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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 10 — May. 20, 2013
  • pp: 12401–12409
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Direct generation of a first-Stokes vortex laser beam from a self-Raman laser

Andrew J. Lee, Takashige Omatsu, and Helen. M. Pask  »View Author Affiliations


Optics Express, Vol. 21, Issue 10, pp. 12401-12409 (2013)
http://dx.doi.org/10.1364/OE.21.012401


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Abstract

We demonstrate the direct generation of a first-order LG01 Laguerre Gaussian (vortex) mode operating at the first-Stokes wavelength of a diode end-pumped, Nd:GdVO4 self-Raman laser. To the best of our knowledge, this is the first report of intracavity stimulated Raman scattering (SRS) being used as a method for frequency conversion of a vortex laser beam and it is effective in enabling the frequency-converted (Stokes) beam to have the same LG01 mode as the fundamental beam.

© 2013 OSA

1. Introduction

Vortex laser beams may be described as having an annular beam profile and orbital angular momentum [1

1. L. Allen, S. M. Barnett, and M. J. Padgett, Optical Angular Momentum (Institute of Physics, Bristol, 2003).

3

3. D. G. Grier, “A revolution in optical manipulation,” Nature 424(6950), 810–816 (2003). [CrossRef] [PubMed]

]. These unique characteristics have seen vortex laser beams applied in a range of cutting edge applications such as optical trapping and manipulation [3

3. D. G. Grier, “A revolution in optical manipulation,” Nature 424(6950), 810–816 (2003). [CrossRef] [PubMed]

], fabrication of nano-needle structures [4

4. K. Toyoda, K. Miyamoto, N. Aoki, R. Morita, and T. Omatsu, “Using optical vortex to control the chirality of twisted metal nanostructures,” Nano Lett. 12(7), 3645–3649 (2012). [CrossRef] [PubMed]

, 5

5. T. Omatsu, K. Chujo, K. Miyamoto, M. Okida, K. Nakamura, N. Aoki, and R. Morita, “Metal microneedle fabrication using twisted light with spin,” Opt. Express 18(17), 17967–17973 (2010). [CrossRef] [PubMed]

], quantum information [2

2. S. Franke-Arnold, L. Allen, and M. Padgett, “Advances in optical angular momentum,” Las. Photon. Rev. 2(4), 299–313 (2008). [CrossRef]

], and ultra-resolution microscopy techniques such as stimulated emission depletion (STED) microscopy [6

6. S. W. Hell and J. Wichmann, “Breaking the diffraction resolution limit by stimulated emission: stimulated-emission-depletion fluorescence microscopy,” Opt. Lett. 19(11), 780–782 (1994). [CrossRef] [PubMed]

].

Vortex laser beams may be produced by converting a Gaussian beam to a Laguerre Gaussian (LG) beam using extra cavity methods such as computer-generated holograms [7

7. N. R. Heckenberg, R. McDuff, C. P. Smith, and A. G. White, “Generation of optical phase singularities by computer-generated holograms,” Opt. Lett. 17(3), 221–223 (1992). [CrossRef] [PubMed]

], spiral phase plates [8

8. V. V. Kotlyar, A. A. Almazov, S. N. Khonina, V. A. Soifer, H. Elfstrom, and J. Turunen, “Generation of phase singularity through diffracting a plane or Gaussian beam by a spiral phase plate,” J. Opt. Soc. Am. A 22(5), 849–861 (2005). [CrossRef] [PubMed]

] and spatial light modulators [9

9. N. Matsumoto, T. Ando, T. Inoue, Y. Ohtake, N. Fukuchi, and T. Hara, “Generation of high-quality higher-order Lagurre-Gaussian beams using liquid-crystal-on-silicon spatial light modulators,” J. Opt. Soc. Am. 25(7), 1642–1651 (2008). [CrossRef]

]. Each of these methods can however, be prone to misalignment and can suffer poor beam quality and/or losses through the conversion process [10

10. A. Ito, Y. Kozawa, and S. Sato, “Generation of hollow scalar and vector beams using a spot-defect mirror,” J. Opt. Soc. Am. A 27(9), 2072–2077 (2010). [CrossRef] [PubMed]

, 11

11. K. Kano, Y. Kozawa, and S. Sato, “Generation of purely single transverse mode vortex beam from a He-Ne laser cavity with a spot-defect mirror,” Int. J. Opt. 2012, 359141 (2012). [CrossRef]

]. In recent years there has been considerable effort devoted to the direct generation of vortex laser beams in solid-state lasers; progress in this area has been recently reviewed by Senatsky et.al [12

12. . Senatsky, J.-F. Bisson, J. Li, A. Shirakawa, M. Thirugnanasambandam, and K.- Ueda, “Laguerre-Gaussian modes selection in diode-pumped solid-state lasers,” Opt. Rev. 19(4), 201–221 (2012). [CrossRef]

]. A variety of methods have been employed to force the laser to oscillate on an LG mode instead of a Gaussian mode, including pumping with an annular shaped beam [13

13. J.-F. Bisson, Y. Senatsky, and K.-I. Ueda, “Generation of Laguerre-Gaussian modes in Nd:YAG laser using diffractive optical pumping,” Laser Phys. Lett. 2(7), 327–333 (2005). [CrossRef]

, 14

14. J. W. Kim, “High-power laser operation of the first-order Laguerre-Gaussian (LG01) mode in a diode-laser-pumped Nd:YAG laser,” J. Korean Phys. Soc. 61(5), 739–743 (2012). [CrossRef]

], using thermal lensing [15

15. M. Okida, T. Omatsu, M. Itoh, and T. Yatagai, “Direct generation of high power Laguerre-Gaussian output from a diode-pumped Nd:YVO4 1.3-mum bounce laser,” Opt. Express 15(12), 7616–7622 (2007). [CrossRef] [PubMed]

], using an intracavity spiral phase plate [16

16. R. Oron, Y. Danziger, N. Davidson, A. A. Friesem, and E. Hasman, “Laser mode discrimination with intra-cavity spiral phase elements,” Opt. Commun. 169(1-6), 115–121 (1999). [CrossRef]

], or by using a defect spot on one of the resonator mirrors [10

10. A. Ito, Y. Kozawa, and S. Sato, “Generation of hollow scalar and vector beams using a spot-defect mirror,” J. Opt. Soc. Am. A 27(9), 2072–2077 (2010). [CrossRef] [PubMed]

, 11

11. K. Kano, Y. Kozawa, and S. Sato, “Generation of purely single transverse mode vortex beam from a He-Ne laser cavity with a spot-defect mirror,” Int. J. Opt. 2012, 359141 (2012). [CrossRef]

]. Until now, the laser wavelengths for which vortex beams have been directly generated are fairly limited, and are based on He-Ne [11

11. K. Kano, Y. Kozawa, and S. Sato, “Generation of purely single transverse mode vortex beam from a He-Ne laser cavity with a spot-defect mirror,” Int. J. Opt. 2012, 359141 (2012). [CrossRef]

], Nd [10

10. A. Ito, Y. Kozawa, and S. Sato, “Generation of hollow scalar and vector beams using a spot-defect mirror,” J. Opt. Soc. Am. A 27(9), 2072–2077 (2010). [CrossRef] [PubMed]

] and Er [17

17. J. W. Kim, J. I. Mackenzie, J. R. Hayes, and W. A. Clarkson, “High power Er:YAG laser with radially-polarized Laguerre-Gaussian (LG01) mode output,” Opt. Express 19(15), 14526–14531 (2011). [CrossRef] [PubMed]

] gain media.

Methods of frequency conversion, such as optical parametric oscillation (OPO) and sum-frequency generation (SFG) are widely used for frequency extension of conventional lasers, yet frequency conversion of optical vortex lasers is not well advanced and is quite a complex topic. As described in [18

18. M. Padgett and L. Allen, “Light with a twist in its tail,” Contemp. Phys. 41(5), 275–285 (2000). [CrossRef]

], conservation of orbital angular momentum in the case of second harmonic generation (SHG) requires two photons, each with angular momentum of , to yield a second harmonic photon with orbital angular momentum 2, and such behaviour has been observed experimentally [18

18. M. Padgett and L. Allen, “Light with a twist in its tail,” Contemp. Phys. 41(5), 275–285 (2000). [CrossRef]

, 19

19. K. Dholakia, N. B. Simpson, M. J. Padgett, and L. Allen, “Second-harmonic generation and the orbital angular momentum of light,” Phys. Rev. A 54(5), R3742–R3745 (1996). [CrossRef] [PubMed]

]. Similar topological charge considerations have been shown to apply for four-wave mixing [20

20. J. Strohaber, M. Zhi, A. V. Sokolov, A. A. Kolomenskii, G. G. Paulus, and H. A. Schuessler, “Coherent transfer of optical orbital angular momentum in multi-order Raman sideband generation,” Opt. Lett. 37(16), 3411–3413 (2012). [CrossRef] [PubMed]

] and OPOs [21

21. M. Martinelli, J. A. O. Huguenin, P. Nussenzveig, and A. Z. Khoury, “Orbital angular momentum exchange in an optical parametric oscillator,” Phys. Rev. A 70(1), 013812 (2004). [CrossRef]

23

23. T. Yusufu, Y. Tokizane, M. Yamada, K. Miyamoto, and T. Omatsu, “Tunable 2-μm optical vortex parametric oscillator,” Opt. Express 20(21), 23666–23675 (2012). [CrossRef] [PubMed]

], and the generation of LG01 modes by frequency conversion is not typical.

In this paper we report intracavity Raman frequency conversion of a continuous wave Nd:GdVO4 laser oscillating on an LG01 mode at 1063 nm, to deliver output at the Stokes wavelength of 1173 nm on the same LG01 mode. The LG01 mode for the fundamental field was preferentially excited by the use of a defect spot on the resonator output coupler, in common with the approach in [10

10. A. Ito, Y. Kozawa, and S. Sato, “Generation of hollow scalar and vector beams using a spot-defect mirror,” J. Opt. Soc. Am. A 27(9), 2072–2077 (2010). [CrossRef] [PubMed]

, 11

11. K. Kano, Y. Kozawa, and S. Sato, “Generation of purely single transverse mode vortex beam from a He-Ne laser cavity with a spot-defect mirror,” Int. J. Opt. 2012, 359141 (2012). [CrossRef]

]. The LG01 mode for the Stokes field result was favoured by a combination of an annular gain profile and the defect spot. We show using interferometry that the helical wavefront of the resonating fundamental field is preserved, and is also present for the resonating Stokes field. Hence we demonstrate for the first time (to the best of our knowledge) the application of SRS for intracavity wavelength conversion of a vortex laser beam, and that using SRS as a means of frequency conversion can enable the frequency-converted (Stokes) beam to have the same orbital angular momentum as the fundamental beam.

2. Experiment

The self-Raman laser cavity was formed using a 20 mm long 0.3 at. % doped Nd:GdVO4, a-cut crystal which had a high-reflecting (HR) coating (M1) applied to its input facet (R> 99.99% from 1063 to 1173 nm) and an anti-reflection coating R<0.05% from 1063 to 1173 nm applied to its output surface, and a 250 mm radius of curvature output coupler (M2) which was HR coated (R = 99.91% at 1063 nm and R = 99.40% at 1173 nm). In this self-Raman configuration, the Nd:GdVO4 crystal performs the dual functions of laser medium (to generate the fundamental field) and Raman medium (to generate the first-Stokes field). The cavity length was typically 22-32 mm. The output coupler was laser micro-machined so as to remove areas of the HR coating to produce regions of low reflectivity (defect spots) which would prevent oscillation of the lowest order Gaussian mode, and tend to force the laser to oscillate on LG modes. The use of similar defect spots to generate LG modes in He-Ne and Nd:YAG lasers has been reported elsewhere [10

10. A. Ito, Y. Kozawa, and S. Sato, “Generation of hollow scalar and vector beams using a spot-defect mirror,” J. Opt. Soc. Am. A 27(9), 2072–2077 (2010). [CrossRef] [PubMed]

, 11

11. K. Kano, Y. Kozawa, and S. Sato, “Generation of purely single transverse mode vortex beam from a He-Ne laser cavity with a spot-defect mirror,” Int. J. Opt. 2012, 359141 (2012). [CrossRef]

]. In order to optimise the diameter of the defect spot for robust generation of the LG01 modes, a 3 × 3 array of spots was produced (with inter-hole spacing of 400 µm), one row consisted of spots of 40 µm diameter, and the other rows consisted of spots which increased in diameter by 20 µm steps from 60 µm to 160 µm. The output coupler was mounted on a 2-axis translation stage to enable alignment of the system with different defect spots. The Nd:GdVO4 crystal was end pumped by a 30 W, 879 nm fibre-coupled (0.22 NA, 100 µm core diameter) laser diode which was focussed to a diameter of 300 µm. The laser resonator layout is shown in Fig. 1
Fig. 1 System layout.
.

The behaviour of the vortex Raman laser was investigated in terms of the fundamental and Stokes field output powers, beam quality and the wavefront characteristics. The order and direction of the vortex beam was determined using the interferometer shown in Fig. 1. A forked interference pattern was produced by expanding the beam (using a × 5 beam expander arrangement with f = 25 mm and f = 125 mm converging lenses) in one arm of the interferometer and combining it with the beam in the other arm. Also, a spiral interference pattern was produced by creating a spherical wavefront in one of the arms of the interferometer [24

24. I. V. Basistiy, M. S. Soskin, and M. V. Vasnetsov, “Optical wavefront dislocations and their properties,” Opt. Commun. 119(5-6), 604–612 (1995). [CrossRef]

] by removing the f = 125 mm lens, and then combining this with the beam in the other arm. The interference patterns generated by the interferometer were recorded using a CCD camera (Cohu 4800). The spatial profile of the laser beam was obtained by simply blocking the arm of the interferometer containing the pair of lenses.

3. Laser performance

Laser action was first investigated without a defect spot, in order to provide a baseline for performance. Fundamental field output at 1063 nm was produced for absorbed pump powers above 80 mW, in a TEM00 mode. For absorbed pump powers above 1 W, Stokes field output at 1173 nm was generated, also in a TEM00 mode.

Lasing of the fundamental field, in the absence of SRS, was then examined with the cavity aligned to lase centred on individual defect spots (through careful positioning of the output coupler). The cavity mode was only able to oscillate on one defect spot at a time as the diameter of the resonator mode was smaller than the spacing between defect spots. Generation of an annular output could only be achieved with the system aligned on a 40 µm diameter defect spot, and with a total cavity length of 32 mm (spacing of 12 mm between the end of the Nd:GdVO4 crystal and the output coupler). Here a threshold absorbed pump power of only ~100 mW was required to oscillate the LG01 fundamental (1063 nm), only slightly above the 80 mW threshold observed without the defect spot.

The power scaling characteristics of the fundamental and Stokes fields are shown in Fig. 2
Fig. 2 Power scaling characteristics of the fundamental and Stokes fields as a function of absorbed pump power.
. The spectral content of the output was investigated using a fibre coupled spectrometer, and it consisted of only two wavelengths: the fundamental at 1063 nm and the first Stokes at 1173 nm. Both fields are linearly polarised along the c-axis of the Nd:GdVO4 crystal and there are no contributions from other Raman-shifts or orthogonal polarisations within the system. Both the fundamental and Stokes fields maintained their annular profiles for absorbed pump powers up to ~7 W, beyond which the output became multi-lobed, no longer resembling an LG01 mode. We believe that this is primarily due to significant thermal lensing manifesting within the Nd:GdVO4 self-Raman crystal; strong thermal lensing is well known in self-Raman systems [25

25. T. Omatsu, M. Okida, A. J. Lee, and H. M. Pask, “Thermal lensing in a diode-end-pumped continuous-wave self-Raman Nd-doped GdVO4 laser,” Appl. Phys. B 108(1), 73–79 (2012). [CrossRef]

, 26

26. P. Dekker, H. M. Pask, D. J. Spence, and J. A. Piper, “Continuous-wave, intracavity doubled, self-Raman laser operation in Nd:GdVO4 at 586.5 nm,” Opt. Express 15(11), 7038–7046 (2007). [CrossRef] [PubMed]

]. As this thermal lens increases in strength with higher pump powers, it causes a contraction of the cavity mode at the output coupler and hence a change in the cavity mode to defect spot diameter ratio, preventing oscillation of the LG01 mode. A maximum fundamental field output power of 400 mW was achieved for 6.8 W absorbed diode pump power. The maximum Stokes power generated from the system was 380 mW for 6.8 W absorbed diode pump power, representing a diode to Stokes generation efficiency of 5.6%. This generation efficiency is lower than what has been reported previously for continuous-wave intra-cavity Stokes lasers [26

26. P. Dekker, H. M. Pask, D. J. Spence, and J. A. Piper, “Continuous-wave, intracavity doubled, self-Raman laser operation in Nd:GdVO4 at 586.5 nm,” Opt. Express 15(11), 7038–7046 (2007). [CrossRef] [PubMed]

, 27

27. L. Fan, Y.-X. Fan, Y.-Q. Li, H. Zhang, Q. Wang, J. Wang, and H.-T. Wang, “High-efficiency continuous-wave Raman conversion with a BaWO4 Raman crystal,” Opt. Lett. 34(11), 1687–1689 (2009). [CrossRef] [PubMed]

]. Compared to the output powers from the laser without the spot defect, which generated 454 mW of fundamental and 420 mW of Stokes output for an absorbed diode pump power of 6.8 W, the output power at the fundamental and Stokes wavelengths were approximately 10% lower when the system lased with an LG01 mode. Again, these results are not unexpected given that the fundamental field power density for the SRS process is lower when the system lases on an LG01 mode.

4. Beam characteristics

The spatial beam profiles and interferograms of the fundamental and Stokes fields are shown in Fig. 3
Fig. 3 Images (a), (b), (c) showing the spatial profile, fork-interferogram, and spiral interferogram respectively for the fundamental field; and (d), (e), (f) showing the spatial profile, fork, and spiral interferograms respectively for the Stokes field. Note that the images show some distortion and diffraction rings, caused by debris on the optics used to capture each image and slight clipping of the beam within the interferometer.
for the case when each field is operating near-threshold. Figures 3(a) and 3(d) show the annular profiles produced at both the fundamental and Stokes fields. The interferograms 3(b) and 3(e) show a single forklet indicating the presence of a first order (LG01) phase singularity in the centre of the beams [24

24. I. V. Basistiy, M. S. Soskin, and M. V. Vasnetsov, “Optical wavefront dislocations and their properties,” Opt. Commun. 119(5-6), 604–612 (1995). [CrossRef]

], and this is supported by the spiral interferograms of Figs. 3(c) and 3(f) which exhibit a single spiral pattern propagating clockwise in both cases. Note that the contrast of the fork and spiral interferograms in the case of the Stokes field is not as good as that obtained for the fundamental field, and this is due to the reflectivity of the mirrors used in the Mach-Zehnder interferometer being lower at the Stokes wavelength.

Once lasing, the laser would operate with a randomly chosen spiral direction, with both the fundamental and Stokes spiral directions always being the same as one another. The fundamental and Stokes field output powers were independent of the spiral direction. This direction did not change with pump power, and could only be changed (albeit randomly) by restarting the laser or making major changes to the alignment or resonator length. As was reported in [10

10. A. Ito, Y. Kozawa, and S. Sato, “Generation of hollow scalar and vector beams using a spot-defect mirror,” J. Opt. Soc. Am. A 27(9), 2072–2077 (2010). [CrossRef] [PubMed]

], the rotation direction of the spiral (indicating the sign of the first order vortex), could not be changed in a controlled way; for example there was no apparent regularity with which the spiral direction would change as the resonator length was increased. Figure 4
Fig. 4 Images showing (a) clockwise; and (b) anti-clockwise spiral waveform generated at the fundamental wavelength when the cavity length was changed.
shows clockwise and anti-clockwise spiral patterns that were generated by the laser cavity at the fundamental wavelength, as the cavity length was changed.

Measurements of the beam quality factor (M2) were undertaken to provide an indicator of the quality of the generated vortex beam, as described in reference [10

10. A. Ito, Y. Kozawa, and S. Sato, “Generation of hollow scalar and vector beams using a spot-defect mirror,” J. Opt. Soc. Am. A 27(9), 2072–2077 (2010). [CrossRef] [PubMed]

]. We note an alternative (and possibly more quantitative) method could be to evaluate the fidelity (quality of the amplitude and phase) of the generated vortex using an element such as a spatial light modulator [28

28. G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3(5), 305–310 (2007). [CrossRef]

], however the process is complex and difficult to implement due to spatial uncertainty in the location of the singularity (dark spot) and was not attempted in this work. The beam quality of the laser output was measured for incident diode pump powers just above the threshold for oscillation of the fundamental (~100 mW incident diode pump power) and the Stokes (~2 W incident diode pump power) fields. In the case of the fundamental field, a beam quality factor (M2) of 2.18 was measured. When pumping just above 2 W, the beam quality of the fundamental field increased to M2 ~3.12, while the beam quality of the Stokes field was M2 ~2.21. As the absorbed diode pump power was further increased to 6.8 W, the beam quality of the Stokes field changed only slightly, increasing to M2 ~2.51. The beam quality factors of the fundamental and Stokes fields being M2~2 is consistent with a first order LG mode being generated within the cavity [10

10. A. Ito, Y. Kozawa, and S. Sato, “Generation of hollow scalar and vector beams using a spot-defect mirror,” J. Opt. Soc. Am. A 27(9), 2072–2077 (2010). [CrossRef] [PubMed]

]. It should be noted that while the M2 of both the fundamental and Stokes fields increased with incident diode pump power, when examining the interferogram produced by the beam across the whole power scaling range, a single fork dislocation was observed for all cases, which indicates that the vortex mode remained single-order [24

24. I. V. Basistiy, M. S. Soskin, and M. V. Vasnetsov, “Optical wavefront dislocations and their properties,” Opt. Commun. 119(5-6), 604–612 (1995). [CrossRef]

]. The fact that the beam quality factor of the fundamental mode increased with pump power suggests that a mixed mode (comprising a first-order LG mode with some higher-order modes) is being produced in this case; it is extremely difficult to de-convolve each of these modes and examine each in isolation.

5. Discussion

It was found that an annular output beam profile (LG mode) could only be achieved when the resonator was aligned to lase on the smallest defect spots, ie those with a diameter of 40 µm, and only for absorbed diode pump powers below ~7 W. At higher absorbed pump powers and/or larger defect spot sizes, the output beam profile was multi-lobed and resembled higher order Hermite Gaussian (HG) modes. We simulated the change in resonator mode diameter using ABCD resonator modelling [29

29. Laser Cavity Analysis and Design software (LasCAD), Germany, www.las-cad.com.

] and found that for pump powers up to 7 W the resonator mode diameter at the output mirror varied from 280 µm to 240 µm, for estimated thermal lens focal lengths between 500 and 140 mm in the Nd:GdVO4 crystal. For 7 W pump power, the ratio of the defect spot diameter to the diameter of the resonator mode at the output coupler is therefore ~0.17 for an intracavity mode diameter of 240 µm. This value is slightly lower than the 0.21 observed in [10

10. A. Ito, Y. Kozawa, and S. Sato, “Generation of hollow scalar and vector beams using a spot-defect mirror,” J. Opt. Soc. Am. A 27(9), 2072–2077 (2010). [CrossRef] [PubMed]

] which used an Nd:YAG laser crystal. For higher pump powers, the stronger thermal lens induced within the Nd:GdVO4 crystal causes significant contraction of the resonator mode at the output coupler and the defect spot is no longer effective at forcing oscillation of an LG mode. Here we note the thermal lensing in a self-Raman laser is substantially stronger than for the corresponding fundamental laser [25

25. T. Omatsu, M. Okida, A. J. Lee, and H. M. Pask, “Thermal lensing in a diode-end-pumped continuous-wave self-Raman Nd-doped GdVO4 laser,” Appl. Phys. B 108(1), 73–79 (2012). [CrossRef]

, 26

26. P. Dekker, H. M. Pask, D. J. Spence, and J. A. Piper, “Continuous-wave, intracavity doubled, self-Raman laser operation in Nd:GdVO4 at 586.5 nm,” Opt. Express 15(11), 7038–7046 (2007). [CrossRef] [PubMed]

], this being due at least in part to the inelastic nature of SRS which contributes additional thermal load.

In the vortex Raman laser, there are at least two contributing mechanisms for generating the Stokes field in a LG01 mode. The first is the spatially-varying Raman gain profile, dictated by the annular profile of the fundamental field. The second is the defect spot on the output coupler, which acts as a spatially-dependent, on-axis loss for the Stokes field.

It is interesting to consider the manner in which orbital momentum is conserved during each SRS event, and this is depicted in Fig. 5
Fig. 5 Concept diagram showing orbital angular momentum states of participating photons and vibration states before and after a SRS event.
. Using a similar approach to that outlined in [18

18. M. Padgett and L. Allen, “Light with a twist in its tail,” Contemp. Phys. 41(5), 275–285 (2000). [CrossRef]

], in which photons are considered to have orbital angular momentum of lћ, the orbital angular momentum states for the fundamental, Stokes and phonon before the scattering event are denoted lF, lS and lR respectively, and those after the event are denoted lF lS and lR . The value of l is frequently called the topological charge. By the nature of the stimulated process, the scattered Stokes photon must have the same l number as the incident Stokes photon, ie. lS = lS. Conservation of orbital angular momentum requires:
lF+lS+lR=2l'S+l'R
(1)
Accordingly, our experimental observations of lF = ± 1 and lS = ± 1 are consistent with orbital angular momentum being conserved with no change to the orbital angular momentum state of the Raman-active medium (lR= l'R)

4. Conclusion

We have demonstrated a continuous-wave Nd:GdVO4 self-Raman laser operating with first-order vortex output at both the fundamental and Stokes wavelengths. 400 mW and 380 mW of output power were achieved at the fundamental and Stokes wavelengths respectively for 6.8 W incident diode pump power. The LG01 mode for the fundamental field was excited by using a defect spot on the output coupler, and this resulted in an annular distribution of Raman gain in the Nd:GdVO4 crystal. This, in combination with the defect spot on the output coupler, resulted in the Stokes field also occurring in a LG01 mode. We considered the conservation of orbital angular momentum in SRS, and found it to be consistent with our observation of LG01 modes for the fundamental and Stokes fields. This result is significant as it demonstrates the application of intracavity SRS to generate high power, high beam-quality vortex beam emission operating at a wide range of wavelengths from a compact all solid-state laser resonator.

Acknowledgments

This work was in-part performed (supported by) at the OptoFab node of the Australian National Fabrication Facility.

References and links

1.

L. Allen, S. M. Barnett, and M. J. Padgett, Optical Angular Momentum (Institute of Physics, Bristol, 2003).

2.

S. Franke-Arnold, L. Allen, and M. Padgett, “Advances in optical angular momentum,” Las. Photon. Rev. 2(4), 299–313 (2008). [CrossRef]

3.

D. G. Grier, “A revolution in optical manipulation,” Nature 424(6950), 810–816 (2003). [CrossRef] [PubMed]

4.

K. Toyoda, K. Miyamoto, N. Aoki, R. Morita, and T. Omatsu, “Using optical vortex to control the chirality of twisted metal nanostructures,” Nano Lett. 12(7), 3645–3649 (2012). [CrossRef] [PubMed]

5.

T. Omatsu, K. Chujo, K. Miyamoto, M. Okida, K. Nakamura, N. Aoki, and R. Morita, “Metal microneedle fabrication using twisted light with spin,” Opt. Express 18(17), 17967–17973 (2010). [CrossRef] [PubMed]

6.

S. W. Hell and J. Wichmann, “Breaking the diffraction resolution limit by stimulated emission: stimulated-emission-depletion fluorescence microscopy,” Opt. Lett. 19(11), 780–782 (1994). [CrossRef] [PubMed]

7.

N. R. Heckenberg, R. McDuff, C. P. Smith, and A. G. White, “Generation of optical phase singularities by computer-generated holograms,” Opt. Lett. 17(3), 221–223 (1992). [CrossRef] [PubMed]

8.

V. V. Kotlyar, A. A. Almazov, S. N. Khonina, V. A. Soifer, H. Elfstrom, and J. Turunen, “Generation of phase singularity through diffracting a plane or Gaussian beam by a spiral phase plate,” J. Opt. Soc. Am. A 22(5), 849–861 (2005). [CrossRef] [PubMed]

9.

N. Matsumoto, T. Ando, T. Inoue, Y. Ohtake, N. Fukuchi, and T. Hara, “Generation of high-quality higher-order Lagurre-Gaussian beams using liquid-crystal-on-silicon spatial light modulators,” J. Opt. Soc. Am. 25(7), 1642–1651 (2008). [CrossRef]

10.

A. Ito, Y. Kozawa, and S. Sato, “Generation of hollow scalar and vector beams using a spot-defect mirror,” J. Opt. Soc. Am. A 27(9), 2072–2077 (2010). [CrossRef] [PubMed]

11.

K. Kano, Y. Kozawa, and S. Sato, “Generation of purely single transverse mode vortex beam from a He-Ne laser cavity with a spot-defect mirror,” Int. J. Opt. 2012, 359141 (2012). [CrossRef]

12.

. Senatsky, J.-F. Bisson, J. Li, A. Shirakawa, M. Thirugnanasambandam, and K.- Ueda, “Laguerre-Gaussian modes selection in diode-pumped solid-state lasers,” Opt. Rev. 19(4), 201–221 (2012). [CrossRef]

13.

J.-F. Bisson, Y. Senatsky, and K.-I. Ueda, “Generation of Laguerre-Gaussian modes in Nd:YAG laser using diffractive optical pumping,” Laser Phys. Lett. 2(7), 327–333 (2005). [CrossRef]

14.

J. W. Kim, “High-power laser operation of the first-order Laguerre-Gaussian (LG01) mode in a diode-laser-pumped Nd:YAG laser,” J. Korean Phys. Soc. 61(5), 739–743 (2012). [CrossRef]

15.

M. Okida, T. Omatsu, M. Itoh, and T. Yatagai, “Direct generation of high power Laguerre-Gaussian output from a diode-pumped Nd:YVO4 1.3-mum bounce laser,” Opt. Express 15(12), 7616–7622 (2007). [CrossRef] [PubMed]

16.

R. Oron, Y. Danziger, N. Davidson, A. A. Friesem, and E. Hasman, “Laser mode discrimination with intra-cavity spiral phase elements,” Opt. Commun. 169(1-6), 115–121 (1999). [CrossRef]

17.

J. W. Kim, J. I. Mackenzie, J. R. Hayes, and W. A. Clarkson, “High power Er:YAG laser with radially-polarized Laguerre-Gaussian (LG01) mode output,” Opt. Express 19(15), 14526–14531 (2011). [CrossRef] [PubMed]

18.

M. Padgett and L. Allen, “Light with a twist in its tail,” Contemp. Phys. 41(5), 275–285 (2000). [CrossRef]

19.

K. Dholakia, N. B. Simpson, M. J. Padgett, and L. Allen, “Second-harmonic generation and the orbital angular momentum of light,” Phys. Rev. A 54(5), R3742–R3745 (1996). [CrossRef] [PubMed]

20.

J. Strohaber, M. Zhi, A. V. Sokolov, A. A. Kolomenskii, G. G. Paulus, and H. A. Schuessler, “Coherent transfer of optical orbital angular momentum in multi-order Raman sideband generation,” Opt. Lett. 37(16), 3411–3413 (2012). [CrossRef] [PubMed]

21.

M. Martinelli, J. A. O. Huguenin, P. Nussenzveig, and A. Z. Khoury, “Orbital angular momentum exchange in an optical parametric oscillator,” Phys. Rev. A 70(1), 013812 (2004). [CrossRef]

22.

K. Miyamoto, S. Miyagi, M. Yamada, K. Furuki, N. Aoki, M. Okida, and T. Omatsu, “Optical vortex pumped mid-infrared optical parametric oscillator,” Opt. Express 19(13), 12220–12226 (2011). [CrossRef] [PubMed]

23.

T. Yusufu, Y. Tokizane, M. Yamada, K. Miyamoto, and T. Omatsu, “Tunable 2-μm optical vortex parametric oscillator,” Opt. Express 20(21), 23666–23675 (2012). [CrossRef] [PubMed]

24.

I. V. Basistiy, M. S. Soskin, and M. V. Vasnetsov, “Optical wavefront dislocations and their properties,” Opt. Commun. 119(5-6), 604–612 (1995). [CrossRef]

25.

T. Omatsu, M. Okida, A. J. Lee, and H. M. Pask, “Thermal lensing in a diode-end-pumped continuous-wave self-Raman Nd-doped GdVO4 laser,” Appl. Phys. B 108(1), 73–79 (2012). [CrossRef]

26.

P. Dekker, H. M. Pask, D. J. Spence, and J. A. Piper, “Continuous-wave, intracavity doubled, self-Raman laser operation in Nd:GdVO4 at 586.5 nm,” Opt. Express 15(11), 7038–7046 (2007). [CrossRef] [PubMed]

27.

L. Fan, Y.-X. Fan, Y.-Q. Li, H. Zhang, Q. Wang, J. Wang, and H.-T. Wang, “High-efficiency continuous-wave Raman conversion with a BaWO4 Raman crystal,” Opt. Lett. 34(11), 1687–1689 (2009). [CrossRef] [PubMed]

28.

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3(5), 305–310 (2007). [CrossRef]

29.

Laser Cavity Analysis and Design software (LasCAD), Germany, www.las-cad.com.

OCIS Codes
(140.3300) Lasers and laser optics : Laser beam shaping
(140.3480) Lasers and laser optics : Lasers, diode-pumped
(140.3550) Lasers and laser optics : Lasers, Raman
(190.5650) Nonlinear optics : Raman effect

ToC Category:
Lasers and Laser Optics

History
Original Manuscript: March 28, 2013
Revised Manuscript: April 27, 2013
Manuscript Accepted: April 28, 2013
Published: May 13, 2013

Citation
Andrew J. Lee, Takashige Omatsu, and Helen. M. Pask, "Direct generation of a first-Stokes vortex laser beam from a self-Raman laser," Opt. Express 21, 12401-12409 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-10-12401


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References

  1. L. Allen, S. M. Barnett, and M. J. Padgett, Optical Angular Momentum (Institute of Physics, Bristol, 2003).
  2. S. Franke-Arnold, L. Allen, and M. Padgett, “Advances in optical angular momentum,” Las. Photon. Rev.2(4), 299–313 (2008). [CrossRef]
  3. D. G. Grier, “A revolution in optical manipulation,” Nature424(6950), 810–816 (2003). [CrossRef] [PubMed]
  4. K. Toyoda, K. Miyamoto, N. Aoki, R. Morita, and T. Omatsu, “Using optical vortex to control the chirality of twisted metal nanostructures,” Nano Lett.12(7), 3645–3649 (2012). [CrossRef] [PubMed]
  5. T. Omatsu, K. Chujo, K. Miyamoto, M. Okida, K. Nakamura, N. Aoki, and R. Morita, “Metal microneedle fabrication using twisted light with spin,” Opt. Express18(17), 17967–17973 (2010). [CrossRef] [PubMed]
  6. S. W. Hell and J. Wichmann, “Breaking the diffraction resolution limit by stimulated emission: stimulated-emission-depletion fluorescence microscopy,” Opt. Lett.19(11), 780–782 (1994). [CrossRef] [PubMed]
  7. N. R. Heckenberg, R. McDuff, C. P. Smith, and A. G. White, “Generation of optical phase singularities by computer-generated holograms,” Opt. Lett.17(3), 221–223 (1992). [CrossRef] [PubMed]
  8. V. V. Kotlyar, A. A. Almazov, S. N. Khonina, V. A. Soifer, H. Elfstrom, and J. Turunen, “Generation of phase singularity through diffracting a plane or Gaussian beam by a spiral phase plate,” J. Opt. Soc. Am. A22(5), 849–861 (2005). [CrossRef] [PubMed]
  9. N. Matsumoto, T. Ando, T. Inoue, Y. Ohtake, N. Fukuchi, and T. Hara, “Generation of high-quality higher-order Lagurre-Gaussian beams using liquid-crystal-on-silicon spatial light modulators,” J. Opt. Soc. Am.25(7), 1642–1651 (2008). [CrossRef]
  10. A. Ito, Y. Kozawa, and S. Sato, “Generation of hollow scalar and vector beams using a spot-defect mirror,” J. Opt. Soc. Am. A27(9), 2072–2077 (2010). [CrossRef] [PubMed]
  11. K. Kano, Y. Kozawa, and S. Sato, “Generation of purely single transverse mode vortex beam from a He-Ne laser cavity with a spot-defect mirror,” Int. J. Opt.2012, 359141 (2012). [CrossRef]
  12. . Senatsky, J.-F. Bisson, J. Li, A. Shirakawa, M. Thirugnanasambandam, and K.- Ueda, “Laguerre-Gaussian modes selection in diode-pumped solid-state lasers,” Opt. Rev.19(4), 201–221 (2012). [CrossRef]
  13. J.-F. Bisson, Y. Senatsky, and K.-I. Ueda, “Generation of Laguerre-Gaussian modes in Nd:YAG laser using diffractive optical pumping,” Laser Phys. Lett.2(7), 327–333 (2005). [CrossRef]
  14. J. W. Kim, “High-power laser operation of the first-order Laguerre-Gaussian (LG01) mode in a diode-laser-pumped Nd:YAG laser,” J. Korean Phys. Soc.61(5), 739–743 (2012). [CrossRef]
  15. M. Okida, T. Omatsu, M. Itoh, and T. Yatagai, “Direct generation of high power Laguerre-Gaussian output from a diode-pumped Nd:YVO4 1.3-mum bounce laser,” Opt. Express15(12), 7616–7622 (2007). [CrossRef] [PubMed]
  16. R. Oron, Y. Danziger, N. Davidson, A. A. Friesem, and E. Hasman, “Laser mode discrimination with intra-cavity spiral phase elements,” Opt. Commun.169(1-6), 115–121 (1999). [CrossRef]
  17. J. W. Kim, J. I. Mackenzie, J. R. Hayes, and W. A. Clarkson, “High power Er:YAG laser with radially-polarized Laguerre-Gaussian (LG01) mode output,” Opt. Express19(15), 14526–14531 (2011). [CrossRef] [PubMed]
  18. M. Padgett and L. Allen, “Light with a twist in its tail,” Contemp. Phys.41(5), 275–285 (2000). [CrossRef]
  19. K. Dholakia, N. B. Simpson, M. J. Padgett, and L. Allen, “Second-harmonic generation and the orbital angular momentum of light,” Phys. Rev. A54(5), R3742–R3745 (1996). [CrossRef] [PubMed]
  20. J. Strohaber, M. Zhi, A. V. Sokolov, A. A. Kolomenskii, G. G. Paulus, and H. A. Schuessler, “Coherent transfer of optical orbital angular momentum in multi-order Raman sideband generation,” Opt. Lett.37(16), 3411–3413 (2012). [CrossRef] [PubMed]
  21. M. Martinelli, J. A. O. Huguenin, P. Nussenzveig, and A. Z. Khoury, “Orbital angular momentum exchange in an optical parametric oscillator,” Phys. Rev. A70(1), 013812 (2004). [CrossRef]
  22. K. Miyamoto, S. Miyagi, M. Yamada, K. Furuki, N. Aoki, M. Okida, and T. Omatsu, “Optical vortex pumped mid-infrared optical parametric oscillator,” Opt. Express19(13), 12220–12226 (2011). [CrossRef] [PubMed]
  23. T. Yusufu, Y. Tokizane, M. Yamada, K. Miyamoto, and T. Omatsu, “Tunable 2-μm optical vortex parametric oscillator,” Opt. Express20(21), 23666–23675 (2012). [CrossRef] [PubMed]
  24. I. V. Basistiy, M. S. Soskin, and M. V. Vasnetsov, “Optical wavefront dislocations and their properties,” Opt. Commun.119(5-6), 604–612 (1995). [CrossRef]
  25. T. Omatsu, M. Okida, A. J. Lee, and H. M. Pask, “Thermal lensing in a diode-end-pumped continuous-wave self-Raman Nd-doped GdVO4 laser,” Appl. Phys. B108(1), 73–79 (2012). [CrossRef]
  26. P. Dekker, H. M. Pask, D. J. Spence, and J. A. Piper, “Continuous-wave, intracavity doubled, self-Raman laser operation in Nd:GdVO4 at 586.5 nm,” Opt. Express15(11), 7038–7046 (2007). [CrossRef] [PubMed]
  27. L. Fan, Y.-X. Fan, Y.-Q. Li, H. Zhang, Q. Wang, J. Wang, and H.-T. Wang, “High-efficiency continuous-wave Raman conversion with a BaWO4 Raman crystal,” Opt. Lett.34(11), 1687–1689 (2009). [CrossRef] [PubMed]
  28. G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys.3(5), 305–310 (2007). [CrossRef]
  29. Laser Cavity Analysis and Design software (LasCAD), Germany, www.las-cad.com .

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