Abstract

We analyse a method to compensate for anisotropy effects in the spatial distribution of parametric down-conversion (PDC) radiation in bulk crystals. In this method, a single nonlinear crystal is replaced by two consecutive crystals with opposite transverse walk-off directions. We implement a simple numerical model to calculate the spatial distribution of intensity and correlations, as well as the Schmidt mode structure, with an account for the anisotropy. Experimental results are presented which prove the validity of both the model and the method.

© 2014 Optical Society of America

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  1. D. C. Burnham, D. L. Weinberg, “Observation of Simultaneity in Parametric Production of Optical Photon Pairs,” Phys. Rev. Lett. 25,84 (1970).
    [CrossRef]
  2. T. Sh. Iskhakov, A. M. Pérez, K. Yu. Spasibko, M. V. Chekhova, G. Leuchs, “Superbunched bright squeezed vacuum state,” Opt. Lett. 37, 1919–1921 (2012).
    [CrossRef] [PubMed]
  3. K. Yu. Spasibko, T. Sh. Iskhakov, M. V. Chekhova, “Spectral properties of high-gain parametric down-conversion,” Opt. Express 20, 7507–7515 (2012).
    [CrossRef] [PubMed]
  4. P. J. Mosley, J. S. Lundeen, B. J. Smith, P. Wasylczyk, A. B. U’Ren, C. Silberhorn, I. A. Walmsley, “Heralded generation of ultrafast single photons in pure quantum states,” Phys. Rev. Lett. 100,133601 (2008).
    [CrossRef] [PubMed]
  5. A. M. Brańczyk, T. C. Ralph, W. Helwig, C. Silberhorn, “Optimized generation of heralded Fock states using parametric down-conversion,” New J. Phys. 12,063001 (2010).
    [CrossRef]
  6. S. S. Straupe, D. P. Ivanov, A. A. Kalinkin, I. B. Bobrov, S. P. Kulik, “Angular Schmidt modes in spontaneous parametric down-conversion,” Phys. Rev. A 83,060302 (2011).
    [CrossRef]
  7. P. B. Dixon, J. H. Shapiro, F. N. C. Wong, “Spectral engineering by Gaussian phase-matching for quantum photonics,” Opt. Express 21, 5879–5890 (2013).
    [CrossRef] [PubMed]
  8. M. V. Fedorov, M. A. Efremov, P. A. Volkov, J. H. Eberly, “Short-pulse or strong-field breakup processes: a route to study entangled wave packets,” J. Phys. B: At. Mol. Opt. Phys. 39,467 (2006).
    [CrossRef]
  9. S. P. Walborn, A. H. Pimentel, “Generalized Hermite-Gauss decomposition of the two-photon state produced by spontaneous parametric down conversion,” J. Phys. B: At. Mol. Opt. Phys. 45,165502 (2012).
    [CrossRef]
  10. M. V. Fedorov, M. A. Efremov, P. A. Volkov, E. V. Moreva, S. S. Straupe, S. P. Kulik, “Anisotropically and High Entanglement of Biphotons States Generated in Spontaneous Parametric Down-Conversion,” Phys. Rev. Lett. 99,063901 (2007).
    [CrossRef]
  11. W. R. Bosenberg, W. S. Pelouch, C. L. Tang, “High-efficiency and narrow-linewidth operation of a two-crystal β-BaB2O4 optical parametric oscillator,” Appl. Phys. Lett. 55,1952 (1989).
    [CrossRef]
  12. D. J. Armstrong, W. J. Alford, T. D. Raymond, A. V. Smith, M. S. Bowers, “Parametric amplification and oscillation with walkoff-compensating crystals,” J. Opt. Soc. Am. B 14, 460–474 (1997).
    [CrossRef]
  13. R. E. Slusher, P. Grangier, A. LaPorta, B. Yurke, M. J. Potasek, “Pulsed Squeezed Light,” Phys. Rev. Lett. 59,2566–2569 (1987).
    [CrossRef]
  14. A. M. Pérez, F. Just, A. Cavanna, M. V. Chekhova, G. Leuchs, “Compensation of anisotropy effects in a nonlinear crystal for squeezed vacuum generation,” Laser Phys. Lett. 10,125201 (2013).
    [CrossRef]
  15. D. Klyshko, Photons and Nonlinear Optics (Gordon and Beach, 1988).
  16. J.-J. Zondy, M. Abed, S. Khodja, “Twin-crystal walk-off-compensated type-II second-harmonic generation: single-pass and cavity-enhanced experiments in KTiOPO4,” J. Opt. Soc. Am. B 11,2368 (1994).
    [CrossRef]
  17. A. V. Burlakov, M. V. Chekhova, D. N. Klyshko, S. P. Kulik, A. N. Penin, Y. H. Shih, D. V. Strekalov, “Interference effects in spontaneous two-photon parametric scattering from two macroscopic regions,” Phys. Rev. A 56,3214 (1997).
    [CrossRef]

2013 (2)

P. B. Dixon, J. H. Shapiro, F. N. C. Wong, “Spectral engineering by Gaussian phase-matching for quantum photonics,” Opt. Express 21, 5879–5890 (2013).
[CrossRef] [PubMed]

A. M. Pérez, F. Just, A. Cavanna, M. V. Chekhova, G. Leuchs, “Compensation of anisotropy effects in a nonlinear crystal for squeezed vacuum generation,” Laser Phys. Lett. 10,125201 (2013).
[CrossRef]

2012 (3)

2011 (1)

S. S. Straupe, D. P. Ivanov, A. A. Kalinkin, I. B. Bobrov, S. P. Kulik, “Angular Schmidt modes in spontaneous parametric down-conversion,” Phys. Rev. A 83,060302 (2011).
[CrossRef]

2010 (1)

A. M. Brańczyk, T. C. Ralph, W. Helwig, C. Silberhorn, “Optimized generation of heralded Fock states using parametric down-conversion,” New J. Phys. 12,063001 (2010).
[CrossRef]

2008 (1)

P. J. Mosley, J. S. Lundeen, B. J. Smith, P. Wasylczyk, A. B. U’Ren, C. Silberhorn, I. A. Walmsley, “Heralded generation of ultrafast single photons in pure quantum states,” Phys. Rev. Lett. 100,133601 (2008).
[CrossRef] [PubMed]

2007 (1)

M. V. Fedorov, M. A. Efremov, P. A. Volkov, E. V. Moreva, S. S. Straupe, S. P. Kulik, “Anisotropically and High Entanglement of Biphotons States Generated in Spontaneous Parametric Down-Conversion,” Phys. Rev. Lett. 99,063901 (2007).
[CrossRef]

2006 (1)

M. V. Fedorov, M. A. Efremov, P. A. Volkov, J. H. Eberly, “Short-pulse or strong-field breakup processes: a route to study entangled wave packets,” J. Phys. B: At. Mol. Opt. Phys. 39,467 (2006).
[CrossRef]

1997 (2)

A. V. Burlakov, M. V. Chekhova, D. N. Klyshko, S. P. Kulik, A. N. Penin, Y. H. Shih, D. V. Strekalov, “Interference effects in spontaneous two-photon parametric scattering from two macroscopic regions,” Phys. Rev. A 56,3214 (1997).
[CrossRef]

D. J. Armstrong, W. J. Alford, T. D. Raymond, A. V. Smith, M. S. Bowers, “Parametric amplification and oscillation with walkoff-compensating crystals,” J. Opt. Soc. Am. B 14, 460–474 (1997).
[CrossRef]

1994 (1)

1989 (1)

W. R. Bosenberg, W. S. Pelouch, C. L. Tang, “High-efficiency and narrow-linewidth operation of a two-crystal β-BaB2O4 optical parametric oscillator,” Appl. Phys. Lett. 55,1952 (1989).
[CrossRef]

1987 (1)

R. E. Slusher, P. Grangier, A. LaPorta, B. Yurke, M. J. Potasek, “Pulsed Squeezed Light,” Phys. Rev. Lett. 59,2566–2569 (1987).
[CrossRef]

1970 (1)

D. C. Burnham, D. L. Weinberg, “Observation of Simultaneity in Parametric Production of Optical Photon Pairs,” Phys. Rev. Lett. 25,84 (1970).
[CrossRef]

Abed, M.

Alford, W. J.

Armstrong, D. J.

Bobrov, I. B.

S. S. Straupe, D. P. Ivanov, A. A. Kalinkin, I. B. Bobrov, S. P. Kulik, “Angular Schmidt modes in spontaneous parametric down-conversion,” Phys. Rev. A 83,060302 (2011).
[CrossRef]

Bosenberg, W. R.

W. R. Bosenberg, W. S. Pelouch, C. L. Tang, “High-efficiency and narrow-linewidth operation of a two-crystal β-BaB2O4 optical parametric oscillator,” Appl. Phys. Lett. 55,1952 (1989).
[CrossRef]

Bowers, M. S.

Branczyk, A. M.

A. M. Brańczyk, T. C. Ralph, W. Helwig, C. Silberhorn, “Optimized generation of heralded Fock states using parametric down-conversion,” New J. Phys. 12,063001 (2010).
[CrossRef]

Burlakov, A. V.

A. V. Burlakov, M. V. Chekhova, D. N. Klyshko, S. P. Kulik, A. N. Penin, Y. H. Shih, D. V. Strekalov, “Interference effects in spontaneous two-photon parametric scattering from two macroscopic regions,” Phys. Rev. A 56,3214 (1997).
[CrossRef]

Burnham, D. C.

D. C. Burnham, D. L. Weinberg, “Observation of Simultaneity in Parametric Production of Optical Photon Pairs,” Phys. Rev. Lett. 25,84 (1970).
[CrossRef]

Cavanna, A.

A. M. Pérez, F. Just, A. Cavanna, M. V. Chekhova, G. Leuchs, “Compensation of anisotropy effects in a nonlinear crystal for squeezed vacuum generation,” Laser Phys. Lett. 10,125201 (2013).
[CrossRef]

Chekhova, M. V.

A. M. Pérez, F. Just, A. Cavanna, M. V. Chekhova, G. Leuchs, “Compensation of anisotropy effects in a nonlinear crystal for squeezed vacuum generation,” Laser Phys. Lett. 10,125201 (2013).
[CrossRef]

T. Sh. Iskhakov, A. M. Pérez, K. Yu. Spasibko, M. V. Chekhova, G. Leuchs, “Superbunched bright squeezed vacuum state,” Opt. Lett. 37, 1919–1921 (2012).
[CrossRef] [PubMed]

K. Yu. Spasibko, T. Sh. Iskhakov, M. V. Chekhova, “Spectral properties of high-gain parametric down-conversion,” Opt. Express 20, 7507–7515 (2012).
[CrossRef] [PubMed]

A. V. Burlakov, M. V. Chekhova, D. N. Klyshko, S. P. Kulik, A. N. Penin, Y. H. Shih, D. V. Strekalov, “Interference effects in spontaneous two-photon parametric scattering from two macroscopic regions,” Phys. Rev. A 56,3214 (1997).
[CrossRef]

Dixon, P. B.

Eberly, J. H.

M. V. Fedorov, M. A. Efremov, P. A. Volkov, J. H. Eberly, “Short-pulse or strong-field breakup processes: a route to study entangled wave packets,” J. Phys. B: At. Mol. Opt. Phys. 39,467 (2006).
[CrossRef]

Efremov, M. A.

M. V. Fedorov, M. A. Efremov, P. A. Volkov, E. V. Moreva, S. S. Straupe, S. P. Kulik, “Anisotropically and High Entanglement of Biphotons States Generated in Spontaneous Parametric Down-Conversion,” Phys. Rev. Lett. 99,063901 (2007).
[CrossRef]

M. V. Fedorov, M. A. Efremov, P. A. Volkov, J. H. Eberly, “Short-pulse or strong-field breakup processes: a route to study entangled wave packets,” J. Phys. B: At. Mol. Opt. Phys. 39,467 (2006).
[CrossRef]

Fedorov, M. V.

M. V. Fedorov, M. A. Efremov, P. A. Volkov, E. V. Moreva, S. S. Straupe, S. P. Kulik, “Anisotropically and High Entanglement of Biphotons States Generated in Spontaneous Parametric Down-Conversion,” Phys. Rev. Lett. 99,063901 (2007).
[CrossRef]

M. V. Fedorov, M. A. Efremov, P. A. Volkov, J. H. Eberly, “Short-pulse or strong-field breakup processes: a route to study entangled wave packets,” J. Phys. B: At. Mol. Opt. Phys. 39,467 (2006).
[CrossRef]

Grangier, P.

R. E. Slusher, P. Grangier, A. LaPorta, B. Yurke, M. J. Potasek, “Pulsed Squeezed Light,” Phys. Rev. Lett. 59,2566–2569 (1987).
[CrossRef]

Helwig, W.

A. M. Brańczyk, T. C. Ralph, W. Helwig, C. Silberhorn, “Optimized generation of heralded Fock states using parametric down-conversion,” New J. Phys. 12,063001 (2010).
[CrossRef]

Iskhakov, T. Sh.

Ivanov, D. P.

S. S. Straupe, D. P. Ivanov, A. A. Kalinkin, I. B. Bobrov, S. P. Kulik, “Angular Schmidt modes in spontaneous parametric down-conversion,” Phys. Rev. A 83,060302 (2011).
[CrossRef]

Just, F.

A. M. Pérez, F. Just, A. Cavanna, M. V. Chekhova, G. Leuchs, “Compensation of anisotropy effects in a nonlinear crystal for squeezed vacuum generation,” Laser Phys. Lett. 10,125201 (2013).
[CrossRef]

Kalinkin, A. A.

S. S. Straupe, D. P. Ivanov, A. A. Kalinkin, I. B. Bobrov, S. P. Kulik, “Angular Schmidt modes in spontaneous parametric down-conversion,” Phys. Rev. A 83,060302 (2011).
[CrossRef]

Khodja, S.

Klyshko, D.

D. Klyshko, Photons and Nonlinear Optics (Gordon and Beach, 1988).

Klyshko, D. N.

A. V. Burlakov, M. V. Chekhova, D. N. Klyshko, S. P. Kulik, A. N. Penin, Y. H. Shih, D. V. Strekalov, “Interference effects in spontaneous two-photon parametric scattering from two macroscopic regions,” Phys. Rev. A 56,3214 (1997).
[CrossRef]

Kulik, S. P.

S. S. Straupe, D. P. Ivanov, A. A. Kalinkin, I. B. Bobrov, S. P. Kulik, “Angular Schmidt modes in spontaneous parametric down-conversion,” Phys. Rev. A 83,060302 (2011).
[CrossRef]

M. V. Fedorov, M. A. Efremov, P. A. Volkov, E. V. Moreva, S. S. Straupe, S. P. Kulik, “Anisotropically and High Entanglement of Biphotons States Generated in Spontaneous Parametric Down-Conversion,” Phys. Rev. Lett. 99,063901 (2007).
[CrossRef]

A. V. Burlakov, M. V. Chekhova, D. N. Klyshko, S. P. Kulik, A. N. Penin, Y. H. Shih, D. V. Strekalov, “Interference effects in spontaneous two-photon parametric scattering from two macroscopic regions,” Phys. Rev. A 56,3214 (1997).
[CrossRef]

LaPorta, A.

R. E. Slusher, P. Grangier, A. LaPorta, B. Yurke, M. J. Potasek, “Pulsed Squeezed Light,” Phys. Rev. Lett. 59,2566–2569 (1987).
[CrossRef]

Leuchs, G.

A. M. Pérez, F. Just, A. Cavanna, M. V. Chekhova, G. Leuchs, “Compensation of anisotropy effects in a nonlinear crystal for squeezed vacuum generation,” Laser Phys. Lett. 10,125201 (2013).
[CrossRef]

T. Sh. Iskhakov, A. M. Pérez, K. Yu. Spasibko, M. V. Chekhova, G. Leuchs, “Superbunched bright squeezed vacuum state,” Opt. Lett. 37, 1919–1921 (2012).
[CrossRef] [PubMed]

Lundeen, J. S.

P. J. Mosley, J. S. Lundeen, B. J. Smith, P. Wasylczyk, A. B. U’Ren, C. Silberhorn, I. A. Walmsley, “Heralded generation of ultrafast single photons in pure quantum states,” Phys. Rev. Lett. 100,133601 (2008).
[CrossRef] [PubMed]

Moreva, E. V.

M. V. Fedorov, M. A. Efremov, P. A. Volkov, E. V. Moreva, S. S. Straupe, S. P. Kulik, “Anisotropically and High Entanglement of Biphotons States Generated in Spontaneous Parametric Down-Conversion,” Phys. Rev. Lett. 99,063901 (2007).
[CrossRef]

Mosley, P. J.

P. J. Mosley, J. S. Lundeen, B. J. Smith, P. Wasylczyk, A. B. U’Ren, C. Silberhorn, I. A. Walmsley, “Heralded generation of ultrafast single photons in pure quantum states,” Phys. Rev. Lett. 100,133601 (2008).
[CrossRef] [PubMed]

Pelouch, W. S.

W. R. Bosenberg, W. S. Pelouch, C. L. Tang, “High-efficiency and narrow-linewidth operation of a two-crystal β-BaB2O4 optical parametric oscillator,” Appl. Phys. Lett. 55,1952 (1989).
[CrossRef]

Penin, A. N.

A. V. Burlakov, M. V. Chekhova, D. N. Klyshko, S. P. Kulik, A. N. Penin, Y. H. Shih, D. V. Strekalov, “Interference effects in spontaneous two-photon parametric scattering from two macroscopic regions,” Phys. Rev. A 56,3214 (1997).
[CrossRef]

Pérez, A. M.

A. M. Pérez, F. Just, A. Cavanna, M. V. Chekhova, G. Leuchs, “Compensation of anisotropy effects in a nonlinear crystal for squeezed vacuum generation,” Laser Phys. Lett. 10,125201 (2013).
[CrossRef]

T. Sh. Iskhakov, A. M. Pérez, K. Yu. Spasibko, M. V. Chekhova, G. Leuchs, “Superbunched bright squeezed vacuum state,” Opt. Lett. 37, 1919–1921 (2012).
[CrossRef] [PubMed]

Pimentel, A. H.

S. P. Walborn, A. H. Pimentel, “Generalized Hermite-Gauss decomposition of the two-photon state produced by spontaneous parametric down conversion,” J. Phys. B: At. Mol. Opt. Phys. 45,165502 (2012).
[CrossRef]

Potasek, M. J.

R. E. Slusher, P. Grangier, A. LaPorta, B. Yurke, M. J. Potasek, “Pulsed Squeezed Light,” Phys. Rev. Lett. 59,2566–2569 (1987).
[CrossRef]

Ralph, T. C.

A. M. Brańczyk, T. C. Ralph, W. Helwig, C. Silberhorn, “Optimized generation of heralded Fock states using parametric down-conversion,” New J. Phys. 12,063001 (2010).
[CrossRef]

Raymond, T. D.

Shapiro, J. H.

Shih, Y. H.

A. V. Burlakov, M. V. Chekhova, D. N. Klyshko, S. P. Kulik, A. N. Penin, Y. H. Shih, D. V. Strekalov, “Interference effects in spontaneous two-photon parametric scattering from two macroscopic regions,” Phys. Rev. A 56,3214 (1997).
[CrossRef]

Silberhorn, C.

A. M. Brańczyk, T. C. Ralph, W. Helwig, C. Silberhorn, “Optimized generation of heralded Fock states using parametric down-conversion,” New J. Phys. 12,063001 (2010).
[CrossRef]

P. J. Mosley, J. S. Lundeen, B. J. Smith, P. Wasylczyk, A. B. U’Ren, C. Silberhorn, I. A. Walmsley, “Heralded generation of ultrafast single photons in pure quantum states,” Phys. Rev. Lett. 100,133601 (2008).
[CrossRef] [PubMed]

Slusher, R. E.

R. E. Slusher, P. Grangier, A. LaPorta, B. Yurke, M. J. Potasek, “Pulsed Squeezed Light,” Phys. Rev. Lett. 59,2566–2569 (1987).
[CrossRef]

Smith, A. V.

Smith, B. J.

P. J. Mosley, J. S. Lundeen, B. J. Smith, P. Wasylczyk, A. B. U’Ren, C. Silberhorn, I. A. Walmsley, “Heralded generation of ultrafast single photons in pure quantum states,” Phys. Rev. Lett. 100,133601 (2008).
[CrossRef] [PubMed]

Spasibko, K. Yu.

Straupe, S. S.

S. S. Straupe, D. P. Ivanov, A. A. Kalinkin, I. B. Bobrov, S. P. Kulik, “Angular Schmidt modes in spontaneous parametric down-conversion,” Phys. Rev. A 83,060302 (2011).
[CrossRef]

M. V. Fedorov, M. A. Efremov, P. A. Volkov, E. V. Moreva, S. S. Straupe, S. P. Kulik, “Anisotropically and High Entanglement of Biphotons States Generated in Spontaneous Parametric Down-Conversion,” Phys. Rev. Lett. 99,063901 (2007).
[CrossRef]

Strekalov, D. V.

A. V. Burlakov, M. V. Chekhova, D. N. Klyshko, S. P. Kulik, A. N. Penin, Y. H. Shih, D. V. Strekalov, “Interference effects in spontaneous two-photon parametric scattering from two macroscopic regions,” Phys. Rev. A 56,3214 (1997).
[CrossRef]

Tang, C. L.

W. R. Bosenberg, W. S. Pelouch, C. L. Tang, “High-efficiency and narrow-linewidth operation of a two-crystal β-BaB2O4 optical parametric oscillator,” Appl. Phys. Lett. 55,1952 (1989).
[CrossRef]

U’Ren, A. B.

P. J. Mosley, J. S. Lundeen, B. J. Smith, P. Wasylczyk, A. B. U’Ren, C. Silberhorn, I. A. Walmsley, “Heralded generation of ultrafast single photons in pure quantum states,” Phys. Rev. Lett. 100,133601 (2008).
[CrossRef] [PubMed]

Volkov, P. A.

M. V. Fedorov, M. A. Efremov, P. A. Volkov, E. V. Moreva, S. S. Straupe, S. P. Kulik, “Anisotropically and High Entanglement of Biphotons States Generated in Spontaneous Parametric Down-Conversion,” Phys. Rev. Lett. 99,063901 (2007).
[CrossRef]

M. V. Fedorov, M. A. Efremov, P. A. Volkov, J. H. Eberly, “Short-pulse or strong-field breakup processes: a route to study entangled wave packets,” J. Phys. B: At. Mol. Opt. Phys. 39,467 (2006).
[CrossRef]

Walborn, S. P.

S. P. Walborn, A. H. Pimentel, “Generalized Hermite-Gauss decomposition of the two-photon state produced by spontaneous parametric down conversion,” J. Phys. B: At. Mol. Opt. Phys. 45,165502 (2012).
[CrossRef]

Walmsley, I. A.

P. J. Mosley, J. S. Lundeen, B. J. Smith, P. Wasylczyk, A. B. U’Ren, C. Silberhorn, I. A. Walmsley, “Heralded generation of ultrafast single photons in pure quantum states,” Phys. Rev. Lett. 100,133601 (2008).
[CrossRef] [PubMed]

Wasylczyk, P.

P. J. Mosley, J. S. Lundeen, B. J. Smith, P. Wasylczyk, A. B. U’Ren, C. Silberhorn, I. A. Walmsley, “Heralded generation of ultrafast single photons in pure quantum states,” Phys. Rev. Lett. 100,133601 (2008).
[CrossRef] [PubMed]

Weinberg, D. L.

D. C. Burnham, D. L. Weinberg, “Observation of Simultaneity in Parametric Production of Optical Photon Pairs,” Phys. Rev. Lett. 25,84 (1970).
[CrossRef]

Wong, F. N. C.

Yurke, B.

R. E. Slusher, P. Grangier, A. LaPorta, B. Yurke, M. J. Potasek, “Pulsed Squeezed Light,” Phys. Rev. Lett. 59,2566–2569 (1987).
[CrossRef]

Zondy, J.-J.

Appl. Phys. Lett. (1)

W. R. Bosenberg, W. S. Pelouch, C. L. Tang, “High-efficiency and narrow-linewidth operation of a two-crystal β-BaB2O4 optical parametric oscillator,” Appl. Phys. Lett. 55,1952 (1989).
[CrossRef]

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

J. Phys. B: At. Mol. Opt. Phys. (2)

M. V. Fedorov, M. A. Efremov, P. A. Volkov, J. H. Eberly, “Short-pulse or strong-field breakup processes: a route to study entangled wave packets,” J. Phys. B: At. Mol. Opt. Phys. 39,467 (2006).
[CrossRef]

S. P. Walborn, A. H. Pimentel, “Generalized Hermite-Gauss decomposition of the two-photon state produced by spontaneous parametric down conversion,” J. Phys. B: At. Mol. Opt. Phys. 45,165502 (2012).
[CrossRef]

Laser Phys. Lett. (1)

A. M. Pérez, F. Just, A. Cavanna, M. V. Chekhova, G. Leuchs, “Compensation of anisotropy effects in a nonlinear crystal for squeezed vacuum generation,” Laser Phys. Lett. 10,125201 (2013).
[CrossRef]

New J. Phys. (1)

A. M. Brańczyk, T. C. Ralph, W. Helwig, C. Silberhorn, “Optimized generation of heralded Fock states using parametric down-conversion,” New J. Phys. 12,063001 (2010).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Phys. Rev. A (2)

A. V. Burlakov, M. V. Chekhova, D. N. Klyshko, S. P. Kulik, A. N. Penin, Y. H. Shih, D. V. Strekalov, “Interference effects in spontaneous two-photon parametric scattering from two macroscopic regions,” Phys. Rev. A 56,3214 (1997).
[CrossRef]

S. S. Straupe, D. P. Ivanov, A. A. Kalinkin, I. B. Bobrov, S. P. Kulik, “Angular Schmidt modes in spontaneous parametric down-conversion,” Phys. Rev. A 83,060302 (2011).
[CrossRef]

Phys. Rev. Lett. (4)

M. V. Fedorov, M. A. Efremov, P. A. Volkov, E. V. Moreva, S. S. Straupe, S. P. Kulik, “Anisotropically and High Entanglement of Biphotons States Generated in Spontaneous Parametric Down-Conversion,” Phys. Rev. Lett. 99,063901 (2007).
[CrossRef]

R. E. Slusher, P. Grangier, A. LaPorta, B. Yurke, M. J. Potasek, “Pulsed Squeezed Light,” Phys. Rev. Lett. 59,2566–2569 (1987).
[CrossRef]

P. J. Mosley, J. S. Lundeen, B. J. Smith, P. Wasylczyk, A. B. U’Ren, C. Silberhorn, I. A. Walmsley, “Heralded generation of ultrafast single photons in pure quantum states,” Phys. Rev. Lett. 100,133601 (2008).
[CrossRef] [PubMed]

D. C. Burnham, D. L. Weinberg, “Observation of Simultaneity in Parametric Production of Optical Photon Pairs,” Phys. Rev. Lett. 25,84 (1970).
[CrossRef]

Other (1)

D. Klyshko, Photons and Nonlinear Optics (Gordon and Beach, 1988).

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Figures (8)

Fig. 1
Fig. 1

(a) Transverse walk-off effect: an extraordinarily polarised beam impinging on a crystal normally is tilted while inside. The walk-off angle ρ depends on the angle of the pump wave vector with the optic axis C and the crystal birefringence. (b) Compensation of the anisotropy effect is obtained by using two crystals with the optic axes tilted in opposite directions. In the two crystals, the walk-off, as well as the anisotropy, manifests itself in the opposite directions, so the effects cancel each other.

Fig. 2
Fig. 2

(a) Front view of the crystal with the principal plane (shown by dashed line) tilted by an angle α with respect to the plane xz in which the angular spectra are considered. (b) Tilted frame of reference in the principal plane for the case α = 0.

Fig. 3
Fig. 3

The experimental setup: L1 is a lens with f = 100 mm, L2 and L3 have f = 200 mm, DM is a dichroic mirror, IF is the interference filter and D1 and D2 are modules containing the detectors.

Fig. 4
Fig. 4

(a) TPA in the far field generated by 1 mm BBO crystal with type-I collinear phase-matching. (b) The measured intensity distribution (blue points) and the theoretical prediction (red line).

Fig. 5
Fig. 5

Theoretical and experimental TPA distributions in the non-compensation configuration.

Fig. 6
Fig. 6

Theoretical and experimental TPA distributions obtained in the configuration of anisotropy compensation.

Fig. 7
Fig. 7

Theoretical and experimental TPA distributions for the ‘weak anisotropy’ configuration.

Fig. 8
Fig. 8

a) First Schmidt mode (red line) for one crystal of 2 mm compared to a gaussian fit (blue line). b) First Schmidt mode for two crystals of 1 mm in the compensation configuration.

Equations (7)

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| ψ = d θ s d θ i F ( θ s , θ i ) a ^ s a ^ i | 0 ,
| ψ = exp ( 1 i h ¯ d t H ) | 0 .
H ^ d V χ ( 2 ) ( E p ( + ) E s ( ) E i ( ) + h . c . ) ,
x = [ ( y sin α + x cos α ) cos ρ z sin ρ ] cos α ( y cos α x sin α ) sin α y = ( y cos α x sin α ) cos α + [ ( y sin α + x cos α ) cos ρ z sin ρ ] sin α z = ( y sin α + x cos α ) sin ρ + z cos ρ .
F ( θ s , θ i ) = d x d y L / 2 cos ρ L / 2 cos ρ d z exp ( x 2 + y 2 2 σ 2 ) exp ( i Δ k x x + i Δ k y y + i Δ k z z ) ,
F ( θ s , θ i ) = F 1 ( θ s , θ i ) exp [ i ϕ ] + F 2 ( θ s , θ i ) ,
| ψ = n = 0 λ n ϕ n ( s ) ϕ n ( i ) ,

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