## Spontaneous parametric down-conversion in periodically poled KTP waveguides and bulk crystals

Optics Express, Vol. 15, Issue 12, pp. 7479-7488 (2007)

http://dx.doi.org/10.1364/OE.15.007479

Acrobat PDF (273 KB)

### Abstract

We present a theoretical and experimental comparison of spontaneous parametric down-conversion in periodically poled waveguides and bulk KTP crystals. We measured a waveguide pair generation rate of 2.9∙10^{6} pairs/s per mW of pump in a 1-nm band: more than 50 times higher than the bulk crystal generation rate.

© 2007 Optical Society of America

## 1. Introduction

8. K. Koch, E. C. Cheung, G. T. Moore, S. H. Chakmakjian, and J. M. Liu, “Hot Spots in Parametric Fluorescence with a Pump Beam of Finite Cross Section,” IEEE J. of Quantum Electron. **31**769 (1995). [CrossRef]

## 2. Theory

*d*is the effective nonlinear coefficient,

*ℒ*is the crystal length,

*ω*are the signal, idler, and pump frequencies,

_{s,i,p}*λ*are the signal idler, and pump wavelengths,

_{s,i,p}*c*is the speed of light in vacuum,

*ε*

_{0}is the permittivity of vacuum,

*n*is the crystal refractive index at the pump wavelength, and

_{p}*𝓟*is the pump power. The function

_{p}*f*(

*λ*) is added to keep into account the collinear geometry and is

_{s}*ω*= 2

_{s}*πc*/

*λ*- and

_{s}*γ*is defined in terms of the derivatives of the phase mismatch Δ

*k*,

*ω¯*is the degenerate frequency for collinear phase matching. Observe that the spectral density in 1 is approximately constant with frequency except for the factor

*f*: for

*ω*≪

_{s}*ω¯f*→ 1 and we recover the result of Ref. [8

8. K. Koch, E. C. Cheung, G. T. Moore, S. H. Chakmakjian, and J. M. Liu, “Hot Spots in Parametric Fluorescence with a Pump Beam of Finite Cross Section,” IEEE J. of Quantum Electron. **31**769 (1995). [CrossRef]

*ω*=

_{s}*ω¯*and

*f*= 1/2. For our simulations it is safe to assume that we are slightly off the perfect collinear condition and take

*f*= 1. Note that the signal power in 1 scales linearly with the pump power and crystal length while it is independent of the pump beam shape (although the result was obtained for gaussian beams). The result in Eq. 1 seems to imply that one cannot expect increased signal power by using waveguides with small modes. As we will see this conclusion is not correct once the effects of waveguides are taken into full account.

8. K. Koch, E. C. Cheung, G. T. Moore, S. H. Chakmakjian, and J. M. Liu, “Hot Spots in Parametric Fluorescence with a Pump Beam of Finite Cross Section,” IEEE J. of Quantum Electron. **31**769 (1995). [CrossRef]

9. P. Baldi, P. Aschieri, S. Nouh, M. De Micheli, D. B. Ostrowsky, D. Delacourt, and M. Papuchon, “Modeling and Experimental Observation of Parametric Fluorescence in Periodically Poled Lithium Niobate Waveguides,” IEEE J. of Quantum Electron. **31**997 (1995). [CrossRef]

7. D. A. Kleinman, “Theory of Optical Parametric Noise,” Phys. Rev. **174**, 1027 (1968). [CrossRef]

9. P. Baldi, P. Aschieri, S. Nouh, M. De Micheli, D. B. Ostrowsky, D. Delacourt, and M. Papuchon, “Modeling and Experimental Observation of Parametric Fluorescence in Periodically Poled Lithium Niobate Waveguides,” IEEE J. of Quantum Electron. **31**997 (1995). [CrossRef]

*ω*

^{(k)}as

*u*satisfies the following conditions

_{k}*V*. We assume that, for a waveguide, the solution is separable and write

*L*is the length of the quantization volume along the propagation axis

*ẑ*,

*β*

^{(k)}is the propagation constant, and ∫

_{A}

*dxdy*|

*U*

^{(k)}|

^{2}= 1 when the integral is carried over the transverse area

*A*of the quantization volume. Observe that

*U*

^{(k)}has dimensions of the inverse of a length. The field can be quantized introducing the electric field operator for signal and idler

*n*are the indexes of refraction for the signal and idler, respectively, and the integration constant is chosen to give the usual commutation rules for the creation and destruction operators. We write the pump field as

_{s,i}*n*is the refractive index for the pump. We assume ∫

_{p}*dxdy*|

*U*|

_{p}^{2}= 1 and choose the normalization so that when we integrate ∫

*dxdycn*

_{p}ε_{0}|

*E*|

_{p}^{2}/2 we obtain the pump power

*P*. The interaction Hamiltonian is then [8

_{p}**31**769 (1995). [CrossRef]

*C*which has a length

*ℒ*along the propagation axis and a transverse area A that coincides with the quantization volume transverse section. We can now calculate the matrix element between the initial state |

*i*〉 = |00〉 with no photons in the signal and idler modes and the final state 〈

*f*| = 〈00|

*â*

_{s}^{(l)}

*â*

_{i}^{(m)}with one photon in each of the modes

*l*and

*m*. By putting

*ω*

_{s}^{(l)}=

*ω*,

_{s}*ω*

_{i}^{(m)}=

*ω*,

_{i}*U*

_{s}^{(l)}=

*U*,

_{s}*U*

_{i}^{(j)}=

*U*and Δ

_{i}*k*=

*β*-

_{p}*β*

_{i}^{(m)}-

*β*

_{s}^{(l)}and enforcing energy conservation

*ω*=

_{p}*ω*+

_{s}*ω*we get

_{i}*A*= (∫

_{I}_{A}

*dxdyU*(

_{p}*U*)

_{i}^{*}(

*U*)

_{s}^{*})

^{-2}is the interaction effective area.

*d𝓝*for a change

*dE*of the energy is

**31**769 (1995). [CrossRef]

*d𝓟*

_{s}^{(W)}=

*h¯ω*emitted in a frequency or wavelength interval is

_{s}𝓦*Ŷ*axis, signal and idler are polarized along the Ŷ and

*Ẑ*axes, respectively, and all beams propagate along the

*X̂*axis. The relevant nonlinear coefficient is

*d*= 2

*d*

_{24}/

*π*where

*d*

_{24}= 3.92 pm/V [11

11. H. Vanherzeele and J. D. Bierlein, “Magnitude of the nonlinear-optical coefficients of KTiOPO_{4},” Opt. Lett. **17**982 (1992). [CrossRef] [PubMed]

*π*is due to the first-order poling. We also put

*ℒ*= 10 mm,

*n*= 1.758,

_{s}*n*= 1.843,

_{i}*n*= 1.840, and

_{p}*𝓟*= 1 mW. Finally we assume

_{p}*π*/Λ to take into account the effect of the poling grating of period Λ = 8.36

*μ*m for the waveguide and Λ = 10

*μ*m for the bulk crystal. To evaluate Δ

*k*we use the pump, signal, and idler wave numbers

*k*and the waveguide contribution to the phase matching Δ

_{p,s,i}*k*. The latter factor has been evaluated empirically to be Δ

_{WG}*k*~ 0.13

_{WG}*μ*m

^{-1}. The dependence of the wave numbers on the wavelengths can be evaluated using the Sellmeier equations for KTP [12

12. J. D. Bierlein and H. Vanherzeele, “Potassium titanyl phospate: properties and new applications,” J. Opt. Soc. Am. B **6**, 622 (1989). [CrossRef]

*A*= 15

_{I}*μ*m

^{2}as calculated from the waveguide eigenmodes which will be derived in the next section.

^{7}pairs/s per mW of pump for the waveguide and ~ 1.6 ∙ 10

^{6}pairs/s for the bulk.

## 3. Waveguide fabrication

*μ*m wide channel waveguides is used to pattern a layer of Al onto the +z surface of the wafer. The wafer is diced into 3 mm × 10 mm chips and polished on the optical surfaces. The chips are placed in a molten bath of RbNO

_{3}salt at 400C for 120 minutes. The bare areas of the patterned surface undergo ion exchange in which Rb

^{+}ions diffuse into the KTP, replacing K

^{+}ions to a depth of around 9

*μ*m, forming an index step of 0.02 relative to the surrounding KTP. After ion exchange the Al layer is removed, and the chip is annealed in air at 325°C for 15 minutes.

15. T. E. Murphy, Ph.D. thesis, MIT (2001). See also the pakage for numerically solving the eigenmode problem at http://www.photonics.umd.edu/software

*μ*m in the lateral direction and a diffusion profile as a function of depth z of the form

*n*(

*z*) = n

_{KTP}+ Δ

*ne*

^{(-z/d)}, with Δ

*n*= 0.02 and

*d*= 8

*μ*m [16

16. M. G. Roelofs, A. Suna, W. Bindloss, and J. D. Bierlein, “Characterization of optical waveguides in KTiOP04 by second harmonic spectroscopy,” J. Appl. Phys. **9**, 4999 (1994). [CrossRef]

*A*used above.

_{I}*μ*m. The patterned electrode was aligned and pressed to the +z surface; a ground electrode consisting of a uniform metal substrate contacted the -z surface. The poling waveform was applied using a Trek 20/20C high voltage amplifier controlled by a computer program that simultaneously monitored the electrode current.

## 4. Experiments

16. M. G. Roelofs, A. Suna, W. Bindloss, and J. D. Bierlein, “Characterization of optical waveguides in KTiOP04 by second harmonic spectroscopy,” J. Appl. Phys. **9**, 4999 (1994). [CrossRef]

^{2}curve yields a FWHM of 0.65 nm which should be compared with the expected width of 0.57 nm calculated using Eq. 16. A possible explanation of the difference between the expected and calculated width is that the crystal length that is effectively poled is shorter than the physical length of the crystal due to imperfections in the poling process.

^{3}and has a poling period of 10

*μ*m that phase matches degenerate type II down-conversion of a pump at 404.85 nm. The second aspheric lens is moved to optimize coupling into the multimode fibers. Given the large numerical aperture of the aspheric lens and the relatively narrow emission cone of the pairs (for the bandwidth we consider) it can be safely assumed that all pairs generated in the band of interest are collected. For a transmitted pump of 440

*μ*W (810

*μ*W injected) with a 1-nm filter we measure

*N*= 149,000 signal counts,

_{s}*N*= 165,000 idler counts, and

_{i}*N*= 24,000 coincidence counts, this corresponds to a rate of 54,000 pairs/s/mW/nm. By changing the crystal temperature we obtain an estimate of the fluorescence photons for the two channels

_{c}*N*= 17,000 counts/s and

_{fs}*N*= 16,500 counts/s, this corresponds to a 9:1 ratio between down-converted and fluorescence photons. Using these numbers we estimate detection and collection efficiencies

_{fi}*η*= 0.18 and

_{s}*η*= 0.16 and an estimated generation rate of 1.8∙10

_{s}^{6}pairs/s/mW in the filter band which is in qualitative agreement with the expected value of 1.5∙10

^{6}pairs/s/mW. The discrepancy is most likely due to our rough estimate of the fluorescence photons. For our experiments the measured pair rate in the waveguide is approximately 50 times larger than the bulk in a 1-nm band.

4. S. Tanzilli, H. De Riedmatten, H. Tittel, H. Zbinden, P. Baldi, M. De Micheli, D. B. Ostrowsky, and N. Gisin, “Highly efficient photon-pair source using periodically poledlithium niobate waveguide,” Electron. Lett. **37**, 28, (2001). [CrossRef]

*μ*W of pump in a 30-nm bandwidth corresponding to 50,000 pairs/s/mW in a 1 nm band or 1.5 · 10

^{6}pairs/s/mW in the aggregate band. Because of the wavelength used Ref. [4

4. S. Tanzilli, H. De Riedmatten, H. Tittel, H. Zbinden, P. Baldi, M. De Micheli, D. B. Ostrowsky, and N. Gisin, “Highly efficient photon-pair source using periodically poledlithium niobate waveguide,” Electron. Lett. **37**, 28, (2001). [CrossRef]

4. S. Tanzilli, H. De Riedmatten, H. Tittel, H. Zbinden, P. Baldi, M. De Micheli, D. B. Ostrowsky, and N. Gisin, “Highly efficient photon-pair source using periodically poledlithium niobate waveguide,” Electron. Lett. **37**, 28, (2001). [CrossRef]

6. A. B. U’Ren, C. Silberhorn, K. Banaszek, and I. A. Walmsley, “Efficient Conditional Preparation of High-Fidelity Single Photon States for Fiber-Optic Quantum Networks,” Phys. Rev. Lett. **93**, 093601 (2004). [CrossRef] [PubMed]

*μ*W pump [18] in a 17-nm bandwidth corresponding to 50,000 pairs/s/mW in a 1 nm band or 8.5·10

^{5}pairs/s/mW in the aggregate band.

19. C. E. Kuklewicz, M. Fiorentino, G. Messin, F. N. C. Wong, and J. H. Shapiro, “High-flux source of polarization entangled photons from a periodically-poled KTiOPO_{4} parametric downconverter,” Phys. Rev. A **69**, 013807 (2004). [CrossRef]

20. M. H. Rubin, D. N. Klyshko, Y. H. Shih, and A. V. Sergienko, “Theory of two-photon entanglement in type-II optical parametric down-conversion,” Phys. Rev. A **50**5122 (1994). [CrossRef] [PubMed]

*N*

_{c}^{(max)}and minima

*N*

_{c}^{(min)}of the interference fringes to obtain a visibility

*V*= (

*N*

_{c}^{(max)}-

*N*

_{c}^{(min)})/(

*N*

_{c}^{(max)}+

*N*

_{c}^{(min)}) = 79%. We attribute the imperfect visibility to a spatial mode mismatch of the signal and idler photons.

## 5. Conclusions

## References and links

1. | P. G. Kwiat, K. Mattle, H. Weinfurter, and A. Zeilinger, “New High-Intensity Source of Polarization-Entangled Photon Pairs,” Phys. Rev Lett. |

2. | P. G. Kwiat, E. Waks, A. G. White1, I. Appelbaum, and P. H. Eberhard, “Ultrabright source of polarization-entangled photons,” Phys. Rev. A |

3. | T. B. Pittman, B. C. Jacobs, and J. D. Franson, “Demonstration of Nondeterministic Quantum Logic Operations Using Linear Optical Elements,” Phys. Rev. Lett. |

4. | S. Tanzilli, H. De Riedmatten, H. Tittel, H. Zbinden, P. Baldi, M. De Micheli, D. B. Ostrowsky, and N. Gisin, “Highly efficient photon-pair source using periodically poledlithium niobate waveguide,” Electron. Lett. |

5. | K. Sanaka, K. Kawahara, and T. Kuga, “New High-Efficiency Source of Photon Pairs for Engineering Quantum Entanglement,” Phys. Rev. Lett. |

6. | A. B. U’Ren, C. Silberhorn, K. Banaszek, and I. A. Walmsley, “Efficient Conditional Preparation of High-Fidelity Single Photon States for Fiber-Optic Quantum Networks,” Phys. Rev. Lett. |

7. | D. A. Kleinman, “Theory of Optical Parametric Noise,” Phys. Rev. |

8. | K. Koch, E. C. Cheung, G. T. Moore, S. H. Chakmakjian, and J. M. Liu, “Hot Spots in Parametric Fluorescence with a Pump Beam of Finite Cross Section,” IEEE J. of Quantum Electron. |

9. | P. Baldi, P. Aschieri, S. Nouh, M. De Micheli, D. B. Ostrowsky, D. Delacourt, and M. Papuchon, “Modeling and Experimental Observation of Parametric Fluorescence in Periodically Poled Lithium Niobate Waveguides,” IEEE J. of Quantum Electron. |

10. | D. F. Walls and G. J. Milburn, “Quantum Optics,” (Springer-Verlag, Berlin, 1995). |

11. | H. Vanherzeele and J. D. Bierlein, “Magnitude of the nonlinear-optical coefficients of KTiOPO |

12. | J. D. Bierlein and H. Vanherzeele, “Potassium titanyl phospate: properties and new applications,” J. Opt. Soc. Am. B |

13. | E. C. Cheung, K. Koch, G. T. Moore, and J. M. Liu, “Measurements of second-order nonlinear optical coefficients from the spectral brightness of parametric fluorescence,” Opt. Lett. |

14. | Z. Y. Ou and Y. J. Lu, “Cavity Enhanced Spontaneous Parametric Down-Conversion for the Prolongation of Correlation Time between Conjugate Photons,” Phys. Rev. Lett. |

15. | T. E. Murphy, Ph.D. thesis, MIT (2001). See also the pakage for numerically solving the eigenmode problem at http://www.photonics.umd.edu/software |

16. | M. G. Roelofs, A. Suna, W. Bindloss, and J. D. Bierlein, “Characterization of optical waveguides in KTiOP04 by second harmonic spectroscopy,” J. Appl. Phys. |

17. | T. Kim, M. Fiorentino, P. V. Gorelik, and F. N. C. Wong, “Low-cost nanosecond electronic coincidence detector,” physics/0501141 (2005). |

18. | A. B. U’ren, |

19. | C. E. Kuklewicz, M. Fiorentino, G. Messin, F. N. C. Wong, and J. H. Shapiro, “High-flux source of polarization entangled photons from a periodically-poled KTiOPO |

20. | M. H. Rubin, D. N. Klyshko, Y. H. Shih, and A. V. Sergienko, “Theory of two-photon entanglement in type-II optical parametric down-conversion,” Phys. Rev. A |

**OCIS Codes**

(190.4410) Nonlinear optics : Nonlinear optics, parametric processes

(270.0270) Quantum optics : Quantum optics

**ToC Category:**

Nonlinear Optics

**History**

Original Manuscript: April 18, 2007

Revised Manuscript: May 24, 2007

Manuscript Accepted: May 31, 2007

Published: June 4, 2007

**Citation**

Marco Fiorentino, Sean M. Spillane, Raymond G. Beausoleil, Tony D. Roberts, Philip Battle, and Mark W. Munro, "Spontaneous parametric down-conversion in periodically poled KTP waveguides and bulk crystals," Opt. Express **15**, 7479-7488 (2007)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-12-7479

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### References

- P. G. Kwiat, K. Mattle, H. Weinfurter, and A. Zeilinger, "New High-Intensity Source of Polarization-Entangled Photon Pairs," Phys. Rev Lett. 75, 4337 (1995). [CrossRef] [PubMed]
- P. G. Kwiat, E. Waks, A. G. White1, I. Appelbaum, and P. H. Eberhard, "Ultrabright source of polarizationentangled photons," Phys. Rev. A 60, R773 (1999). [CrossRef]
- T. B. Pittman, B. C. Jacobs, and J. D. Franson, "Demonstration of Nondeterministic Quantum Logic Operations Using Linear Optical Elements," Phys. Rev. Lett. 88, 257902 (2002). [CrossRef] [PubMed]
- S. Tanzilli, H. De Riedmatten, H. Tittel, H. Zbinden, P. Baldi, M. De Micheli, D. B. Ostrowsky, N. Gisin, " Highly efficient photon-pair source using periodically poledlithium niobate waveguide," Electron. Lett. 37, 28, (2001). [CrossRef]
- K. Sanaka, K. Kawahara, and T. Kuga, "New High-Efficiency Source of Photon Pairs for Engineering Quantum Entanglement," Phys. Rev. Lett. 86, 5620 (2001). [CrossRef] [PubMed]
- A. B. U’Ren, C. Silberhorn, K. Banaszek, and I. A.Walmsley, "Efficient Conditional Preparation of High-Fidelity Single Photon States for Fiber-Optic Quantum Networks," Phys. Rev. Lett. 93, 093601 (2004). [CrossRef] [PubMed]
- D. A. Kleinman, "Theory of Optical Parametric Noise," Phys. Rev. 174, 1027 (1968). [CrossRef]
- K. Koch, E. C. Cheung, G. T. Moore, S. H. Chakmakjian, and J. M. Liu, "Hot Spots in Parametric Fluorescence with a Pump Beam of Finite Cross Section," IEEE J. of Quantum Electron. 31769 (1995). [CrossRef]
- P. Baldi, P. Aschieri, S. Nouh, M. De Micheli, D. B. Ostrowsky, D. Delacourt, and M. Papuchon, "Modeling and Experimental Observation of Parametric Fluorescence in Periodically Poled Lithium Niobate Waveguides," IEEE J. of Quantum Electron. 31997 (1995). [CrossRef]
- D. F. Walls and G. J. Milburn, "Quantum Optics," (Springer-Verlag, Berlin, 1995).
- H. Vanherzeele and J. D. Bierlein, "Magnitude of the nonlinear-optical coefficients of KTiOPO4," Opt. Lett. 17982 (1992). [CrossRef] [PubMed]
- J. D. Bierlein and H. Vanherzeele, "Potassium titanyl phospate: properties and new applications," J. Opt. Soc. Am. B 6, 622 (1989). [CrossRef]
- E. C. Cheung, K. Koch, G. T. Moore, J. M. Liu, "Measurements of second-order nonlinear optical coefficients from the spectral brightness of parametric fluorescence," Opt. Lett. 19168 (1994). [CrossRef] [PubMed]
- Z. Y. Ou and Y. J. Lu, "Cavity Enhanced Spontaneous Parametric Down-Conversion for the Prolongation of Correlation Time between Conjugate Photons," Phys. Rev. Lett. 83, 2556 (1999). [CrossRef]
- T. E. Murphy, Ph.D. thesis, MIT (2001). See also the pakage for numerically solving the eigenmode problem at http://www.photonics.umd.edu/software
- M. G. Roelofs, A. Suna, W. Bindloss, and J. D. Bierlein, "Characterization of optical waveguides in KTiOP04 by second harmonic spectroscopy," J. Appl. Phys. 9, 4999 (1994). [CrossRef]
- T. Kim, M. Fiorentino, P. V. Gorelik and F. N. C. Wong, "Low-cost nanosecond electronic coincidence detector," physics/0501141 (2005).
- A. B. U’ren, personal communication.
- C. E. Kuklewicz, M. Fiorentino, G. Messin, F. N. C. Wong, and J. H. Shapiro, "High-flux source of polarization entangled photons from a periodically-poled KTiOPO4 parametric downconverter," Phys. Rev. A 69, 013807 (2004). [CrossRef]
- M. H. Rubin, D. N. Klyshko, Y. H. Shih, and A. V. Sergienko, "Theory of two-photon entanglement in type-II optical parametric down-conversion," Phys. Rev. A 505122 (1994). [CrossRef] [PubMed]

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