Abstract

An analysis of the output polarization of a noncollinear type I optical parametric downconversion source is presented. Such a source can be made by pumping a nonlinear crystal with an extraordinary-polarized beam to produce pairs of ordinary-polarized photons. A polarization map of the output light illustrates dramatic variation in the polarization direction at large scattering angles. The effect of this variation in polarization direction is seen on a map of the nonlinear conversion efficiency. The apparent ambiguity in the polarization for the particular case in which one of the outputs propagates along the crystal optic axis is also discussed.

© 1997 Optical Society of America

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References

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  1. A. Einstein, B. Podolsky, and N. Rosen, “Can quantum-mechanical description of physical reality be considered complete?” Phys. Rev. 47, 777–780 (1935).
    [CrossRef]
  2. Z. Y. Ou and L. Mandel, “Violation of Bell’s inequality and classical probability in a two-photon correlation experiment,” Phys. Rev. Lett. 61, 50–53 (1988).
    [CrossRef] [PubMed]
  3. Y. H. Shih and C. O. Alley, “New type of Einstein–Podolsky–Rosen–Bohm experiment using pairs of light quanta produced by optical parametric downconversion,” Phys. Rev. Lett. 61, 2921–2924 (1988).
    [CrossRef] [PubMed]
  4. T. E. Kiess, Y. H. Shih, A. V. Sergienko, and C. O. Alley, “Einstein–Podolsky–Rosen–Bohm experiment using pairs of light quanta produced by type-II parametric downconversion,” Phys. Rev. Lett. 71, 3893–3897 (1993).
    [CrossRef] [PubMed]
  5. R. Y. Chiao, P. G. Kwait, and A. Steinberg, “Quantum nonlocality in two-photon experiments at Berkeley,” Quantum Semiclassic. Opt. 7, 259–278 (1995).
    [CrossRef]
  6. T. B. Pittman, D. V. Strekalov, A. Migdall, M. H. Rubin, A. V. Sergienko, and Y. H. Shih, “Can two-photon interference be considered the interference of two-photon?” Phys. Rev. Lett. 77, 1917–1920 (1996).
    [CrossRef] [PubMed]
  7. A. Yariv, Optical Electronics, 3rd ed. (Holt, Rinehart, & Winston, New York, 1985), Chap. 8, pp. 227–273.
  8. D. N. Klyshko, Photons and Nonlinear Optics (Gordon & Breach, New York, 1988), Chap. 1, pp. 1–64; Chap. 6, pp. 285–357.
  9. M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1993), pp. 679–680.
  10. D. N. Klyshko, “Utilization of vacuum fluctuations as an optical brightness standard,” Sov. J. Quantum Electron. 7, 591–595 (1977).
    [CrossRef]
  11. K. Koch, E. C. Cheung, G. T. Moore, S. H. Chakmakjian, and J. M. Liu, “Hot spots in parametric fluorescence with pump beam of finite cross section,” IEEE J. Quantum Electron. 31, 769–781 (1995).
    [CrossRef]
  12. F. Zernike and J. E. Midwinter, Applied Nonlinear Optics (Wiley, New York, 1973), pp. 34–41.
  13. Although this Kleinman symmetry assumption is best met for wavelengths shorter than 5 μm, where LiIO3 transmittance begins to fall off, the calculations here are carried out to 9 μm for better viewing of the results.
  14. M. Choy and R. L. Byer, “Accurate second-order susceptibility measurements of visible and infrared nonlinear crystals,” Phys. Rev. B 14, 1693–1706 (1976).
    [CrossRef]

1996 (1)

T. B. Pittman, D. V. Strekalov, A. Migdall, M. H. Rubin, A. V. Sergienko, and Y. H. Shih, “Can two-photon interference be considered the interference of two-photon?” Phys. Rev. Lett. 77, 1917–1920 (1996).
[CrossRef] [PubMed]

1995 (2)

K. Koch, E. C. Cheung, G. T. Moore, S. H. Chakmakjian, and J. M. Liu, “Hot spots in parametric fluorescence with pump beam of finite cross section,” IEEE J. Quantum Electron. 31, 769–781 (1995).
[CrossRef]

R. Y. Chiao, P. G. Kwait, and A. Steinberg, “Quantum nonlocality in two-photon experiments at Berkeley,” Quantum Semiclassic. Opt. 7, 259–278 (1995).
[CrossRef]

1993 (1)

T. E. Kiess, Y. H. Shih, A. V. Sergienko, and C. O. Alley, “Einstein–Podolsky–Rosen–Bohm experiment using pairs of light quanta produced by type-II parametric downconversion,” Phys. Rev. Lett. 71, 3893–3897 (1993).
[CrossRef] [PubMed]

1988 (2)

Z. Y. Ou and L. Mandel, “Violation of Bell’s inequality and classical probability in a two-photon correlation experiment,” Phys. Rev. Lett. 61, 50–53 (1988).
[CrossRef] [PubMed]

Y. H. Shih and C. O. Alley, “New type of Einstein–Podolsky–Rosen–Bohm experiment using pairs of light quanta produced by optical parametric downconversion,” Phys. Rev. Lett. 61, 2921–2924 (1988).
[CrossRef] [PubMed]

1977 (1)

D. N. Klyshko, “Utilization of vacuum fluctuations as an optical brightness standard,” Sov. J. Quantum Electron. 7, 591–595 (1977).
[CrossRef]

1976 (1)

M. Choy and R. L. Byer, “Accurate second-order susceptibility measurements of visible and infrared nonlinear crystals,” Phys. Rev. B 14, 1693–1706 (1976).
[CrossRef]

1935 (1)

A. Einstein, B. Podolsky, and N. Rosen, “Can quantum-mechanical description of physical reality be considered complete?” Phys. Rev. 47, 777–780 (1935).
[CrossRef]

Alley, C. O.

T. E. Kiess, Y. H. Shih, A. V. Sergienko, and C. O. Alley, “Einstein–Podolsky–Rosen–Bohm experiment using pairs of light quanta produced by type-II parametric downconversion,” Phys. Rev. Lett. 71, 3893–3897 (1993).
[CrossRef] [PubMed]

Y. H. Shih and C. O. Alley, “New type of Einstein–Podolsky–Rosen–Bohm experiment using pairs of light quanta produced by optical parametric downconversion,” Phys. Rev. Lett. 61, 2921–2924 (1988).
[CrossRef] [PubMed]

Byer, R. L.

M. Choy and R. L. Byer, “Accurate second-order susceptibility measurements of visible and infrared nonlinear crystals,” Phys. Rev. B 14, 1693–1706 (1976).
[CrossRef]

Chakmakjian, S. H.

K. Koch, E. C. Cheung, G. T. Moore, S. H. Chakmakjian, and J. M. Liu, “Hot spots in parametric fluorescence with pump beam of finite cross section,” IEEE J. Quantum Electron. 31, 769–781 (1995).
[CrossRef]

Cheung, E. C.

K. Koch, E. C. Cheung, G. T. Moore, S. H. Chakmakjian, and J. M. Liu, “Hot spots in parametric fluorescence with pump beam of finite cross section,” IEEE J. Quantum Electron. 31, 769–781 (1995).
[CrossRef]

Chiao, R. Y.

R. Y. Chiao, P. G. Kwait, and A. Steinberg, “Quantum nonlocality in two-photon experiments at Berkeley,” Quantum Semiclassic. Opt. 7, 259–278 (1995).
[CrossRef]

Choy, M.

M. Choy and R. L. Byer, “Accurate second-order susceptibility measurements of visible and infrared nonlinear crystals,” Phys. Rev. B 14, 1693–1706 (1976).
[CrossRef]

Einstein, A.

A. Einstein, B. Podolsky, and N. Rosen, “Can quantum-mechanical description of physical reality be considered complete?” Phys. Rev. 47, 777–780 (1935).
[CrossRef]

Kiess, T. E.

T. E. Kiess, Y. H. Shih, A. V. Sergienko, and C. O. Alley, “Einstein–Podolsky–Rosen–Bohm experiment using pairs of light quanta produced by type-II parametric downconversion,” Phys. Rev. Lett. 71, 3893–3897 (1993).
[CrossRef] [PubMed]

Klyshko, D. N.

D. N. Klyshko, “Utilization of vacuum fluctuations as an optical brightness standard,” Sov. J. Quantum Electron. 7, 591–595 (1977).
[CrossRef]

Koch, K.

K. Koch, E. C. Cheung, G. T. Moore, S. H. Chakmakjian, and J. M. Liu, “Hot spots in parametric fluorescence with pump beam of finite cross section,” IEEE J. Quantum Electron. 31, 769–781 (1995).
[CrossRef]

Kwait, P. G.

R. Y. Chiao, P. G. Kwait, and A. Steinberg, “Quantum nonlocality in two-photon experiments at Berkeley,” Quantum Semiclassic. Opt. 7, 259–278 (1995).
[CrossRef]

Liu, J. M.

K. Koch, E. C. Cheung, G. T. Moore, S. H. Chakmakjian, and J. M. Liu, “Hot spots in parametric fluorescence with pump beam of finite cross section,” IEEE J. Quantum Electron. 31, 769–781 (1995).
[CrossRef]

Mandel, L.

Z. Y. Ou and L. Mandel, “Violation of Bell’s inequality and classical probability in a two-photon correlation experiment,” Phys. Rev. Lett. 61, 50–53 (1988).
[CrossRef] [PubMed]

Migdall, A.

T. B. Pittman, D. V. Strekalov, A. Migdall, M. H. Rubin, A. V. Sergienko, and Y. H. Shih, “Can two-photon interference be considered the interference of two-photon?” Phys. Rev. Lett. 77, 1917–1920 (1996).
[CrossRef] [PubMed]

Moore, G. T.

K. Koch, E. C. Cheung, G. T. Moore, S. H. Chakmakjian, and J. M. Liu, “Hot spots in parametric fluorescence with pump beam of finite cross section,” IEEE J. Quantum Electron. 31, 769–781 (1995).
[CrossRef]

Ou, Z. Y.

Z. Y. Ou and L. Mandel, “Violation of Bell’s inequality and classical probability in a two-photon correlation experiment,” Phys. Rev. Lett. 61, 50–53 (1988).
[CrossRef] [PubMed]

Pittman, T. B.

T. B. Pittman, D. V. Strekalov, A. Migdall, M. H. Rubin, A. V. Sergienko, and Y. H. Shih, “Can two-photon interference be considered the interference of two-photon?” Phys. Rev. Lett. 77, 1917–1920 (1996).
[CrossRef] [PubMed]

Podolsky, B.

A. Einstein, B. Podolsky, and N. Rosen, “Can quantum-mechanical description of physical reality be considered complete?” Phys. Rev. 47, 777–780 (1935).
[CrossRef]

Rosen, N.

A. Einstein, B. Podolsky, and N. Rosen, “Can quantum-mechanical description of physical reality be considered complete?” Phys. Rev. 47, 777–780 (1935).
[CrossRef]

Rubin, M. H.

T. B. Pittman, D. V. Strekalov, A. Migdall, M. H. Rubin, A. V. Sergienko, and Y. H. Shih, “Can two-photon interference be considered the interference of two-photon?” Phys. Rev. Lett. 77, 1917–1920 (1996).
[CrossRef] [PubMed]

Sergienko, A. V.

T. B. Pittman, D. V. Strekalov, A. Migdall, M. H. Rubin, A. V. Sergienko, and Y. H. Shih, “Can two-photon interference be considered the interference of two-photon?” Phys. Rev. Lett. 77, 1917–1920 (1996).
[CrossRef] [PubMed]

T. E. Kiess, Y. H. Shih, A. V. Sergienko, and C. O. Alley, “Einstein–Podolsky–Rosen–Bohm experiment using pairs of light quanta produced by type-II parametric downconversion,” Phys. Rev. Lett. 71, 3893–3897 (1993).
[CrossRef] [PubMed]

Shih, Y. H.

T. B. Pittman, D. V. Strekalov, A. Migdall, M. H. Rubin, A. V. Sergienko, and Y. H. Shih, “Can two-photon interference be considered the interference of two-photon?” Phys. Rev. Lett. 77, 1917–1920 (1996).
[CrossRef] [PubMed]

T. E. Kiess, Y. H. Shih, A. V. Sergienko, and C. O. Alley, “Einstein–Podolsky–Rosen–Bohm experiment using pairs of light quanta produced by type-II parametric downconversion,” Phys. Rev. Lett. 71, 3893–3897 (1993).
[CrossRef] [PubMed]

Y. H. Shih and C. O. Alley, “New type of Einstein–Podolsky–Rosen–Bohm experiment using pairs of light quanta produced by optical parametric downconversion,” Phys. Rev. Lett. 61, 2921–2924 (1988).
[CrossRef] [PubMed]

Steinberg, A.

R. Y. Chiao, P. G. Kwait, and A. Steinberg, “Quantum nonlocality in two-photon experiments at Berkeley,” Quantum Semiclassic. Opt. 7, 259–278 (1995).
[CrossRef]

Strekalov, D. V.

T. B. Pittman, D. V. Strekalov, A. Migdall, M. H. Rubin, A. V. Sergienko, and Y. H. Shih, “Can two-photon interference be considered the interference of two-photon?” Phys. Rev. Lett. 77, 1917–1920 (1996).
[CrossRef] [PubMed]

IEEE J. Quantum Electron. (1)

K. Koch, E. C. Cheung, G. T. Moore, S. H. Chakmakjian, and J. M. Liu, “Hot spots in parametric fluorescence with pump beam of finite cross section,” IEEE J. Quantum Electron. 31, 769–781 (1995).
[CrossRef]

Phys. Rev. (1)

A. Einstein, B. Podolsky, and N. Rosen, “Can quantum-mechanical description of physical reality be considered complete?” Phys. Rev. 47, 777–780 (1935).
[CrossRef]

Phys. Rev. B (1)

M. Choy and R. L. Byer, “Accurate second-order susceptibility measurements of visible and infrared nonlinear crystals,” Phys. Rev. B 14, 1693–1706 (1976).
[CrossRef]

Phys. Rev. Lett. (4)

Z. Y. Ou and L. Mandel, “Violation of Bell’s inequality and classical probability in a two-photon correlation experiment,” Phys. Rev. Lett. 61, 50–53 (1988).
[CrossRef] [PubMed]

Y. H. Shih and C. O. Alley, “New type of Einstein–Podolsky–Rosen–Bohm experiment using pairs of light quanta produced by optical parametric downconversion,” Phys. Rev. Lett. 61, 2921–2924 (1988).
[CrossRef] [PubMed]

T. E. Kiess, Y. H. Shih, A. V. Sergienko, and C. O. Alley, “Einstein–Podolsky–Rosen–Bohm experiment using pairs of light quanta produced by type-II parametric downconversion,” Phys. Rev. Lett. 71, 3893–3897 (1993).
[CrossRef] [PubMed]

T. B. Pittman, D. V. Strekalov, A. Migdall, M. H. Rubin, A. V. Sergienko, and Y. H. Shih, “Can two-photon interference be considered the interference of two-photon?” Phys. Rev. Lett. 77, 1917–1920 (1996).
[CrossRef] [PubMed]

Quantum Semiclassic. Opt. (1)

R. Y. Chiao, P. G. Kwait, and A. Steinberg, “Quantum nonlocality in two-photon experiments at Berkeley,” Quantum Semiclassic. Opt. 7, 259–278 (1995).
[CrossRef]

Sov. J. Quantum Electron. (1)

D. N. Klyshko, “Utilization of vacuum fluctuations as an optical brightness standard,” Sov. J. Quantum Electron. 7, 591–595 (1977).
[CrossRef]

Other (5)

F. Zernike and J. E. Midwinter, Applied Nonlinear Optics (Wiley, New York, 1973), pp. 34–41.

Although this Kleinman symmetry assumption is best met for wavelengths shorter than 5 μm, where LiIO3 transmittance begins to fall off, the calculations here are carried out to 9 μm for better viewing of the results.

A. Yariv, Optical Electronics, 3rd ed. (Holt, Rinehart, & Winston, New York, 1985), Chap. 8, pp. 227–273.

D. N. Klyshko, Photons and Nonlinear Optics (Gordon & Breach, New York, 1988), Chap. 1, pp. 1–64; Chap. 6, pp. 285–357.

M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1993), pp. 679–680.

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Figures (4)

Fig. 1
Fig. 1

Pump beam, crystal, crystal optic axis C, and signal and idler PDC output cones at angles As and Ai. The azimuthal coordinate angle B is referenced to the y-axis direction.

Fig. 2
Fig. 2

ϕ, γ, β, coordinate system and the crystal optic axis tilted by angle Θ in the xz plane; β is the angle between z and P in the xz plane.

Fig. 3
Fig. 3

(a) Polarization angle β versus azimuthal angle B for various polar output angles A. (For polarization, 0° and 180° are not physically distinct, so the discontinuities shown are indicative of a nonzero winding number of the polarization direction.) (b) Polarization of PDC light emitted along any direction (ϕ, γ) is indicated by the angle of the dashes at that location. The center of symmetry at (ϕ, γ)=(0°, 35.3°) coincides with the crystal optic axis tilt, indicated by the black dot.

Fig. 4
Fig. 4

Left, relative map of PDC conversion efficiency versus ϕ and γ. To guide the eye, the gray scale from white to black indicates the graduation from high to low efficiency. The outer annulus covers the directions of idler output in the spectral region from 2.5 µm to 9.0 µm. The overlaid dashes show the polarization directions of PDC output light. (The efficiency along the positive γ axis near the optic axis is unity. The fact that the contours cut across the axis is an artifact of the contour plotting routine.) Right, the inner annulus covering the signal output directions is shown enlarged. The spectral range of this annulus covers 0.478 µm at its inner edge to 0.560 µm at the outer edge. This region is correlated to the 2.5–9.0 µm idler spectral range of the outer annulus.

Equations (11)

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ωp=ωs+ωi,
kp=ks+ki,
P(A, B)·C(Θ)=0,
β=tan-1-cos Θ cos ϕ sin γ+sin Θ cos γcos Θ sin ϕ.
ϕ=tan-1[tan A cos B],
γ=sin-1[sin A sin B],
P(ωs+ωi)=DEx(ωs)Ex(ωi)Ey(ωs)Ey(ωi)Ez(ωs)Ez(ωi)Ey(ωs)Ez(ωi)+Ez(ωs)Ey(ωi)Ez(ωs)Ex(ωi)+Ex(ωs)Ez(ωi)Ex(ωs)Ey(ωi)+Ey(ωs)Ex(ωi.
D=00d3100d3100d330d310d3100000,
Pzc(ωs+ωi)=d31[Exc(ωs)Exc(ωi)+Eyc(ωs)Eyc(ωi)]=d31(sin v sin w+cos v cos w)EsEi=d31 cos(v-w)EsEi.
Pz(ωs+ωi)=d31 sin Θ cos(v-w)EsEi,
deff=d31 cos Θ cos(v-w).

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