Abstract

We have analyzed squeezing of the fundamental field by means of traveling-wave, type-II phase-matched, second-harmonic generation, taking into account depletion of the fundamental field and phase mismatch between the fundamental and the harmonic fields. For the phase-matched case we show that the generated squeezing is S = 1 − γ, where γ is the harmonic conversion efficiency. In the case of a large phase-mismatch we have identified a new mechanism that generates squeezing. It is the nonlinear phase shift of the fundamental field that is due to the cascaded χ(2) nonlinearity.

© 1993 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. L. A. Wu, M. Xiao, H. J. Kimble, J. Opt. Soc. Am. B 4, 1465 (1987); E. S. Polzik, J. Carri, H. J. Kimble, Phys. Rev. Lett. 68, 3020 (1992).
    [CrossRef] [PubMed]
  2. O. Aytür, P. Kumar, Opt. Lett. 17, 529 (1992); C. Kim, R. D. Li, P. Kumar, in Quantum Electronics and Laser Science, Vol. 12 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), p. 214.
    [CrossRef] [PubMed]
  3. S. F. Pereira, M. Xiao, H. J. Kimble, J. L. Hall, Phys. Rev. A 38, 4931 (1988); P. Kürz, R. Paschotta, K. Fiedler, A. Sizmann, G. Leuchs, J. Mlynek, Appl. Phys. B 55, 216 (1992).
    [CrossRef] [PubMed]
  4. G. J. Milburn, D. F. Walls, Phys. Rev. A 27, 392 (1983); L. A. Lugiato, G. Strini, F. DeMartini, Opt. Lett. 8, 256 (1983); M. J. Collet, C. W. Gardiner, Phys. Rev. A 30, 1386 (1984); T. A. B. Kennedy, T. B. Anderson, D. F. Walls, Phys. Rev. A 40, 1385 (1989).
    [CrossRef] [PubMed]
  5. L. Mandel, Opt. Commun. 42, 437 (1982); S. Kielich, R. Tanaś, R. Zawodny, J. Mod. Opt. 34, 979 (1987).
    [CrossRef]
  6. J. A. Armstrong, N. Bloembergen, J. Ducuing, P. S. Pershan, Phys. Rev. 127, 1918 (1962).
    [CrossRef]
  7. M. Shirasaki, H. A. Haus, J. Opt. Soc. Am. B 8, 681 (1991); K. J. Blow, R. Loudon, S. J. D. Phoenix, Phys. Rev. A 45, 8064 (1992).
    [CrossRef] [PubMed]
  8. G. Stegeman, M. Sheik-Bahae, E. W. Van Stryland, G. Assanto, Opt. Lett. 18, 13 (1992); D. C. Hutchings, J. S. Aitchison, C. N. Ironside, Opt. Lett. 18, 793 (1993).
    [CrossRef] [PubMed]
  9. K. Bergman, H. A. Haus, Opt. Lett. 16, 663 (1991); M. Rosenbluh, R. M. Shelby, Phys. Rev. Lett. 66, 153 (1991).
    [CrossRef] [PubMed]
  10. By treating A classically, we in essence ignore the coherent-state fluctuations ΔA of the strong fundamental input beam. A more detailed linearization analysis, in which ΔA is retained, shows that these fluctuations also get squeezed. Along with the mean field, the fluctuations in Aout, however, get separated from âout after passage through half-wave plate HWP2 and polarization beam splitter PBS2 (see Fig. 1).
  11. H. P. Yuen, Phys. Rev. A 13, 2226 (1976).
    [CrossRef]
  12. M. I. Kolobov, P. Kumar, Opt. Lett. 18, 849 (1993).
    [CrossRef] [PubMed]
  13. A. J. W. Brown, M. S. Bowers, K. W. Kangas, C. H. Fisher, Opt. Lett. 17, 109 (1992).
    [CrossRef] [PubMed]

1993 (1)

1992 (3)

1991 (2)

1988 (1)

S. F. Pereira, M. Xiao, H. J. Kimble, J. L. Hall, Phys. Rev. A 38, 4931 (1988); P. Kürz, R. Paschotta, K. Fiedler, A. Sizmann, G. Leuchs, J. Mlynek, Appl. Phys. B 55, 216 (1992).
[CrossRef] [PubMed]

1987 (1)

1983 (1)

G. J. Milburn, D. F. Walls, Phys. Rev. A 27, 392 (1983); L. A. Lugiato, G. Strini, F. DeMartini, Opt. Lett. 8, 256 (1983); M. J. Collet, C. W. Gardiner, Phys. Rev. A 30, 1386 (1984); T. A. B. Kennedy, T. B. Anderson, D. F. Walls, Phys. Rev. A 40, 1385 (1989).
[CrossRef] [PubMed]

1982 (1)

L. Mandel, Opt. Commun. 42, 437 (1982); S. Kielich, R. Tanaś, R. Zawodny, J. Mod. Opt. 34, 979 (1987).
[CrossRef]

1976 (1)

H. P. Yuen, Phys. Rev. A 13, 2226 (1976).
[CrossRef]

1962 (1)

J. A. Armstrong, N. Bloembergen, J. Ducuing, P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[CrossRef]

Armstrong, J. A.

J. A. Armstrong, N. Bloembergen, J. Ducuing, P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[CrossRef]

Assanto, G.

Aytür, O.

Bergman, K.

Bloembergen, N.

J. A. Armstrong, N. Bloembergen, J. Ducuing, P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[CrossRef]

Bowers, M. S.

Brown, A. J. W.

Ducuing, J.

J. A. Armstrong, N. Bloembergen, J. Ducuing, P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[CrossRef]

Fisher, C. H.

Hall, J. L.

S. F. Pereira, M. Xiao, H. J. Kimble, J. L. Hall, Phys. Rev. A 38, 4931 (1988); P. Kürz, R. Paschotta, K. Fiedler, A. Sizmann, G. Leuchs, J. Mlynek, Appl. Phys. B 55, 216 (1992).
[CrossRef] [PubMed]

Haus, H. A.

Kangas, K. W.

Kimble, H. J.

S. F. Pereira, M. Xiao, H. J. Kimble, J. L. Hall, Phys. Rev. A 38, 4931 (1988); P. Kürz, R. Paschotta, K. Fiedler, A. Sizmann, G. Leuchs, J. Mlynek, Appl. Phys. B 55, 216 (1992).
[CrossRef] [PubMed]

L. A. Wu, M. Xiao, H. J. Kimble, J. Opt. Soc. Am. B 4, 1465 (1987); E. S. Polzik, J. Carri, H. J. Kimble, Phys. Rev. Lett. 68, 3020 (1992).
[CrossRef] [PubMed]

Kolobov, M. I.

Kumar, P.

Mandel, L.

L. Mandel, Opt. Commun. 42, 437 (1982); S. Kielich, R. Tanaś, R. Zawodny, J. Mod. Opt. 34, 979 (1987).
[CrossRef]

Milburn, G. J.

G. J. Milburn, D. F. Walls, Phys. Rev. A 27, 392 (1983); L. A. Lugiato, G. Strini, F. DeMartini, Opt. Lett. 8, 256 (1983); M. J. Collet, C. W. Gardiner, Phys. Rev. A 30, 1386 (1984); T. A. B. Kennedy, T. B. Anderson, D. F. Walls, Phys. Rev. A 40, 1385 (1989).
[CrossRef] [PubMed]

Pereira, S. F.

S. F. Pereira, M. Xiao, H. J. Kimble, J. L. Hall, Phys. Rev. A 38, 4931 (1988); P. Kürz, R. Paschotta, K. Fiedler, A. Sizmann, G. Leuchs, J. Mlynek, Appl. Phys. B 55, 216 (1992).
[CrossRef] [PubMed]

Pershan, P. S.

J. A. Armstrong, N. Bloembergen, J. Ducuing, P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[CrossRef]

Sheik-Bahae, M.

Shirasaki, M.

Stegeman, G.

Van Stryland, E. W.

Walls, D. F.

G. J. Milburn, D. F. Walls, Phys. Rev. A 27, 392 (1983); L. A. Lugiato, G. Strini, F. DeMartini, Opt. Lett. 8, 256 (1983); M. J. Collet, C. W. Gardiner, Phys. Rev. A 30, 1386 (1984); T. A. B. Kennedy, T. B. Anderson, D. F. Walls, Phys. Rev. A 40, 1385 (1989).
[CrossRef] [PubMed]

Wu, L. A.

Xiao, M.

S. F. Pereira, M. Xiao, H. J. Kimble, J. L. Hall, Phys. Rev. A 38, 4931 (1988); P. Kürz, R. Paschotta, K. Fiedler, A. Sizmann, G. Leuchs, J. Mlynek, Appl. Phys. B 55, 216 (1992).
[CrossRef] [PubMed]

L. A. Wu, M. Xiao, H. J. Kimble, J. Opt. Soc. Am. B 4, 1465 (1987); E. S. Polzik, J. Carri, H. J. Kimble, Phys. Rev. Lett. 68, 3020 (1992).
[CrossRef] [PubMed]

Yuen, H. P.

H. P. Yuen, Phys. Rev. A 13, 2226 (1976).
[CrossRef]

J. Opt. Soc. Am. B (2)

Opt. Commun. (1)

L. Mandel, Opt. Commun. 42, 437 (1982); S. Kielich, R. Tanaś, R. Zawodny, J. Mod. Opt. 34, 979 (1987).
[CrossRef]

Opt. Lett. (5)

Phys. Rev. (1)

J. A. Armstrong, N. Bloembergen, J. Ducuing, P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[CrossRef]

Phys. Rev. A (3)

S. F. Pereira, M. Xiao, H. J. Kimble, J. L. Hall, Phys. Rev. A 38, 4931 (1988); P. Kürz, R. Paschotta, K. Fiedler, A. Sizmann, G. Leuchs, J. Mlynek, Appl. Phys. B 55, 216 (1992).
[CrossRef] [PubMed]

G. J. Milburn, D. F. Walls, Phys. Rev. A 27, 392 (1983); L. A. Lugiato, G. Strini, F. DeMartini, Opt. Lett. 8, 256 (1983); M. J. Collet, C. W. Gardiner, Phys. Rev. A 30, 1386 (1984); T. A. B. Kennedy, T. B. Anderson, D. F. Walls, Phys. Rev. A 40, 1385 (1989).
[CrossRef] [PubMed]

H. P. Yuen, Phys. Rev. A 13, 2226 (1976).
[CrossRef]

Other (1)

By treating A classically, we in essence ignore the coherent-state fluctuations ΔA of the strong fundamental input beam. A more detailed linearization analysis, in which ΔA is retained, shows that these fluctuations also get squeezed. Along with the mean field, the fluctuations in Aout, however, get separated from âout after passage through half-wave plate HWP2 and polarization beam splitter PBS2 (see Fig. 1).

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 (2)

Fig. 1
Fig. 1

Schematic of a commonly employed, type-II phase-matched, SHG scheme. The principal axes of the KTP crystal are parallel to the S- and P-polarization directions. The harmonic field, which is S polarized because of the type-II phase matching, can be separated by use of a prism or a dichroic beam splitter (not shown).

Fig. 2
Fig. 2

Obtainable squeezing as a function of the intensity of the fundamental field (∝|A|2) for various phase-mismatch parameters.

Equations (13)

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

A 1 ( 2 ) ( 0 ) = 2 1 / 2 ( A + Δ A a ˆ ) ,
d A 1 ( 2 ) d z = κ A 2 ( 1 ) * A 3 exp ( i Δ k z ) , d A 3 d z = κ A 1 A 2 exp ( i Δ k z ) ,
A 1 ( L ) = η 1 A 1 ( 0 ) exp ( i Φ NL 1 ) , A 2 ( L ) = η 2 A 2 ( 0 ) exp ( i Φ NL 2 ) ,
η 1 [ | A 1 ( 0 ) | 2 , | A 2 ( 0 ) | 2 ] = η 1 ( | A | 2 / 2 , | A | 2 / 2 ) + 1 2 ( η 1 u 2 η 1 u 1 ) ( A * a ˆ + A a ˆ ) ,
A 1 ( 2 ) ( L ) = 2 1 / 2 ( η A ± μ a ˆ ± ν a ˆ ) exp ( i Φ NL ) ,
μ = η + | A | 2 2 [ i η ( u 2 u 1 ) Φ NL 1 + ( η 1 u 2 η 1 u 1 ) ] , ν = A 2 2 [ i η ( u 2 u 1 ) Φ NL 1 + ( η 1 u 2 η 1 u 1 ) ] .
η 1 u 2 η 1 u 1 = 1 | A | 2 [ η 1 + 1 η 1 ( u 2 u 1 ) | A 1 ( L ) | 2 ]
| A 1 ( L ) | 2 u 2 | A 1 ( L ) | 2 u 1 = 1 ,
μ = 1 2 [ i η | A | 2 ( u 2 u 1 ) Φ NL 1 ( 1 η + η ) ] , ν = 1 2 [ i η A 2 ( u 2 u 1 ) Φ NL 1 + A 2 | A | 2 ( η 1 η ) ] ,
a ˆ out = 2 1 / 2 [ A 1 ( L ) A 2 ( L ) ] = μ a ˆ + ν a ˆ ,
S = ( | μ | | ν | ) 2 = 1 4 { [ ( η 1 + η ) 2 + 4 Φ eff 2 ] 1 / 2 [ ( η 1 η ) 2 + 4 Φ eff 2 ] 1 / 2 } 2 ,
S = η 2 = 1 γ ,
S = η 2 = [ sech ( κ | A | L / 2 1 / 2 ) ] 2 .

Metrics