Abstract

We introduce two static methods to break the phase-matching symmetry in third harmonic generation with a focused Gaussian beam in the tight focusing limit, dramatically increasing the conversion efficiency and mode quality. Both rely on inhibiting harmonic generation immediately after the beam waist, preventing the near perfect cancellation of the third harmonic generation (THG) from before and after the focus. The first method involves placing a thin metal septum at the waist: the laser drills a small pinhole, which, in turn, disrupts the beam focus after the pinhole. The second method is based on placing a large χ(3) gas before the focus and a small χ(3) gas after the focus.

© 2012 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, Phys. Rev. Lett. 7, 118 (1961).
    [CrossRef]
  2. A. L’Huillier, L. A. Lompre, M. Ferray, X. F. Li, G. Mainfray, and C. Manus, Europhys. Lett. 5, 601 (1988).
    [CrossRef]
  3. J. Comly and E. Garmire, Appl. Phys. Lett. 12, 7 (1968).
    [CrossRef]
  4. For example, R. A. Ganeev, M. Suzuki, M. Baba, H. Kuroda, and I. A. Kulagin, Appl. Opt. 45, 748 (2006), and references therein.
    [CrossRef]
  5. J. F. Ward and G. H. C. New, Phys. Rev. 185, 57 (1969).
    [CrossRef]
  6. R. W. Boyd, Nonlinear Optics, 3rd ed. (Academic Press, 2008) p. 121.
  7. M. S. Malcuit, R. W. Boyd, W. V. Davis, and K. Rzyzewski, Phys. Rev. A 41, 3822 (1990).
    [CrossRef]
  8. R. Eramo and M. Matera, Appl. Opt. 33, 1691 (1994);
  9. D. S. Steingrube, T. Vockerodt, E. Schulz, U. Morgner, and M. Kovăcev, Phys. Rev. A 80, 043819 (2009).
    [CrossRef]
  10. G. N. Gibson and E. Sergan are preparing a manuscript to be titled “Third-harmonic generation in the semi-infinite phase-matching limit.”
  11. X. Liu, D. Du, and G. Mourou, IEEE J. Quantum Electron. 33, 1706 (1997).
    [CrossRef]
  12. P. T. Mannion, J. Magee, E. Coyne, G. M. OConnor, and T. J. Glynn, Appl. Surf. Sci. 233, 275 (2004).
    [CrossRef]
  13. M. P. Bogaard and B. J. Orr, in International Review of Science, Molecular Structure and Properties, Physical Chemistry, Series 2 (London, 1975), pp. 186–187.
  14. Due to space limitations, we do not include a detailed study of the pressure dependence and simply keep the pressure fixed throughout at 100 torr. In fact, the pressure dependence is quite weak from 100 to 700 torr.

2009 (1)

D. S. Steingrube, T. Vockerodt, E. Schulz, U. Morgner, and M. Kovăcev, Phys. Rev. A 80, 043819 (2009).
[CrossRef]

2006 (1)

2004 (1)

P. T. Mannion, J. Magee, E. Coyne, G. M. OConnor, and T. J. Glynn, Appl. Surf. Sci. 233, 275 (2004).
[CrossRef]

1997 (1)

X. Liu, D. Du, and G. Mourou, IEEE J. Quantum Electron. 33, 1706 (1997).
[CrossRef]

1994 (1)

1990 (1)

M. S. Malcuit, R. W. Boyd, W. V. Davis, and K. Rzyzewski, Phys. Rev. A 41, 3822 (1990).
[CrossRef]

1988 (1)

A. L’Huillier, L. A. Lompre, M. Ferray, X. F. Li, G. Mainfray, and C. Manus, Europhys. Lett. 5, 601 (1988).
[CrossRef]

1969 (1)

J. F. Ward and G. H. C. New, Phys. Rev. 185, 57 (1969).
[CrossRef]

1968 (1)

J. Comly and E. Garmire, Appl. Phys. Lett. 12, 7 (1968).
[CrossRef]

1961 (1)

P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, Phys. Rev. Lett. 7, 118 (1961).
[CrossRef]

Baba, M.

Bogaard, M. P.

M. P. Bogaard and B. J. Orr, in International Review of Science, Molecular Structure and Properties, Physical Chemistry, Series 2 (London, 1975), pp. 186–187.

Boyd, R. W.

M. S. Malcuit, R. W. Boyd, W. V. Davis, and K. Rzyzewski, Phys. Rev. A 41, 3822 (1990).
[CrossRef]

R. W. Boyd, Nonlinear Optics, 3rd ed. (Academic Press, 2008) p. 121.

Comly, J.

J. Comly and E. Garmire, Appl. Phys. Lett. 12, 7 (1968).
[CrossRef]

Coyne, E.

P. T. Mannion, J. Magee, E. Coyne, G. M. OConnor, and T. J. Glynn, Appl. Surf. Sci. 233, 275 (2004).
[CrossRef]

Davis, W. V.

M. S. Malcuit, R. W. Boyd, W. V. Davis, and K. Rzyzewski, Phys. Rev. A 41, 3822 (1990).
[CrossRef]

Du, D.

X. Liu, D. Du, and G. Mourou, IEEE J. Quantum Electron. 33, 1706 (1997).
[CrossRef]

Eramo, R.

Ferray, M.

A. L’Huillier, L. A. Lompre, M. Ferray, X. F. Li, G. Mainfray, and C. Manus, Europhys. Lett. 5, 601 (1988).
[CrossRef]

Franken, P. A.

P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, Phys. Rev. Lett. 7, 118 (1961).
[CrossRef]

Ganeev, R. A.

Garmire, E.

J. Comly and E. Garmire, Appl. Phys. Lett. 12, 7 (1968).
[CrossRef]

Gibson, G. N.

G. N. Gibson and E. Sergan are preparing a manuscript to be titled “Third-harmonic generation in the semi-infinite phase-matching limit.”

Glynn, T. J.

P. T. Mannion, J. Magee, E. Coyne, G. M. OConnor, and T. J. Glynn, Appl. Surf. Sci. 233, 275 (2004).
[CrossRef]

Hill, A. E.

P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, Phys. Rev. Lett. 7, 118 (1961).
[CrossRef]

Kovacev, M.

D. S. Steingrube, T. Vockerodt, E. Schulz, U. Morgner, and M. Kovăcev, Phys. Rev. A 80, 043819 (2009).
[CrossRef]

Kulagin, I. A.

Kuroda, H.

L’Huillier, A.

A. L’Huillier, L. A. Lompre, M. Ferray, X. F. Li, G. Mainfray, and C. Manus, Europhys. Lett. 5, 601 (1988).
[CrossRef]

Li, X. F.

A. L’Huillier, L. A. Lompre, M. Ferray, X. F. Li, G. Mainfray, and C. Manus, Europhys. Lett. 5, 601 (1988).
[CrossRef]

Liu, X.

X. Liu, D. Du, and G. Mourou, IEEE J. Quantum Electron. 33, 1706 (1997).
[CrossRef]

Lompre, L. A.

A. L’Huillier, L. A. Lompre, M. Ferray, X. F. Li, G. Mainfray, and C. Manus, Europhys. Lett. 5, 601 (1988).
[CrossRef]

Magee, J.

P. T. Mannion, J. Magee, E. Coyne, G. M. OConnor, and T. J. Glynn, Appl. Surf. Sci. 233, 275 (2004).
[CrossRef]

Mainfray, G.

A. L’Huillier, L. A. Lompre, M. Ferray, X. F. Li, G. Mainfray, and C. Manus, Europhys. Lett. 5, 601 (1988).
[CrossRef]

Malcuit, M. S.

M. S. Malcuit, R. W. Boyd, W. V. Davis, and K. Rzyzewski, Phys. Rev. A 41, 3822 (1990).
[CrossRef]

Mannion, P. T.

P. T. Mannion, J. Magee, E. Coyne, G. M. OConnor, and T. J. Glynn, Appl. Surf. Sci. 233, 275 (2004).
[CrossRef]

Manus, C.

A. L’Huillier, L. A. Lompre, M. Ferray, X. F. Li, G. Mainfray, and C. Manus, Europhys. Lett. 5, 601 (1988).
[CrossRef]

Matera, M.

Morgner, U.

D. S. Steingrube, T. Vockerodt, E. Schulz, U. Morgner, and M. Kovăcev, Phys. Rev. A 80, 043819 (2009).
[CrossRef]

Mourou, G.

X. Liu, D. Du, and G. Mourou, IEEE J. Quantum Electron. 33, 1706 (1997).
[CrossRef]

New, G. H. C.

J. F. Ward and G. H. C. New, Phys. Rev. 185, 57 (1969).
[CrossRef]

OConnor, G. M.

P. T. Mannion, J. Magee, E. Coyne, G. M. OConnor, and T. J. Glynn, Appl. Surf. Sci. 233, 275 (2004).
[CrossRef]

Orr, B. J.

M. P. Bogaard and B. J. Orr, in International Review of Science, Molecular Structure and Properties, Physical Chemistry, Series 2 (London, 1975), pp. 186–187.

Peters, C. W.

P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, Phys. Rev. Lett. 7, 118 (1961).
[CrossRef]

Rzyzewski, K.

M. S. Malcuit, R. W. Boyd, W. V. Davis, and K. Rzyzewski, Phys. Rev. A 41, 3822 (1990).
[CrossRef]

Schulz, E.

D. S. Steingrube, T. Vockerodt, E. Schulz, U. Morgner, and M. Kovăcev, Phys. Rev. A 80, 043819 (2009).
[CrossRef]

Sergan, E.

G. N. Gibson and E. Sergan are preparing a manuscript to be titled “Third-harmonic generation in the semi-infinite phase-matching limit.”

Steingrube, D. S.

D. S. Steingrube, T. Vockerodt, E. Schulz, U. Morgner, and M. Kovăcev, Phys. Rev. A 80, 043819 (2009).
[CrossRef]

Suzuki, M.

Vockerodt, T.

D. S. Steingrube, T. Vockerodt, E. Schulz, U. Morgner, and M. Kovăcev, Phys. Rev. A 80, 043819 (2009).
[CrossRef]

Ward, J. F.

J. F. Ward and G. H. C. New, Phys. Rev. 185, 57 (1969).
[CrossRef]

Weinreich, G.

P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, Phys. Rev. Lett. 7, 118 (1961).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. Lett. (1)

J. Comly and E. Garmire, Appl. Phys. Lett. 12, 7 (1968).
[CrossRef]

Appl. Surf. Sci. (1)

P. T. Mannion, J. Magee, E. Coyne, G. M. OConnor, and T. J. Glynn, Appl. Surf. Sci. 233, 275 (2004).
[CrossRef]

Europhys. Lett. (1)

A. L’Huillier, L. A. Lompre, M. Ferray, X. F. Li, G. Mainfray, and C. Manus, Europhys. Lett. 5, 601 (1988).
[CrossRef]

IEEE J. Quantum Electron. (1)

X. Liu, D. Du, and G. Mourou, IEEE J. Quantum Electron. 33, 1706 (1997).
[CrossRef]

Phys. Rev. (1)

J. F. Ward and G. H. C. New, Phys. Rev. 185, 57 (1969).
[CrossRef]

Phys. Rev. A (2)

M. S. Malcuit, R. W. Boyd, W. V. Davis, and K. Rzyzewski, Phys. Rev. A 41, 3822 (1990).
[CrossRef]

D. S. Steingrube, T. Vockerodt, E. Schulz, U. Morgner, and M. Kovăcev, Phys. Rev. A 80, 043819 (2009).
[CrossRef]

Phys. Rev. Lett. (1)

P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, Phys. Rev. Lett. 7, 118 (1961).
[CrossRef]

Other (4)

R. W. Boyd, Nonlinear Optics, 3rd ed. (Academic Press, 2008) p. 121.

G. N. Gibson and E. Sergan are preparing a manuscript to be titled “Third-harmonic generation in the semi-infinite phase-matching limit.”

M. P. Bogaard and B. J. Orr, in International Review of Science, Molecular Structure and Properties, Physical Chemistry, Series 2 (London, 1975), pp. 186–187.

Due to space limitations, we do not include a detailed study of the pressure dependence and simply keep the pressure fixed throughout at 100 torr. In fact, the pressure dependence is quite weak from 100 to 700 torr.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1.
Fig. 1.

Schematic of experimental setup.

Fig. 2.
Fig. 2.

Intensity dependence of THG for different septum thicknesses.

Fig. 3.
Fig. 3.

Modes of the third harmonic beam at the highest input energy. (a)–(c) 0.010”, 0.020”, 0.025” septa. The increasing beam size corresponds to smaller pinholes. (d) No septum. (e) and (f) CO2/He with a 0.002” septum. All images are taken at 2×1014W/cm2 except (f) at 7×1013W/cm2. Images (a)–(c) and (f) are smooth round modes, while (d) and (e) have a ring structure. The axes units are millimeters.

Fig. 4.
Fig. 4.

Intensity dependence of THG for the two-gas geometry. Also shown is the dependence for a freely propagating beam in CO2 (same data shown with black dots in Fig. 2) and results from simulations.

Equations (2)

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

J3(Δk,zo,z)=zozeiΔkzdz(1+2iz/b)2,
J3SIL(Δk)=ib2[1+bΔk2ebΔk/2Γ(0,bΔk2)],

Metrics