## Spectral study of photon pairs generated in dispersion shifted fiber with a pulsed pump

Optics Express, Vol. 16, Issue 1, pp. 32-44 (2008)

http://dx.doi.org/10.1364/OE.16.000032

Acrobat PDF (3142 KB)

### Abstract

Spectral correlation of photon pairs generated in dispersion shifted fiber by a pulsed pump is theoretically analyzed and experimentally investigated. We first calculate the spectral function of photon pairs according to the deduced two-photon state generated by spontaneous four wave mixing under the assumptions close to the real experimental conditions. We then experimentally study the spectral property of the signal and idler photon pairs generated in optical fiber by photon correlation measurements, and the experimental results agree with the calculation. The investigation is useful for developing fiber-based sources of entangled photon pairs and for studying multi-photon quantum interference with multiple photon pairs.

© 2008 Optical Society of America

## 1. Introduction

12. M. Fiorentino, P. L. Voss, J. E. Sharping, and P. Kumar, “All-fiber photon-pair source for quantum communication,” Photon. Technol. Lett. **14**, 983–985 (2002). [CrossRef]

13. X. Li, P. L. Voss, J. E. Sharping, and P. Kumar, “Optical-fiber source of polarization-entangled photons in the 1550 nm telecom band,” Phys. Rev. Lett. **94**, 053,601 (2005). [CrossRef]

14. H. Takesue and K. Inoue, “Generation of 1.5-um band time-bin entanglement using spontaneous fiber four-wave mixing and planar lightwave circuit interferometers,” Phys. Rev. A **72**, 041,804 (2005). [CrossRef]

15. J. Fan, A. Dogariu, and L. J. Wang, “Generation of correlated photon pairs in a microstructure fiber,” Opt. Lett. **30**, 1530–1532 (2005). [CrossRef] [PubMed]

16. J. Fulconis, O. Alibart, W. J. Wadsworth, P. S. Russell, and J. G. Rarity, “High brightness single mode source of correlated photon pairs using a photonic crystal fiber,” Opt. Express **13**, 7572–7582 (2005). [CrossRef] [PubMed]

17. K. F. Lee, J. Chen, C. Liang, X. Li, P. L. Voss, and P. Kumar, “Generation of high-purity telecom-band entangled photon pairs in dispersion-shifted fiber,” Opt. Lett. **31**, 1905–1907 (2006). [CrossRef] [PubMed]

^{(2)}nonlinear crystals. Although Raman scattering (RS) may degrade the fidelity of such sources [18

18. X. Li, J. Chen, P. L. Voss, J. Sharping, and P. Kumar, “All-fiber photon-pair source for quantum communications: Improved generation of correlated photons,” Opt. Express **12**, 3737–3744 (2004). [CrossRef] [PubMed]

19. K. Inoue and K. Shimizu, “Generation of Quantum-Correlated Photon Pairs in Optical Fiber: Influence of Spontaneous Raman Scattering,” Jpn. J. Appl. Phys **43**, 8048–8052 (2004). [CrossRef]

20. H. Takesue and K. Inoue, “1.5 um band quantum-correlated photon pair generation in dispersion-shifted fiber: suppression of noise photons by cooling fiber,” Opt. Express **13**, 7832–7839 (2005). [CrossRef] [PubMed]

17. K. F. Lee, J. Chen, C. Liang, X. Li, P. L. Voss, and P. Kumar, “Generation of high-purity telecom-band entangled photon pairs in dispersion-shifted fiber,” Opt. Lett. **31**, 1905–1907 (2006). [CrossRef] [PubMed]

21. J. G. Rarity, J. Fulconis, J. Duligall, W. J. Wadsworth, and P. S. J. Russell, “Photonic crystal fiber source of correlated photon pairs,” Opt. Express **13**, 534–544 (2005). [CrossRef] [PubMed]

16. J. Fulconis, O. Alibart, W. J. Wadsworth, P. S. Russell, and J. G. Rarity, “High brightness single mode source of correlated photon pairs using a photonic crystal fiber,” Opt. Express **13**, 7572–7582 (2005). [CrossRef] [PubMed]

12. M. Fiorentino, P. L. Voss, J. E. Sharping, and P. Kumar, “All-fiber photon-pair source for quantum communication,” Photon. Technol. Lett. **14**, 983–985 (2002). [CrossRef]

13. X. Li, P. L. Voss, J. E. Sharping, and P. Kumar, “Optical-fiber source of polarization-entangled photons in the 1550 nm telecom band,” Phys. Rev. Lett. **94**, 053,601 (2005). [CrossRef]

21. J. G. Rarity, J. Fulconis, J. Duligall, W. J. Wadsworth, and P. S. J. Russell, “Photonic crystal fiber source of correlated photon pairs,” Opt. Express **13**, 534–544 (2005). [CrossRef] [PubMed]

14. H. Takesue and K. Inoue, “Generation of 1.5-um band time-bin entanglement using spontaneous fiber four-wave mixing and planar lightwave circuit interferometers,” Phys. Rev. A **72**, 041,804 (2005). [CrossRef]

15. J. Fan, A. Dogariu, and L. J. Wang, “Generation of correlated photon pairs in a microstructure fiber,” Opt. Lett. **30**, 1530–1532 (2005). [CrossRef] [PubMed]

16. J. Fulconis, O. Alibart, W. J. Wadsworth, P. S. Russell, and J. G. Rarity, “High brightness single mode source of correlated photon pairs using a photonic crystal fiber,” Opt. Express **13**, 7572–7582 (2005). [CrossRef] [PubMed]

17. K. F. Lee, J. Chen, C. Liang, X. Li, P. L. Voss, and P. Kumar, “Generation of high-purity telecom-band entangled photon pairs in dispersion-shifted fiber,” Opt. Lett. **31**, 1905–1907 (2006). [CrossRef] [PubMed]

22. J. Chen, X. Li, and P. Kumar, “Two-photon-state generation via four-wave mixing in optical fibers,” Phys. Rev. A **72**, 033,801 (2005). [CrossRef]

23
. O. Alibart, J. Fulconis, G. K. L. Wong, S. G. Murdoch, W. J. Wadsworth, and J. G. Rarity, “Photon pair generation using four-wave mixing in a microstructured fibre: theory versus experiment,” New J. of Phys. **8**, 67 (2006). [CrossRef]

24. K. Garay-Palmett, H. J. McGuinness, O. Cohen, J. S. Lundeen, R. Rangel-Rojo, A. B. U’Ren, M. G. Raymer, C. J. McKinstrie, S. Radic, and I. A. Walmsley, “Photon pair-state preparation with tailored spectral properties by spontaneous four-wave mixing in photonic-crystal fiber,” Opt. Express **15**, 14,870–14,886 (2007). [CrossRef]

^{(2)}crystal counterparts, the characteristics of the χ

^{(3)}based fiber source, such as the spectral and temporal mode properties of various fiber sources, have not been fully explored.

^{(3)}-based two-photon state in DSF [22

22. J. Chen, X. Li, and P. Kumar, “Two-photon-state generation via four-wave mixing in optical fibers,” Phys. Rev. A **72**, 033,801 (2005). [CrossRef]

22. J. Chen, X. Li, and P. Kumar, “Two-photon-state generation via four-wave mixing in optical fibers,” Phys. Rev. A **72**, 033,801 (2005). [CrossRef]

## 2. Theory

*E*

^{(+)}

*(*

_{p}*t*,

*z*) in Eq. (1) is taken to be a classical narrow pulse, having a Gaussian spectral envelope. For the fiber with a length of hundreds meters, its propagation loss can be neglected. Therefore the self phase modulation (SPM) of pump can be included in a straightforward manner [22

**72**, 033,801 (2005). [CrossRef]

*ω*

_{p0}is the central frequency of pump pulse,

*σ*is the optical bandwidth of the pump,

_{p}*P*is the peak pump power,

_{p}*k*is the wave-vector of pump,

_{p}*γ*is the nonlinear coefficient of the optical fiber, and Ω

*=*

_{p}*ω*-

_{p}*ω*

_{p0}.

*λ*

_{0}and a duration

*T*

_{0}of a few picoseconds, if the fiber length L is of the order of hundreds meters, the pulse broadening due to group velocity dispersion (GVD) and third order dispersion can be neglected [25]. This is because the fiber length satisfies the relations:

*F*(

*ω*,

_{s}*ω*) is simplified as

_{i}*γP*can cancel out each other when the central wavelength of the pump pulse

_{p}L*λ*

_{p0}in the anomalous dispersion region of DSF is properly optimized and |

*ω*

_{p0}-

*ω*

_{0}|≪Δ. Under this condition, we have

*ϕ*(

*ω*,

_{s}*ω*) is the sum of the frequencies Ω

_{i}*and Ω*

_{s}*, which indicates the sinc function has the property of exchange symmetry:*

_{i}*ϕ*(

*ω*,

_{s}*ω*)=

_{i}*ϕ*(

*ω*,

_{i}*ω*).

_{s}*F*(

*ω*,

_{s}*ω*)|

_{i}^{2}, proportional to the two-photon joint spectral correlation of photon pairs, depends on the functions |

*α*(

*ω*,

_{s}*ω*)|

_{i}^{2}and |

*ϕ*(

*ω*,

_{s}*ω*)|

_{i}^{2}, which are determined by the spectrum of pump field and the phase matching condition of FWM, respectively. To understand the relationship between |

*F*(

*ω*,

_{s}*ω*)|

_{i}^{2}, |

*α*(

*ω*,

_{s}*ω*)|

_{i}^{2}and |

*ϕ*(

*ω*,

_{s}*ω*)|

_{i}^{2}, it is instructive to examine plots of these functions individually at various conditions. Figure 1 shows the envelop of |

*α*(

*ω*,

_{s}*ω*)|

_{i}^{2}for the pump with

*λ*

_{p0}=1541 nm and full-widthhalf-maximum (FWHM) of 1 nm (

*σ*/2

_{p}*π*=75 GHz). Since the argument of |

*α*(

*ω*,

_{s}*ω*)|

_{i}^{2}is the sum of the frequencies Ω

*and Ω*

_{s}*, the function has constant value along lines defined by Ω*

_{i}*+Ω*

_{s}*=*

_{i}*const*, namely,

*ω*+

_{s}*ω*=

_{i}*const*, which reaches its peak value at every point on the line

*ω*+

_{s}*ω*= 2

_{i}*ω*

_{p0}. The graphical representation in Fig. 2, (a), (b) and (c) are the sinc function |

*ϕ*(

*ω*,

_{s}*ω*)|

_{i}^{2}in DSF with

*λ*

_{0}=1540 nm and

*γP*=1 for the frequency difference Δ/2

_{p}L*π*=2.17 THz, 2.67 THz, and 3.18 THz, respectively. For each frequency difference Δ, the frequency of the signal and idler photon pairs satisfying the relation Ω

*=Ω*

_{i}*=0 is labeled by a crosshairs. For Δ/2*

_{s}*π*=2.67 THz, the sum of the second order dispersion term and SPM is negligibly small, so that the sinc function can be approximated as

*ω*+

_{s}*ω*=2

_{i}*ω*

_{p0}when Δ/2

*π*is not equal to 2.67 THz, as shown in Fig. 2(a) and (c), respectively. Figure 2(d), (e) and (f) are the normalized joint spectral intensity |

*F*(

*ω*,

_{s}*ω*)|

_{i}^{2}corresponding to Fig. 2(a), (b), and (c), respectively. It is clear that the spectral property of the function |

*F*(

*ω*,

_{s}*ω*)|

_{i}^{2}highly depends on that of the sinc function

*ϕ*(

*ω*,

_{s}*ω*).

_{i}*F*(

*ω*,

_{s}*ω*), it is useful to study the conditional spectrum

_{i}*S*

_{s(i)}(

*ω*) of the individual signal (idler) photon wave packets for a given Gaussian shaped filter with width

*σ*

_{0}at the idler (signal) field

*and Ω*

_{s}*, associated with the bandwidths of signal and idler fields, are much less than Δ, i.e., |Ω*

_{i}*|, |Ω*

_{s}*|≪Δ, and the sum of the second order dispersion term and SPM term in the function*

_{i}*ϕ*(

*ω*,

_{s}*ω*) (see Eq. (11)) is negligibly small, the sinc function

_{i}*ϕ*(

*ω*,

_{s}*ω*) in Eq. (12) can be approximated to the Gaussian function:

_{i}*ϕ*=(

*k*″′

*L*/8)Δ

^{2}(Ω

*+Ω*

_{s}*), and Γ=0.04822. In this case, the conditional spectrum*

_{i}*S*

_{s(i)}(

*ω*) can be expressed as

*S*(

_{s}*ω*) and

*S*(

_{i}*ω*), are identical. Moreover, if the condition

*σ*′″

_{p}k*L*Δ

^{2}/4<1 is satisfied, we have

*S*

_{s(i)}(Ω) only depends on the bandwidth of pump and that of the filter placed in idler (signal) field, which implies the sinc function

*ϕ*(

*ω*,

_{s}*ω*) in Eq. (12) does not play a role. We note that the required conditions |Ω

_{i}*|, |Ω*

_{s}*|≪Δ and*

_{i}*σ*′″

_{p}k*L*Δ

^{2}/4<1 are practically realizable. For example, the signal and idler photon pairs at telecom band, with the frequency difference Δ/2

*π*=1.8 THz (15 nm) and bandwidth

*σ*

_{0}/2

*π*=25 GHz, can be obtained by pumping 300m DSF with a pulsed pump and by using the off-the-shelf filters, such as fiber Bragg-grating filters and fiber-pigtailed wavelength-division-multiplexing filters. For the pump pulse with a bandwidth

*σ*/2

_{p}*π*=100 GHz, we have

*σ*′″

_{p}k*L*Δ

^{2}/4=0.13<1.

*ϕ*(

*ω*,

_{s}*ω*) has the value of about 1 and can be viewed as nonexistence, we investigate how to deduce the spectral property of the spectral function

_{i}*F*(

*ω*,

_{s}*ω*) in the whole range of the frequency difference Δ from the function

_{i}*S*

_{s(i)}(Ω). Assuming the bandwidth in idler field

*σ*

_{0}is much less than that of the pump

*σ*, so that Ω

_{p}*≈*

_{i}_{0}is valid, then the trait of

*S*(Ω) can be found by projecting the joint spectral intensity |

_{s}*F*(

*ω*,

_{s}*ω*)|

_{i}^{2}onto the

*ω*axis for a given frequency difference Δ. Under this condition, we have

_{s}## 3. Experiment

*ω*and

_{s}*ω*, respectively, are produced in 300m DSF by a pulsed pump. The zero-dispersion wavelength

_{i}*λ*

_{0}of the DSF is about 1539±2nm. The efficiency of spontaneous FWM in DSF is low because of the relatively low magnitude of Kerr (χ

^{(3)}) nonlinearity. To reliably detect the scattered photon-pairs, a pump to photon-pair rejection ratio in excess of 100 dB is required. This is achieved with a filter F

_{2}by cascading a free-space double-grating spectral filter (DGSF) that provides a pump-rejection ratio in excess of 90 dB [13

13. X. Li, P. L. Voss, J. E. Sharping, and P. Kumar, “Optical-fiber source of polarization-entangled photons in the 1550 nm telecom band,” Phys. Rev. Lett. **94**, 053,601 (2005). [CrossRef]

_{1}, whose FWHM is about 1 nm. Single photon detectors (SPD, id200) operated in the gated Geiger mode are used to detect the signal and idler photons. The 2.5-ns-wide gate pulses arrive at a rate of about 600 KHz, which is 1/64 of the repetition rate of the pump pulses, and the deadtime of the gate is set to be 10

*µ*s to suppress the after-pulse effect. The electrical signals produced by the SPDs in response to the incoming photons (and dark counts) are acquired by a photon-counting system. Thus, single counts in both the signal and idler bands and coincidences acquired from different time bins can be determined. The quantum efficiency of SPD1 (SPD2) is about 10% (7%), with a corresponding dark-count probability of 1.5×10

^{-4}(2×10

^{-5}) /pulse. The total detection efficiencies for both the signal and idler photons are about 1%, when the transmission efficiencies of DSF (~90%), and F

_{2}composed of DGSF (~40%), TF(~40%), and AWG (~30%) are included.

*S*(Ω) in Eq. (12). In the first experiment, the average power of pump is about 0.4mW (corresponding to

_{s}*γP*≈1), the central wavelength of the pump pulses is fixed at 1540.65±0.05nm, the central wavelength of the detected idler photons is fixed at 1530.18±0.02nm, 1531.74±0.02nm, and 1533.30±0.02nm, respectively. For each setting of the pump and idler photons, we scan the central wavelength of signal channel and conduct the photon counting measurement. At each wavelength, we measure the single counts in both the signal and idler channels, and record the coincidence rate between the detected signal and idler photons. The true coincidence rate is obtained by subtracting the accidental coincidence rate produced by the adjacent pump pulses from the coincidence rate produced by the same pulse. For each set of data, after subtracting the Raman contribution [18

_{p}L18. X. Li, J. Chen, P. L. Voss, J. Sharping, and P. Kumar, “All-fiber photon-pair source for quantum communications: Improved generation of correlated photons,” Opt. Express **12**, 3737–3744 (2004). [CrossRef] [PubMed]

*λ*=

_{i}*λ*

_{s}λ_{p0}/(2

*λ*-

_{s}*λ*

_{p0}) is also plotted in Fig. 5(b). One sees that all the three data points are sat on the symmetry line, indicating the source has the property of spectral symmetry when the wavelength of the idler (signal) photon is in the range from 1530nm to 1533.30nm (1551nm to 1548.30nm).

*γP*≈0.5), we obtain three sets of data for the three kinds of experimental settings, as shown in Fig. 6(a) and (b), and Fig. 6(c) and (d), respectively. We find each set of data in Fig. 6(a) and Fig. 6(c) fits well with a Gaussian function, and their FWHM are about the same at a certain pump level. The FWHM in Fig. 6(a) is wider than that in Fig. 6(c), because the SPM induced pump pulse broadening increases with the increasing pump power. At the lower pump level of 0.2mW, taking the slight broadening of pump pulse due to SPM into account, we find the FWHMs of the fitting curves, pump pulse and the filter in the idler band in Fig. 6(c), which are about 1.4 nm, 0.9 nm, and 0.35 nm, respectively, satisfy the relation shown in Eq. (14) [26]. In Fig. 6(b), the cross points of central wavelengths of idler and signal are not all sat on the symmetry line, some of them are below the line, and the offset increases with the increase of the frequency difference Δ; while in Fig. 6(d), all the three data points sit on the symmetry line. The results agree with the calculated results: when the pump power decreases, although the frequency difference Δ

_{p}L_{0}decreases, the spectral range within which |

*F*(

*ω*,

_{s}*ω*)|

_{i}^{2}exhibits spectral symmetry broadens.

*λ*

_{p0}from

*λ*

_{0}. Comparing Fig. 6(b) with Fig. 5(b), one sees the spectrum of the photon pairs shown in Fig. 6(b) starts to become asymmetry when the idler (signal) photon is within the range from 1531.7nm to 1534.9nm (1551.5nm to 1548.5nm). The results agree with the theoretical prediction: when the deviation of

*λ*from λ

_{p}_{0}increases, Δ

_{0}decreases; and when Δ is greater than Δ

_{0}, the symmetry direction of the function |

*F*(

*ω*,

_{s}*ω*)|

_{i}^{2}will shift away from that of the pump, and the offset increases with the increase of Δ, as shown in Fig. 2 and Fig. 3.

18. X. Li, J. Chen, P. L. Voss, J. Sharping, and P. Kumar, “All-fiber photon-pair source for quantum communications: Improved generation of correlated photons,” Opt. Express **12**, 3737–3744 (2004). [CrossRef] [PubMed]

19. K. Inoue and K. Shimizu, “Generation of Quantum-Correlated Photon Pairs in Optical Fiber: Influence of Spontaneous Raman Scattering,” Jpn. J. Appl. Phys **43**, 8048–8052 (2004). [CrossRef]

**31**, 1905–1907 (2006). [CrossRef] [PubMed]

**12**, 3737–3744 (2004). [CrossRef] [PubMed]

**12**, 3737–3744 (2004). [CrossRef] [PubMed]

**94**, 053,601 (2005). [CrossRef]

## 4. Summary and discussion

3. E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature **409**, 46–52 (2001). [CrossRef] [PubMed]

*F*(

*ω*,

_{s}*ω*) [10

_{i}10. Z. Y. Ou, “Parametric Down-Conversion with Coherent Pulse Pumping and Quantum Interference between Independent Fields,” Quantum Semiclass Opt. **9**, 599–614 (1997). [CrossRef]

24. K. Garay-Palmett, H. J. McGuinness, O. Cohen, J. S. Lundeen, R. Rangel-Rojo, A. B. U’Ren, M. G. Raymer, C. J. McKinstrie, S. Radic, and I. A. Walmsley, “Photon pair-state preparation with tailored spectral properties by spontaneous four-wave mixing in photonic-crystal fiber,” Opt. Express **15**, 14,870–14,886 (2007). [CrossRef]

27. Z. Y. Ou, J. K. Rhee, and L. J. Wang, “Photon Bunching and Multiphoton Interference in Parametric Down-Conversion,” Phys. Rev. A **60**, 593–604 (1999). [CrossRef]

*,Ω*

_{s}*(≪Δ). When we properly adjust the power and the second order dispersion*

_{i}*k*″ so that the first two terms cancel, the function becomes

*A*≡

*k*″

*L*Δ/4,

*B*≡

*k*′″

*L*Δ

^{2}/16. Normally, this function shows a stripe with a slope of

*tanδ*=(

*A*+

*B*)/(

*A*-

*B*) and this will not produce a factorized

*F*(

*ω*,

_{s}*ω*). But an interesting case occurs when

_{i}*A*≫

*B*so that

*δ*≈45°. Combining with the pump spectral function

*α*(

*ω*,

_{s}*ω*), which lies in 135°,

_{i}*ϕ*(

*ω*,

_{s}*ω*) may provide a factorized joint spectral function

_{i}*F*(

*ω*,

_{s}*ω*) for proper value of the pump band width

_{i}*σ*. As shown in Fig. 7, plots (a) and (b) show a non-factorized joint spectral function with too large or too small

_{p}*σ*, but Fig. 7(c) shows a factorized F-function with

_{p}*σ*=1.1/

_{p}*A*. Furthermore when

*A*=±

*B*and

*σ*≫1/|

_{p}*A*|, an asymmetric but factorized F-function can be obtained as shown in Fig. 8. The ideas employed here are the same as those from Ref. [24

24. K. Garay-Palmett, H. J. McGuinness, O. Cohen, J. S. Lundeen, R. Rangel-Rojo, A. B. U’Ren, M. G. Raymer, C. J. McKinstrie, S. Radic, and I. A. Walmsley, “Photon pair-state preparation with tailored spectral properties by spontaneous four-wave mixing in photonic-crystal fiber,” Opt. Express **15**, 14,870–14,886 (2007). [CrossRef]

*λ*

_{p0}is close to the zero-dispersion wavelength

*λ*

_{0}, we have |

*A*|≪|

*B*|, and therefore are unable to achieve the conditions mentioned above. But a micro-structured fiber will have all the freedom to adjust

*k*″ and

*k*″′ to achieve these.

## Acknowledgement

## References and links

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13. | X. Li, P. L. Voss, J. E. Sharping, and P. Kumar, “Optical-fiber source of polarization-entangled photons in the 1550 nm telecom band,” Phys. Rev. Lett. |

14. | H. Takesue and K. Inoue, “Generation of 1.5-um band time-bin entanglement using spontaneous fiber four-wave mixing and planar lightwave circuit interferometers,” Phys. Rev. A |

15. | J. Fan, A. Dogariu, and L. J. Wang, “Generation of correlated photon pairs in a microstructure fiber,” Opt. Lett. |

16. | J. Fulconis, O. Alibart, W. J. Wadsworth, P. S. Russell, and J. G. Rarity, “High brightness single mode source of correlated photon pairs using a photonic crystal fiber,” Opt. Express |

17. | K. F. Lee, J. Chen, C. Liang, X. Li, P. L. Voss, and P. Kumar, “Generation of high-purity telecom-band entangled photon pairs in dispersion-shifted fiber,” Opt. Lett. |

18. | X. Li, J. Chen, P. L. Voss, J. Sharping, and P. Kumar, “All-fiber photon-pair source for quantum communications: Improved generation of correlated photons,” Opt. Express |

19. | K. Inoue and K. Shimizu, “Generation of Quantum-Correlated Photon Pairs in Optical Fiber: Influence of Spontaneous Raman Scattering,” Jpn. J. Appl. Phys |

20. | H. Takesue and K. Inoue, “1.5 um band quantum-correlated photon pair generation in dispersion-shifted fiber: suppression of noise photons by cooling fiber,” Opt. Express |

21. | J. G. Rarity, J. Fulconis, J. Duligall, W. J. Wadsworth, and P. S. J. Russell, “Photonic crystal fiber source of correlated photon pairs,” Opt. Express |

22. | J. Chen, X. Li, and P. Kumar, “Two-photon-state generation via four-wave mixing in optical fibers,” Phys. Rev. A |

23 . | O. Alibart, J. Fulconis, G. K. L. Wong, S. G. Murdoch, W. J. Wadsworth, and J. G. Rarity, “Photon pair generation using four-wave mixing in a microstructured fibre: theory versus experiment,” New J. of Phys. |

24. | K. Garay-Palmett, H. J. McGuinness, O. Cohen, J. S. Lundeen, R. Rangel-Rojo, A. B. U’Ren, M. G. Raymer, C. J. McKinstrie, S. Radic, and I. A. Walmsley, “Photon pair-state preparation with tailored spectral properties by spontaneous four-wave mixing in photonic-crystal fiber,” Opt. Express |

25. | G. P. Agrawal, |

26. | X. Li, J. Chen, K. F. Lee, P. L. Voss, and P. Kumar, “All-fiber photon-pair source for quantum communication: Influence of spectra,” Proceeding of Quantum Communication and Measurement |

27. | Z. Y. Ou, J. K. Rhee, and L. J. Wang, “Photon Bunching and Multiphoton Interference in Parametric Down-Conversion,” Phys. Rev. A |

**OCIS Codes**

(190.4370) Nonlinear optics : Nonlinear optics, fibers

(190.4410) Nonlinear optics : Nonlinear optics, parametric processes

(270.0270) Quantum optics : Quantum optics

**ToC Category:**

Quantum Optics

**History**

Original Manuscript: October 22, 2007

Revised Manuscript: December 3, 2007

Manuscript Accepted: December 14, 2007

Published: December 21, 2007

**Citation**

Xiaoying Li, Xiaoxin Ma, Zhe Yu Ou, Lei Yang, Liang Cui, and Daoyin Yu, "Spectral study of photon pairs generated in dispersion shifted fiber with a pulsed pump," Opt. Express **16**, 32-44 (2008)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-1-32

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