Abstract

The greater confinement of light that is possible in photonic crystal fibers (PCFs) leads to greater effective nonlinearity, which promises to yield greater quantum squeezing than is possible in standard optical fiber. However, experimental work to date has not achieved improvements over standard fiber. We present a comprehensive numerical investigation of polarization squeezing in PCF in a Sagnac configuration. By including loss, a noninstantaneous Raman response, excess phase-noise, second- and third-order dispersion, and self-steepening, the simulations are able to identify the physical factors that limit current PCF squeezing experiments.

© 2013 Optical Society of America

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  1. J. S. Neergaard-Nielsen, M. Takeuchi, K. Wakui, H. Takahashi, K. Hayasaka, M. Takeoka, and M. Sasaki, Phys. Rev. Lett. 105, 053602 (2010).
    [CrossRef]
  2. S. L. Braunstein, Rev. Mod. Phys. 77, 513 (2005).
    [CrossRef]
  3. W. P. Bowen, N. Treps, R. Schnabel, and P. K. Lam, Phys. Rev. Lett. 89, 253601 (2002).
    [CrossRef]
  4. N. Korolkova, G. Leuchs, R. Loudon, T. C. Ralph, and C. Silberhorn, Phys. Rev. A 65, 052306 (2002).
    [CrossRef]
  5. K. Wagner, J. Janousek, V. Delaubert, H. Zou, C. Harb, N. Treps, J. F. Morizur, P. K. Lam, and H.-A. Bachor, Science 321, 541 (2008).
    [CrossRef]
  6. T. L. S. Collaboration, Nat. Phys. 7, 962 (2011).
    [CrossRef]
  7. P. D. Drummond, R. M. Shelby, S. R. Friberg, and Y. Yamamoto, Nature 365, 307 (1993).
    [CrossRef]
  8. R. H. Stolen and A. Ashkin, Appl. Phys. Lett. 22, 294 (1973).
    [CrossRef]
  9. R. Dong, J. Heersink, J. F. Corney, P. D. Drummond, U. L. Andersen, and G. Leuchs, Opt. Lett. 33, 116 (2008).
    [CrossRef]
  10. J. Milanovic, J. Heersink, C. Marquardt, A. Huck, U. L. Andersen, and G. Leuchs, Laser Phys. 17, 559 (2007).
    [CrossRef]
  11. J. Milanovic, M. Lassen, U. L. Andersen, and G. Leuchs, Opt. Express 18, 1521 (2010).
    [CrossRef]
  12. J. F. Corney, J. Heersink, R. Dong, V. Josse, P. D. Drummond, G. Leuchs, and U. L. Andersen, Phys. Rev. A 78, 023831 (2008).
    [CrossRef]
  13. P. D. Drummond and A. D. Hardman, Europhys. Lett. 21, 279 (1993).
    [CrossRef]
  14. J. F. Corney and M. J. Tacey, in Proceedings of the International Quantum Electronics Conference and Conference on Lasers and Electro-Optics Pacific Rim, Sydney, Australia, August28–September 1, 2011, paper I889.
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    [CrossRef]
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  17. J. P. Gordon, Opt. Lett. 11, 662 (1986).
    [CrossRef]
  18. NKT Photonics, , 2010, available at http://www.nktphotonics.com/files/files/NL-PM-750.pdf .

2011 (1)

T. L. S. Collaboration, Nat. Phys. 7, 962 (2011).
[CrossRef]

2010 (2)

J. S. Neergaard-Nielsen, M. Takeuchi, K. Wakui, H. Takahashi, K. Hayasaka, M. Takeoka, and M. Sasaki, Phys. Rev. Lett. 105, 053602 (2010).
[CrossRef]

J. Milanovic, M. Lassen, U. L. Andersen, and G. Leuchs, Opt. Express 18, 1521 (2010).
[CrossRef]

2008 (3)

J. F. Corney, J. Heersink, R. Dong, V. Josse, P. D. Drummond, G. Leuchs, and U. L. Andersen, Phys. Rev. A 78, 023831 (2008).
[CrossRef]

R. Dong, J. Heersink, J. F. Corney, P. D. Drummond, U. L. Andersen, and G. Leuchs, Opt. Lett. 33, 116 (2008).
[CrossRef]

K. Wagner, J. Janousek, V. Delaubert, H. Zou, C. Harb, N. Treps, J. F. Morizur, P. K. Lam, and H.-A. Bachor, Science 321, 541 (2008).
[CrossRef]

2007 (1)

J. Milanovic, J. Heersink, C. Marquardt, A. Huck, U. L. Andersen, and G. Leuchs, Laser Phys. 17, 559 (2007).
[CrossRef]

2005 (1)

S. L. Braunstein, Rev. Mod. Phys. 77, 513 (2005).
[CrossRef]

2002 (2)

W. P. Bowen, N. Treps, R. Schnabel, and P. K. Lam, Phys. Rev. Lett. 89, 253601 (2002).
[CrossRef]

N. Korolkova, G. Leuchs, R. Loudon, T. C. Ralph, and C. Silberhorn, Phys. Rev. A 65, 052306 (2002).
[CrossRef]

2001 (1)

1993 (2)

P. D. Drummond and A. D. Hardman, Europhys. Lett. 21, 279 (1993).
[CrossRef]

P. D. Drummond, R. M. Shelby, S. R. Friberg, and Y. Yamamoto, Nature 365, 307 (1993).
[CrossRef]

1986 (1)

1973 (1)

R. H. Stolen and A. Ashkin, Appl. Phys. Lett. 22, 294 (1973).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2007).

Andersen, U. L.

J. Milanovic, M. Lassen, U. L. Andersen, and G. Leuchs, Opt. Express 18, 1521 (2010).
[CrossRef]

R. Dong, J. Heersink, J. F. Corney, P. D. Drummond, U. L. Andersen, and G. Leuchs, Opt. Lett. 33, 116 (2008).
[CrossRef]

J. F. Corney, J. Heersink, R. Dong, V. Josse, P. D. Drummond, G. Leuchs, and U. L. Andersen, Phys. Rev. A 78, 023831 (2008).
[CrossRef]

J. Milanovic, J. Heersink, C. Marquardt, A. Huck, U. L. Andersen, and G. Leuchs, Laser Phys. 17, 559 (2007).
[CrossRef]

Ashkin, A.

R. H. Stolen and A. Ashkin, Appl. Phys. Lett. 22, 294 (1973).
[CrossRef]

Bachor, H.-A.

K. Wagner, J. Janousek, V. Delaubert, H. Zou, C. Harb, N. Treps, J. F. Morizur, P. K. Lam, and H.-A. Bachor, Science 321, 541 (2008).
[CrossRef]

Bowen, W. P.

W. P. Bowen, N. Treps, R. Schnabel, and P. K. Lam, Phys. Rev. Lett. 89, 253601 (2002).
[CrossRef]

Braunstein, S. L.

S. L. Braunstein, Rev. Mod. Phys. 77, 513 (2005).
[CrossRef]

Collaboration, T. L. S.

T. L. S. Collaboration, Nat. Phys. 7, 962 (2011).
[CrossRef]

Corney, J. F.

J. F. Corney, J. Heersink, R. Dong, V. Josse, P. D. Drummond, G. Leuchs, and U. L. Andersen, Phys. Rev. A 78, 023831 (2008).
[CrossRef]

R. Dong, J. Heersink, J. F. Corney, P. D. Drummond, U. L. Andersen, and G. Leuchs, Opt. Lett. 33, 116 (2008).
[CrossRef]

J. F. Corney and M. J. Tacey, in Proceedings of the International Quantum Electronics Conference and Conference on Lasers and Electro-Optics Pacific Rim, Sydney, Australia, August28–September 1, 2011, paper I889.

Delaubert, V.

K. Wagner, J. Janousek, V. Delaubert, H. Zou, C. Harb, N. Treps, J. F. Morizur, P. K. Lam, and H.-A. Bachor, Science 321, 541 (2008).
[CrossRef]

Dong, R.

R. Dong, J. Heersink, J. F. Corney, P. D. Drummond, U. L. Andersen, and G. Leuchs, Opt. Lett. 33, 116 (2008).
[CrossRef]

J. F. Corney, J. Heersink, R. Dong, V. Josse, P. D. Drummond, G. Leuchs, and U. L. Andersen, Phys. Rev. A 78, 023831 (2008).
[CrossRef]

Drummond, P. D.

J. F. Corney, J. Heersink, R. Dong, V. Josse, P. D. Drummond, G. Leuchs, and U. L. Andersen, Phys. Rev. A 78, 023831 (2008).
[CrossRef]

R. Dong, J. Heersink, J. F. Corney, P. D. Drummond, U. L. Andersen, and G. Leuchs, Opt. Lett. 33, 116 (2008).
[CrossRef]

P. D. Drummond, J. Opt. Soc. Am. B 18, 139 (2001).
[CrossRef]

P. D. Drummond, R. M. Shelby, S. R. Friberg, and Y. Yamamoto, Nature 365, 307 (1993).
[CrossRef]

P. D. Drummond and A. D. Hardman, Europhys. Lett. 21, 279 (1993).
[CrossRef]

Friberg, S. R.

P. D. Drummond, R. M. Shelby, S. R. Friberg, and Y. Yamamoto, Nature 365, 307 (1993).
[CrossRef]

Gordon, J. P.

Harb, C.

K. Wagner, J. Janousek, V. Delaubert, H. Zou, C. Harb, N. Treps, J. F. Morizur, P. K. Lam, and H.-A. Bachor, Science 321, 541 (2008).
[CrossRef]

Hardman, A. D.

P. D. Drummond and A. D. Hardman, Europhys. Lett. 21, 279 (1993).
[CrossRef]

Hayasaka, K.

J. S. Neergaard-Nielsen, M. Takeuchi, K. Wakui, H. Takahashi, K. Hayasaka, M. Takeoka, and M. Sasaki, Phys. Rev. Lett. 105, 053602 (2010).
[CrossRef]

Heersink, J.

J. F. Corney, J. Heersink, R. Dong, V. Josse, P. D. Drummond, G. Leuchs, and U. L. Andersen, Phys. Rev. A 78, 023831 (2008).
[CrossRef]

R. Dong, J. Heersink, J. F. Corney, P. D. Drummond, U. L. Andersen, and G. Leuchs, Opt. Lett. 33, 116 (2008).
[CrossRef]

J. Milanovic, J. Heersink, C. Marquardt, A. Huck, U. L. Andersen, and G. Leuchs, Laser Phys. 17, 559 (2007).
[CrossRef]

Huck, A.

J. Milanovic, J. Heersink, C. Marquardt, A. Huck, U. L. Andersen, and G. Leuchs, Laser Phys. 17, 559 (2007).
[CrossRef]

Janousek, J.

K. Wagner, J. Janousek, V. Delaubert, H. Zou, C. Harb, N. Treps, J. F. Morizur, P. K. Lam, and H.-A. Bachor, Science 321, 541 (2008).
[CrossRef]

Josse, V.

J. F. Corney, J. Heersink, R. Dong, V. Josse, P. D. Drummond, G. Leuchs, and U. L. Andersen, Phys. Rev. A 78, 023831 (2008).
[CrossRef]

Korolkova, N.

N. Korolkova, G. Leuchs, R. Loudon, T. C. Ralph, and C. Silberhorn, Phys. Rev. A 65, 052306 (2002).
[CrossRef]

Lam, P. K.

K. Wagner, J. Janousek, V. Delaubert, H. Zou, C. Harb, N. Treps, J. F. Morizur, P. K. Lam, and H.-A. Bachor, Science 321, 541 (2008).
[CrossRef]

W. P. Bowen, N. Treps, R. Schnabel, and P. K. Lam, Phys. Rev. Lett. 89, 253601 (2002).
[CrossRef]

Lassen, M.

Leuchs, G.

J. Milanovic, M. Lassen, U. L. Andersen, and G. Leuchs, Opt. Express 18, 1521 (2010).
[CrossRef]

R. Dong, J. Heersink, J. F. Corney, P. D. Drummond, U. L. Andersen, and G. Leuchs, Opt. Lett. 33, 116 (2008).
[CrossRef]

J. F. Corney, J. Heersink, R. Dong, V. Josse, P. D. Drummond, G. Leuchs, and U. L. Andersen, Phys. Rev. A 78, 023831 (2008).
[CrossRef]

J. Milanovic, J. Heersink, C. Marquardt, A. Huck, U. L. Andersen, and G. Leuchs, Laser Phys. 17, 559 (2007).
[CrossRef]

N. Korolkova, G. Leuchs, R. Loudon, T. C. Ralph, and C. Silberhorn, Phys. Rev. A 65, 052306 (2002).
[CrossRef]

Loudon, R.

N. Korolkova, G. Leuchs, R. Loudon, T. C. Ralph, and C. Silberhorn, Phys. Rev. A 65, 052306 (2002).
[CrossRef]

Marquardt, C.

J. Milanovic, J. Heersink, C. Marquardt, A. Huck, U. L. Andersen, and G. Leuchs, Laser Phys. 17, 559 (2007).
[CrossRef]

Milanovic, J.

J. Milanovic, M. Lassen, U. L. Andersen, and G. Leuchs, Opt. Express 18, 1521 (2010).
[CrossRef]

J. Milanovic, J. Heersink, C. Marquardt, A. Huck, U. L. Andersen, and G. Leuchs, Laser Phys. 17, 559 (2007).
[CrossRef]

Morizur, J. F.

K. Wagner, J. Janousek, V. Delaubert, H. Zou, C. Harb, N. Treps, J. F. Morizur, P. K. Lam, and H.-A. Bachor, Science 321, 541 (2008).
[CrossRef]

Neergaard-Nielsen, J. S.

J. S. Neergaard-Nielsen, M. Takeuchi, K. Wakui, H. Takahashi, K. Hayasaka, M. Takeoka, and M. Sasaki, Phys. Rev. Lett. 105, 053602 (2010).
[CrossRef]

Ralph, T. C.

N. Korolkova, G. Leuchs, R. Loudon, T. C. Ralph, and C. Silberhorn, Phys. Rev. A 65, 052306 (2002).
[CrossRef]

Sasaki, M.

J. S. Neergaard-Nielsen, M. Takeuchi, K. Wakui, H. Takahashi, K. Hayasaka, M. Takeoka, and M. Sasaki, Phys. Rev. Lett. 105, 053602 (2010).
[CrossRef]

Schnabel, R.

W. P. Bowen, N. Treps, R. Schnabel, and P. K. Lam, Phys. Rev. Lett. 89, 253601 (2002).
[CrossRef]

Shelby, R. M.

P. D. Drummond, R. M. Shelby, S. R. Friberg, and Y. Yamamoto, Nature 365, 307 (1993).
[CrossRef]

Silberhorn, C.

N. Korolkova, G. Leuchs, R. Loudon, T. C. Ralph, and C. Silberhorn, Phys. Rev. A 65, 052306 (2002).
[CrossRef]

Stolen, R. H.

R. H. Stolen and A. Ashkin, Appl. Phys. Lett. 22, 294 (1973).
[CrossRef]

Tacey, M. J.

J. F. Corney and M. J. Tacey, in Proceedings of the International Quantum Electronics Conference and Conference on Lasers and Electro-Optics Pacific Rim, Sydney, Australia, August28–September 1, 2011, paper I889.

Takahashi, H.

J. S. Neergaard-Nielsen, M. Takeuchi, K. Wakui, H. Takahashi, K. Hayasaka, M. Takeoka, and M. Sasaki, Phys. Rev. Lett. 105, 053602 (2010).
[CrossRef]

Takeoka, M.

J. S. Neergaard-Nielsen, M. Takeuchi, K. Wakui, H. Takahashi, K. Hayasaka, M. Takeoka, and M. Sasaki, Phys. Rev. Lett. 105, 053602 (2010).
[CrossRef]

Takeuchi, M.

J. S. Neergaard-Nielsen, M. Takeuchi, K. Wakui, H. Takahashi, K. Hayasaka, M. Takeoka, and M. Sasaki, Phys. Rev. Lett. 105, 053602 (2010).
[CrossRef]

Treps, N.

K. Wagner, J. Janousek, V. Delaubert, H. Zou, C. Harb, N. Treps, J. F. Morizur, P. K. Lam, and H.-A. Bachor, Science 321, 541 (2008).
[CrossRef]

W. P. Bowen, N. Treps, R. Schnabel, and P. K. Lam, Phys. Rev. Lett. 89, 253601 (2002).
[CrossRef]

Wagner, K.

K. Wagner, J. Janousek, V. Delaubert, H. Zou, C. Harb, N. Treps, J. F. Morizur, P. K. Lam, and H.-A. Bachor, Science 321, 541 (2008).
[CrossRef]

Wakui, K.

J. S. Neergaard-Nielsen, M. Takeuchi, K. Wakui, H. Takahashi, K. Hayasaka, M. Takeoka, and M. Sasaki, Phys. Rev. Lett. 105, 053602 (2010).
[CrossRef]

Yamamoto, Y.

P. D. Drummond, R. M. Shelby, S. R. Friberg, and Y. Yamamoto, Nature 365, 307 (1993).
[CrossRef]

Zou, H.

K. Wagner, J. Janousek, V. Delaubert, H. Zou, C. Harb, N. Treps, J. F. Morizur, P. K. Lam, and H.-A. Bachor, Science 321, 541 (2008).
[CrossRef]

Appl. Phys. Lett. (1)

R. H. Stolen and A. Ashkin, Appl. Phys. Lett. 22, 294 (1973).
[CrossRef]

Europhys. Lett. (1)

P. D. Drummond and A. D. Hardman, Europhys. Lett. 21, 279 (1993).
[CrossRef]

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

Laser Phys. (1)

J. Milanovic, J. Heersink, C. Marquardt, A. Huck, U. L. Andersen, and G. Leuchs, Laser Phys. 17, 559 (2007).
[CrossRef]

Nat. Phys. (1)

T. L. S. Collaboration, Nat. Phys. 7, 962 (2011).
[CrossRef]

Nature (1)

P. D. Drummond, R. M. Shelby, S. R. Friberg, and Y. Yamamoto, Nature 365, 307 (1993).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Phys. Rev. A (2)

J. F. Corney, J. Heersink, R. Dong, V. Josse, P. D. Drummond, G. Leuchs, and U. L. Andersen, Phys. Rev. A 78, 023831 (2008).
[CrossRef]

N. Korolkova, G. Leuchs, R. Loudon, T. C. Ralph, and C. Silberhorn, Phys. Rev. A 65, 052306 (2002).
[CrossRef]

Phys. Rev. Lett. (2)

J. S. Neergaard-Nielsen, M. Takeuchi, K. Wakui, H. Takahashi, K. Hayasaka, M. Takeoka, and M. Sasaki, Phys. Rev. Lett. 105, 053602 (2010).
[CrossRef]

W. P. Bowen, N. Treps, R. Schnabel, and P. K. Lam, Phys. Rev. Lett. 89, 253601 (2002).
[CrossRef]

Rev. Mod. Phys. (1)

S. L. Braunstein, Rev. Mod. Phys. 77, 513 (2005).
[CrossRef]

Science (1)

K. Wagner, J. Janousek, V. Delaubert, H. Zou, C. Harb, N. Treps, J. F. Morizur, P. K. Lam, and H.-A. Bachor, Science 321, 541 (2008).
[CrossRef]

Other (3)

G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2007).

NKT Photonics, , 2010, available at http://www.nktphotonics.com/files/files/NL-PM-750.pdf .

J. F. Corney and M. J. Tacey, in Proceedings of the International Quantum Electronics Conference and Conference on Lasers and Electro-Optics Pacific Rim, Sydney, Australia, August28–September 1, 2011, paper I889.

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Figures (2)

Fig. 1.
Fig. 1.

(a) Squeezing and (b) antisqueezing as a function of the total pulse energy. Pluses show the pure squeezing, with no higher-order dispersive effects (B3=0, s=0), GAWBS noise (G=0) or loss. The remaining curves successively add in the effects of the 13% linear loss (diamonds), imperfect spectral overlap (squares), and GAWBS noise (circles). The shading on the latter indicates the effect of a ±0.03 uncertainty in the experimentally determined spectral overlap [11]. Experimentally measured squeezing is given by the triangles. The vertical dashed line indicates the energy of two soliton inputs. (c) Squeezing and (d) antisqueezing for various amounts of third-order dispersion B3: 0 (pluses), 0.3 (circles), 0.5 (squares), 1.0 (diamonds), 3.0 (crosses), and 6.0 (stars). Other parameters are in Figs. 1(a) and 1(b), with experimental results again plotted as triangles. 104 stochastic paths were used in the simulation to give a maximum sampling error of ±6.3×102dB.

Fig. 2.
Fig. 2.

Fiber length (shaded green line, left axis) for optimal squeezing with GAWBS noise (shaded–dashed blue line, right axis, with maximum sampling error of ±0.2dB) as a function of total pulse energy, with (dashed line) and without (dashed–dotted line) GAWBS noise. The green shading shows the range of fiber lengths that give squeezing within 5% of the optimum. For some of the small pulse energies (between 3.00 and 4.57 pJ), the trend indicates marginally better squeezing for fiber lengths larger than 30 m. Linear loss and finite spectral overlap effects have not been included. 103 stochastic paths were used in the simulation.

Equations (3)

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

M=(1ϵ)S^θ+ϵS^0S^0,
ϕ(z,t)z=i[122t2iB3163t3+Gη+dth(tt)|ϕ(z,t)|2+Γ(z,t)]ϕ(z,t)s|ϕ(z,t)|2ϕ(z,t)t.
Γ(z,Ω)Γ(z,Ω)=αR(|Ω|)[nth(|Ω|)+12]δΩΩδ(zz),

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