## Degenerate noncollinear emission from a type I collinear parametric oscillator

Optics Express, Vol. 9, Issue 1, pp. 16-23 (2001)

http://dx.doi.org/10.1364/OE.9.000016

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### Abstract

Noncollinear emission occurs in a free running type I parametric oscillator beyond the theoretical tuning curve for collinear oscillation. The noncollinear emission is described in terms of the emission angle and the corresponding angle of divergence. Experimentally recorded single captures of the transverse profile for the noncollinear regime are presented. A theoretical description of the degenerate tuning is described to explain the noncollinear regime.

© Optical Society of America

## Introduction

1. L. A. W. Gloster, Z. X. Jiang, and T. A. King, “Characterisation of a Nd:YAG Pumped β-BaB_{2}O_{4} Optical Parametric Oscillator in Collinear and Noncollinear phase matched configurations,” Quant. Elect. **30**, 2961–2969 (1994). [CrossRef]

## Theory of noncollinear interactions

1. L. A. W. Gloster, Z. X. Jiang, and T. A. King, “Characterisation of a Nd:YAG Pumped β-BaB_{2}O_{4} Optical Parametric Oscillator in Collinear and Noncollinear phase matched configurations,” Quant. Elect. **30**, 2961–2969 (1994). [CrossRef]

*p*,

*s*,

*i*represent the pump, signal and idler waves respectively. The noncollinearity, α, is the angle between the noncollinear and the corresponding collinear interactions. The frequencies, wavelengths and refractive indices of the three interacting waves are given by

*ω*,

_{j}*λ*and

_{j}*n*respectively. Tuning is achieved in the same way as in the collinear case by rotation of the non-linear optic crystal.

_{j}1. L. A. W. Gloster, Z. X. Jiang, and T. A. King, “Characterisation of a Nd:YAG Pumped β-BaB_{2}O_{4} Optical Parametric Oscillator in Collinear and Noncollinear phase matched configurations,” Quant. Elect. **30**, 2961–2969 (1994). [CrossRef]

## Observations of noncollinear emission

_{s}=ω

_{i}). The noncollinear emission angles presented in figure 4 are less than a factor of 2 smaller than the theoretical walk-off [2] experienced by the extraordinarily polarised pump beam, of 74 mrad, when passing through the non-linear BBO crystal. The theoretical pump walk-off changes less than 0.5 % over the non-collinear range presented. The divergence of the noncollinear emission is presented in Fig. 5. As can be deduced from Fig. 4 and 5 the larger the emission angle the smaller the divergence.

3. V. Krylov, A. Kalintsev, A. Rebane, D. Erni, and Urs P. Wild, “Noncollinear parametric generation in LiIO3 and β-barium borate by frequency-doubled femtosecond Ti:sapphire laser pulses,” Opt. Lett. **20**, 151–153 (1995). [CrossRef] [PubMed]

5. A. Berzanskis, W. Chinaglia, L. A. Lugiato, K. H. Feller, and P. Di Trapani, “Spatial structures in optical parametric amplification,” Phys. Rev. A **60**, 1626–1635 (1999). [CrossRef]

6. B. M. Jost, A. V. Sergienko, A. F. Arbouraddy, B. E. A. Saleh, and M. C. Teich, “Spatial correlation of spontaneously down-converted photon pairs detected with a single-photon-sensitive CCD camera,” Opt. Express **3**, 81–88 (1998), http://www.opticsexpress.org/oearchive/source/4652.htm. [CrossRef] [PubMed]

7. G-L. Oppo, M. Brambilla, and L. A. Lugiato, “Formation and evolution of roll patterns in optical parametric oscillators,” Phys. Rev. A **49**, 2028–2032 (1994). [CrossRef] [PubMed]

4. A. Gatti, L. A. Lugiato, G-L. Oppo, R. Martin, P. Di Trappani, and A. Berzanskis, “From quantum to classical images,” Opt. Express **1**, 21–30 (1997), http://www.opticsexpress.org/oearchive/source/1986.htm. [CrossRef] [PubMed]

7. G-L. Oppo, M. Brambilla, and L. A. Lugiato, “Formation and evolution of roll patterns in optical parametric oscillators,” Phys. Rev. A **49**, 2028–2032 (1994). [CrossRef] [PubMed]

## Discussion

3. V. Krylov, A. Kalintsev, A. Rebane, D. Erni, and Urs P. Wild, “Noncollinear parametric generation in LiIO3 and β-barium borate by frequency-doubled femtosecond Ti:sapphire laser pulses,” Opt. Lett. **20**, 151–153 (1995). [CrossRef] [PubMed]

## Acknowledgements

## References and links

1. | L. A. W. Gloster, Z. X. Jiang, and T. A. King, “Characterisation of a Nd:YAG Pumped β-BaB |

2. | V. G. Dmitriev, G. G. Gurzadayan, and D. N. Nikogosyan, “Handbook of nonlinear optic crystals,” Springer-Verlag, (1991). |

3. | V. Krylov, A. Kalintsev, A. Rebane, D. Erni, and Urs P. Wild, “Noncollinear parametric generation in LiIO3 and β-barium borate by frequency-doubled femtosecond Ti:sapphire laser pulses,” Opt. Lett. |

4. | A. Gatti, L. A. Lugiato, G-L. Oppo, R. Martin, P. Di Trappani, and A. Berzanskis, “From quantum to classical images,” Opt. Express |

5. | A. Berzanskis, W. Chinaglia, L. A. Lugiato, K. H. Feller, and P. Di Trapani, “Spatial structures in optical parametric amplification,” Phys. Rev. A |

6. | B. M. Jost, A. V. Sergienko, A. F. Arbouraddy, B. E. A. Saleh, and M. C. Teich, “Spatial correlation of spontaneously down-converted photon pairs detected with a single-photon-sensitive CCD camera,” Opt. Express |

7. | G-L. Oppo, M. Brambilla, and L. A. Lugiato, “Formation and evolution of roll patterns in optical parametric oscillators,” Phys. Rev. A |

**OCIS Codes**

(140.4780) Lasers and laser optics : Optical resonators

(190.4410) Nonlinear optics : Nonlinear optics, parametric processes

(190.4420) Nonlinear optics : Nonlinear optics, transverse effects in

(190.4970) Nonlinear optics : Parametric oscillators and amplifiers

**ToC Category:**

Research Papers

**History**

Original Manuscript: May 8, 2001

Published: July 2, 2001

**Citation**

Matthew Shelton and David West, "Degenerate noncollinear emission from a type I collinear parametric oscillator," Opt. Express **9**, 16-23 (2001)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-9-1-16

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### References

- L. A. W. Gloster, Z. X. Jiang, and T. A. King, "Characterisation of a Nd:YAG Pumped � -BaB2O4 Optical Parametric Oscillator in Collinear and Noncollinear phase matched configurations," Quant. Elect. 30, 2961- 2969 (1994). [CrossRef]
- V. G. Dmitriev, G. G. Gurzadayan, D. N. Nikogosyan, "Handbook of nonlinear optic crystals," Springer-Verlag, (1991).
- V. Krylov, A. Kalintsev, A. Rebane, D. Erni and Urs P. Wild, "Noncollinear parametric generation in LiIO3 and �-barium borate by frequency-doubled femtosecond Ti:sapphire laser pulses," Opt. Lett. 20, 151-153 (1995). [CrossRef] [PubMed]
- A. Gatti, L. A. Lugiato, G-L. Oppo, R. Martin, P. Di Trappani and A. Berzanskis, "From quantum to classical images," Opt. Express 1, 21-30 (1997), http://www.opticsexpress.org/oearchive/source/1986.htm. [CrossRef] [PubMed]
- A. Berzanskis, W. Chinaglia, L. A. Lugiato, K. H. Feller and P. Di Trapani, "Spatial structures in optical parametric amplification," Phys. Rev. A 60, 1626-1635 (1999). [CrossRef]
- B. M. Jost, A. V. Sergienko, A. F. Arbouraddy, B. E. A. Saleh and M. C. Teich, "Spatial correlation of spontaneously down-converted photon pairs detected with a single-photon-sensitive CCD camera," Opt. Express 3, 81-88 (1998), http://www.opticsexpress.org/oearchive/source/4652.htm. [CrossRef] [PubMed]
- G-L. Oppo, M. Brambilla, L. A. Lugiato, "Formation and evolution of roll patterns in optical parametric oscillators," Phys. Rev. A 49, 2028-2032 (1994). [CrossRef] [PubMed]

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