Abstract

In this Letter, the optical forces on an electric dipole generated by a beam made up of two circularly polarized Hermite–Gaussian modes have been analyzed. When the intensity of the two modes is not the same, the mechanical action of the scattering force is completely different from the behavior of the Poynting vector. The dynamics of resonant metallic nanoparticles under this field have been calculated by means of Langevin molecular dynamic simulations. This configuration could be useful to experimentally verify how radiation pressure on a Rayleigh particle is due to the transfer of linear momentum coming solely from the orbital part of the Poynting vector.

© 2014 Optical Society of America

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References

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    [CrossRef]
  2. D. G. Grier, Nature 424, 810 (2003).
    [CrossRef]
  3. J. Chen, J. Ng, Z. Lin, and C. T. Chan, Nat. Photonics 5, 531 (2011).
    [CrossRef]
  4. J. J. Sáenz, Nat. Photonics 5, 514 (2011).
    [CrossRef]
  5. L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge University, 2006).
  6. M. Nieto-Vesperinas, P. C. Chaumet, and A. Rahmani, Phil. Trans. R. Soc. A 362, 719 (2004).
    [CrossRef]
  7. C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Atom-Photon Interactions: Basic Processes and Applications (Wiley-Interscience, 1992).
  8. A. Hemmerich and T. W. Hansch, Phys. Rev. Lett. 68, 1492 (1992).
    [CrossRef]
  9. Y. Roichman, B. Sun, Y. Roichman, J. Amato-Grill, and D. G. Grier, Phys. Rev. Lett. 100, 013602 (2008).
    [CrossRef]
  10. L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
    [CrossRef]
  11. J. R. Arias-Gonzalez and M. Nieto-Vesperinas, J. Opt. Soc. Am. A 20, 1201 (2003).
    [CrossRef]
  12. V. Wong and M. Ratner, Phys. Rev. B 73, 075416 (2006).
    [CrossRef]
  13. S. Albaladejo, M. I. Marqués, M. Laroche, and J. J. Sáenz, Phys. Rev. Lett. 102, 113602 (2009).
    [CrossRef]
  14. M. V. Berry, J. Opt. A Pure Appl. Opt. 11, 094001 (2009).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  22. L. Allen and M. J. Padgett, Opt. Commun. 184, 67 (2000).
    [CrossRef]
  23. K. Volke-Sepulveda, V. Garcés-Chávez, S. Chávez-Cerda, J. Arlt, and K. Dholakia, J. Opt. B 4, S82 (2002).
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  28. D. B. Ruffner and D. G. Grier, Phys. Rev. Lett 108, 173602 (2012).
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    [CrossRef]
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  35. B. T. Draine, Astrophys. J. 333, 848 (1988).
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    [CrossRef]

2013 (4)

A. Y. Bekshaev, J. Opt. 15, 044004 (2013).
[CrossRef]

D. B. Ruffner and D. G. Grier, Phys. Rev. Lett. 111, 059301 (2013).
[CrossRef]

M. I. Marqués and J. J. Sáenz, Phys. Rev. Lett. 111, 059302 (2013).
[CrossRef]

A. Canaguier-Durand, A. Cuche, C. Genet, and T. W. Ebbesen, Phys. Rev. A 88, 033831 (2013).
[CrossRef]

2012 (5)

2011 (2)

J. Chen, J. Ng, Z. Lin, and C. T. Chan, Nat. Photonics 5, 531 (2011).
[CrossRef]

J. J. Sáenz, Nat. Photonics 5, 514 (2011).
[CrossRef]

2010 (1)

G. Baffou, R. Quidant, and F. J. G. de Abajo, ACS Nano 4, 709 (2010).
[CrossRef]

2009 (4)

S. Albaladejo, M. I. Marqués, M. Laroche, and J. J. Sáenz, Phys. Rev. Lett. 102, 113602 (2009).
[CrossRef]

M. V. Berry, J. Opt. A Pure Appl. Opt. 11, 094001 (2009).
[CrossRef]

Q. Zhan, Adv. Opt. Photon. 1, 1 (2009).
[CrossRef]

Y. Zhao, D. Shapiro, D. McGloin, D. T. Chiu, and S. Marchesini, Opt. Express 17, 23316 (2009).
[CrossRef]

2008 (1)

Y. Roichman, B. Sun, Y. Roichman, J. Amato-Grill, and D. G. Grier, Phys. Rev. Lett. 100, 013602 (2008).
[CrossRef]

2007 (2)

Y. Zhao, J. S. Edgar, G. D. M. Jeffries, D. McGloin, and D. T. Chiu, Phys. Rev. Lett. 99, 073901 (2007).
[CrossRef]

P. Vaveliuk, B. Ruiz, and A. Lencina, Opt. Lett. 32, 927 (2007).
[CrossRef]

2006 (1)

V. Wong and M. Ratner, Phys. Rev. B 73, 075416 (2006).
[CrossRef]

2005 (1)

D. McGloin and K. Dholakia, Contemp. Phys. 46, 15 (2005).
[CrossRef]

2004 (1)

M. Nieto-Vesperinas, P. C. Chaumet, and A. Rahmani, Phil. Trans. R. Soc. A 362, 719 (2004).
[CrossRef]

2003 (2)

2002 (1)

K. Volke-Sepulveda, V. Garcés-Chávez, S. Chávez-Cerda, J. Arlt, and K. Dholakia, J. Opt. B 4, S82 (2002).
[CrossRef]

2000 (3)

L. Allen and M. J. Padgett, Opt. Commun. 184, 67 (2000).
[CrossRef]

P. C. Chaumet and M. Nieto-Vesperinas, Opt. Lett. 25, 1065 (2000).
[CrossRef]

M. Padgett and L. Allen, Contemp. Phys. 41, 275 (2000).
[CrossRef]

1997 (1)

1994 (1)

W. L. Erikson and S. Singh, Phys. Rev. E 49, 5778 (1994).
[CrossRef]

1992 (2)

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef]

A. Hemmerich and T. W. Hansch, Phys. Rev. Lett. 68, 1492 (1992).
[CrossRef]

1988 (1)

B. T. Draine, Astrophys. J. 333, 848 (1988).
[CrossRef]

1970 (1)

A. Ashkin, Phys. Rev. Lett. 24, 156 (1970).
[CrossRef]

Albaladejo, S.

S. Albaladejo, M. I. Marqués, M. Laroche, and J. J. Sáenz, Phys. Rev. Lett. 102, 113602 (2009).
[CrossRef]

Allen, L.

M. Padgett and L. Allen, Contemp. Phys. 41, 275 (2000).
[CrossRef]

L. Allen and M. J. Padgett, Opt. Commun. 184, 67 (2000).
[CrossRef]

N. B. Simpson, K. Dholakia, L. Allen, and M. J. Padgett, Opt. Lett. 22, 52 (1997).
[CrossRef]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef]

Amato-Grill, J.

Y. Roichman, B. Sun, Y. Roichman, J. Amato-Grill, and D. G. Grier, Phys. Rev. Lett. 100, 013602 (2008).
[CrossRef]

Angelsky, O. V.

Arias-Gonzalez, J. R.

Arlt, J.

K. Volke-Sepulveda, V. Garcés-Chávez, S. Chávez-Cerda, J. Arlt, and K. Dholakia, J. Opt. B 4, S82 (2002).
[CrossRef]

Ashkin, A.

A. Ashkin, Phys. Rev. Lett. 24, 156 (1970).
[CrossRef]

Baffou, G.

G. Baffou, R. Quidant, and F. J. G. de Abajo, ACS Nano 4, 709 (2010).
[CrossRef]

Beijersbergen, M. W.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef]

Bekshaev, A. Y.

Berry, M. V.

M. V. Berry, J. Opt. A Pure Appl. Opt. 11, 094001 (2009).
[CrossRef]

Canaguier-Durand, A.

A. Canaguier-Durand, A. Cuche, C. Genet, and T. W. Ebbesen, Phys. Rev. A 88, 033831 (2013).
[CrossRef]

Chan, C. T.

J. Chen, J. Ng, Z. Lin, and C. T. Chan, Nat. Photonics 5, 531 (2011).
[CrossRef]

Chaumet, P. C.

M. Nieto-Vesperinas, P. C. Chaumet, and A. Rahmani, Phil. Trans. R. Soc. A 362, 719 (2004).
[CrossRef]

P. C. Chaumet and M. Nieto-Vesperinas, Opt. Lett. 25, 1065 (2000).
[CrossRef]

Chávez-Cerda, S.

K. Volke-Sepulveda, V. Garcés-Chávez, S. Chávez-Cerda, J. Arlt, and K. Dholakia, J. Opt. B 4, S82 (2002).
[CrossRef]

Chen, J.

J. Chen, J. Ng, Z. Lin, and C. T. Chan, Nat. Photonics 5, 531 (2011).
[CrossRef]

Chiu, D. T.

Y. Zhao, D. Shapiro, D. McGloin, D. T. Chiu, and S. Marchesini, Opt. Express 17, 23316 (2009).
[CrossRef]

Y. Zhao, J. S. Edgar, G. D. M. Jeffries, D. McGloin, and D. T. Chiu, Phys. Rev. Lett. 99, 073901 (2007).
[CrossRef]

Cohen-Tannoudji, C.

C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Atom-Photon Interactions: Basic Processes and Applications (Wiley-Interscience, 1992).

Cuche, A.

A. Canaguier-Durand, A. Cuche, C. Genet, and T. W. Ebbesen, Phys. Rev. A 88, 033831 (2013).
[CrossRef]

de Abajo, F. J. G.

G. Baffou, R. Quidant, and F. J. G. de Abajo, ACS Nano 4, 709 (2010).
[CrossRef]

Dholakia, K.

D. McGloin and K. Dholakia, Contemp. Phys. 46, 15 (2005).
[CrossRef]

K. Volke-Sepulveda, V. Garcés-Chávez, S. Chávez-Cerda, J. Arlt, and K. Dholakia, J. Opt. B 4, S82 (2002).
[CrossRef]

N. B. Simpson, K. Dholakia, L. Allen, and M. J. Padgett, Opt. Lett. 22, 52 (1997).
[CrossRef]

Draine, B. T.

B. T. Draine, Astrophys. J. 333, 848 (1988).
[CrossRef]

Dupont-Roc, J.

C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Atom-Photon Interactions: Basic Processes and Applications (Wiley-Interscience, 1992).

Ebbesen, T. W.

A. Canaguier-Durand, A. Cuche, C. Genet, and T. W. Ebbesen, Phys. Rev. A 88, 033831 (2013).
[CrossRef]

Edgar, J. S.

Y. Zhao, J. S. Edgar, G. D. M. Jeffries, D. McGloin, and D. T. Chiu, Phys. Rev. Lett. 99, 073901 (2007).
[CrossRef]

Erikson, W. L.

W. L. Erikson and S. Singh, Phys. Rev. E 49, 5778 (1994).
[CrossRef]

Garcés-Chávez, V.

K. Volke-Sepulveda, V. Garcés-Chávez, S. Chávez-Cerda, J. Arlt, and K. Dholakia, J. Opt. B 4, S82 (2002).
[CrossRef]

Genet, C.

A. Canaguier-Durand, A. Cuche, C. Genet, and T. W. Ebbesen, Phys. Rev. A 88, 033831 (2013).
[CrossRef]

Grier, D. G.

D. B. Ruffner and D. G. Grier, Phys. Rev. Lett. 111, 059301 (2013).
[CrossRef]

D. B. Ruffner and D. G. Grier, Phys. Rev. Lett 108, 173602 (2012).
[CrossRef]

Y. Roichman, B. Sun, Y. Roichman, J. Amato-Grill, and D. G. Grier, Phys. Rev. Lett. 100, 013602 (2008).
[CrossRef]

D. G. Grier, Nature 424, 810 (2003).
[CrossRef]

Grynberg, G.

C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Atom-Photon Interactions: Basic Processes and Applications (Wiley-Interscience, 1992).

Hansch, T. W.

A. Hemmerich and T. W. Hansch, Phys. Rev. Lett. 68, 1492 (1992).
[CrossRef]

Hanson, S. G.

Hecht, B.

L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge University, 2006).

Hemmerich, A.

A. Hemmerich and T. W. Hansch, Phys. Rev. Lett. 68, 1492 (1992).
[CrossRef]

Jeffries, G. D. M.

Y. Zhao, J. S. Edgar, G. D. M. Jeffries, D. McGloin, and D. T. Chiu, Phys. Rev. Lett. 99, 073901 (2007).
[CrossRef]

Laroche, M.

S. Albaladejo, M. I. Marqués, M. Laroche, and J. J. Sáenz, Phys. Rev. Lett. 102, 113602 (2009).
[CrossRef]

Lencina, A.

Lin, Z.

J. Chen, J. Ng, Z. Lin, and C. T. Chan, Nat. Photonics 5, 531 (2011).
[CrossRef]

Maksimyak, A. P.

Maksimyak, P. P.

Marchesini, S.

Marqués, M. I.

M. I. Marqués and J. J. Sáenz, Phys. Rev. Lett. 111, 059302 (2013).
[CrossRef]

S. Albaladejo, M. I. Marqués, M. Laroche, and J. J. Sáenz, Phys. Rev. Lett. 102, 113602 (2009).
[CrossRef]

McGloin, D.

Y. Zhao, D. Shapiro, D. McGloin, D. T. Chiu, and S. Marchesini, Opt. Express 17, 23316 (2009).
[CrossRef]

Y. Zhao, J. S. Edgar, G. D. M. Jeffries, D. McGloin, and D. T. Chiu, Phys. Rev. Lett. 99, 073901 (2007).
[CrossRef]

D. McGloin and K. Dholakia, Contemp. Phys. 46, 15 (2005).
[CrossRef]

Mokhun, I. I.

Ng, J.

J. Chen, J. Ng, Z. Lin, and C. T. Chan, Nat. Photonics 5, 531 (2011).
[CrossRef]

Nieto-Vesperinas, M.

Novotny, L.

L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge University, 2006).

Padgett, M.

M. Padgett and L. Allen, Contemp. Phys. 41, 275 (2000).
[CrossRef]

Padgett, M. J.

Quidant, R.

G. Baffou, R. Quidant, and F. J. G. de Abajo, ACS Nano 4, 709 (2010).
[CrossRef]

Rahmani, A.

M. Nieto-Vesperinas, P. C. Chaumet, and A. Rahmani, Phil. Trans. R. Soc. A 362, 719 (2004).
[CrossRef]

Ratner, M.

V. Wong and M. Ratner, Phys. Rev. B 73, 075416 (2006).
[CrossRef]

Roichman, Y.

Y. Roichman, B. Sun, Y. Roichman, J. Amato-Grill, and D. G. Grier, Phys. Rev. Lett. 100, 013602 (2008).
[CrossRef]

Y. Roichman, B. Sun, Y. Roichman, J. Amato-Grill, and D. G. Grier, Phys. Rev. Lett. 100, 013602 (2008).
[CrossRef]

Ruffner, D. B.

D. B. Ruffner and D. G. Grier, Phys. Rev. Lett. 111, 059301 (2013).
[CrossRef]

D. B. Ruffner and D. G. Grier, Phys. Rev. Lett 108, 173602 (2012).
[CrossRef]

Ruiz, B.

Sáenz, J. J.

M. I. Marqués and J. J. Sáenz, Phys. Rev. Lett. 111, 059302 (2013).
[CrossRef]

J. J. Sáenz, Nat. Photonics 5, 514 (2011).
[CrossRef]

S. Albaladejo, M. I. Marqués, M. Laroche, and J. J. Sáenz, Phys. Rev. Lett. 102, 113602 (2009).
[CrossRef]

Shapiro, D.

Simpson, N. B.

Singh, S.

W. L. Erikson and S. Singh, Phys. Rev. E 49, 5778 (1994).
[CrossRef]

Spreeuw, R. J. C.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef]

Sun, B.

Y. Roichman, B. Sun, Y. Roichman, J. Amato-Grill, and D. G. Grier, Phys. Rev. Lett. 100, 013602 (2008).
[CrossRef]

Tyurin, A. V.

Vaveliuk, P.

Volke-Sepulveda, K.

K. Volke-Sepulveda, V. Garcés-Chávez, S. Chávez-Cerda, J. Arlt, and K. Dholakia, J. Opt. B 4, S82 (2002).
[CrossRef]

Wang, L. G.

Woerdman, J. P.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef]

Wong, V.

V. Wong and M. Ratner, Phys. Rev. B 73, 075416 (2006).
[CrossRef]

Zenkova, C. Y.

Zhan, Q.

Zhao, Y.

Y. Zhao, D. Shapiro, D. McGloin, D. T. Chiu, and S. Marchesini, Opt. Express 17, 23316 (2009).
[CrossRef]

Y. Zhao, J. S. Edgar, G. D. M. Jeffries, D. McGloin, and D. T. Chiu, Phys. Rev. Lett. 99, 073901 (2007).
[CrossRef]

ACS Nano (1)

G. Baffou, R. Quidant, and F. J. G. de Abajo, ACS Nano 4, 709 (2010).
[CrossRef]

Adv. Opt. Photon. (1)

Astrophys. J. (1)

B. T. Draine, Astrophys. J. 333, 848 (1988).
[CrossRef]

Contemp. Phys. (2)

M. Padgett and L. Allen, Contemp. Phys. 41, 275 (2000).
[CrossRef]

D. McGloin and K. Dholakia, Contemp. Phys. 46, 15 (2005).
[CrossRef]

J. Opt. (1)

A. Y. Bekshaev, J. Opt. 15, 044004 (2013).
[CrossRef]

J. Opt. A Pure Appl. Opt. (1)

M. V. Berry, J. Opt. A Pure Appl. Opt. 11, 094001 (2009).
[CrossRef]

J. Opt. B (1)

K. Volke-Sepulveda, V. Garcés-Chávez, S. Chávez-Cerda, J. Arlt, and K. Dholakia, J. Opt. B 4, S82 (2002).
[CrossRef]

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

Nat. Photonics (2)

J. Chen, J. Ng, Z. Lin, and C. T. Chan, Nat. Photonics 5, 531 (2011).
[CrossRef]

J. J. Sáenz, Nat. Photonics 5, 514 (2011).
[CrossRef]

Nature (1)

D. G. Grier, Nature 424, 810 (2003).
[CrossRef]

Opt. Commun. (1)

L. Allen and M. J. Padgett, Opt. Commun. 184, 67 (2000).
[CrossRef]

Opt. Express (4)

Opt. Lett. (3)

Phil. Trans. R. Soc. A (1)

M. Nieto-Vesperinas, P. C. Chaumet, and A. Rahmani, Phil. Trans. R. Soc. A 362, 719 (2004).
[CrossRef]

Phys. Rev. A (3)

A. Y. Bekshaev, O. V. Angelsky, S. G. Hanson, and C. Y. Zenkova, Phys. Rev. A 86, 023847 (2012).
[CrossRef]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef]

A. Canaguier-Durand, A. Cuche, C. Genet, and T. W. Ebbesen, Phys. Rev. A 88, 033831 (2013).
[CrossRef]

Phys. Rev. B (1)

V. Wong and M. Ratner, Phys. Rev. B 73, 075416 (2006).
[CrossRef]

Phys. Rev. E (1)

W. L. Erikson and S. Singh, Phys. Rev. E 49, 5778 (1994).
[CrossRef]

Phys. Rev. Lett (1)

D. B. Ruffner and D. G. Grier, Phys. Rev. Lett 108, 173602 (2012).
[CrossRef]

Phys. Rev. Lett. (7)

Y. Zhao, J. S. Edgar, G. D. M. Jeffries, D. McGloin, and D. T. Chiu, Phys. Rev. Lett. 99, 073901 (2007).
[CrossRef]

S. Albaladejo, M. I. Marqués, M. Laroche, and J. J. Sáenz, Phys. Rev. Lett. 102, 113602 (2009).
[CrossRef]

D. B. Ruffner and D. G. Grier, Phys. Rev. Lett. 111, 059301 (2013).
[CrossRef]

M. I. Marqués and J. J. Sáenz, Phys. Rev. Lett. 111, 059302 (2013).
[CrossRef]

A. Hemmerich and T. W. Hansch, Phys. Rev. Lett. 68, 1492 (1992).
[CrossRef]

Y. Roichman, B. Sun, Y. Roichman, J. Amato-Grill, and D. G. Grier, Phys. Rev. Lett. 100, 013602 (2008).
[CrossRef]

A. Ashkin, Phys. Rev. Lett. 24, 156 (1970).
[CrossRef]

Other (2)

L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge University, 2006).

C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Atom-Photon Interactions: Basic Processes and Applications (Wiley-Interscience, 1992).

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Figures (2)

Fig. 1.
Fig. 1.

(a) Scattering force and (b) Poynting vector in the focal plane of a beam with spot size (ω0) composed of the fields from Eqs. (1)–(3) with A=0.15. Intensity in the cross section is represented by a color map (white corresponds to high intensity; dark corresponds to low intensity).

Fig. 2.
Fig. 2.

(a) Molecular dynamics simulation of the trajectories performed by 10 resonant nanoparticles with 50 nm radii embedded in water. Particles are illuminated with a beam with spot size (ω0) composed of the fields from Eqs. (1)–(3) with A=0.15. Radiation wavelength is λ=530nm, and the trajectory lasts 0.01 s. Intensity in the focal plane is represented by a color map (white corresponds to high intensity; dark corresponds to low intensity). (b) Trajectories in the hypothetical situation of scattering forces coming from the full Poynting vector.

Equations (11)

Equations on this page are rendered with MathJax. Learn more.

Ex=Pw2nϵ0c(Ψ01+iAΨ10),
Ey=Pw2nϵ0c(iΨ01AΨ10),
Ez=12kω0Pwnϵ0c(i(A1)Ψ112(A+1)Ψ00+AΨ20+Ψ02),
Ψmn(x,y,z=0)=2πω02Hm(X)Hn(Y)e(x2+y2)/ω02,
Fi=12ϵϵ0I(α)I(ExiEx*+EyiEy*+EziEz*),
Fx=42PwAnI(α)cπω03e2((x2+y2)/ω02)Y,
Fy=42PwAnI(α)cπω03e2((x2+y2)/ω02)X.
Sx=Ce2((x2+y2)/ω02)Y((A+1)A2X2Y2),
Sy=Ce2((x2+y2)/ω02)X(A(A+1)A2X2Y2),
C=42Pwω03πk.
α=α01iα0k3/(6π),

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