Abstract

The inter-conversion between the Hermite-Gaussian (HG) modes and the Laguerre-Gaussian (LG) modes is discussed. The HG beams carrying a cross phase can evolve into the LG modes, and vice versa, a LG mode with the cross phase can also transform to the HG mode. This conversion process is accompanied by the intensity rotations of optical beams, and their angular velocities and acceleration are both radially dependent. Initially, the outer intensity peak and the inner intensity hollow rotate in the opposite directions. After that they tend to rotate in the same direction with different velocities. Different patterns can be generated in a controllable way by adjusting the cross phase coefficients. The theoretical results provide a controllable approach for modes generation by engineering the phase structure.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. M. Born and E. Wolf, Principles of Optics (Macmillan, 1964).
  2. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968).
  3. H. Kogelnik, “On the Propagation of Gaussian Beams of Light Through Lenslike Media Including those with a Loss or Gain Variation,” Appl. Opt. 4(12), 1562–1569 (1965).
    [Crossref]
  4. H. Kogelnik and T. Li, “Laser Beams and Resonators,” Appl. Opt. 5(10), 1550–1567 (1966).
    [Crossref] [PubMed]
  5. L. Allen, M. J. Padgett, and M. Babiker, “The orbital angular momentum of light,” Prog. Opt. 39, 291–372 (1999).
    [Crossref]
  6. S. Franke-Arnold, L. Allen, and M. Padgett, “Advances in optical angular momentum,” Laser Photon. Rev. 2(4), 299–313 (2008).
    [Crossref]
  7. M. S. Soskin and M.V. Vasnetsov, “Singular optics,” Prog. Opt. 42, 219–276 (2001).
    [Crossref]
  8. M. R. Dennis, K. O’Holleran, and M. J. Padgett, “Singular optics: optical vortices and polarization singularities,” Prog. Opt. 53, 293–359 (2009).
    [Crossref]
  9. A. S. Desyatnikov, T.A. Fadeyeva, and M. R. Dennis, “Special issue on singular optics,” J. Opt. 15(4), 040201 (2013).
    [Crossref]
  10. A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature (London) 412, 313–316 (2001).
    [Crossref]
  11. M. Padgett and R. Bowman, “Tweezers with a twist,” Nat. Photonics 5, 343–348 (2011).
    [Crossref]
  12. J. Wang, J.Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6, 488–496 (2012).
    [Crossref]
  13. 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]
  14. M.W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wave-front laser-beams produced with a spiral phaseplate,” Opt. Commun. 112(5–6), 321–327 (1994).
    [Crossref]
  15. V. Peet, “Biaxial crystal as a versatile mode converter,” J. Opt. 12(9), 095706 (2010).
    [Crossref]
  16. J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207(1), 169–175 (2002).
    [Crossref]
  17. J. Courtial, K. Dholakia, L. Allen, and M.J. Padgett, “Gaussian beam with very high orbital angular momentum,” Opt. Commun. 144(4–6), 210–213 (1997).
    [Crossref]
  18. G. Liang, Y. Wang, Q. Guo, and H. Zhang, “Anisotropic diffraction induced by orbital angular momentum during propagations of optical beams,” Opt. Express. 26(7), 8084–8094 (2018).
    [Crossref] [PubMed]
  19. J. Webster, C. Rosales-Guzmán, and A. Forbes, “Radially dependent angular acceleration of twisted light,” Opt. Lett. 42(4), 675–678 (2015).
    [Crossref]
  20. M. Padgett, J. Arlt, N. Simpson, and L. Allen, “An experiment to observe the intensity and phase structure of Laguerre-Gaussian laser modes,” Am. J. Phys. 64(1), 77–82 (1996).
    [Crossref]
  21. H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, 1984).
  22. W. Miller, Symmetry and Separation of Variables (Addison-Wesley, 1977).
  23. G. Liang and Q. Guo, “Spiraling elliptic solitons in nonlocal nonlinear media without anisotropy,” Phys. Rev. A 88(4), 043825 (2013).
    [Crossref]
  24. G. Liang, Q. Guo, W. Cheng, N. Yin, P. Wu, and H. Cao, “Spiraling elliptic beam in nonlocal nonlinear media,” Opt. Express. 23(19), 24612–24625 (2015).
    [Crossref] [PubMed]
  25. G. Liang and Z. Yang, “Controllable diffraction of Gaussian kbeams with initial cross phase in nonlocal nonlinear media,” Laser Phys. 28(3), 035402 (2018).
    [Crossref]
  26. D. Deng and Q. Guo, “Airy complex variable function Gaussian beams,” New J. Phys. 11(10), 103029 (2009).
    [Crossref]
  27. C. Schulze, F. S. Roux, A. Dudley, R. Rop, M. Duparré, and A. Forbes, “Accelerated rotation with orbital angular momentum modes,” Phys. Rev. A 91(4), 043821 (2015).
    [Crossref]

2018 (2)

G. Liang, Y. Wang, Q. Guo, and H. Zhang, “Anisotropic diffraction induced by orbital angular momentum during propagations of optical beams,” Opt. Express. 26(7), 8084–8094 (2018).
[Crossref] [PubMed]

G. Liang and Z. Yang, “Controllable diffraction of Gaussian kbeams with initial cross phase in nonlocal nonlinear media,” Laser Phys. 28(3), 035402 (2018).
[Crossref]

2015 (3)

G. Liang, Q. Guo, W. Cheng, N. Yin, P. Wu, and H. Cao, “Spiraling elliptic beam in nonlocal nonlinear media,” Opt. Express. 23(19), 24612–24625 (2015).
[Crossref] [PubMed]

C. Schulze, F. S. Roux, A. Dudley, R. Rop, M. Duparré, and A. Forbes, “Accelerated rotation with orbital angular momentum modes,” Phys. Rev. A 91(4), 043821 (2015).
[Crossref]

J. Webster, C. Rosales-Guzmán, and A. Forbes, “Radially dependent angular acceleration of twisted light,” Opt. Lett. 42(4), 675–678 (2015).
[Crossref]

2013 (2)

A. S. Desyatnikov, T.A. Fadeyeva, and M. R. Dennis, “Special issue on singular optics,” J. Opt. 15(4), 040201 (2013).
[Crossref]

G. Liang and Q. Guo, “Spiraling elliptic solitons in nonlocal nonlinear media without anisotropy,” Phys. Rev. A 88(4), 043825 (2013).
[Crossref]

2012 (1)

J. Wang, J.Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6, 488–496 (2012).
[Crossref]

2011 (1)

M. Padgett and R. Bowman, “Tweezers with a twist,” Nat. Photonics 5, 343–348 (2011).
[Crossref]

2010 (1)

V. Peet, “Biaxial crystal as a versatile mode converter,” J. Opt. 12(9), 095706 (2010).
[Crossref]

2009 (2)

M. R. Dennis, K. O’Holleran, and M. J. Padgett, “Singular optics: optical vortices and polarization singularities,” Prog. Opt. 53, 293–359 (2009).
[Crossref]

D. Deng and Q. Guo, “Airy complex variable function Gaussian beams,” New J. Phys. 11(10), 103029 (2009).
[Crossref]

2008 (1)

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

2002 (1)

J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207(1), 169–175 (2002).
[Crossref]

2001 (2)

M. S. Soskin and M.V. Vasnetsov, “Singular optics,” Prog. Opt. 42, 219–276 (2001).
[Crossref]

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature (London) 412, 313–316 (2001).
[Crossref]

1999 (1)

L. Allen, M. J. Padgett, and M. Babiker, “The orbital angular momentum of light,” Prog. Opt. 39, 291–372 (1999).
[Crossref]

1997 (1)

J. Courtial, K. Dholakia, L. Allen, and M.J. Padgett, “Gaussian beam with very high orbital angular momentum,” Opt. Commun. 144(4–6), 210–213 (1997).
[Crossref]

1996 (1)

M. Padgett, J. Arlt, N. Simpson, and L. Allen, “An experiment to observe the intensity and phase structure of Laguerre-Gaussian laser modes,” Am. J. Phys. 64(1), 77–82 (1996).
[Crossref]

1994 (1)

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

1992 (1)

1966 (1)

1965 (1)

Ahmed, N.

J. Wang, J.Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6, 488–496 (2012).
[Crossref]

Allen, L.

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

L. Allen, M. J. Padgett, and M. Babiker, “The orbital angular momentum of light,” Prog. Opt. 39, 291–372 (1999).
[Crossref]

J. Courtial, K. Dholakia, L. Allen, and M.J. Padgett, “Gaussian beam with very high orbital angular momentum,” Opt. Commun. 144(4–6), 210–213 (1997).
[Crossref]

M. Padgett, J. Arlt, N. Simpson, and L. Allen, “An experiment to observe the intensity and phase structure of Laguerre-Gaussian laser modes,” Am. J. Phys. 64(1), 77–82 (1996).
[Crossref]

Arlt, J.

M. Padgett, J. Arlt, N. Simpson, and L. Allen, “An experiment to observe the intensity and phase structure of Laguerre-Gaussian laser modes,” Am. J. Phys. 64(1), 77–82 (1996).
[Crossref]

Babiker, M.

L. Allen, M. J. Padgett, and M. Babiker, “The orbital angular momentum of light,” Prog. Opt. 39, 291–372 (1999).
[Crossref]

Beijersbergen, M.W.

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

Born, M.

M. Born and E. Wolf, Principles of Optics (Macmillan, 1964).

Bowman, R.

M. Padgett and R. Bowman, “Tweezers with a twist,” Nat. Photonics 5, 343–348 (2011).
[Crossref]

Cao, H.

G. Liang, Q. Guo, W. Cheng, N. Yin, P. Wu, and H. Cao, “Spiraling elliptic beam in nonlocal nonlinear media,” Opt. Express. 23(19), 24612–24625 (2015).
[Crossref] [PubMed]

Cheng, W.

G. Liang, Q. Guo, W. Cheng, N. Yin, P. Wu, and H. Cao, “Spiraling elliptic beam in nonlocal nonlinear media,” Opt. Express. 23(19), 24612–24625 (2015).
[Crossref] [PubMed]

Coerwinkel, R. P. C.

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

Courtial, J.

J. Courtial, K. Dholakia, L. Allen, and M.J. Padgett, “Gaussian beam with very high orbital angular momentum,” Opt. Commun. 144(4–6), 210–213 (1997).
[Crossref]

Curtis, J. E.

J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207(1), 169–175 (2002).
[Crossref]

Deng, D.

D. Deng and Q. Guo, “Airy complex variable function Gaussian beams,” New J. Phys. 11(10), 103029 (2009).
[Crossref]

Dennis, M. R.

A. S. Desyatnikov, T.A. Fadeyeva, and M. R. Dennis, “Special issue on singular optics,” J. Opt. 15(4), 040201 (2013).
[Crossref]

M. R. Dennis, K. O’Holleran, and M. J. Padgett, “Singular optics: optical vortices and polarization singularities,” Prog. Opt. 53, 293–359 (2009).
[Crossref]

Desyatnikov, A. S.

A. S. Desyatnikov, T.A. Fadeyeva, and M. R. Dennis, “Special issue on singular optics,” J. Opt. 15(4), 040201 (2013).
[Crossref]

Dholakia, K.

J. Courtial, K. Dholakia, L. Allen, and M.J. Padgett, “Gaussian beam with very high orbital angular momentum,” Opt. Commun. 144(4–6), 210–213 (1997).
[Crossref]

Dolinar, S.

J. Wang, J.Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6, 488–496 (2012).
[Crossref]

Dudley, A.

C. Schulze, F. S. Roux, A. Dudley, R. Rop, M. Duparré, and A. Forbes, “Accelerated rotation with orbital angular momentum modes,” Phys. Rev. A 91(4), 043821 (2015).
[Crossref]

Duparré, M.

C. Schulze, F. S. Roux, A. Dudley, R. Rop, M. Duparré, and A. Forbes, “Accelerated rotation with orbital angular momentum modes,” Phys. Rev. A 91(4), 043821 (2015).
[Crossref]

Fadeyeva, T.A.

A. S. Desyatnikov, T.A. Fadeyeva, and M. R. Dennis, “Special issue on singular optics,” J. Opt. 15(4), 040201 (2013).
[Crossref]

Fazal, I. M.

J. Wang, J.Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6, 488–496 (2012).
[Crossref]

Forbes, A.

C. Schulze, F. S. Roux, A. Dudley, R. Rop, M. Duparré, and A. Forbes, “Accelerated rotation with orbital angular momentum modes,” Phys. Rev. A 91(4), 043821 (2015).
[Crossref]

J. Webster, C. Rosales-Guzmán, and A. Forbes, “Radially dependent angular acceleration of twisted light,” Opt. Lett. 42(4), 675–678 (2015).
[Crossref]

Franke-Arnold, S.

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

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968).

Grier, D. G.

J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207(1), 169–175 (2002).
[Crossref]

Guo, Q.

G. Liang, Y. Wang, Q. Guo, and H. Zhang, “Anisotropic diffraction induced by orbital angular momentum during propagations of optical beams,” Opt. Express. 26(7), 8084–8094 (2018).
[Crossref] [PubMed]

G. Liang, Q. Guo, W. Cheng, N. Yin, P. Wu, and H. Cao, “Spiraling elliptic beam in nonlocal nonlinear media,” Opt. Express. 23(19), 24612–24625 (2015).
[Crossref] [PubMed]

G. Liang and Q. Guo, “Spiraling elliptic solitons in nonlocal nonlinear media without anisotropy,” Phys. Rev. A 88(4), 043825 (2013).
[Crossref]

D. Deng and Q. Guo, “Airy complex variable function Gaussian beams,” New J. Phys. 11(10), 103029 (2009).
[Crossref]

Haus, H. A.

H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, 1984).

Heckenberg, N. R.

Huang, H.

J. Wang, J.Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6, 488–496 (2012).
[Crossref]

Kogelnik, H.

Koss, B. A.

J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207(1), 169–175 (2002).
[Crossref]

Kristensen, M.

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

Li, T.

Liang, G.

G. Liang, Y. Wang, Q. Guo, and H. Zhang, “Anisotropic diffraction induced by orbital angular momentum during propagations of optical beams,” Opt. Express. 26(7), 8084–8094 (2018).
[Crossref] [PubMed]

G. Liang and Z. Yang, “Controllable diffraction of Gaussian kbeams with initial cross phase in nonlocal nonlinear media,” Laser Phys. 28(3), 035402 (2018).
[Crossref]

G. Liang, Q. Guo, W. Cheng, N. Yin, P. Wu, and H. Cao, “Spiraling elliptic beam in nonlocal nonlinear media,” Opt. Express. 23(19), 24612–24625 (2015).
[Crossref] [PubMed]

G. Liang and Q. Guo, “Spiraling elliptic solitons in nonlocal nonlinear media without anisotropy,” Phys. Rev. A 88(4), 043825 (2013).
[Crossref]

Mair, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature (London) 412, 313–316 (2001).
[Crossref]

McDuff, R.

Miller, W.

W. Miller, Symmetry and Separation of Variables (Addison-Wesley, 1977).

O’Holleran, K.

M. R. Dennis, K. O’Holleran, and M. J. Padgett, “Singular optics: optical vortices and polarization singularities,” Prog. Opt. 53, 293–359 (2009).
[Crossref]

Padgett, M.

M. Padgett and R. Bowman, “Tweezers with a twist,” Nat. Photonics 5, 343–348 (2011).
[Crossref]

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

M. Padgett, J. Arlt, N. Simpson, and L. Allen, “An experiment to observe the intensity and phase structure of Laguerre-Gaussian laser modes,” Am. J. Phys. 64(1), 77–82 (1996).
[Crossref]

Padgett, M. J.

M. R. Dennis, K. O’Holleran, and M. J. Padgett, “Singular optics: optical vortices and polarization singularities,” Prog. Opt. 53, 293–359 (2009).
[Crossref]

L. Allen, M. J. Padgett, and M. Babiker, “The orbital angular momentum of light,” Prog. Opt. 39, 291–372 (1999).
[Crossref]

Padgett, M.J.

J. Courtial, K. Dholakia, L. Allen, and M.J. Padgett, “Gaussian beam with very high orbital angular momentum,” Opt. Commun. 144(4–6), 210–213 (1997).
[Crossref]

Peet, V.

V. Peet, “Biaxial crystal as a versatile mode converter,” J. Opt. 12(9), 095706 (2010).
[Crossref]

Ren, Y.

J. Wang, J.Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6, 488–496 (2012).
[Crossref]

Rop, R.

C. Schulze, F. S. Roux, A. Dudley, R. Rop, M. Duparré, and A. Forbes, “Accelerated rotation with orbital angular momentum modes,” Phys. Rev. A 91(4), 043821 (2015).
[Crossref]

Rosales-Guzmán, C.

Roux, F. S.

C. Schulze, F. S. Roux, A. Dudley, R. Rop, M. Duparré, and A. Forbes, “Accelerated rotation with orbital angular momentum modes,” Phys. Rev. A 91(4), 043821 (2015).
[Crossref]

Schulze, C.

C. Schulze, F. S. Roux, A. Dudley, R. Rop, M. Duparré, and A. Forbes, “Accelerated rotation with orbital angular momentum modes,” Phys. Rev. A 91(4), 043821 (2015).
[Crossref]

Simpson, N.

M. Padgett, J. Arlt, N. Simpson, and L. Allen, “An experiment to observe the intensity and phase structure of Laguerre-Gaussian laser modes,” Am. J. Phys. 64(1), 77–82 (1996).
[Crossref]

Smith, C. P.

Soskin, M. S.

M. S. Soskin and M.V. Vasnetsov, “Singular optics,” Prog. Opt. 42, 219–276 (2001).
[Crossref]

Tur, M.

J. Wang, J.Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6, 488–496 (2012).
[Crossref]

Vasnetsov, M.V.

M. S. Soskin and M.V. Vasnetsov, “Singular optics,” Prog. Opt. 42, 219–276 (2001).
[Crossref]

Vaziri, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature (London) 412, 313–316 (2001).
[Crossref]

Wang, J.

J. Wang, J.Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6, 488–496 (2012).
[Crossref]

Wang, Y.

G. Liang, Y. Wang, Q. Guo, and H. Zhang, “Anisotropic diffraction induced by orbital angular momentum during propagations of optical beams,” Opt. Express. 26(7), 8084–8094 (2018).
[Crossref] [PubMed]

Webster, J.

Weihs, G.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature (London) 412, 313–316 (2001).
[Crossref]

White, A. G.

Willner, A. E.

J. Wang, J.Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6, 488–496 (2012).
[Crossref]

Woerdman, J. P.

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

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Macmillan, 1964).

Wu, P.

G. Liang, Q. Guo, W. Cheng, N. Yin, P. Wu, and H. Cao, “Spiraling elliptic beam in nonlocal nonlinear media,” Opt. Express. 23(19), 24612–24625 (2015).
[Crossref] [PubMed]

Yan, Y.

J. Wang, J.Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6, 488–496 (2012).
[Crossref]

Yang, J.Y.

J. Wang, J.Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6, 488–496 (2012).
[Crossref]

Yang, Z.

G. Liang and Z. Yang, “Controllable diffraction of Gaussian kbeams with initial cross phase in nonlocal nonlinear media,” Laser Phys. 28(3), 035402 (2018).
[Crossref]

Yin, N.

G. Liang, Q. Guo, W. Cheng, N. Yin, P. Wu, and H. Cao, “Spiraling elliptic beam in nonlocal nonlinear media,” Opt. Express. 23(19), 24612–24625 (2015).
[Crossref] [PubMed]

Yue, Y.

J. Wang, J.Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6, 488–496 (2012).
[Crossref]

Zeilinger, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature (London) 412, 313–316 (2001).
[Crossref]

Zhang, H.

G. Liang, Y. Wang, Q. Guo, and H. Zhang, “Anisotropic diffraction induced by orbital angular momentum during propagations of optical beams,” Opt. Express. 26(7), 8084–8094 (2018).
[Crossref] [PubMed]

Am. J. Phys. (1)

M. Padgett, J. Arlt, N. Simpson, and L. Allen, “An experiment to observe the intensity and phase structure of Laguerre-Gaussian laser modes,” Am. J. Phys. 64(1), 77–82 (1996).
[Crossref]

Appl. Opt. (2)

J. Opt. (2)

A. S. Desyatnikov, T.A. Fadeyeva, and M. R. Dennis, “Special issue on singular optics,” J. Opt. 15(4), 040201 (2013).
[Crossref]

V. Peet, “Biaxial crystal as a versatile mode converter,” J. Opt. 12(9), 095706 (2010).
[Crossref]

Laser Photon. Rev. (1)

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

Laser Phys. (1)

G. Liang and Z. Yang, “Controllable diffraction of Gaussian kbeams with initial cross phase in nonlocal nonlinear media,” Laser Phys. 28(3), 035402 (2018).
[Crossref]

Nat. Photonics (2)

M. Padgett and R. Bowman, “Tweezers with a twist,” Nat. Photonics 5, 343–348 (2011).
[Crossref]

J. Wang, J.Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6, 488–496 (2012).
[Crossref]

Nature (London) (1)

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature (London) 412, 313–316 (2001).
[Crossref]

New J. Phys. (1)

D. Deng and Q. Guo, “Airy complex variable function Gaussian beams,” New J. Phys. 11(10), 103029 (2009).
[Crossref]

Opt. Commun. (3)

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

J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207(1), 169–175 (2002).
[Crossref]

J. Courtial, K. Dholakia, L. Allen, and M.J. Padgett, “Gaussian beam with very high orbital angular momentum,” Opt. Commun. 144(4–6), 210–213 (1997).
[Crossref]

Opt. Express. (2)

G. Liang, Y. Wang, Q. Guo, and H. Zhang, “Anisotropic diffraction induced by orbital angular momentum during propagations of optical beams,” Opt. Express. 26(7), 8084–8094 (2018).
[Crossref] [PubMed]

G. Liang, Q. Guo, W. Cheng, N. Yin, P. Wu, and H. Cao, “Spiraling elliptic beam in nonlocal nonlinear media,” Opt. Express. 23(19), 24612–24625 (2015).
[Crossref] [PubMed]

Opt. Lett. (2)

Phys. Rev. A (2)

G. Liang and Q. Guo, “Spiraling elliptic solitons in nonlocal nonlinear media without anisotropy,” Phys. Rev. A 88(4), 043825 (2013).
[Crossref]

C. Schulze, F. S. Roux, A. Dudley, R. Rop, M. Duparré, and A. Forbes, “Accelerated rotation with orbital angular momentum modes,” Phys. Rev. A 91(4), 043821 (2015).
[Crossref]

Prog. Opt. (3)

M. S. Soskin and M.V. Vasnetsov, “Singular optics,” Prog. Opt. 42, 219–276 (2001).
[Crossref]

M. R. Dennis, K. O’Holleran, and M. J. Padgett, “Singular optics: optical vortices and polarization singularities,” Prog. Opt. 53, 293–359 (2009).
[Crossref]

L. Allen, M. J. Padgett, and M. Babiker, “The orbital angular momentum of light,” Prog. Opt. 39, 291–372 (1999).
[Crossref]

Other (4)

M. Born and E. Wolf, Principles of Optics (Macmillan, 1964).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968).

H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, 1984).

W. Miller, Symmetry and Separation of Variables (Addison-Wesley, 1977).

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Figures (8)

Fig. 1
Fig. 1 Different intensity patterns for different Θ at the propagation z = 30.
Fig. 2
Fig. 2 Transformation process from (1,0) Hermite Gaussian mode with the phase exp   ( i x y ) to (0,-1) Laguerre Gaussian mode. (a1-d1) transformation of intensity profiles; while (a2-d2) transformation of phase profiles.
Fig. 3
Fig. 3 Angular velocities ωo [green curves in (a)], accelerations Ωo [green curves in (b)] of the outer peaks and ωi [red curves in (a)], accelerations Ωi [red curves in (b)] of the inner hollow during the same transformation process as Fig. 2. Dashed curves are plotted for Θ = 0.5, while solid curves are plotted for Θ = 1.
Fig. 4
Fig. 4 Transformation from (1,0) [(a1),(a2)] and (2,0) [(c1),(c2)] Hermite Gaussian mode with the phase exp   ( i x y ) to (0,-1) [(b1),(b2)] and (0,-2) [(d1),(d2)] Laguerre Gaussian mode. (a1-d1) transformation of intensity profiles; while (a2-d2) transformation of phase profiles.
Fig. 5
Fig. 5 Transformation from (1,0) [(a1),(a2)] and (3,2) [(c1),(c2)] Hermite Gaussian mode with the phase exp   ( i x y ) to (0,-1) [(b1),(b2)] and (2,-1) [(d1),(d2)] Laguerre Gaussian mode. (a1-d1) transformation of intensity profiles; while (a2-d2) transformation of phase profiles.
Fig. 6
Fig. 6 Evolutions of (0,0) [(a1),(a2)] and (1,1) [(c1),(c2)] Hermite Gaussian mode with the phase exp   ( i x y ). (a1-d1) evolutions of intensity profiles; while (a2-d2) evolutions of phase profiles.
Fig. 7
Fig. 7 Transformation process from (2,1) Hermite Gaussian mode with the phase exp   ( i x y ) to (1,-1) Laguerre Gaussian mode. (a1-d1) transformation of intensity profiles; while (a2-d2) transformation of phase profiles.
Fig. 8
Fig. 8 Transformation process from (0,-2) Laguerre Gaussian mode with the phase exp   ( i x y ) to (2,0) Hermite Gaussian mode. (a1-d1) transformation of intensity profiles; while (a2-d2) transformation of phase profiles.

Equations (7)

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2 i k φ Z + ( 2 φ X 2 + 2 φ Y 2 ) = 0 ,
i φ z + 1 2 ( 2 φ x 2 + 2 φ y 2 ) = 0 .
φ ( x , y , z ) = i exp  ( i z ) 2 π z φ ( x , y , 0 ) exp  [ i ( x x ) 2 + ( y y ) 2 2 z ] d x d y ,
φ ( x , y , 0 ) = H m ( x ) H n ( y ) exp  ( x 2 + y 2 2 ) exp  ( i Θ x y ) ,
φ ( x , y , z ) = A ( x z Θ 1 + i z y ) exp   ( x 2 + y 2 2 w 1 2 x y 2 w 2 ) × exp   [ i c 1 ( x 2 + y 2 ) + i c 2 x y ] ,
φ ( x , y , 0 ) = ( x i y ) exp  ( x 2 + y 2 2 ) exp  ( i Θ x y ) ,
φ ( x , y , z ) = B [ x 1 i z ( Θ 1 ) ( Θ + 1 ) z i y ] exp   ( x 2 + y 2 2 w 1 2 x y 2 w 2 ) × exp   [ i c 1 ( x 2 + y 2 ) + i c 2 x y ] ,

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