Abstract

We demonstrate second-harmonic generation from a (110)ZnSe crystal for focused, axially symmetric polarized beams. Distinctive distributions in polarization and intensity accompanying transverse mode conversion to higher-order Hermite–Gaussian or Laguerre–Gaussian modes are observed. A longitudinal electric field generated by a radially polarized beam is verified by the variation in the intensity distribution.

© 2008 Optical Society of America

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References

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  1. N. B. Baranova, M. O. Scully, and B. Ya. Zeldovich, "Acceleration of charged particles by laser beams," Zh. Eksp. Teor. Fiz. 105, 469-486 (1994) N. B. Baranova, M. O. Scully, and B. Ya. Zeldovich,[JETP 78, 249-258 (1994)].
  2. K. S. Youngworth and T. G. Brown, "Focusing of high numerical aperture cylindrical vector beams," Opt. Express 7, 77-87 (2000).
    [CrossRef] [PubMed]
  3. Q. Zhan, "Trapping metallic Rayleigh particles with radial polarization," Opt. Express 12, 3377-3382 (2004).
    [CrossRef] [PubMed]
  4. S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, "Focusing light to a tighter spot," Opt. Commun. 179, 1-7 (2000).
    [CrossRef]
  5. A. Bouhelier, M. Beversluis, A. Hartschuh, and L. Novotny, "Near-field second-harmonic generation induced by local field enhancement," Phys. Rev. Lett. 90, 013903 (2003).
    [CrossRef] [PubMed]
  6. 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]
  7. 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] [PubMed]
  8. 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] [PubMed]
  9. Y. Kozawa, K. Yonezawa, and S. Sato, "Generation of cylindrical vector beams from a Nd:YAG laser cavity including a c-cut YVO4 crystal, in Conference on Lasers and Electro-Optics, Technical Digest (Optical Society of America, 2007), paper CFA4.
  10. H. P. Wagner, M. Kühnelt, W. Langbein, and J. M. Hvam, "Dispersion of the second-order nonlinear susceptibility in ZnTe, ZnSe, and ZnS," Phys. Rev. B 58, 10494-10501 (1998).
    [CrossRef]
  11. R. Bernal and J. A. Maytorena, "Second harmonic generation from centrosymmetric thin films by a focused beam with arbitrary transverse structure," Phys. Rev. B 70, 125420 (2004).
    [CrossRef]
  12. S. Carrasco, B. E. A. Saleh, M. C. Teich, and J. T. Fourkas, "Second- and third-harmonic generation with vector Gaussian beams," J. Opt. Soc. Am. B 23, 2134-2141 (2006).
    [CrossRef]
  13. V. Delaubert, M. Lassen, D. R. N. Pulford, H.-A. Bachor, and C. C. Harb, "Spatial mode discrimination using second harmonic generation," Opt. Express 15, 5815-5826 (2007).
    [CrossRef] [PubMed]
  14. D. P. Biss and T. G. Brown, "Cylindrical vector beam focusing through a dielectric interface," Opt. Express 9, 490-497 (2001).
    [CrossRef] [PubMed]
  15. D. T. F. Marple, "Refractive index of ZnSe, ZnTe, and CdTe," J. Appl. Phys. 35, 539-542 (1964).
    [CrossRef]
  16. R. W. Schoonover and T. D. Visser, "Polarization singularities of focused, radially polarized fields," Opt. Express 14, 5733-5745 (2006).
    [CrossRef] [PubMed]

2007 (2)

2006 (3)

S. Carrasco, B. E. A. Saleh, M. C. Teich, and J. T. Fourkas, "Second- and third-harmonic generation with vector Gaussian beams," J. Opt. Soc. Am. B 23, 2134-2141 (2006).
[CrossRef]

R. W. Schoonover and T. D. Visser, "Polarization singularities of focused, radially polarized fields," Opt. Express 14, 5733-5745 (2006).
[CrossRef] [PubMed]

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 (2)

Q. Zhan, "Trapping metallic Rayleigh particles with radial polarization," Opt. Express 12, 3377-3382 (2004).
[CrossRef] [PubMed]

R. Bernal and J. A. Maytorena, "Second harmonic generation from centrosymmetric thin films by a focused beam with arbitrary transverse structure," Phys. Rev. B 70, 125420 (2004).
[CrossRef]

2003 (1)

A. Bouhelier, M. Beversluis, A. Hartschuh, and L. Novotny, "Near-field second-harmonic generation induced by local field enhancement," Phys. Rev. Lett. 90, 013903 (2003).
[CrossRef] [PubMed]

2001 (2)

D. P. Biss and T. G. Brown, "Cylindrical vector beam focusing through a dielectric interface," Opt. Express 9, 490-497 (2001).
[CrossRef] [PubMed]

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] [PubMed]

2000 (2)

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, "Focusing light to a tighter spot," Opt. Commun. 179, 1-7 (2000).
[CrossRef]

K. S. Youngworth and T. G. Brown, "Focusing of high numerical aperture cylindrical vector beams," Opt. Express 7, 77-87 (2000).
[CrossRef] [PubMed]

1998 (1)

H. P. Wagner, M. Kühnelt, W. Langbein, and J. M. Hvam, "Dispersion of the second-order nonlinear susceptibility in ZnTe, ZnSe, and ZnS," Phys. Rev. B 58, 10494-10501 (1998).
[CrossRef]

1994 (1)

N. B. Baranova, M. O. Scully, and B. Ya. Zeldovich, "Acceleration of charged particles by laser beams," Zh. Eksp. Teor. Fiz. 105, 469-486 (1994) N. B. Baranova, M. O. Scully, and B. Ya. Zeldovich,[JETP 78, 249-258 (1994)].

1964 (1)

D. T. F. Marple, "Refractive index of ZnSe, ZnTe, and CdTe," J. Appl. Phys. 35, 539-542 (1964).
[CrossRef]

J. Appl. Phys. (2)

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]

D. T. F. Marple, "Refractive index of ZnSe, ZnTe, and CdTe," J. Appl. Phys. 35, 539-542 (1964).
[CrossRef]

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

Opt. Commun. (1)

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, "Focusing light to a tighter spot," Opt. Commun. 179, 1-7 (2000).
[CrossRef]

Opt. Express (6)

Phys. Rev. B (2)

H. P. Wagner, M. Kühnelt, W. Langbein, and J. M. Hvam, "Dispersion of the second-order nonlinear susceptibility in ZnTe, ZnSe, and ZnS," Phys. Rev. B 58, 10494-10501 (1998).
[CrossRef]

R. Bernal and J. A. Maytorena, "Second harmonic generation from centrosymmetric thin films by a focused beam with arbitrary transverse structure," Phys. Rev. B 70, 125420 (2004).
[CrossRef]

Phys. Rev. Lett. (2)

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] [PubMed]

A. Bouhelier, M. Beversluis, A. Hartschuh, and L. Novotny, "Near-field second-harmonic generation induced by local field enhancement," Phys. Rev. Lett. 90, 013903 (2003).
[CrossRef] [PubMed]

Zh. Eksp. Teor. Fiz. (1)

N. B. Baranova, M. O. Scully, and B. Ya. Zeldovich, "Acceleration of charged particles by laser beams," Zh. Eksp. Teor. Fiz. 105, 469-486 (1994) N. B. Baranova, M. O. Scully, and B. Ya. Zeldovich,[JETP 78, 249-258 (1994)].

Other (1)

Y. Kozawa, K. Yonezawa, and S. Sato, "Generation of cylindrical vector beams from a Nd:YAG laser cavity including a c-cut YVO4 crystal, in Conference on Lasers and Electro-Optics, Technical Digest (Optical Society of America, 2007), paper CFA4.

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Figures (5)

Fig. 1
Fig. 1

Schematic of a fundamental laser beam and a ( 110 ) ZnSe crystal used for second-harmonic generation. (a) Side view and (b) top view. Dotted curves indicate the fundamental beam.

Fig. 2
Fig. 2

Amplitude patterns of fundamental beam (left-hand side of the heavy arrows in the center) and second-harmonic waves (right-hand side of the heavy arrows) for (a) azimutally and (b) radially polarized beams. Each arrow indicates the direction of instantaneous electric field. Total intensity pattern of the second-harmonic wave is depicted in the right-hand side.

Fig. 3
Fig. 3

Calculated intensity profile of second-harmonic wave at ζ = 1000 z 0 along the direction transverse to the optical axis when a fundamental HG 01 mode beam is focused.

Fig. 4
Fig. 4

Measured intensity pattern of second-harmonic wave in logarithmic scale for several axially symmetric, polarized beams as illustrated in the first column. In the second column, total intensity pattern is shown. In the last three columns, intensity patterns for different polarization as indicated by an arrow in the top of the figure are shown.

Fig. 5
Fig. 5

Intensity patterns of second-harmonic wave with horizontal polarization after passing through a linear polarizer. The patterns are plotted in linear scale. From left to right, the fundamental beam is changed from a radially polarized beam to an azimuthally polarized one through a beam with windmill polarization.

Equations (5)

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u 01 S H G ( ξ , ψ , ζ ) γ 1 u 02 ( ξ , ψ , ζ ) + γ 2 2 u 00 ( ξ , ψ , ζ ) ,
γ 1 = ζ 1 ζ 2 i exp ( i Δ k ζ ) ζ + i z 0 d ζ ,
γ 2 = ζ 1 ζ 2 i ( ζ i z 0 ) exp ( i Δ k ζ ) ( ζ + i z 0 ) 2 d ζ = ζ 1 ζ 2 i exp ( i Δ k ζ ) ζ + i z 0 d ζ 2 z 0 ζ 1 ζ 2 exp ( i Δ k ζ ) ( ζ + i z 0 ) 2 d ζ ,
u 00 ( ξ , ψ , ζ ) = 1 ω 0 2 π i z 0 ζ + i z 0 exp ( i k ξ 2 + ψ 2 2 ( ζ + i z 0 ) ) exp ( i k ζ ) ,
u 02 ( ξ , ψ , ζ ) = 1 2 ω 0 1 π i z 0 ζ + i z 0 ( 8 ω 2 ( ζ ) ξ 2 2 ) exp ( i k ξ 2 + ψ 2 2 ( ζ + i z 0 ) ) exp ( i 2 η ) exp ( i k ζ ) = 2 2 ξ 2 ω 0 2 ( i z 0 ζ + i z 0 ) 2 u 00 ( ξ , ψ , ζ ) 1 2 exp ( i 2 η ) u 00 ( ξ , ψ , ζ ) ,

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