Abstract

A self-imaging resonator can be simultaneously resonant for many transverse modes and therefore allows cavity build-up for images of various shapes. The stability properties of such a cavity are reviewed. We have used this device for the first time to enhance the efficiency of second harmonic generation of weak images. We characterize the global and local efficiency of the second harmonic generation, and discuss its limitation due to the spatial bandwidth of the cavity and the diffraction along the crystal length.

© 2010 Optical Society of America

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References

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  1. V. Khokhlov, "Wave propagation in nonlinear dispersive lines" Radiotek. Electron 6, 1116-1130 (1961).
  2. P. A. Franken, A. E. Hill, C. W. Peters and G. Weinreich, "Generation of Optical Harmonics," Phys. Rev. Lett. 7, 118-119 (1961).
    [CrossRef]
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  4. Z. Y. Ou, S. F. Pereira, E. S. Polzik and H. J. Kimble, "85% efficiency for cw frequency doubling from 1.08 to 0.54μm," Opt. Lett. 17, 640-642 (1992).
    [CrossRef] [PubMed]
  5. R. Paschotta, P. Kurz, R. Henking, S. Schiller and J. Mlynek, "82% efficient continuous-wave frequency doubling of 1.06μm with a monolithic MgO:LiNbO3 resonator," Opt. Lett. 19, 1325-1327 (1994).
    [CrossRef] [PubMed]
  6. M. Kolobov editor, Quantum Imaging, (Springer-Verlag, 2006).
  7. V. Delaubert, M. Lassen, D. R. N. Pulford, H. A. Bachor and C. C. Harb, "Spatial mode discrimination using second harmonic generation," Opt. Express 155815-5826 (2007).
    [CrossRef]
  8. J. A. Arnaud, "Degenerate optical cavities" App. Opt. 8 (1), 189-195 (1969).
    [CrossRef]
  9. A. E. Siegman, Lasers (University Science Books, Mill Valley, 1986).
  10. S. Gigan, L. Lopez, N. Treps, A. Maître, C. Fabre, "Image transmission through a stable paraxial cavity," Phys. Rev. A. 72, 023804 (2005).
    [CrossRef]
  11. B. Chalopin, "Optique quantique multimode : des images aux impulsions," PhD Thesis, http://tel.archives-ouvertes.fr/tel-00431648/fr/ (2009).
  12. L. Lopez, B. Chalopin, A. Rivière de la Souchère, C. Fabre, A. Maître, and N. Treps, "Multimode quantum properties of a self-imaging OPO: squeezed vacuum and EPR beams generation", Phys. Rev. A 80043816 (2009).
    [CrossRef]
  13. G. Boyd, D. Kleinman, "Parametric interaction of focused Gaussian light beams," IEEE J. Quantum Electron., (1968).
    [CrossRef]
  14. P. Scotto, P. Colet, M. San Miguel, "All-optical image processing with cavity type II second-harmonic generation," Opt. Lett. 28, 1695-1697 (2003).
    [CrossRef] [PubMed]

2009 (1)

L. Lopez, B. Chalopin, A. Rivière de la Souchère, C. Fabre, A. Maître, and N. Treps, "Multimode quantum properties of a self-imaging OPO: squeezed vacuum and EPR beams generation", Phys. Rev. A 80043816 (2009).
[CrossRef]

2007 (1)

2005 (1)

S. Gigan, L. Lopez, N. Treps, A. Maître, C. Fabre, "Image transmission through a stable paraxial cavity," Phys. Rev. A. 72, 023804 (2005).
[CrossRef]

2003 (1)

1994 (1)

1992 (1)

1987 (1)

1969 (1)

J. A. Arnaud, "Degenerate optical cavities" App. Opt. 8 (1), 189-195 (1969).
[CrossRef]

1968 (1)

G. Boyd, D. Kleinman, "Parametric interaction of focused Gaussian light beams," IEEE J. Quantum Electron., (1968).
[CrossRef]

1961 (2)

V. Khokhlov, "Wave propagation in nonlinear dispersive lines" Radiotek. Electron 6, 1116-1130 (1961).

P. A. Franken, A. E. Hill, C. W. Peters and G. Weinreich, "Generation of Optical Harmonics," Phys. Rev. Lett. 7, 118-119 (1961).
[CrossRef]

Arnaud, J. A.

J. A. Arnaud, "Degenerate optical cavities" App. Opt. 8 (1), 189-195 (1969).
[CrossRef]

Bachor, H. A.

Boyd, G.

G. Boyd, D. Kleinman, "Parametric interaction of focused Gaussian light beams," IEEE J. Quantum Electron., (1968).
[CrossRef]

Chalopin, B.

L. Lopez, B. Chalopin, A. Rivière de la Souchère, C. Fabre, A. Maître, and N. Treps, "Multimode quantum properties of a self-imaging OPO: squeezed vacuum and EPR beams generation", Phys. Rev. A 80043816 (2009).
[CrossRef]

Colet, P.

Delaubert, V.

Fabre, C.

L. Lopez, B. Chalopin, A. Rivière de la Souchère, C. Fabre, A. Maître, and N. Treps, "Multimode quantum properties of a self-imaging OPO: squeezed vacuum and EPR beams generation", Phys. Rev. A 80043816 (2009).
[CrossRef]

S. Gigan, L. Lopez, N. Treps, A. Maître, C. Fabre, "Image transmission through a stable paraxial cavity," Phys. Rev. A. 72, 023804 (2005).
[CrossRef]

Franken, P. A.

P. A. Franken, A. E. Hill, C. W. Peters and G. Weinreich, "Generation of Optical Harmonics," Phys. Rev. Lett. 7, 118-119 (1961).
[CrossRef]

Gigan, S.

S. Gigan, L. Lopez, N. Treps, A. Maître, C. Fabre, "Image transmission through a stable paraxial cavity," Phys. Rev. A. 72, 023804 (2005).
[CrossRef]

Harb, C. C.

Henking, R.

Hill, A. E.

P. A. Franken, A. E. Hill, C. W. Peters and G. Weinreich, "Generation of Optical Harmonics," Phys. Rev. Lett. 7, 118-119 (1961).
[CrossRef]

Khokhlov, V.

V. Khokhlov, "Wave propagation in nonlinear dispersive lines" Radiotek. Electron 6, 1116-1130 (1961).

Kimble, H. J.

Kleinman, D.

G. Boyd, D. Kleinman, "Parametric interaction of focused Gaussian light beams," IEEE J. Quantum Electron., (1968).
[CrossRef]

Kurz, P.

Lassen, M.

Lopez, L.

L. Lopez, B. Chalopin, A. Rivière de la Souchère, C. Fabre, A. Maître, and N. Treps, "Multimode quantum properties of a self-imaging OPO: squeezed vacuum and EPR beams generation", Phys. Rev. A 80043816 (2009).
[CrossRef]

S. Gigan, L. Lopez, N. Treps, A. Maître, C. Fabre, "Image transmission through a stable paraxial cavity," Phys. Rev. A. 72, 023804 (2005).
[CrossRef]

Lue, J. T.

Maître, A.

L. Lopez, B. Chalopin, A. Rivière de la Souchère, C. Fabre, A. Maître, and N. Treps, "Multimode quantum properties of a self-imaging OPO: squeezed vacuum and EPR beams generation", Phys. Rev. A 80043816 (2009).
[CrossRef]

S. Gigan, L. Lopez, N. Treps, A. Maître, C. Fabre, "Image transmission through a stable paraxial cavity," Phys. Rev. A. 72, 023804 (2005).
[CrossRef]

Mlynek, J.

Ou, Z. Y.

Paschotta, R.

Pereira, S. F.

Peters, C. W.

P. A. Franken, A. E. Hill, C. W. Peters and G. Weinreich, "Generation of Optical Harmonics," Phys. Rev. Lett. 7, 118-119 (1961).
[CrossRef]

Polzik, E. S.

Pulford, D. R. N.

Rivière de la Souchère, A.

L. Lopez, B. Chalopin, A. Rivière de la Souchère, C. Fabre, A. Maître, and N. Treps, "Multimode quantum properties of a self-imaging OPO: squeezed vacuum and EPR beams generation", Phys. Rev. A 80043816 (2009).
[CrossRef]

San Miguel, M.

Schiller, S.

Scotto, P.

Sun, C. J

Treps, N.

L. Lopez, B. Chalopin, A. Rivière de la Souchère, C. Fabre, A. Maître, and N. Treps, "Multimode quantum properties of a self-imaging OPO: squeezed vacuum and EPR beams generation", Phys. Rev. A 80043816 (2009).
[CrossRef]

S. Gigan, L. Lopez, N. Treps, A. Maître, C. Fabre, "Image transmission through a stable paraxial cavity," Phys. Rev. A. 72, 023804 (2005).
[CrossRef]

Weinreich, G.

P. A. Franken, A. E. Hill, C. W. Peters and G. Weinreich, "Generation of Optical Harmonics," Phys. Rev. Lett. 7, 118-119 (1961).
[CrossRef]

App. Opt. (1)

J. A. Arnaud, "Degenerate optical cavities" App. Opt. 8 (1), 189-195 (1969).
[CrossRef]

IEEE J. Quantum Electron. (1)

G. Boyd, D. Kleinman, "Parametric interaction of focused Gaussian light beams," IEEE J. Quantum Electron., (1968).
[CrossRef]

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

Opt. Express (1)

Opt. Lett. (3)

Phys. Rev. A (1)

L. Lopez, B. Chalopin, A. Rivière de la Souchère, C. Fabre, A. Maître, and N. Treps, "Multimode quantum properties of a self-imaging OPO: squeezed vacuum and EPR beams generation", Phys. Rev. A 80043816 (2009).
[CrossRef]

Phys. Rev. A. (1)

S. Gigan, L. Lopez, N. Treps, A. Maître, C. Fabre, "Image transmission through a stable paraxial cavity," Phys. Rev. A. 72, 023804 (2005).
[CrossRef]

Phys. Rev. Lett. (1)

P. A. Franken, A. E. Hill, C. W. Peters and G. Weinreich, "Generation of Optical Harmonics," Phys. Rev. Lett. 7, 118-119 (1961).
[CrossRef]

Radiotek. Electron (1)

V. Khokhlov, "Wave propagation in nonlinear dispersive lines" Radiotek. Electron 6, 1116-1130 (1961).

Other (3)

A. E. Siegman, Lasers (University Science Books, Mill Valley, 1986).

M. Kolobov editor, Quantum Imaging, (Springer-Verlag, 2006).

B. Chalopin, "Optique quantique multimode : des images aux impulsions," PhD Thesis, http://tel.archives-ouvertes.fr/tel-00431648/fr/ (2009).

Supplementary Material (1)

» Media 1: AVI (3946 KB)     

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Figures (8)

Fig. 1.
Fig. 1.

Linear self-imaging cavity. From a geometrical point-of-view, after a round-trip, any ray will retraces its own path. From a mode point of view, all the transverse TEM mn are simultanously resonant.

Fig. 2.
Fig. 2.

Normalized frequency difference between transverse modes α 2 π with respect to the distances from the full degeneracy ε = L 1 - L 1deg and δ = L 2 - L 2deg for experimental values f = 50mm and R = 38mm. The white regions are the configurations where the cavity is unstable.

Fig. 3.
Fig. 3.

Experimental setup. A Yag laser is sent through a mask and injected into a self-imaging cavity. The transmitted and frequency doubled images are recorded on two cameras, one for each wavelength, placed in the near field plane of the mask.

Fig. 4.
Fig. 4.

Transmitted infrared images through the imaging system with or without the self imaging cavity and with or without the crystal. The length scale corresponds to the size of the image in the cavity.

Fig. 5.
Fig. 5.

Infrared images and the corresponding second harmonic ones.

Fig. 6.
Fig. 6.

Single frame from a video (Media 1) recording the multimode properties of the cavity and the second harmonic generation, and the stability of the locking system while the input image is being continuously changed.

Fig. 7.
Fig. 7.

Experimental values of the doubling efficiency as a function of input infrared power, for a gaussian mode resonating in the self-imaging cavity.

Fig. 8.
Fig. 8.

Doubling efficiency (defined as the ratio between the green power and the infrared one) of a beam intercepted by vertical (a) and horizontal (b) slits as a function of their width in the crystal plane. The theoretical calculation (c) show the same behaviour. The small negative slope observed for large slits is due to the gaussian shape of the beam, not taken into account in the calculation.

Equations (7)

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2 π c = 2 π p + ( n + m + 1 ) α
A B C D = 1 0 0 1
L 1 = L 1 , deg = f + f 2 R
L 2 = L 2 , deg = f + R
B ( ρ ) d ρ ' A ( ρ ρ ' ) A ( ρ + ρ ' ) [ π 2 Si ( | ρ | 2 l coh 2 ) ]
l coh = λ 0 l c 4 πn
Si ( x ) = 0 x sin u u du

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