 9, 2014 We demonstrated a continuous-wave (cw) and pulsed optical vortex with topological charges driven by heat generated during the lasing process without introducing the astigmatism effect and reducing lasing efficiency. During the lasing process, the topological charges were changeable by the thermal-induced lens and selected by the modematching between the pump and oscillating beams. With a graphene sample as the saturable absorber, a pulsed optical vortex was achieved at a wavelength of 1.36 μm, which identified that graphene could be used as a pulse modulator for the generation of a pulsed optical vortex. Thermally driven cw and pulsed optical vortexes should have various promising applications based on the compact structure, changeable topological charges, and specific wavelength. © 2014 Optical Society of America OCIS codes: (140.3538) Lasers, pulsed; (140.3480) Lasers, diode-pumped; (050.4865) Optical vortices; (070.2580) Paraxial wave optics. http://dx.doi.org/10.1364/OL.39.002366
Angular momentum (AM) is a universal physical concept and can be carried by a rotated particle. Orbital and spin are two types of AM. Similar to rotated particles such as electrons, light can also have AM when it has a helical phase or rotated polarization direction [1,2]. Both of them can transfer torque [3,4]. However, spin AM per photon has only three values, 0 and ℏ, corresponding to linear and circular polarizations with different rotated directions, and orbital AM per photon is lℏ, generated by the helical phase and determined by the topological charge or azimuthal mode index l [2]. Their generation [4–7], propagation dynamics [8,9], entanglement [10], interaction with matter [11], etc., have been drawing much attention over the past few decades, since they belong to the wave–particle duality [2] and can reveal the nature of the optical AM [12]. Laguerre–Gaussian (LGp;l ) laser modes are a type of eigenmodes of the laser cavity and carry orbital AM equal to lℏ per photon. The previous investigation [13] has identified that the astigmatism effect is essential for the generation of high-order eigen laser modes, in spite of the Hermite–Gaussian (HGp;l ) or LGp;l laser modes. However, the introduction of astigmatism effects into the laser cavity would reduce the lasing efficiency, since the astigmatism would reduce the mode-matching degree between the pump and oscillating beams [14]. In the lasing process, heat is unavoidable and is caused mainly by quantum defects [15]. The thermal effects generated are considered to be deleterious to the laser output performance, especially in high-power lasers. Thermal-induced lensing is a direct result of thermal effects whose focal length is tunable by the absorbed pump power [16] and change the sizes of oscillating modes. The size of oscillating high-order eigenmodes of the laser cavity is proportional to their order and the sizes of the fundamental modes determined by the laser cavity. By mode matching between the pump and oscillating beams, the order of achieved laser modes can be driven 0146-9592/14/082366-04$15.00/0
thermally and no obvious reduction of the optical efficiency is generated [15]. In the universal neodymiumdoped crystal lasers, the most serious thermal effects are generated during the lasing process at a wavelength of 1.3 μm laser with 808 nm LD pumped quantum defects are the largest. Lasers with wavelengths of about have many applications in some specific fields, such as medical treatment, optical fiber communication, and efficient production of red radiation by frequency doubling [17], aside from the absorption of some specific matter at this wavelength. However, most previous studies were focused on the operation of lasers at 1.06 μm [7,12– 14,18]. In this Letter, we demonstrate thermally driven continuous-wave (cw) and pulsed LGp;l laser modes at the wavelength of 1.3 μm with tunable topological charges. It also identified that graphene can be used as a saturable absorber for the generation of a pulsed optical vortex. The pump source was a commercial fiber-coupled laser diode (LD) with a central wavelength around 808 nm. The core size of the fiber was 100 μm in radius, and the numerical aperture was 0.22. The output intensity from the fiber distributes as a doughnut shape [19]. The symmetry of the doughnut-shaped distribution determined that the laser system could be described with a cylindrical coordinate that meets the requirement of generation within LG eigenmodes within a cavity. Using an imaging unit with a beam compression ratio of 1:1, the pump light was focused into a crystal with a beam waist that is 100 μm in radius. The experimental configuration used for the generation of cw and a pulsed optical vortex is shown in Fig. 1. The gain medium was Nd-doped Lu0.5 Y0.5 2 SiO5 (Nd:LYSO) crystal with a size of 3 mm× 3 mm × 10 mm, whose end faces were polished and uncoated. The crystal, cut along c axis, was chosen as the gain material in the laser experiments, since the crystallographic axes b and a have small thermal conductivities [20]. The crystal was wrapped with indium foil and © 2014 Optical Society of America
April 15, 2014 / Vol. 39, No. 8 / OPTICS LETTERS
Fig. 1. Experimental configuration of cw and pulsed optical vortex.
mounted in a water-cooled copper block with cooling temperature of 20°C. The emission peak with the longest wavelength was located at about 1.36 μm [21], which determined the quantum defect of 40.5% during the lasing process at this wavelength. A plane–concave resonant cavity was used to realize the laser. A concave mirror (M1) with a curvature radius of 200 mm, which was high-transmission (HT) coated at 808 nm and 1.06 to 1.08 μm, and highly reflective at 1.3 to 1.4 μm, was used as the input mirror. The output coupler (M2) was a flat mirror, which was also HT coated at 1.06 to 1.08 μm and had an optimized transmission of 5% between 1.3 and 1.4 μm. The oscillation at 1.06 to 1.08 μm in the cavity was suppressed by the HT coating at this wavelength band. The length of the cavity was about 20 mm in the laser experiments. For the pulsed lasers, multilayered graphene with initial transmission of 87% was used as the saturable absorber, which was inset between the gain material and the output coupler. The output power performance is shown in Fig. 2. The absorbed pump power was measured by removing the output coupler, since the laser at 1.3 μm is a four-level system. The threshold was measured to be 0.45 W and the maximum output power was 1.36 W under the absorbed pump power of 6.7 W with optical conversion and slope efficiency of 20.3% and 21.8%, respectively. The orders of the achieved modes are also shown in this figure, corresponding to the output power and absorbed pump power. From this figure, it can be found that the output transverse modes belong to LGp;l with topological charge of lℏ. Based on the ABCD matrix, the oscillating
Fig. 2. Dependence of the cw and pulsed output power of LGp;l modes on the absorbed pump power.
2367
modes in the crystal would be large if there was no thermal lens generated in the crystal. The LG0;l mode size can be approximately shown as ω0 2p l 11∕2 [22,23], where ω0 is the fundamental mode size, which can be calculated by the ABCD matrix. With the method presented by Song et al. [24], the thermal focal length can be measured with this cavity. Based on the calculation and measurement of the thermal focal length, it can be found that, in the laser cavity used, the LGp;;l mode size was reduced with the decrease of the thermally induced focal length if the focal length was larger than about 3 mm. The modes with l 1 matched well with the pump beam in the pump power range from 2.86 to 4.99 W; however, the modes with l 2 matched well from 4.99 to 5.7 W. When the pump power increased to over 5.7 W, a p 1 mode appeared, as shown in Fig. 2. Considering the large quantum defects (40.5%), the relatively poor thermal properties of the crystal used [20,24], and its low absorption efficiency (30.8%) at the pump beam, we did not increase the pump power further to avoid cracking of the crystal. Based on the cw laser experiments and calculation, it can be found that the radius of oscillating modes decreased with the increase of the pump power and the thermal focal effect, and higher order modes with large radii became mode-matched with the pump mode. Therefore, it could be concluded that the optical vortex generated was thermally driven and that mode matching was the selection rule for the order and topological charge of LG0;l modes. To further identify the LGp;l modes driven thermally, the cooling temperature was tuned to 25°C and 10°C, which generated higher (over 3 W) and lower (about 2.5 W) LG0;1 mode thresholds, respectively, since the thermal focal length is determined by the difference in temperature between the cooling sides on and the pump core in the crystal [16]. To confirm the topological charge of the achieved LGp;l modes, a mode converter made up of two identical cylindrical lenses, which introduced ik to the decomposition of LGp;l [2], was used to transform the LGp;l to HGm;n modes, here, k is the order of the decomposition components, p minm; n, and l jm − nj. The plain surfaces of the two lenses were set to be parallel to each other with the axis of the cylinder pointing vertically. In the experiment, we prepared the distance p between the two cylindrical lenses to be precisely 2f where f was the focal length of the two lenses. Figure 3 shows the transverse patterns of the LGp;l modes and converted HGm;n modes. From this figure, we can identify the LGp;l modes that possess topological charges of l 0, 1, and 2. In the entire lasing process, there was no astigmatism effect in the lasing cavity and the slope efficiency of 21.8% was normal for quantum defects of 40.5%. We believe that the efficiency could be improved if the laser crystal was suitably coated at the lasing wavelength. Graphene has been investigated as a universal saturable absorber for the generation of pulsed lasers. By inserting the graphene into the cavity, optical pulses were generated. The passively Q-switched laser performance is also presented in Fig. 2. The threshold was 0.47 W, a bit larger than the cw one. The highest output power was 0.53 W under absorbed pump power of 6.7 W, with slope efficiency of 8.5%. The repetition rate and pulse width were recorded with a DPO7104 digital
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OPTICS LETTERS / Vol. 39, No. 8 / April 15, 2014
Fig. 3. Transverse pattern of the laser beam. Top row, the achieved LGp;l modes. Bottom row, the converted HGm;n modes corresponding the LGp;l modes.
oscilloscope (1 GHz bandwidth and 10 Gs∕s sampling rate, Tektronix Inc.). As shown in Fig. 4, the repetition rate increased from 8.4 to 79 kHz and the pulse energy increased from 5.69 to 6.71 μJ in the entire pump power range. The shortest pulse was 102 ns under pump power of 6.7 W. The pulse profile with a width of 102 ns and typical repetition rate of 79 kHz is also presented in the inset of Fig. 4. It should be noted that the thresholds of the LG0;1 , LG0;2 , and LG1;0 modes were, respectively, 2.46, 4.5, and 5.3 W, obviously smaller than the corresponding cw thresholds. The observed LG0;1 , LG0;2 , and LG1;0 modes were similar to those shown in Fig. 4. In the cw lasers, the intracavity intensity was low and the change of the topological charge was contributed mainly by the thermal focal effect. However, the intracavity peak intensity of the pulsed lasers was about 48 times larger than the cw one, which indicated that the focal effects consisted of the thermal focal lens and nonlinear refractive index effects in the pulsed lasers. In other words, the nonlinear refractive index effects in the pulsed regime should be responsible for the lower threshold of high-order modes, since the radii of the oscillating
Fig. 4. Dependence of the repetition rate and pulse energy on the absorbed pump power. Inset: pulse profile with a width of 102 ns and a repetition rate of 79 kHz.
Fig. 5.
Laser spectrum of cw and pulsed vortex.
modes were determined by the cavity and focal effects. From the pulsed results, no topological charge was found to be lost, which showed that there was no AM transfer between the graphene and vortex pulses, and that graphene can be used as a saturable absorber for the vortex pulses. Using an optical spectrum analyzer, the laser spectrum was measured to be at about 1.36 μm, which is shown in Fig. 5. In conclusion, thermally driven cw and a pulsed optical vortex were directly generated by the mode-matching selection. Considering the large quantum defects and specific applications, optical vortices at a wavelength of 1.36 μm were demonstrated. The results also showed that graphene can be used as a vortex pulse modulator. We believe that the generated cw and pulsed optical vortex will find some promising applications in quantum optics, investigation of the interaction of orbital angular momentum of photons and matter, nonlinear optics, optical communications, etc. This work is supported by the National Natural Science Foundation of China (Nos. 51025210, 51102156 and 51272131) and the Shangdong Province Young and Middle-Aged Scientists Research Awards Fund (BS2011CL024). †These authors contributed equally to this work. References 1. L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992). 2. L. Allen, M. J. Padgett, and M. Babiker, Prog. Opt. 39, 291 (1999). 3. P. Němec, E. Rozkotová, N. Tesařová, F. Trojánek, E. De Ranieri, K. Olejník, J. Zemen, V. Novák, M. Cukr, P. Malý, and T. Jungwirth, Nat. Phys. 8, 411 (2012). 4. K. Toyoda, F. Takahashi, S. Takizawa, Y. Tokizane, K. Miyamoto, R. Morita, and T. Omatsu, Phys. Rev. Lett. 110, 143603 (2013). 5. C. Hernández-García, A. Picón, J. S. Román, and L. Plaja, Phys. Rev. Lett. 111, 083602 (2013). 6. L. Carbone, C. Bogan, P. Fulda, A. Freise, and B. Willke, Phys. Rev. Lett. 110, 251101 (2013). 7. J. F. Bisson, Y. Senatsky, and K. I. Ueda, Laser Phys. Lett. 2, 327 (2005). 8. D. Rozas, C. T. Law, and G. A. Swartzlander, Jr., J. Opt. Soc. Am. B 14, 3054 (1997).
April 15, 2014 / Vol. 39, No. 8 / OPTICS LETTERS 9. J. Leach, M. R. Dennis, J. Courtial, and M. J. Padgett, Nature 432, 165 (2004). 10. J. Romero, J. Leach, B. Jack, M. R. Dennis, S. FrankeArnold, S. M. Barnett, and M. J. Padgett, Phys. Rev. Lett. 106, 100407 (2011). 11. M. Zürch, C. Kern, P. Hansinger, A. Dreischuh, and Ch. Spielmann, Nat. Phys. 8, 743 (2012). 12. Y. Zhao, Z. Wang, H. Yu, S. Zhuang, H. Zhang, X. Xu, J. Xu, X. Xu, and J. Wang, Appl. Phys. Lett. 101, 031113 (2012). 13. T. H. Lu, Y. C. Lin, H. C. Liang, Y. J. Huang, Y. F. Chen, and K. F. Huang, Opt. Lett. 35, 345 (2010). 14. Y. F. Chen, Y. P. Lan, and S. C. Wang, Appl. Phys. B 72, 167 (2001). 15. Y. F. Chen, IEEE J. Quantum Electron. 33, 1424 (1997). 16. R. C. C. Leite, S. P. S. Porto, and T. C. Damen, Appl. Phys. Lett. 10, 100 (1967).
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17. C. Du, S. Ruan, H. Zhang, Y. Yu, F. Zeng, J. Wang, and M. Jiang, Appl. Phys. B 80, 45 (2005). 18. D. J. Kim, J. W. Kim, and W. A. Clarkson, Opt. Express 21, 29449 (2013). 19. H. H. Yu, H. J. Zhang, Y. C. Wang, Z. P. Wang, J. Y. Wang, and V. Petrov, Sci. Rep. 3, 1085 (2013). 20. Y. G. Zhao, S. D. Zhuang, X. D. Xu, J. Xu, H. H. Yu, Z. P. Wang, and X. G. Xu, Opt. Express 22, 2228 (2014). 21. D. Z. Li, X. D. Xu, D. H. Zhou, S. D. Zhuang, Z. P. Wang, C. T. Xia, F. Wu, and J. Xu, Laser Phys. Lett. 7, 798 (2010). 22. R. J. Freiberg and A. S. Halsted, Appl. Opt. 8, 355 (1969). 23. S. M. Baumann, D. M. Kalb, L. H. MacMillan, and E. J. Galvez, Opt. Express 17, 9818 (2009). 24. F. Song, C. Zhang, X. Ding, J. Xu, G. Zhang, M. Leigh, and N. Peyghambarian, Appl. Phys. Lett. 81, 2145 (2002).
OPTICS LETTERS / Vol. 39, No. 8 / April 15, 2014
Thermally driven continuous-wave and pulsed optical vortex Yitian Ding,1,2,† Miaomiao Xu,1,3,† Yongguang Zhao,1 Haohai Yu,1,* Huaijin Zhang,1 Zhengping Wang,1 and Jiyang Wang1 1
State Key Laboratory of Crystal Materials and Institute of Crystal Materials, Shandong University, Jinan 250100, China 2
Department of Physics, Shandong University, Jinan 250100, China 3 Taishan College, Shandong University, Jinan 250100, China *Corresponding author: [email protected]
Received November 21, 2013; revised March 16, 2014; accepted March 17, 2014; posted March 18, 2014 (Doc. ID 201751); published April 9, 2014 We demonstrated a continuous-wave (cw) and pulsed optical vortex with topological charges driven by heat generated during the lasing process without introducing the astigmatism effect and reducing lasing efficiency. During the lasing process, the topological charges were changeable by the thermal-induced lens and selected by the modematching between the pump and oscillating beams. With a graphene sample as the saturable absorber, a pulsed optical vortex was achieved at a wavelength of 1.36 μm, which identified that graphene could be used as a pulse modulator for the generation of a pulsed optical vortex. Thermally driven cw and pulsed optical vortexes should have various promising applications based on the compact structure, changeable topological charges, and specific wavelength. © 2014 Optical Society of America OCIS codes: (140.3538) Lasers, pulsed; (140.3480) Lasers, diode-pumped; (050.4865) Optical vortices; (070.2580) Paraxial wave optics. http://dx.doi.org/10.1364/OL.39.002366
Angular momentum (AM) is a universal physical concept and can be carried by a rotated particle. Orbital and spin are two types of AM. Similar to rotated particles such as electrons, light can also have AM when it has a helical phase or rotated polarization direction [1,2]. Both of them can transfer torque [3,4]. However, spin AM per photon has only three values, 0 and ℏ, corresponding to linear and circular polarizations with different rotated directions, and orbital AM per photon is lℏ, generated by the helical phase and determined by the topological charge or azimuthal mode index l [2]. Their generation [4–7], propagation dynamics [8,9], entanglement [10], interaction with matter [11], etc., have been drawing much attention over the past few decades, since they belong to the wave–particle duality [2] and can reveal the nature of the optical AM [12]. Laguerre–Gaussian (LGp;l ) laser modes are a type of eigenmodes of the laser cavity and carry orbital AM equal to lℏ per photon. The previous investigation [13] has identified that the astigmatism effect is essential for the generation of high-order eigen laser modes, in spite of the Hermite–Gaussian (HGp;l ) or LGp;l laser modes. However, the introduction of astigmatism effects into the laser cavity would reduce the lasing efficiency, since the astigmatism would reduce the mode-matching degree between the pump and oscillating beams [14]. In the lasing process, heat is unavoidable and is caused mainly by quantum defects [15]. The thermal effects generated are considered to be deleterious to the laser output performance, especially in high-power lasers. Thermal-induced lensing is a direct result of thermal effects whose focal length is tunable by the absorbed pump power [16] and change the sizes of oscillating modes. The size of oscillating high-order eigenmodes of the laser cavity is proportional to their order and the sizes of the fundamental modes determined by the laser cavity. By mode matching between the pump and oscillating beams, the order of achieved laser modes can be driven 0146-9592/14/082366-04$15.00/0
thermally and no obvious reduction of the optical efficiency is generated [15]. In the universal neodymiumdoped crystal lasers, the most serious thermal effects are generated during the lasing process at a wavelength of 1.3 μm laser with 808 nm LD pumped quantum defects are the largest. Lasers with wavelengths of about have many applications in some specific fields, such as medical treatment, optical fiber communication, and efficient production of red radiation by frequency doubling [17], aside from the absorption of some specific matter at this wavelength. However, most previous studies were focused on the operation of lasers at 1.06 μm [7,12– 14,18]. In this Letter, we demonstrate thermally driven continuous-wave (cw) and pulsed LGp;l laser modes at the wavelength of 1.3 μm with tunable topological charges. It also identified that graphene can be used as a saturable absorber for the generation of a pulsed optical vortex. The pump source was a commercial fiber-coupled laser diode (LD) with a central wavelength around 808 nm. The core size of the fiber was 100 μm in radius, and the numerical aperture was 0.22. The output intensity from the fiber distributes as a doughnut shape [19]. The symmetry of the doughnut-shaped distribution determined that the laser system could be described with a cylindrical coordinate that meets the requirement of generation within LG eigenmodes within a cavity. Using an imaging unit with a beam compression ratio of 1:1, the pump light was focused into a crystal with a beam waist that is 100 μm in radius. The experimental configuration used for the generation of cw and a pulsed optical vortex is shown in Fig. 1. The gain medium was Nd-doped Lu0.5 Y0.5 2 SiO5 (Nd:LYSO) crystal with a size of 3 mm× 3 mm × 10 mm, whose end faces were polished and uncoated. The crystal, cut along c axis, was chosen as the gain material in the laser experiments, since the crystallographic axes b and a have small thermal conductivities [20]. The crystal was wrapped with indium foil and © 2014 Optical Society of America
April 15, 2014 / Vol. 39, No. 8 / OPTICS LETTERS
Fig. 1. Experimental configuration of cw and pulsed optical vortex.
mounted in a water-cooled copper block with cooling temperature of 20°C. The emission peak with the longest wavelength was located at about 1.36 μm [21], which determined the quantum defect of 40.5% during the lasing process at this wavelength. A plane–concave resonant cavity was used to realize the laser. A concave mirror (M1) with a curvature radius of 200 mm, which was high-transmission (HT) coated at 808 nm and 1.06 to 1.08 μm, and highly reflective at 1.3 to 1.4 μm, was used as the input mirror. The output coupler (M2) was a flat mirror, which was also HT coated at 1.06 to 1.08 μm and had an optimized transmission of 5% between 1.3 and 1.4 μm. The oscillation at 1.06 to 1.08 μm in the cavity was suppressed by the HT coating at this wavelength band. The length of the cavity was about 20 mm in the laser experiments. For the pulsed lasers, multilayered graphene with initial transmission of 87% was used as the saturable absorber, which was inset between the gain material and the output coupler. The output power performance is shown in Fig. 2. The absorbed pump power was measured by removing the output coupler, since the laser at 1.3 μm is a four-level system. The threshold was measured to be 0.45 W and the maximum output power was 1.36 W under the absorbed pump power of 6.7 W with optical conversion and slope efficiency of 20.3% and 21.8%, respectively. The orders of the achieved modes are also shown in this figure, corresponding to the output power and absorbed pump power. From this figure, it can be found that the output transverse modes belong to LGp;l with topological charge of lℏ. Based on the ABCD matrix, the oscillating
Fig. 2. Dependence of the cw and pulsed output power of LGp;l modes on the absorbed pump power.
2367
modes in the crystal would be large if there was no thermal lens generated in the crystal. The LG0;l mode size can be approximately shown as ω0 2p l 11∕2 [22,23], where ω0 is the fundamental mode size, which can be calculated by the ABCD matrix. With the method presented by Song et al. [24], the thermal focal length can be measured with this cavity. Based on the calculation and measurement of the thermal focal length, it can be found that, in the laser cavity used, the LGp;;l mode size was reduced with the decrease of the thermally induced focal length if the focal length was larger than about 3 mm. The modes with l 1 matched well with the pump beam in the pump power range from 2.86 to 4.99 W; however, the modes with l 2 matched well from 4.99 to 5.7 W. When the pump power increased to over 5.7 W, a p 1 mode appeared, as shown in Fig. 2. Considering the large quantum defects (40.5%), the relatively poor thermal properties of the crystal used [20,24], and its low absorption efficiency (30.8%) at the pump beam, we did not increase the pump power further to avoid cracking of the crystal. Based on the cw laser experiments and calculation, it can be found that the radius of oscillating modes decreased with the increase of the pump power and the thermal focal effect, and higher order modes with large radii became mode-matched with the pump mode. Therefore, it could be concluded that the optical vortex generated was thermally driven and that mode matching was the selection rule for the order and topological charge of LG0;l modes. To further identify the LGp;l modes driven thermally, the cooling temperature was tuned to 25°C and 10°C, which generated higher (over 3 W) and lower (about 2.5 W) LG0;1 mode thresholds, respectively, since the thermal focal length is determined by the difference in temperature between the cooling sides on and the pump core in the crystal [16]. To confirm the topological charge of the achieved LGp;l modes, a mode converter made up of two identical cylindrical lenses, which introduced ik to the decomposition of LGp;l [2], was used to transform the LGp;l to HGm;n modes, here, k is the order of the decomposition components, p minm; n, and l jm − nj. The plain surfaces of the two lenses were set to be parallel to each other with the axis of the cylinder pointing vertically. In the experiment, we prepared the distance p between the two cylindrical lenses to be precisely 2f where f was the focal length of the two lenses. Figure 3 shows the transverse patterns of the LGp;l modes and converted HGm;n modes. From this figure, we can identify the LGp;l modes that possess topological charges of l 0, 1, and 2. In the entire lasing process, there was no astigmatism effect in the lasing cavity and the slope efficiency of 21.8% was normal for quantum defects of 40.5%. We believe that the efficiency could be improved if the laser crystal was suitably coated at the lasing wavelength. Graphene has been investigated as a universal saturable absorber for the generation of pulsed lasers. By inserting the graphene into the cavity, optical pulses were generated. The passively Q-switched laser performance is also presented in Fig. 2. The threshold was 0.47 W, a bit larger than the cw one. The highest output power was 0.53 W under absorbed pump power of 6.7 W, with slope efficiency of 8.5%. The repetition rate and pulse width were recorded with a DPO7104 digital
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OPTICS LETTERS / Vol. 39, No. 8 / April 15, 2014
Fig. 3. Transverse pattern of the laser beam. Top row, the achieved LGp;l modes. Bottom row, the converted HGm;n modes corresponding the LGp;l modes.
oscilloscope (1 GHz bandwidth and 10 Gs∕s sampling rate, Tektronix Inc.). As shown in Fig. 4, the repetition rate increased from 8.4 to 79 kHz and the pulse energy increased from 5.69 to 6.71 μJ in the entire pump power range. The shortest pulse was 102 ns under pump power of 6.7 W. The pulse profile with a width of 102 ns and typical repetition rate of 79 kHz is also presented in the inset of Fig. 4. It should be noted that the thresholds of the LG0;1 , LG0;2 , and LG1;0 modes were, respectively, 2.46, 4.5, and 5.3 W, obviously smaller than the corresponding cw thresholds. The observed LG0;1 , LG0;2 , and LG1;0 modes were similar to those shown in Fig. 4. In the cw lasers, the intracavity intensity was low and the change of the topological charge was contributed mainly by the thermal focal effect. However, the intracavity peak intensity of the pulsed lasers was about 48 times larger than the cw one, which indicated that the focal effects consisted of the thermal focal lens and nonlinear refractive index effects in the pulsed lasers. In other words, the nonlinear refractive index effects in the pulsed regime should be responsible for the lower threshold of high-order modes, since the radii of the oscillating
Fig. 4. Dependence of the repetition rate and pulse energy on the absorbed pump power. Inset: pulse profile with a width of 102 ns and a repetition rate of 79 kHz.
Fig. 5.
Laser spectrum of cw and pulsed vortex.
modes were determined by the cavity and focal effects. From the pulsed results, no topological charge was found to be lost, which showed that there was no AM transfer between the graphene and vortex pulses, and that graphene can be used as a saturable absorber for the vortex pulses. Using an optical spectrum analyzer, the laser spectrum was measured to be at about 1.36 μm, which is shown in Fig. 5. In conclusion, thermally driven cw and a pulsed optical vortex were directly generated by the mode-matching selection. Considering the large quantum defects and specific applications, optical vortices at a wavelength of 1.36 μm were demonstrated. The results also showed that graphene can be used as a vortex pulse modulator. We believe that the generated cw and pulsed optical vortex will find some promising applications in quantum optics, investigation of the interaction of orbital angular momentum of photons and matter, nonlinear optics, optical communications, etc. This work is supported by the National Natural Science Foundation of China (Nos. 51025210, 51102156 and 51272131) and the Shangdong Province Young and Middle-Aged Scientists Research Awards Fund (BS2011CL024). †These authors contributed equally to this work. References 1. L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992). 2. L. Allen, M. J. Padgett, and M. Babiker, Prog. Opt. 39, 291 (1999). 3. P. Němec, E. Rozkotová, N. Tesařová, F. Trojánek, E. De Ranieri, K. Olejník, J. Zemen, V. Novák, M. Cukr, P. Malý, and T. Jungwirth, Nat. Phys. 8, 411 (2012). 4. K. Toyoda, F. Takahashi, S. Takizawa, Y. Tokizane, K. Miyamoto, R. Morita, and T. Omatsu, Phys. Rev. Lett. 110, 143603 (2013). 5. C. Hernández-García, A. Picón, J. S. Román, and L. Plaja, Phys. Rev. Lett. 111, 083602 (2013). 6. L. Carbone, C. Bogan, P. Fulda, A. Freise, and B. Willke, Phys. Rev. Lett. 110, 251101 (2013). 7. J. F. Bisson, Y. Senatsky, and K. I. Ueda, Laser Phys. Lett. 2, 327 (2005). 8. D. Rozas, C. T. Law, and G. A. Swartzlander, Jr., J. Opt. Soc. Am. B 14, 3054 (1997).
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