Abstract

It is theoretically demonstrated that the planar geometric mode with a π/2 mode converter, so called the circularly geometric mode, can be solved from the inhomogeneous Helmholtz equation by considering the pump distribution on the lasing mode. Theoretical analysis clearly reveal that the vortex structures of circularly geometric modes are determined by the minimum order of transverse lasing modes, the total number of transverse lasing modes and the degenerate condition in the cavity. Moreover, we experimentally manifest that the circularly geometric mode can be generated from the selective pumped solid-state laser with an external π/2 mode converter. To explore the vortex structures of the generated geometric modes, the interference patterns are performed by an experimental apparatus consisting of a Mach-Zehnder interferometer. The good agreement between experimental observations and numerical calculations confirms the analysis of vortex structures is reliable.

© 2016 Optical Society of America

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References

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    [Crossref]

2013 (2)

Y. F. Chen, J. C. Tung, P. Y. Chiang, H. C. Liang, and K. F. Huang, “Exploring the effect of fractional degeneracy and the emergence of ray-wave duality in solid-state lasers with off-axis pumping,” Phys. Rev. A 88(1), 013827 (2013).
[Crossref]

K. Toyoda, F. Takahashi, S. Takizawa, Y. Tokizane, K. Miyamoto, R. Morita, and T. Omatsu, “Transfer of light helicity to nanostructures,” Phys. Rev. Lett. 110(14), 143603 (2013).
[Crossref] [PubMed]

2012 (1)

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]

2011 (1)

T. H. Lu, Y. C. Lin, Y. F. Chen, and K. F. Huang, “Generation of multi-axis Laguerre–Gaussian beams from geometric modes of a hemiconfocal cavity,” Appl. Phys. B 103(4), 991–999 (2011).
[Crossref]

2010 (1)

C. H. Chen, P. Y. Huang, and C. W. Kuo, “Geometric modes outside the multi-bouncing fundamental Gaussian beam model,” J. Opt. 12(1), 015708 (2010).
[Crossref]

2008 (3)

A. A. Malyutin, “Closed laser-beam trajectories in plano-spherical resonators with Gaussian apertures,” Quantum Electron. 38(2), 181–186 (2008).
[Crossref]

Y. J. Liu, X. W. Sun, D. Luo, and Z. Raszewski, “Generating electrically tunable optical vortices by a liquid crystal cell with patterned electrode,” Appl. Phys. Lett. 92(10), 101114 (2008).
[Crossref]

M. Dienerowitz, M. Mazilu, P. J. Reece, T. F. Krauss, and K. Dholakia, “Optical vortex trap for resonant confinement of metal nanoparticles,” Opt. Express 16(7), 4991–4999 (2008).
[Crossref] [PubMed]

2007 (2)

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

A. A. Malyutin, “Modes of a plano-spherical laser resonator with the Gaussian gain distribution of the active medium,” Quantum Electron. 37(3), 299–306 (2007).
[Crossref]

2006 (1)

2005 (2)

Ya. Izdebskaya, V. Shvedov, and A. Volyar, “Generation of higher-order optical vortices by a dielectric wedge,” Opt. Lett. 30(18), 2472–2474 (2005).
[Crossref] [PubMed]

A. B. Matsko, A. A. Savchenkov, D. Strekalov, and L. Maleki, “Whispering gallery resonators for studying orbital angular momentum of a photon,” Phys. Rev. Lett. 95(14), 143904 (2005).
[Crossref] [PubMed]

2004 (2)

Y. F. Chen, C. H. Jiang, Y. P. Lan, and K. F. Huang, “Wave representation of geometrical laser beam trajectories in a hemiconfocal cavity,” Phys. Rev. A 69(5), 053807 (2004).
[Crossref]

G. Gibson, J. Courtial, M. Padgett, M. Vasnetsov, V. Pas’ko, S. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Express 12(22), 5448–5456 (2004).
[Crossref] [PubMed]

2003 (1)

M. P. MacDonald, G. C. Spalding, and K. Dholakia, “Microfluidic sorting in an optical lattice,” Nature 426(6965), 421–424 (2003).
[Crossref] [PubMed]

2001 (2)

J. Dingjan, M. P. van Exter, and J. P. Woerdman, “Geometric modes in a single-frequency Nd: YVO4 laser,” Opt. Commun. 188(5–6), 345–351 (2001).
[Crossref]

Y. F. Chen, Y. P. Lan, and S. C. Wang, “Generation of Laguerre–Gaussian modes in fiber-coupled laser diode end-pumped lasers,” Appl. Phys. B 72(2), 167–170 (2001).
[Crossref]

1999 (1)

Q. Zhang, B. Ozygus, and H. Weber, “Degeneration effects in laser cavities,” Eur. Phys. J. Appl. Phys. 6(3), 293–298 (1999).
[Crossref]

1996 (1)

1994 (1)

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112(5–6), 321–327 (1994).
[Crossref]

1993 (1)

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96(1–3), 123–132 (1993).
[Crossref]

1992 (2)

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]

V. Yu. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, “Screw dislocations in light wavefronts,” J. Mod. Opt. 39(5), 985–990 (1992).
[Crossref]

1991 (1)

E. Abramochkin and V. Volostnikov, “Beam transformations and nontransformed beams,” Opt. Commun. 83(1–2), 123–135 (1991).
[Crossref]

Abramochkin, E.

E. Abramochkin and V. Volostnikov, “Beam transformations and nontransformed beams,” Opt. Commun. 83(1–2), 123–135 (1991).
[Crossref]

Allen, L.

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96(1–3), 123–132 (1993).
[Crossref]

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]

Aoki, N.

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]

Barnett, S.

Bazhenov, V. Yu.

V. Yu. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, “Screw dislocations in light wavefronts,” J. Mod. Opt. 39(5), 985–990 (1992).
[Crossref]

Beijersbergen, M. W.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112(5–6), 321–327 (1994).
[Crossref]

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96(1–3), 123–132 (1993).
[Crossref]

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]

Bernet, S.

Chen, C. H.

C. H. Chen, P. Y. Huang, and C. W. Kuo, “Geometric modes outside the multi-bouncing fundamental Gaussian beam model,” J. Opt. 12(1), 015708 (2010).
[Crossref]

Chen, Y. F.

Y. F. Chen, J. C. Tung, P. Y. Chiang, H. C. Liang, and K. F. Huang, “Exploring the effect of fractional degeneracy and the emergence of ray-wave duality in solid-state lasers with off-axis pumping,” Phys. Rev. A 88(1), 013827 (2013).
[Crossref]

T. H. Lu, Y. C. Lin, Y. F. Chen, and K. F. Huang, “Generation of multi-axis Laguerre–Gaussian beams from geometric modes of a hemiconfocal cavity,” Appl. Phys. B 103(4), 991–999 (2011).
[Crossref]

Y. F. Chen, C. H. Jiang, Y. P. Lan, and K. F. Huang, “Wave representation of geometrical laser beam trajectories in a hemiconfocal cavity,” Phys. Rev. A 69(5), 053807 (2004).
[Crossref]

Y. F. Chen, Y. P. Lan, and S. C. Wang, “Generation of Laguerre–Gaussian modes in fiber-coupled laser diode end-pumped lasers,” Appl. Phys. B 72(2), 167–170 (2001).
[Crossref]

Chiang, P. Y.

Y. F. Chen, J. C. Tung, P. Y. Chiang, H. C. Liang, and K. F. Huang, “Exploring the effect of fractional degeneracy and the emergence of ray-wave duality in solid-state lasers with off-axis pumping,” Phys. Rev. A 88(1), 013827 (2013).
[Crossref]

Coerwinkel, R. P. C.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112(5–6), 321–327 (1994).
[Crossref]

Courtial, J.

Dholakia, K.

Dienerowitz, M.

Dingjan, J.

J. Dingjan, M. P. van Exter, and J. P. Woerdman, “Geometric modes in a single-frequency Nd: YVO4 laser,” Opt. Commun. 188(5–6), 345–351 (2001).
[Crossref]

Franke-Arnold, S.

Fürhapter, S.

Gahagan, K. T.

Gibson, G.

Huang, K. F.

Y. F. Chen, J. C. Tung, P. Y. Chiang, H. C. Liang, and K. F. Huang, “Exploring the effect of fractional degeneracy and the emergence of ray-wave duality in solid-state lasers with off-axis pumping,” Phys. Rev. A 88(1), 013827 (2013).
[Crossref]

T. H. Lu, Y. C. Lin, Y. F. Chen, and K. F. Huang, “Generation of multi-axis Laguerre–Gaussian beams from geometric modes of a hemiconfocal cavity,” Appl. Phys. B 103(4), 991–999 (2011).
[Crossref]

Y. F. Chen, C. H. Jiang, Y. P. Lan, and K. F. Huang, “Wave representation of geometrical laser beam trajectories in a hemiconfocal cavity,” Phys. Rev. A 69(5), 053807 (2004).
[Crossref]

Huang, P. Y.

C. H. Chen, P. Y. Huang, and C. W. Kuo, “Geometric modes outside the multi-bouncing fundamental Gaussian beam model,” J. Opt. 12(1), 015708 (2010).
[Crossref]

Izdebskaya, Ya.

Jesacher, A.

Jiang, C. H.

Y. F. Chen, C. H. Jiang, Y. P. Lan, and K. F. Huang, “Wave representation of geometrical laser beam trajectories in a hemiconfocal cavity,” Phys. Rev. A 69(5), 053807 (2004).
[Crossref]

Krauss, T. F.

Kristensen, M.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112(5–6), 321–327 (1994).
[Crossref]

Kuo, C. W.

C. H. Chen, P. Y. Huang, and C. W. Kuo, “Geometric modes outside the multi-bouncing fundamental Gaussian beam model,” J. Opt. 12(1), 015708 (2010).
[Crossref]

Lan, Y. P.

Y. F. Chen, C. H. Jiang, Y. P. Lan, and K. F. Huang, “Wave representation of geometrical laser beam trajectories in a hemiconfocal cavity,” Phys. Rev. A 69(5), 053807 (2004).
[Crossref]

Y. F. Chen, Y. P. Lan, and S. C. Wang, “Generation of Laguerre–Gaussian modes in fiber-coupled laser diode end-pumped lasers,” Appl. Phys. B 72(2), 167–170 (2001).
[Crossref]

Liang, H. C.

Y. F. Chen, J. C. Tung, P. Y. Chiang, H. C. Liang, and K. F. Huang, “Exploring the effect of fractional degeneracy and the emergence of ray-wave duality in solid-state lasers with off-axis pumping,” Phys. Rev. A 88(1), 013827 (2013).
[Crossref]

Lin, Y. C.

T. H. Lu, Y. C. Lin, Y. F. Chen, and K. F. Huang, “Generation of multi-axis Laguerre–Gaussian beams from geometric modes of a hemiconfocal cavity,” Appl. Phys. B 103(4), 991–999 (2011).
[Crossref]

Liu, Y. J.

Y. J. Liu, X. W. Sun, D. Luo, and Z. Raszewski, “Generating electrically tunable optical vortices by a liquid crystal cell with patterned electrode,” Appl. Phys. Lett. 92(10), 101114 (2008).
[Crossref]

Lu, T. H.

T. H. Lu, Y. C. Lin, Y. F. Chen, and K. F. Huang, “Generation of multi-axis Laguerre–Gaussian beams from geometric modes of a hemiconfocal cavity,” Appl. Phys. B 103(4), 991–999 (2011).
[Crossref]

Luo, D.

Y. J. Liu, X. W. Sun, D. Luo, and Z. Raszewski, “Generating electrically tunable optical vortices by a liquid crystal cell with patterned electrode,” Appl. Phys. Lett. 92(10), 101114 (2008).
[Crossref]

MacDonald, M. P.

M. P. MacDonald, G. C. Spalding, and K. Dholakia, “Microfluidic sorting in an optical lattice,” Nature 426(6965), 421–424 (2003).
[Crossref] [PubMed]

Maleki, L.

A. B. Matsko, A. A. Savchenkov, D. Strekalov, and L. Maleki, “Whispering gallery resonators for studying orbital angular momentum of a photon,” Phys. Rev. Lett. 95(14), 143904 (2005).
[Crossref] [PubMed]

Malyutin, A. A.

A. A. Malyutin, “Closed laser-beam trajectories in plano-spherical resonators with Gaussian apertures,” Quantum Electron. 38(2), 181–186 (2008).
[Crossref]

A. A. Malyutin, “Modes of a plano-spherical laser resonator with the Gaussian gain distribution of the active medium,” Quantum Electron. 37(3), 299–306 (2007).
[Crossref]

Matsko, A. B.

A. B. Matsko, A. A. Savchenkov, D. Strekalov, and L. Maleki, “Whispering gallery resonators for studying orbital angular momentum of a photon,” Phys. Rev. Lett. 95(14), 143904 (2005).
[Crossref] [PubMed]

Mazilu, M.

Miyamoto, K.

K. Toyoda, F. Takahashi, S. Takizawa, Y. Tokizane, K. Miyamoto, R. Morita, and T. Omatsu, “Transfer of light helicity to nanostructures,” Phys. Rev. Lett. 110(14), 143603 (2013).
[Crossref] [PubMed]

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]

Molina-Terriza, G.

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

Morita, R.

K. Toyoda, F. Takahashi, S. Takizawa, Y. Tokizane, K. Miyamoto, R. Morita, and T. Omatsu, “Transfer of light helicity to nanostructures,” Phys. Rev. Lett. 110(14), 143603 (2013).
[Crossref] [PubMed]

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]

Omatsu, T.

K. Toyoda, F. Takahashi, S. Takizawa, Y. Tokizane, K. Miyamoto, R. Morita, and T. Omatsu, “Transfer of light helicity to nanostructures,” Phys. Rev. Lett. 110(14), 143603 (2013).
[Crossref] [PubMed]

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]

Ozygus, B.

Q. Zhang, B. Ozygus, and H. Weber, “Degeneration effects in laser cavities,” Eur. Phys. J. Appl. Phys. 6(3), 293–298 (1999).
[Crossref]

Padgett, M.

Pas’ko, V.

Raszewski, Z.

Y. J. Liu, X. W. Sun, D. Luo, and Z. Raszewski, “Generating electrically tunable optical vortices by a liquid crystal cell with patterned electrode,” Appl. Phys. Lett. 92(10), 101114 (2008).
[Crossref]

Reece, P. J.

Ritsch-Marte, M.

Savchenkov, A. A.

A. B. Matsko, A. A. Savchenkov, D. Strekalov, and L. Maleki, “Whispering gallery resonators for studying orbital angular momentum of a photon,” Phys. Rev. Lett. 95(14), 143904 (2005).
[Crossref] [PubMed]

Shvedov, V.

Soskin, M. S.

V. Yu. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, “Screw dislocations in light wavefronts,” J. Mod. Opt. 39(5), 985–990 (1992).
[Crossref]

Spalding, G. C.

M. P. MacDonald, G. C. Spalding, and K. Dholakia, “Microfluidic sorting in an optical lattice,” Nature 426(6965), 421–424 (2003).
[Crossref] [PubMed]

Spreeuw, R. J. C.

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]

Strekalov, D.

A. B. Matsko, A. A. Savchenkov, D. Strekalov, and L. Maleki, “Whispering gallery resonators for studying orbital angular momentum of a photon,” Phys. Rev. Lett. 95(14), 143904 (2005).
[Crossref] [PubMed]

Sun, X. W.

Y. J. Liu, X. W. Sun, D. Luo, and Z. Raszewski, “Generating electrically tunable optical vortices by a liquid crystal cell with patterned electrode,” Appl. Phys. Lett. 92(10), 101114 (2008).
[Crossref]

Swartzlander, G. A.

Takahashi, F.

K. Toyoda, F. Takahashi, S. Takizawa, Y. Tokizane, K. Miyamoto, R. Morita, and T. Omatsu, “Transfer of light helicity to nanostructures,” Phys. Rev. Lett. 110(14), 143603 (2013).
[Crossref] [PubMed]

Takizawa, S.

K. Toyoda, F. Takahashi, S. Takizawa, Y. Tokizane, K. Miyamoto, R. Morita, and T. Omatsu, “Transfer of light helicity to nanostructures,” Phys. Rev. Lett. 110(14), 143603 (2013).
[Crossref] [PubMed]

Tokizane, Y.

K. Toyoda, F. Takahashi, S. Takizawa, Y. Tokizane, K. Miyamoto, R. Morita, and T. Omatsu, “Transfer of light helicity to nanostructures,” Phys. Rev. Lett. 110(14), 143603 (2013).
[Crossref] [PubMed]

Torner, L.

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

Torres, J. P.

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

Toyoda, K.

K. Toyoda, F. Takahashi, S. Takizawa, Y. Tokizane, K. Miyamoto, R. Morita, and T. Omatsu, “Transfer of light helicity to nanostructures,” Phys. Rev. Lett. 110(14), 143603 (2013).
[Crossref] [PubMed]

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]

Tung, J. C.

Y. F. Chen, J. C. Tung, P. Y. Chiang, H. C. Liang, and K. F. Huang, “Exploring the effect of fractional degeneracy and the emergence of ray-wave duality in solid-state lasers with off-axis pumping,” Phys. Rev. A 88(1), 013827 (2013).
[Crossref]

van der Veen, H. E. L. O.

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96(1–3), 123–132 (1993).
[Crossref]

van Exter, M. P.

J. Dingjan, M. P. van Exter, and J. P. Woerdman, “Geometric modes in a single-frequency Nd: YVO4 laser,” Opt. Commun. 188(5–6), 345–351 (2001).
[Crossref]

Vasnetsov, M.

Vasnetsov, M. V.

V. Yu. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, “Screw dislocations in light wavefronts,” J. Mod. Opt. 39(5), 985–990 (1992).
[Crossref]

Volostnikov, V.

E. Abramochkin and V. Volostnikov, “Beam transformations and nontransformed beams,” Opt. Commun. 83(1–2), 123–135 (1991).
[Crossref]

Volyar, A.

Wang, S. C.

Y. F. Chen, Y. P. Lan, and S. C. Wang, “Generation of Laguerre–Gaussian modes in fiber-coupled laser diode end-pumped lasers,” Appl. Phys. B 72(2), 167–170 (2001).
[Crossref]

Weber, H.

Q. Zhang, B. Ozygus, and H. Weber, “Degeneration effects in laser cavities,” Eur. Phys. J. Appl. Phys. 6(3), 293–298 (1999).
[Crossref]

Woerdman, J. P.

J. Dingjan, M. P. van Exter, and J. P. Woerdman, “Geometric modes in a single-frequency Nd: YVO4 laser,” Opt. Commun. 188(5–6), 345–351 (2001).
[Crossref]

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112(5–6), 321–327 (1994).
[Crossref]

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96(1–3), 123–132 (1993).
[Crossref]

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]

Zhang, Q.

Q. Zhang, B. Ozygus, and H. Weber, “Degeneration effects in laser cavities,” Eur. Phys. J. Appl. Phys. 6(3), 293–298 (1999).
[Crossref]

Appl. Phys. B (2)

Y. F. Chen, Y. P. Lan, and S. C. Wang, “Generation of Laguerre–Gaussian modes in fiber-coupled laser diode end-pumped lasers,” Appl. Phys. B 72(2), 167–170 (2001).
[Crossref]

T. H. Lu, Y. C. Lin, Y. F. Chen, and K. F. Huang, “Generation of multi-axis Laguerre–Gaussian beams from geometric modes of a hemiconfocal cavity,” Appl. Phys. B 103(4), 991–999 (2011).
[Crossref]

Appl. Phys. Lett. (1)

Y. J. Liu, X. W. Sun, D. Luo, and Z. Raszewski, “Generating electrically tunable optical vortices by a liquid crystal cell with patterned electrode,” Appl. Phys. Lett. 92(10), 101114 (2008).
[Crossref]

Eur. Phys. J. Appl. Phys. (1)

Q. Zhang, B. Ozygus, and H. Weber, “Degeneration effects in laser cavities,” Eur. Phys. J. Appl. Phys. 6(3), 293–298 (1999).
[Crossref]

J. Mod. Opt. (1)

V. Yu. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, “Screw dislocations in light wavefronts,” J. Mod. Opt. 39(5), 985–990 (1992).
[Crossref]

J. Opt. (1)

C. H. Chen, P. Y. Huang, and C. W. Kuo, “Geometric modes outside the multi-bouncing fundamental Gaussian beam model,” J. Opt. 12(1), 015708 (2010).
[Crossref]

J. Opt. Soc. Am. A (1)

Nano Lett. (1)

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]

Nat. Phys. (1)

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

Nature (1)

M. P. MacDonald, G. C. Spalding, and K. Dholakia, “Microfluidic sorting in an optical lattice,” Nature 426(6965), 421–424 (2003).
[Crossref] [PubMed]

Opt. Commun. (4)

E. Abramochkin and V. Volostnikov, “Beam transformations and nontransformed beams,” Opt. Commun. 83(1–2), 123–135 (1991).
[Crossref]

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96(1–3), 123–132 (1993).
[Crossref]

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112(5–6), 321–327 (1994).
[Crossref]

J. Dingjan, M. P. van Exter, and J. P. Woerdman, “Geometric modes in a single-frequency Nd: YVO4 laser,” Opt. Commun. 188(5–6), 345–351 (2001).
[Crossref]

Opt. Express (2)

Opt. Lett. (2)

Phys. Rev. A (3)

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]

Y. F. Chen, C. H. Jiang, Y. P. Lan, and K. F. Huang, “Wave representation of geometrical laser beam trajectories in a hemiconfocal cavity,” Phys. Rev. A 69(5), 053807 (2004).
[Crossref]

Y. F. Chen, J. C. Tung, P. Y. Chiang, H. C. Liang, and K. F. Huang, “Exploring the effect of fractional degeneracy and the emergence of ray-wave duality in solid-state lasers with off-axis pumping,” Phys. Rev. A 88(1), 013827 (2013).
[Crossref]

Phys. Rev. Lett. (2)

A. B. Matsko, A. A. Savchenkov, D. Strekalov, and L. Maleki, “Whispering gallery resonators for studying orbital angular momentum of a photon,” Phys. Rev. Lett. 95(14), 143904 (2005).
[Crossref] [PubMed]

K. Toyoda, F. Takahashi, S. Takizawa, Y. Tokizane, K. Miyamoto, R. Morita, and T. Omatsu, “Transfer of light helicity to nanostructures,” Phys. Rev. Lett. 110(14), 143603 (2013).
[Crossref] [PubMed]

Quantum Electron. (2)

A. A. Malyutin, “Modes of a plano-spherical laser resonator with the Gaussian gain distribution of the active medium,” Quantum Electron. 37(3), 299–306 (2007).
[Crossref]

A. A. Malyutin, “Closed laser-beam trajectories in plano-spherical resonators with Gaussian apertures,” Quantum Electron. 38(2), 181–186 (2008).
[Crossref]

Other (1)

J. Erhard, H. Laabs, B. Ozygus, and H. Weber, “Diode-pumped multipath laser oscillators,” in Laser Resonators II, A. V. Kudryashov, ed., Proc. SPIE 3611, 2–10 (1999)

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Figures (7)

Fig. 1
Fig. 1 (a)-(c) Calculated wave patterns | Ψ ( + ) (ρ,ϕ,z) | 2 for the case of nmin < Q with nmin = 3, Q = 4, no = 7, 11 and 15 and K = 1, 2 and 3, respectively; (d)-(f) Numerical patterns of phase angle fields for Ψ ( + ) (ρ,ϕ,z) corresponding to (a)-(c), respectively.
Fig. 2
Fig. 2 (a)-(c) Calculated wave patterns | Ψ ( + ) (ρ,ϕ,z) | 2 for the case of nmin = Q = 3 with no = 6, 9 and 12 and K = 1, 2 and 3, respectively; (d)-(f) Numerical patterns of phase angle fields for Ψ ( + ) (ρ,ϕ,z) corresponding to (a)-(c), respectively.
Fig. 3
Fig. 3 (a)-(c) Calculated wave patterns | Ψ ( + ) (ρ,ϕ,z) | 2 for the case of nmin > Q with nmin = 4, Q = 3, no = 7, 10 and 13 and K = 1, 2 and 3, respectively; (d)-(f) Numerical patterns of phase angle fields for Ψ ( + ) (ρ,ϕ,z) corresponding to (a)-(c), respectively.
Fig. 4
Fig. 4 Experimental setup for generating the interference patterns between plane waves and circularly geometric modes from a selective pumped solid-state lasers with an external π/2-cylindrical-lens mode converter.
Fig. 5
Fig. 5 (first row) Experimental interference patterns for LG0,n modes with various azimuthal-order n; (second row) Numerical patterns of phase angle fields for LG0,n modes; (third row) Calculated wave patterns corresponding to experimental results in the first row.
Fig. 6
Fig. 6 (a) and (c) Experimental patterns of circularly geometric modes; (e) and (g) Calculated wave patterns | Ψ ( + ) (ρ,ϕ,z) | 2 and | Ψ ( ) (ρ,ϕ,z) | 2 for Ω=1/3 corresponding to experimental results shown in (a) and (c), respectively; (b) and (d) Experimental interference patterns for circularly geometric modes; (f) and (h) Calculated wave patterns corresponding to experimental results in (b) and (d), respectively.
Fig. 7
Fig. 7 (a) Experimental pattern of the circularly geometric mode; (b) and (c) Experimental interference patterns formed by tilted plane waves and circularly geometric modes; (d) Calculated wave patterns corresponding to experimental results in (a); (e) and (f) Calculated wave patterns with parameters θ z =6× 10 3 π , θ t =0.2π and θ z =9× 10 3 π , θ t =1.1π corresponding to experimental results in (b) and (c), respectively.

Equations (7)

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ψ n,s (x,y,z)= Φ n (x,y,z)exp( i k n,s z ˜ )exp[ i(n+1) θ G (z) ],
Φ n (x,y,z)= 2 2 n πn! 1 w(z) H n ( 2 x w(z) )exp[ x 2 + y 2 w (z) 2 ],
ψ ˜ n,s (±) (ρ,ϕ,z)= Φ ˜ n (±) (ρ,ϕ,z)exp( i k n,s z ˜ )exp[ i(n+1) θ G (z) ],
Φ ˜ n (±) (ρ,ϕ,z)= 2 πn! 1 w(z) ( 2 ρ w(z) ) n exp[ ρ 2 w (z) 2 ]exp( ±inϕ ).
Ψ (±) (ρ,ϕ,z)= ηλ L 4 π 2 L c 2 π w 2 ( z c ) 1 2π n o ×{ s= s o J s o +J n= n o N n o +N exp[ (n n o ) 2 / 4 n o ] [( s o s)+( n o n)Ω]+iγ ψ ˜ n,s (±) (ρ,ϕ,z) },
Ψ (±) (ρ,ϕ,z)= η L c 2 π w 2 ( z c ) exp(ik z ˜ ) 2π n o ×[ n= n o +QK e (n n o ) 2 4 n o Φ ˜ n (±) (ρ,ϕ,z) e i(n+1) θ G (z) ],
E(ρ,ϕ,z)= ψ ˜ n,s (+) (ρ,ϕ,z)+Aexp[ i( k z z+ k t ρ ) ],

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