Abstract

Evolution of transverse intensity profiles for the dominant and cross-polarization components of linearly polarized Hermite–Gauss laser beams is studied experimentally as the beams propagate away from their waist. Measured intensity profiles and their evolution with propagation are in good agreement with the theoretical predictions.

© 2012 Optical Society of America

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    [CrossRef]
  2. L. W. Davis, “Theory of electromagnetic beams,” Phys. Rev. A 19, 1177–1179 (1979).
    [CrossRef]
  3. D. N. Pattanayak and G. P. Agrawal, “Representation of vector electromagnetic beams,” Phys. Rev. A 22, 1159–1164 (1980).
  4. Y. Fainman and J. Shamir, “Polarization of nonplanar wave fronts,” Appl. Opt. 23, 3188–3195 (1984).
    [CrossRef]
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    [CrossRef]
  6. J. P. Barton, D. R. Alexander, and S. A. Schaub, “Internal and near-surface electromagnetic fields for a spherical particle irradiated by a focused laser beam,” J. Appl. Phys. 64, 1632–1639 (1988).
    [CrossRef]
  7. J. P. Barton and D. R. Alexander, “Fifth-order corrected electro-magnetic field components for a fundamental Gaussian beam,” J. Appl. Phys. 66, 2800–2802 (1989).
    [CrossRef]
  8. W. L. Erikson and S. Singh, “Polarization properties of Maxwell-Gaussian laser beams,” Phys. Rev. E 49, 5778–5786 (1994).
    [CrossRef]
  9. J. W. Moore, R. Vyas, and S. Singh, “The hidden side of a laser beam,” in Proceedings of the John Hall Symposium, J. C. Bergquist, S. A. Diddams, L. Hollberg, C, Oates, J. Ye, and L. Kaleth, eds. (World Scientific, 2006), pp. 97–99.
  10. H.-C. Kim and Y. H. Lee, “Higher-order corrections to the electric field vector of a Gaussian beam,” J. Opt. Soc. Am. A 16, 2232–2238 (1999).
    [CrossRef]
  11. H.-C. Kim and Y. H. Lee, “Hermite-Gaussian and Laguerre-Gaussian beams beyond the paraxial approximation,” Opt. Commun. 169, 9–16 (1999).
    [CrossRef]
  12. L. Fratta, P. Debernardi, G. P. Bava, C. Degen, J. Kaiser, I. Fischer, and W. Elsaber, “Spatially inhomogeneously polarized transverse modes in vertical-cavity surface-emitting lasers,” Phys. Rev. A 64, 031803(R) (2001).
    [CrossRef]
  13. A. Ciattoni, B. Crosignani, and P. Di Porto, “Vectorial theory of propagation in uniaxially anisotropic media,” J. Opt. Soc. Am. A 18, 1656–1661 (2001).
    [CrossRef]
  14. G. Cincotti, A. Ciattoni, and C. Palma, “Hermite-Gauss beams in uniaxially anisotropic crystal,” IEEE J. Quantum Electron. 37, 1517–1524 (2001).
    [CrossRef]
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  18. C. J. R. Sheppard and S. Saghafi, “Transverse-electric and transverse-magnetic beam modes beyond the paraxial approximation,” Opt. Lett. 24, 1543–1545 (1999).
    [CrossRef]
  19. J. Vickers, M. Burch, R. Vyas, and S. Singh, “Phase and interference properties of optical vortex beams,” J. Opt. Soc. Am. A 25, 823–827 (2008).
    [CrossRef]
  20. T. A. Fadeyeva and A. V. Volyar, “Extreme spin-orbit coupling in crystal-traveling paraxial beams,” J. Opt. Soc. Am. A 27, 381–389 (2010).
    [CrossRef]
  21. B. Hao and J. Leger, “Experimental measurement of longitudinal component in the vicinity of focused radially polarized beam,” Opt. Express 15, 3550–3556 (2007).
    [CrossRef]
  22. W. Nasalski, “Elegant Hermite-Gaussian and Laguerre-Gaussian beams at a dielectric interface,” Opt. Applicata 40, 615–622 (2010).
  23. L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, “Longitudinal field modes probed by single molecules,” Phys. Rev. Lett. 86, 5251–5254 (2001).
    [CrossRef]
  24. G. Kihara Rurimo, M. Schardt, S. Quabis, S. Malzer, Ch. Dotzler, A. Winkler, G. Leuchs, G. H. Döhler, D. Driscoll, M. Hanson, A. C. Gossard, and S. F. Pereira, “Using a quantum well heterostructure to study the longitudinal and transverse electric field components of a strongly focused laser beam,” J. Appl. Phys. 100, 023112 (2006).
    [CrossRef]
  25. Y. Kozawa and S. Sato, “Observation of the longitudinal field of a focused laser beam by second-harmonic generation,” J. Opt. Soc. Am. B 25, 175–179 (2008).
    [CrossRef]
  26. M. O. Scully and M. S. Zubairy, “Simple laser accelerator: Optics and particle dynamics,” Phys. Rev. A 44, 2656–2663 (1991).
    [CrossRef]
  27. P. Banzer, U. Peschel, S. Quabis, and G. Leuchs, “On the experimental investigation of the electric and magnetic response of a single nano-structure,” Opt. Express 18, 10905–10923 (2010).
    [CrossRef]
  28. S. Liu, H. Guo, H. Tanga, and M. Liua, “Direct acceleration of electrons using single Hermite-Gaussian beam and Bessel beam in vacuum,” Phys. Lett. A 324, 104–113 (2004).
    [CrossRef]

2010 (3)

2008 (2)

2007 (1)

2006 (1)

G. Kihara Rurimo, M. Schardt, S. Quabis, S. Malzer, Ch. Dotzler, A. Winkler, G. Leuchs, G. H. Döhler, D. Driscoll, M. Hanson, A. C. Gossard, and S. F. Pereira, “Using a quantum well heterostructure to study the longitudinal and transverse electric field components of a strongly focused laser beam,” J. Appl. Phys. 100, 023112 (2006).
[CrossRef]

2004 (1)

S. Liu, H. Guo, H. Tanga, and M. Liua, “Direct acceleration of electrons using single Hermite-Gaussian beam and Bessel beam in vacuum,” Phys. Lett. A 324, 104–113 (2004).
[CrossRef]

2001 (4)

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, “Longitudinal field modes probed by single molecules,” Phys. Rev. Lett. 86, 5251–5254 (2001).
[CrossRef]

L. Fratta, P. Debernardi, G. P. Bava, C. Degen, J. Kaiser, I. Fischer, and W. Elsaber, “Spatially inhomogeneously polarized transverse modes in vertical-cavity surface-emitting lasers,” Phys. Rev. A 64, 031803(R) (2001).
[CrossRef]

A. Ciattoni, B. Crosignani, and P. Di Porto, “Vectorial theory of propagation in uniaxially anisotropic media,” J. Opt. Soc. Am. A 18, 1656–1661 (2001).
[CrossRef]

G. Cincotti, A. Ciattoni, and C. Palma, “Hermite-Gauss beams in uniaxially anisotropic crystal,” IEEE J. Quantum Electron. 37, 1517–1524 (2001).
[CrossRef]

1999 (3)

1998 (1)

1996 (2)

1994 (1)

W. L. Erikson and S. Singh, “Polarization properties of Maxwell-Gaussian laser beams,” Phys. Rev. E 49, 5778–5786 (1994).
[CrossRef]

1991 (1)

M. O. Scully and M. S. Zubairy, “Simple laser accelerator: Optics and particle dynamics,” Phys. Rev. A 44, 2656–2663 (1991).
[CrossRef]

1989 (1)

J. P. Barton and D. R. Alexander, “Fifth-order corrected electro-magnetic field components for a fundamental Gaussian beam,” J. Appl. Phys. 66, 2800–2802 (1989).
[CrossRef]

1988 (1)

J. P. Barton, D. R. Alexander, and S. A. Schaub, “Internal and near-surface electromagnetic fields for a spherical particle irradiated by a focused laser beam,” J. Appl. Phys. 64, 1632–1639 (1988).
[CrossRef]

1987 (1)

1984 (1)

1980 (1)

D. N. Pattanayak and G. P. Agrawal, “Representation of vector electromagnetic beams,” Phys. Rev. A 22, 1159–1164 (1980).

1979 (1)

L. W. Davis, “Theory of electromagnetic beams,” Phys. Rev. A 19, 1177–1179 (1979).
[CrossRef]

1975 (1)

M. Lax, W. H. Louisell, and W. B. McKnight, “From Maxwell to paraxial wave optics,” Phys. Rev. A 11, 1365–1370 (1975).
[CrossRef]

Agrawal, G. P.

D. N. Pattanayak and G. P. Agrawal, “Representation of vector electromagnetic beams,” Phys. Rev. A 22, 1159–1164 (1980).

Alexander, D. R.

J. P. Barton and D. R. Alexander, “Fifth-order corrected electro-magnetic field components for a fundamental Gaussian beam,” J. Appl. Phys. 66, 2800–2802 (1989).
[CrossRef]

J. P. Barton, D. R. Alexander, and S. A. Schaub, “Internal and near-surface electromagnetic fields for a spherical particle irradiated by a focused laser beam,” J. Appl. Phys. 64, 1632–1639 (1988).
[CrossRef]

Banzer, P.

Barton, J. P.

J. P. Barton and D. R. Alexander, “Fifth-order corrected electro-magnetic field components for a fundamental Gaussian beam,” J. Appl. Phys. 66, 2800–2802 (1989).
[CrossRef]

J. P. Barton, D. R. Alexander, and S. A. Schaub, “Internal and near-surface electromagnetic fields for a spherical particle irradiated by a focused laser beam,” J. Appl. Phys. 64, 1632–1639 (1988).
[CrossRef]

Bava, G. P.

L. Fratta, P. Debernardi, G. P. Bava, C. Degen, J. Kaiser, I. Fischer, and W. Elsaber, “Spatially inhomogeneously polarized transverse modes in vertical-cavity surface-emitting lasers,” Phys. Rev. A 64, 031803(R) (2001).
[CrossRef]

Beversluis, M. R.

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, “Longitudinal field modes probed by single molecules,” Phys. Rev. Lett. 86, 5251–5254 (2001).
[CrossRef]

Brown, T. G.

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, “Longitudinal field modes probed by single molecules,” Phys. Rev. Lett. 86, 5251–5254 (2001).
[CrossRef]

Burch, M.

Ciattoni, A.

A. Ciattoni, B. Crosignani, and P. Di Porto, “Vectorial theory of propagation in uniaxially anisotropic media,” J. Opt. Soc. Am. A 18, 1656–1661 (2001).
[CrossRef]

G. Cincotti, A. Ciattoni, and C. Palma, “Hermite-Gauss beams in uniaxially anisotropic crystal,” IEEE J. Quantum Electron. 37, 1517–1524 (2001).
[CrossRef]

Cincotti, G.

G. Cincotti, A. Ciattoni, and C. Palma, “Hermite-Gauss beams in uniaxially anisotropic crystal,” IEEE J. Quantum Electron. 37, 1517–1524 (2001).
[CrossRef]

Crosignani, B.

Davis, L. W.

L. W. Davis, “Theory of electromagnetic beams,” Phys. Rev. A 19, 1177–1179 (1979).
[CrossRef]

Debernardi, P.

L. Fratta, P. Debernardi, G. P. Bava, C. Degen, J. Kaiser, I. Fischer, and W. Elsaber, “Spatially inhomogeneously polarized transverse modes in vertical-cavity surface-emitting lasers,” Phys. Rev. A 64, 031803(R) (2001).
[CrossRef]

Degen, C.

L. Fratta, P. Debernardi, G. P. Bava, C. Degen, J. Kaiser, I. Fischer, and W. Elsaber, “Spatially inhomogeneously polarized transverse modes in vertical-cavity surface-emitting lasers,” Phys. Rev. A 64, 031803(R) (2001).
[CrossRef]

Di Porto, P.

Döhler, G. H.

G. Kihara Rurimo, M. Schardt, S. Quabis, S. Malzer, Ch. Dotzler, A. Winkler, G. Leuchs, G. H. Döhler, D. Driscoll, M. Hanson, A. C. Gossard, and S. F. Pereira, “Using a quantum well heterostructure to study the longitudinal and transverse electric field components of a strongly focused laser beam,” J. Appl. Phys. 100, 023112 (2006).
[CrossRef]

Dotzler, Ch.

G. Kihara Rurimo, M. Schardt, S. Quabis, S. Malzer, Ch. Dotzler, A. Winkler, G. Leuchs, G. H. Döhler, D. Driscoll, M. Hanson, A. C. Gossard, and S. F. Pereira, “Using a quantum well heterostructure to study the longitudinal and transverse electric field components of a strongly focused laser beam,” J. Appl. Phys. 100, 023112 (2006).
[CrossRef]

Driscoll, D.

G. Kihara Rurimo, M. Schardt, S. Quabis, S. Malzer, Ch. Dotzler, A. Winkler, G. Leuchs, G. H. Döhler, D. Driscoll, M. Hanson, A. C. Gossard, and S. F. Pereira, “Using a quantum well heterostructure to study the longitudinal and transverse electric field components of a strongly focused laser beam,” J. Appl. Phys. 100, 023112 (2006).
[CrossRef]

Elsaber, W.

L. Fratta, P. Debernardi, G. P. Bava, C. Degen, J. Kaiser, I. Fischer, and W. Elsaber, “Spatially inhomogeneously polarized transverse modes in vertical-cavity surface-emitting lasers,” Phys. Rev. A 64, 031803(R) (2001).
[CrossRef]

Erikson, W. L.

W. L. Erikson and S. Singh, “Polarization properties of Maxwell-Gaussian laser beams,” Phys. Rev. E 49, 5778–5786 (1994).
[CrossRef]

Fadeyeva, T. A.

Fainman, Y.

Fischer, I.

L. Fratta, P. Debernardi, G. P. Bava, C. Degen, J. Kaiser, I. Fischer, and W. Elsaber, “Spatially inhomogeneously polarized transverse modes in vertical-cavity surface-emitting lasers,” Phys. Rev. A 64, 031803(R) (2001).
[CrossRef]

Fratta, L.

L. Fratta, P. Debernardi, G. P. Bava, C. Degen, J. Kaiser, I. Fischer, and W. Elsaber, “Spatially inhomogeneously polarized transverse modes in vertical-cavity surface-emitting lasers,” Phys. Rev. A 64, 031803(R) (2001).
[CrossRef]

Gossard, A. C.

G. Kihara Rurimo, M. Schardt, S. Quabis, S. Malzer, Ch. Dotzler, A. Winkler, G. Leuchs, G. H. Döhler, D. Driscoll, M. Hanson, A. C. Gossard, and S. F. Pereira, “Using a quantum well heterostructure to study the longitudinal and transverse electric field components of a strongly focused laser beam,” J. Appl. Phys. 100, 023112 (2006).
[CrossRef]

Greene, P. L.

Guo, H.

S. Liu, H. Guo, H. Tanga, and M. Liua, “Direct acceleration of electrons using single Hermite-Gaussian beam and Bessel beam in vacuum,” Phys. Lett. A 324, 104–113 (2004).
[CrossRef]

Hall, D. G.

Hanson, M.

G. Kihara Rurimo, M. Schardt, S. Quabis, S. Malzer, Ch. Dotzler, A. Winkler, G. Leuchs, G. H. Döhler, D. Driscoll, M. Hanson, A. C. Gossard, and S. F. Pereira, “Using a quantum well heterostructure to study the longitudinal and transverse electric field components of a strongly focused laser beam,” J. Appl. Phys. 100, 023112 (2006).
[CrossRef]

Hao, B.

Kaiser, J.

L. Fratta, P. Debernardi, G. P. Bava, C. Degen, J. Kaiser, I. Fischer, and W. Elsaber, “Spatially inhomogeneously polarized transverse modes in vertical-cavity surface-emitting lasers,” Phys. Rev. A 64, 031803(R) (2001).
[CrossRef]

Kihara Rurimo, G.

G. Kihara Rurimo, M. Schardt, S. Quabis, S. Malzer, Ch. Dotzler, A. Winkler, G. Leuchs, G. H. Döhler, D. Driscoll, M. Hanson, A. C. Gossard, and S. F. Pereira, “Using a quantum well heterostructure to study the longitudinal and transverse electric field components of a strongly focused laser beam,” J. Appl. Phys. 100, 023112 (2006).
[CrossRef]

Kim, H.-C.

H.-C. Kim and Y. H. Lee, “Hermite-Gaussian and Laguerre-Gaussian beams beyond the paraxial approximation,” Opt. Commun. 169, 9–16 (1999).
[CrossRef]

H.-C. Kim and Y. H. Lee, “Higher-order corrections to the electric field vector of a Gaussian beam,” J. Opt. Soc. Am. A 16, 2232–2238 (1999).
[CrossRef]

Kozawa, Y.

Lax, M.

M. Lax, W. H. Louisell, and W. B. McKnight, “From Maxwell to paraxial wave optics,” Phys. Rev. A 11, 1365–1370 (1975).
[CrossRef]

Lee, Y. H.

H.-C. Kim and Y. H. Lee, “Higher-order corrections to the electric field vector of a Gaussian beam,” J. Opt. Soc. Am. A 16, 2232–2238 (1999).
[CrossRef]

H.-C. Kim and Y. H. Lee, “Hermite-Gaussian and Laguerre-Gaussian beams beyond the paraxial approximation,” Opt. Commun. 169, 9–16 (1999).
[CrossRef]

Leger, J.

Leuchs, G.

P. Banzer, U. Peschel, S. Quabis, and G. Leuchs, “On the experimental investigation of the electric and magnetic response of a single nano-structure,” Opt. Express 18, 10905–10923 (2010).
[CrossRef]

G. Kihara Rurimo, M. Schardt, S. Quabis, S. Malzer, Ch. Dotzler, A. Winkler, G. Leuchs, G. H. Döhler, D. Driscoll, M. Hanson, A. C. Gossard, and S. F. Pereira, “Using a quantum well heterostructure to study the longitudinal and transverse electric field components of a strongly focused laser beam,” J. Appl. Phys. 100, 023112 (2006).
[CrossRef]

Liu, S.

S. Liu, H. Guo, H. Tanga, and M. Liua, “Direct acceleration of electrons using single Hermite-Gaussian beam and Bessel beam in vacuum,” Phys. Lett. A 324, 104–113 (2004).
[CrossRef]

Liua, M.

S. Liu, H. Guo, H. Tanga, and M. Liua, “Direct acceleration of electrons using single Hermite-Gaussian beam and Bessel beam in vacuum,” Phys. Lett. A 324, 104–113 (2004).
[CrossRef]

Louisell, W. H.

M. Lax, W. H. Louisell, and W. B. McKnight, “From Maxwell to paraxial wave optics,” Phys. Rev. A 11, 1365–1370 (1975).
[CrossRef]

Malzer, S.

G. Kihara Rurimo, M. Schardt, S. Quabis, S. Malzer, Ch. Dotzler, A. Winkler, G. Leuchs, G. H. Döhler, D. Driscoll, M. Hanson, A. C. Gossard, and S. F. Pereira, “Using a quantum well heterostructure to study the longitudinal and transverse electric field components of a strongly focused laser beam,” J. Appl. Phys. 100, 023112 (2006).
[CrossRef]

McKnight, W. B.

M. Lax, W. H. Louisell, and W. B. McKnight, “From Maxwell to paraxial wave optics,” Phys. Rev. A 11, 1365–1370 (1975).
[CrossRef]

Moore, J. W.

J. W. Moore, R. Vyas, and S. Singh, “The hidden side of a laser beam,” in Proceedings of the John Hall Symposium, J. C. Bergquist, S. A. Diddams, L. Hollberg, C, Oates, J. Ye, and L. Kaleth, eds. (World Scientific, 2006), pp. 97–99.

Mukunda, N.

Nasalski, W.

W. Nasalski, “Elegant Hermite-Gaussian and Laguerre-Gaussian beams at a dielectric interface,” Opt. Applicata 40, 615–622 (2010).

Novotny, L.

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, “Longitudinal field modes probed by single molecules,” Phys. Rev. Lett. 86, 5251–5254 (2001).
[CrossRef]

Palma, C.

G. Cincotti, A. Ciattoni, and C. Palma, “Hermite-Gauss beams in uniaxially anisotropic crystal,” IEEE J. Quantum Electron. 37, 1517–1524 (2001).
[CrossRef]

Pattanayak, D. N.

D. N. Pattanayak and G. P. Agrawal, “Representation of vector electromagnetic beams,” Phys. Rev. A 22, 1159–1164 (1980).

Pereira, S. F.

G. Kihara Rurimo, M. Schardt, S. Quabis, S. Malzer, Ch. Dotzler, A. Winkler, G. Leuchs, G. H. Döhler, D. Driscoll, M. Hanson, A. C. Gossard, and S. F. Pereira, “Using a quantum well heterostructure to study the longitudinal and transverse electric field components of a strongly focused laser beam,” J. Appl. Phys. 100, 023112 (2006).
[CrossRef]

Peschel, U.

Quabis, S.

P. Banzer, U. Peschel, S. Quabis, and G. Leuchs, “On the experimental investigation of the electric and magnetic response of a single nano-structure,” Opt. Express 18, 10905–10923 (2010).
[CrossRef]

G. Kihara Rurimo, M. Schardt, S. Quabis, S. Malzer, Ch. Dotzler, A. Winkler, G. Leuchs, G. H. Döhler, D. Driscoll, M. Hanson, A. C. Gossard, and S. F. Pereira, “Using a quantum well heterostructure to study the longitudinal and transverse electric field components of a strongly focused laser beam,” J. Appl. Phys. 100, 023112 (2006).
[CrossRef]

Saghafi, S.

Sato, S.

Schardt, M.

G. Kihara Rurimo, M. Schardt, S. Quabis, S. Malzer, Ch. Dotzler, A. Winkler, G. Leuchs, G. H. Döhler, D. Driscoll, M. Hanson, A. C. Gossard, and S. F. Pereira, “Using a quantum well heterostructure to study the longitudinal and transverse electric field components of a strongly focused laser beam,” J. Appl. Phys. 100, 023112 (2006).
[CrossRef]

Schaub, S. A.

J. P. Barton, D. R. Alexander, and S. A. Schaub, “Internal and near-surface electromagnetic fields for a spherical particle irradiated by a focused laser beam,” J. Appl. Phys. 64, 1632–1639 (1988).
[CrossRef]

Scully, M. O.

M. O. Scully and M. S. Zubairy, “Simple laser accelerator: Optics and particle dynamics,” Phys. Rev. A 44, 2656–2663 (1991).
[CrossRef]

Shamir, J.

Sheppard, C. J. R.

Simon, R.

Singh, S.

J. Vickers, M. Burch, R. Vyas, and S. Singh, “Phase and interference properties of optical vortex beams,” J. Opt. Soc. Am. A 25, 823–827 (2008).
[CrossRef]

W. L. Erikson and S. Singh, “Polarization properties of Maxwell-Gaussian laser beams,” Phys. Rev. E 49, 5778–5786 (1994).
[CrossRef]

J. W. Moore, R. Vyas, and S. Singh, “The hidden side of a laser beam,” in Proceedings of the John Hall Symposium, J. C. Bergquist, S. A. Diddams, L. Hollberg, C, Oates, J. Ye, and L. Kaleth, eds. (World Scientific, 2006), pp. 97–99.

Sudarshan, E. C.

Tanga, H.

S. Liu, H. Guo, H. Tanga, and M. Liua, “Direct acceleration of electrons using single Hermite-Gaussian beam and Bessel beam in vacuum,” Phys. Lett. A 324, 104–113 (2004).
[CrossRef]

Vickers, J.

Volyar, A. V.

Vyas, R.

J. Vickers, M. Burch, R. Vyas, and S. Singh, “Phase and interference properties of optical vortex beams,” J. Opt. Soc. Am. A 25, 823–827 (2008).
[CrossRef]

J. W. Moore, R. Vyas, and S. Singh, “The hidden side of a laser beam,” in Proceedings of the John Hall Symposium, J. C. Bergquist, S. A. Diddams, L. Hollberg, C, Oates, J. Ye, and L. Kaleth, eds. (World Scientific, 2006), pp. 97–99.

Winkler, A.

G. Kihara Rurimo, M. Schardt, S. Quabis, S. Malzer, Ch. Dotzler, A. Winkler, G. Leuchs, G. H. Döhler, D. Driscoll, M. Hanson, A. C. Gossard, and S. F. Pereira, “Using a quantum well heterostructure to study the longitudinal and transverse electric field components of a strongly focused laser beam,” J. Appl. Phys. 100, 023112 (2006).
[CrossRef]

Youngworth, K. S.

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, “Longitudinal field modes probed by single molecules,” Phys. Rev. Lett. 86, 5251–5254 (2001).
[CrossRef]

Zubairy, M. S.

M. O. Scully and M. S. Zubairy, “Simple laser accelerator: Optics and particle dynamics,” Phys. Rev. A 44, 2656–2663 (1991).
[CrossRef]

Appl. Opt. (2)

IEEE J. Quantum Electron. (1)

G. Cincotti, A. Ciattoni, and C. Palma, “Hermite-Gauss beams in uniaxially anisotropic crystal,” IEEE J. Quantum Electron. 37, 1517–1524 (2001).
[CrossRef]

J. Appl. Phys. (3)

J. P. Barton, D. R. Alexander, and S. A. Schaub, “Internal and near-surface electromagnetic fields for a spherical particle irradiated by a focused laser beam,” J. Appl. Phys. 64, 1632–1639 (1988).
[CrossRef]

J. P. Barton and D. R. Alexander, “Fifth-order corrected electro-magnetic field components for a fundamental Gaussian beam,” J. Appl. Phys. 66, 2800–2802 (1989).
[CrossRef]

G. Kihara Rurimo, M. Schardt, S. Quabis, S. Malzer, Ch. Dotzler, A. Winkler, G. Leuchs, G. H. Döhler, D. Driscoll, M. Hanson, A. C. Gossard, and S. F. Pereira, “Using a quantum well heterostructure to study the longitudinal and transverse electric field components of a strongly focused laser beam,” J. Appl. Phys. 100, 023112 (2006).
[CrossRef]

J. Opt. Soc. Am. A (6)

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

Opt. Applicata (1)

W. Nasalski, “Elegant Hermite-Gaussian and Laguerre-Gaussian beams at a dielectric interface,” Opt. Applicata 40, 615–622 (2010).

Opt. Commun. (1)

H.-C. Kim and Y. H. Lee, “Hermite-Gaussian and Laguerre-Gaussian beams beyond the paraxial approximation,” Opt. Commun. 169, 9–16 (1999).
[CrossRef]

Opt. Express (2)

Opt. Lett. (2)

Phys. Lett. A (1)

S. Liu, H. Guo, H. Tanga, and M. Liua, “Direct acceleration of electrons using single Hermite-Gaussian beam and Bessel beam in vacuum,” Phys. Lett. A 324, 104–113 (2004).
[CrossRef]

Phys. Rev. A (5)

M. O. Scully and M. S. Zubairy, “Simple laser accelerator: Optics and particle dynamics,” Phys. Rev. A 44, 2656–2663 (1991).
[CrossRef]

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Figures (4)

Fig. 1.
Fig. 1.

Outline of the experimental setup. P1 and P2 are linear polarizers and L is a lens. Distance z is measured from the external beam waist.

Fig. 2.
Fig. 2.

Evolution of the dominant (x-component) and cross-polarization (y-component) field component intensities I1(mn) and I2(mn) for Nm+n=0, one HG beams at (left to right) z=0, z=12zR, z=zR, z=2zR, and z=4zR. In each frame the top row contains computed profiles and directly below are the experimentally recorded intensity profiles. The subscripts 1 and 2 on intensities refer, respectively, to the x and y components of the electric field.

Fig. 3.
Fig. 3.

Evolution of the dominant and cross-polarization field component intensities I1(mn) and I2(mn) for Nm+n=2 HG beams at (left to right) z=0, z=12zR, z=zR, z=2zR, and z=4zR. In each frame the top row shows computed intensity profiles and directly below are the experimentally recorded profiles.

Fig. 4.
Fig. 4.

Evolution of the dominant and cross-polarization field component intensities I1(mn) and I2(mn) for Nm+n=3 HG beams at (left to right) z=0, z=12zR, z=zR, z=2zR, and z=4zR. In each frame the top row contains computed profiles and directly below are the experimentally recorded intensity profiles.

Equations (21)

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(r,t)E(r)ei(kzωt)=[e1E1(r)+e2E2(r)+e3E3(r)]ei(kzωt),
E1(mn)(r)=Amnψmn(r),
E2(mn)(r)=Amn12k22ψmn(r)xy,
E3(mn)(r)=Amnikψmn(r)x,
[2x2+2y2+2ikz]ψmn(r)=0
ψmn(r)=2πw2(z)Hm(2xw(z))Hn(2yw(z))×exp[i(m+n+1)θ(z)+ikρ2/2R(z)ρ2/w2(z)],
θ(z)=tan1(z/zR),
w(z)=wo1+(z/zR)2,
R(z)=z+zR2/z.
E1(mn)(r)=Amnψmn(r),
E2(mn)(r)=Amn4(kwo)2(4mnψm1,n12mψm1,n+12nψm+1,n1+ψm+1,n+1),
E3(mn)(r)=Amni2kwo(2mψm1,nψm+1,n).
U2(mn)U1(mn)=(2m+1)(2n+1)4(kwo)4,
U3(mn)U1(mn)=(2m+1)(kwo)2.
E1(mn)(r)=Amn(i)m+n+12πw2Hm(2xw)Hn(2yw)eikρ2/2Rρ2/w2,
E2(mn)(r)=1(kwo)22xyw2E1(mn)(r),
E3(mn)(r)=2i(kwo)xwE1(mn)(r).
I1(r)=[Po2m+nn!m!πw2]Hm2(2xw)Hn2(2yw)e2(ρ2)/w2,
I2(r)=4(kwo)4x2y2w4I1(r)
I3(r)=4(kwo)2x2w2I1(r),
I210=1(kwo)42Poπw2(z)[Y2e(X2+Y2)][(1X2)2cos2θ(z)+X4sin2θ(z)],

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