## Generation of broadband spontaneous parametric fluorescence using multiple bulk nonlinear crystals |

Optics Express, Vol. 20, Issue 13, pp. 13977-13987 (2012)

http://dx.doi.org/10.1364/OE.20.013977

Acrobat PDF (1089 KB)

### Abstract

We propose a novel method for generating broadband spontaneous parametric fluorescence by using a set of bulk nonlinear crystals (NLCs). We also demonstrate this scheme experimentally. Our method employs a superposition of spontaneous parametric fluorescence spectra generated using multiple bulk NLCs. A typical bandwidth of 160 nm (73 THz) with a degenerate wavelength of 808 nm was achieved using two *β*-barium-borate (BBO) crystals, whereas a typical bandwidth of 75 nm (34 THz) was realized using a single BBO crystal. We also observed coincidence counts of generated photon pairs in a non-collinear configuration. The bandwidth could be further broadened by increasing the number of NLCs. Our demonstration suggests that a set of four BBO crystals could realize a bandwidth of approximately 215 nm (100 THz). We also discuss the stability of Hong-Ou-Mandel two-photon interference between the parametric fluorescence generated by this scheme. Our simple scheme is easy to implement with conventional NLCs and does not require special devices.

© 2012 OSA

## 1. Introduction

14. S. Carrasco, M. B. Nasr, A. V. Sergienko, B. E. A. Saleh, M. C. Teich, J. P. Torres, and L. Torner, “Broadband light generation by non-collinear parametric downconversion,” Opt. Lett. **31**(2), 253–255 (2006). [CrossRef] [PubMed]

15. M. Hendrych, X. Shi, A. Valencia, and J. Torres, “Broadening the bandwidth of entangled photons: A step towards the generation of extremely short biphotons,” Phys. Rev. A **79**(2), 023817 (2009). [CrossRef]

16. K. O’Donnell and A. U’Ren, “Observation of ultrabroadband, beamlike parametric downconversion,” Opt. Lett. **32**(7), 817–819 (2007). [CrossRef]

*β*-barium-borate (BBO) crystals. We also measured the coincidence counts of generated photon pairs in a non-collinear configuration. Calculations based on the experimental results suggest that it should be possible to realize a bandwidth of approximately 215 nm (100 THz) by using a set of four BBO crystals.

17. C. Hong, Z. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. **59**(18), 2044–2046 (1987). [CrossRef] [PubMed]

## 2. Proposed scheme

*ω*and a momentum

_{p}*k*is down converted to a pair of photons, which are signal and idler photons with frequencies

_{p}*ω*and

_{s}*ω*and momenta

_{i}*k*and

_{s}*k*, respectively. Due to energy conservation,

_{i}*ω*=

_{p}*ω*+

_{s}*ω*must be satisfied so that the momentum mismatch Δ

_{i}*k*=

*k*−

_{p}*k*−

_{s}*k*must be zero to satisfy the critical phase-matching condition [18]. The frequency spectrum

_{i}*F*(

*ω*) for spontaneous parametric fluorescence, which consists of pairs of signal

*F*(

*ω*) and idler

_{s}*F*(

*ω*) photons, can be assumed to be symmetric relative to the center frequency

_{i}*F*(

*ω*), which is

*z*is the position in the NLC along the pump beam axis. and

*L*is the length of the NLC along the

*z*axis. The momentum mismatch Δ

*k*in the NLC depends on the frequencies of the generated signal and idler photons. Thus, the frequency spectrum

*F*(

*ω*) has a finite bandwidth that is determined by the frequency-dependent momentum mismatch Δ

*k*(Ω).

*θ*and the wavelength

*λ*of the generated parametric fluorescence as tuning curves that indicate the phase-matching conditions. The three different tilt angles

*θ*of the three NLCs (

_{t}*θ*,

_{ta}*θ*,

_{tb}*θ*) lead to three different tuning curves. When the generated signal and idler photons are collected at emission angles of

_{tc}*θ*=

*θ*and −

_{d}*θ*, respectively, the parametric fluorescence spectra generated by the NLCs have different peaks and bandwidths, as shown in the lower left figure of Fig. 2. The broadband spontaneous parametric fluorescence can be obtained at the detection angle

_{d}*θ*as a superposition of these spectra, as shown in the lower right figure of Fig. 2. Following the proposed method, the spectral bandwidth can be broadened by increasing the number of crystals. The expected broadening of the bandwidth with increasing number of crystals will be discussed later in Sec. 4.1 based on experimentally measured spectra.

_{d}## 3. Experimental setup

*θ*

_{t1}(

*θ*

_{t2}) relative to the cut angle (28.9°) of the BBO crystal. The signal and idler photons generated by type-I phase-matching parametric down conversion are collected by two fiber couplers (FCs) with an emission angle

*θ*of 1° relative to the pump beam. Long pass filters (LPFs) are placed in front of the FCs to filter the pump beam. Collected photons are transferred through polarization-maintaining fibers (PMFs) to the 300-mm spectrograph with a 300-grooves/mm grating blazed at 750 nm (SP-2358, Princeton Instruments) and detected by a charge coupled device (Pixis:100BRX, Princeton Instruments) to measure the frequency spectrum. The phase-matching conditions of the two BBO crystals are controlled by rotating the BBO crystals to vary the tilt angles

*θ*

_{t}_{1}and

*θ*

_{t}_{2}.

## 4. Results and discussion

### 4.1. Observation of broadband spontaneous parametric fluorescence

*θ*

_{t}_{2}was varied from −0.05° to −0.40° in 0.05° steps. As a result, the spectrum could be controlled by varying the phase-matching conditions, as shown in Fig. 2. The transmission efficiency of the spectrograph was calibrated in these spectra; however, the intensity reduction in the long wavelength region may be due to a reduction in the fiber coupling efficiency. When the tilt angle

*θ*

_{t2}was set to −0.05°, the spectrum was degenerate at the center wavelength of 808 nm and the bandwidth (FWHM) was typically 75 nm (34 THz). Thus, a broadband spectrum is expected when spectra with different tilt angles are superimposed. As an example, Fig. 4(b) shows calculated spectra as a superposition of these measured spectra. The bandwidth of the spectra obtained by summing two measured spectra obtained for tilt angles

*θ*

_{t2}of −0.05° and −0.15° is approximately 130 nm (60 THz), as plotted by the blue line in Fig. 4(b). A bandwidth of approximately 215 nm (100 THz), which is almost three times that of one degenerate spectrum, can be expected from the sum of four measured spectra with

*θ*

_{t2}of −0.10°, −0.20°, −0.30°, and −0.40°, as plotted by the red line in Fig. 4(b).

19. S. Baek and Y. Kim, “Spectral properties of entangled photon pairs generated via frequency-degenerate type-i spontaneous parametric down-conversion,” Phys. Rev. A **77**(4), 043807 (2008). [CrossRef]

### 4.2. Effect of the air gap between the nonlinear crystals in the proposed scheme

*u*are the group velocities for ordinary and extraordinary rays in a medium [20

_{o,e}20. G. D. Giuseppe, M. Atatüre, M. D. Shaw, A. V. Sergienko, B. E. A. Saleh, and M. C. Teich, “Entangled-photon generation from parametric down-conversion in media with inhomogeneous nonlinearity,” Phys. Rev. A **66**(1), 013801 (2002). [CrossRef]

*l*of the pump and signal (idler) photons after passing through the medium with a length

*d*can be given by Δ

*l*=

*cdD*. If the coherence length of the pump beam is shorter than this separation, this separation causes a loss of the coherence between photons generated from separated multiple NLCs and thus only an incoherent mixture of photons can be obtained [21

21. Y. -H. Kim, S. P. Kulik, and Y. Shih, “High-intensity pulsed source of space-time and polarization double-entangled photon pairs,” Phys. Rev. A **62**(1), 011802 (2000). [CrossRef]

22. R. Rangarajan, M. Goggin, and P. Kwiat, “Optimizing type-I polarization-entangled photons,” Opt. Express **17**(21), 18920–18933 (2009). [CrossRef]

*l*in the BBO crystal is approximately 0.1 mm and that in the air gap is less than 1

*μ*m. In our experimental setup shown in Sec. 3, the CW pump laser with a narrow linewidth (∼ 100 kHz) is used. The coherence length of the laser is an order of 1 km and is much longer than these separations (0.1 mm and 1

*μ*m). In this condition, the effect of group velocity mismatch is negligible and it is not necessary to stabilize the distance between crystals with interferometric accuracy. Note that similar condition has been widely used for the polarization-entanglement sources [23

23. P. G. Kwiat, E. Waks, A. G. White, I. Appelbaum, and P. H. Eberhard, “Ultrabright source of polarization-entangled photons,” Phys. Rev. A **60**(2), R773–R776 (1999). [CrossRef]

25. H. Fujiwara, Y. Kawabe, R. Okamoto, S. Takeuchi, and K. Sasaki, “Quantum lithography under imperfect conditions effects of loss and dephasing on two-photon interference fringes,” J. Opt. Soc. Am. B **28**(3), 422–431 (2011). [CrossRef]

21. Y. -H. Kim, S. P. Kulik, and Y. Shih, “High-intensity pulsed source of space-time and polarization double-entangled photon pairs,” Phys. Rev. A **62**(1), 011802 (2000). [CrossRef]

22. R. Rangarajan, M. Goggin, and P. Kwiat, “Optimizing type-I polarization-entangled photons,” Opt. Express **17**(21), 18920–18933 (2009). [CrossRef]

26. M. Atatüre, A. V. Sergienko, B. E. A. Saleh, and M. C. Teich, “Entanglement in cascaded-crystal parametric down-conversion,” Phys. Rev. Lett. **86**(18), 4013–4016 (2002). [CrossRef]

20. G. D. Giuseppe, M. Atatüre, M. D. Shaw, A. V. Sergienko, B. E. A. Saleh, and M. C. Teich, “Entangled-photon generation from parametric down-conversion in media with inhomogeneous nonlinearity,” Phys. Rev. A **66**(1), 013801 (2002). [CrossRef]

*F*(+Ω) =

_{i}*F*(−Ω) (

_{i}*i*=

*a,b*) is a symmetric frequency spectrum of photons generated from

*i*th NLC as explained in Sec. 2 and

*ϕ*(Ω) is a phase term. This phase term can be given by

_{d}*ϕ*(Ω) = Δ

_{d}*k*(Ω)

*d*, where Δ

*k*(Ω) is a momentum mismatch between the pump beam, signal and idler photons in the air gap. This momentum mismatch can be written by

*n*(

*ω*) is a refractive index of the air at the frequency

*ω*.

17. C. Hong, Z. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. **59**(18), 2044–2046 (1987). [CrossRef] [PubMed]

*P*(

_{c}*τ*) between two separated output ports A and B of the HOM interferometer with the slow single photon detectors can be written by where

*τ*is a relative time delay between signal and idler photons,

*a*(

_{j}*ω*)(

_{j}*j*=

*A*,

*B*) is an annihilation operator for the mode coupled to the output port

*j*=

*A*,

*B*at the frequency

*ω*and

_{j}*a*(Ω

_{j}*)(*

_{k}*j*=

*s*,

*i*and

*k*=

*A*,

*B*) is an annihilation operator for the mode of signal (

*j*=

*s*) and idler (

*j*=

*i*) photons at the frequency Ω

*[27*

_{k}27. A. Steinberg, P. Kwiat, and R. Chiao, “Dispersion cancellation and high-resolution time measurements in a fourth-order optical interferometer,” Phys. Rev. A **45**(9), 6659–6665 (1992). [CrossRef] [PubMed]

*F*(Ω)(

_{i}*i*=

*a,b*) of photons generated from

*i*th NLC is assumed to be different from each other (cf. Fig. 2). Then a sum of two spectra

*F*(Ω) +

_{a}*F*(Ω) has broadened bandwidth (Ω/2

_{b}*π*∼ 70 THz in this case).

*ϕ*= 0); (2) The case of our experimental condition, with the pump laser wavelength

_{d}*λ*of 404 nm and the air gap distance

_{p}*d*of 10 mm (The average of

*ϕ*over the fluorescence spectrum is approximately 0.37

_{d}*π*); (3) The worst case (

*ϕ*=

_{d}*π*), which corresponds to the air gap distance approximately 27 mm for

*λ*of 404 nm. Note that the phase term

_{p}*ϕ*is a function of the gap distance

_{d}*d*between the crystals and refractive indices

*n*of the pump and signal (idler) photons. The results of the calculations for these three cases are shown in Fig. 6(b). The solid black line, the dashed blue line, and the dashed-dotted red line corresponds to case (1), (2), and (3) respectively. In case (1), the HOM interference curve is simply the inverse Fourier transform of the absolute value squared of the sum of the two spectra (

*F*(Ω) +

_{a}*F*(Ω)), which is shown as the black line in Fig. 6(a). The width of this HOM dip (

_{b}*cτ*∼ 3

*μ*m) corresponds to the time correlation of the signal and the idler photon (

*τ*∼ 9 fs). Note that the difference between the dashed blue line (case (2)) and the solid black line (case (1)) is negligibly small. In the worst case (case (3)), the width of the HOM dip is almost the same with the HOM dip given solely by the first crystal (

*F*(Ω)). Note that the difference between the curves becomes less significant when the overlap of

_{a}*F*(Ω) and

_{a}*F*(Ω) become smaller. Note also that this effect caused by momentum mismatch changes has a sinusoidal dependence on the gap distance

_{b}*d*, with a period of 54 mm in our experimental condition. Thus, it is not necessary to stabilize the distance between crystals with interferometric accuracy for this effect, too.

## 5. Conclusion

## Acknowledgments

## References and links

1. | E. Knill, R. Laflamme, and G. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature |

2. | L. -M. Duan, M. Lukin, J. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature |

3. | S. E. Harris, “Chirp and compress: Toward single-cycle biphotons,” Phys. Rev. Lett. |

4. | G. Brida, V. Caricato, M. V. Fedorov, M. Genovese, M. Gramegna, and S. P. Kulik, “Characterization of spectral entanglement of spontaneous parametric-down conversion biphotons in femtosecond pulsed regime,” Europhys. Lett. |

5. | M. B. Nasr, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Demonstration of dispersion-canceled quantum-optical coherence tomography,” Phys. Rev. Lett. |

6. | B. Dayan, A. Pe’er, A. A. Friesem, and Y. Silberberg, “Two photon absorption and coherent control with broadband down-converted light,” Phys. Rev. Lett. |

7. | S. M. Hendrickson, M. M. Lai, T. B. Pittman, and J. D. Franson, “Observation of two-photon absorption at low power levels using tapered optical fibers in rubidium vapor,” Phys. Rev. Lett. |

8. | V. Giovannetti, S. Lloyd, L. Maccone, and F. N. C. Wong, “Clock synchronization with dispersion cancellation,” Phys. Rev. Lett. |

9. | N. Mohan, O. Minaeva, G. Goltsman, M. Saleh, M. Nasr, A. Sergienko, B. Saleh, and M. Teich, “Ultrabroadband coherence-domain imaging using parametric downconversion and superconducting single-photon detectors at 1064 nm,” Appl. Opt. |

10. | M. Nasr, S. Carrasco, B. Saleh, A. Sergienko, M. Teich, J. Torres, L. Torner, D. Hum, and M. Fejer, “Ultra-broadband biphotons generated via chirped quasi-phase-matched optical parametric down-conversion,” Phys. Rev. Lett. |

11. | A. M. Brańczyk, A. Fedrizzi, T. M. Stace, T. C. Ralph, and A. G. White, “Engineered optical nonlinearity for quantum light sources,” Opt. Express |

12. | K. G. Katamadze and S. P. Kulik, “Control of the spectrum of the biphoton field,” JETP |

13. | E. Dauler, G. Jaeger, A. Muller, A. Migdall, and A. Sergienko, “Tests of a two-photon technique for measuring polarization mode dispersion with subfemtosecond precision,” J. Res. Natl. Inst. Stand. Technol. |

14. | S. Carrasco, M. B. Nasr, A. V. Sergienko, B. E. A. Saleh, M. C. Teich, J. P. Torres, and L. Torner, “Broadband light generation by non-collinear parametric downconversion,” Opt. Lett. |

15. | M. Hendrych, X. Shi, A. Valencia, and J. Torres, “Broadening the bandwidth of entangled photons: A step towards the generation of extremely short biphotons,” Phys. Rev. A |

16. | K. O’Donnell and A. U’Ren, “Observation of ultrabroadband, beamlike parametric downconversion,” Opt. Lett. |

17. | C. Hong, Z. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. |

18. | R. Boyd, |

19. | S. Baek and Y. Kim, “Spectral properties of entangled photon pairs generated via frequency-degenerate type-i spontaneous parametric down-conversion,” Phys. Rev. A |

20. | G. D. Giuseppe, M. Atatüre, M. D. Shaw, A. V. Sergienko, B. E. A. Saleh, and M. C. Teich, “Entangled-photon generation from parametric down-conversion in media with inhomogeneous nonlinearity,” Phys. Rev. A |

21. | Y. -H. Kim, S. P. Kulik, and Y. Shih, “High-intensity pulsed source of space-time and polarization double-entangled photon pairs,” Phys. Rev. A |

22. | R. Rangarajan, M. Goggin, and P. Kwiat, “Optimizing type-I polarization-entangled photons,” Opt. Express |

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

24. | Y. Kawabe, H. Fujiwara, R. Okamoto, K. Sasaki, and S. Takeuchi, “Quantum interference fringes beating the diffraction limit,” Opt. Express |

25. | H. Fujiwara, Y. Kawabe, R. Okamoto, S. Takeuchi, and K. Sasaki, “Quantum lithography under imperfect conditions effects of loss and dephasing on two-photon interference fringes,” J. Opt. Soc. Am. B |

26. | M. Atatüre, A. V. Sergienko, B. E. A. Saleh, and M. C. Teich, “Entanglement in cascaded-crystal parametric down-conversion,” Phys. Rev. Lett. |

27. | A. Steinberg, P. Kwiat, and R. Chiao, “Dispersion cancellation and high-resolution time measurements in a fourth-order optical interferometer,” Phys. Rev. A |

28. | A. Pe’er, Y. Bromberg, B. Dayan, Y. Silberberg, and A. A. Friesem, “Broadband sum-frequency generation as an efficient two-photon detector for optical tomography,” Opt. Express |

29. | R. Kaltenbaek, J. Lavoie, D. N. Biggerstaff, and K. J. Resch, “Quantum-inspired interferometry with chirped laser pulses,” Nat. Phys. |

**OCIS Codes**

(190.4410) Nonlinear optics : Nonlinear optics, parametric processes

(270.0270) Quantum optics : Quantum optics

**ToC Category:**

Quantum Optics

**History**

Original Manuscript: April 26, 2012

Revised Manuscript: May 18, 2012

Manuscript Accepted: May 21, 2012

Published: June 8, 2012

**Citation**

Masayuki Okano, Ryo Okamoto, Akira Tanaka, Shanthi Subashchandran, and Shigeki Takeuchi, "Generation of broadband spontaneous parametric fluorescence using multiple bulk nonlinear crystals," Opt. Express **20**, 13977-13987 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-13-13977

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### References

- E. Knill, R. Laflamme, and G. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature409(6816), 46–52 (2001). [CrossRef] [PubMed]
- L. -M. Duan, M. Lukin, J. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature414(6862), 413–418 (2001). [CrossRef] [PubMed]
- S. E. Harris, “Chirp and compress: Toward single-cycle biphotons,” Phys. Rev. Lett.98(6), 063602 (2007). [CrossRef] [PubMed]
- G. Brida, V. Caricato, M. V. Fedorov, M. Genovese, M. Gramegna, and S. P. Kulik, “Characterization of spectral entanglement of spontaneous parametric-down conversion biphotons in femtosecond pulsed regime,” Europhys. Lett.87(6), 64003 (2009). [CrossRef]
- M. B. Nasr, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Demonstration of dispersion-canceled quantum-optical coherence tomography,” Phys. Rev. Lett.91(8), 083601 (2003). [CrossRef] [PubMed]
- B. Dayan, A. Pe’er, A. A. Friesem, and Y. Silberberg, “Two photon absorption and coherent control with broadband down-converted light,” Phys. Rev. Lett.93(2), 023005 (2004). [CrossRef] [PubMed]
- S. M. Hendrickson, M. M. Lai, T. B. Pittman, and J. D. Franson, “Observation of two-photon absorption at low power levels using tapered optical fibers in rubidium vapor,” Phys. Rev. Lett.105(17), 173602 (2010). [CrossRef]
- V. Giovannetti, S. Lloyd, L. Maccone, and F. N. C. Wong, “Clock synchronization with dispersion cancellation,” Phys. Rev. Lett.87(11), 117902 (2001). [CrossRef] [PubMed]
- N. Mohan, O. Minaeva, G. Goltsman, M. Saleh, M. Nasr, A. Sergienko, B. Saleh, and M. Teich, “Ultrabroadband coherence-domain imaging using parametric downconversion and superconducting single-photon detectors at 1064 nm,” Appl. Opt.48(20), 4009–4017 (2009). [CrossRef] [PubMed]
- M. Nasr, S. Carrasco, B. Saleh, A. Sergienko, M. Teich, J. Torres, L. Torner, D. Hum, and M. Fejer, “Ultra-broadband biphotons generated via chirped quasi-phase-matched optical parametric down-conversion,” Phys. Rev. Lett.100(18), 183601 (2008). [CrossRef] [PubMed]
- A. M. Brańczyk, A. Fedrizzi, T. M. Stace, T. C. Ralph, and A. G. White, “Engineered optical nonlinearity for quantum light sources,” Opt. Express19(1), 55–65 (2011). [CrossRef]
- K. G. Katamadze and S. P. Kulik, “Control of the spectrum of the biphoton field,” JETP112(1), 20–37 (2011). [CrossRef]
- E. Dauler, G. Jaeger, A. Muller, A. Migdall, and A. Sergienko, “Tests of a two-photon technique for measuring polarization mode dispersion with subfemtosecond precision,” J. Res. Natl. Inst. Stand. Technol.104(1), 1–10 (1999). [CrossRef]
- S. Carrasco, M. B. Nasr, A. V. Sergienko, B. E. A. Saleh, M. C. Teich, J. P. Torres, and L. Torner, “Broadband light generation by non-collinear parametric downconversion,” Opt. Lett.31(2), 253–255 (2006). [CrossRef] [PubMed]
- M. Hendrych, X. Shi, A. Valencia, and J. Torres, “Broadening the bandwidth of entangled photons: A step towards the generation of extremely short biphotons,” Phys. Rev. A79(2), 023817 (2009). [CrossRef]
- K. O’Donnell and A. U’Ren, “Observation of ultrabroadband, beamlike parametric downconversion,” Opt. Lett.32(7), 817–819 (2007). [CrossRef]
- C. Hong, Z. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett.59(18), 2044–2046 (1987). [CrossRef] [PubMed]
- R. Boyd, Nonlinear optics (Academic Press, 2003).
- S. Baek and Y. Kim, “Spectral properties of entangled photon pairs generated via frequency-degenerate type-i spontaneous parametric down-conversion,” Phys. Rev. A77(4), 043807 (2008). [CrossRef]
- G. D. Giuseppe, M. Atatüre, M. D. Shaw, A. V. Sergienko, B. E. A. Saleh, and M. C. Teich, “Entangled-photon generation from parametric down-conversion in media with inhomogeneous nonlinearity,” Phys. Rev. A66(1), 013801 (2002). [CrossRef]
- Y. -H. Kim, S. P. Kulik, and Y. Shih, “High-intensity pulsed source of space-time and polarization double-entangled photon pairs,” Phys. Rev. A62(1), 011802 (2000). [CrossRef]
- R. Rangarajan, M. Goggin, and P. Kwiat, “Optimizing type-I polarization-entangled photons,” Opt. Express17(21), 18920–18933 (2009). [CrossRef]
- P. G. Kwiat, E. Waks, A. G. White, I. Appelbaum, and P. H. Eberhard, “Ultrabright source of polarization-entangled photons,” Phys. Rev. A60(2), R773–R776 (1999). [CrossRef]
- Y. Kawabe, H. Fujiwara, R. Okamoto, K. Sasaki, and S. Takeuchi, “Quantum interference fringes beating the diffraction limit,” Opt. Express15(21), 14244–14250 (2007). [CrossRef] [PubMed]
- H. Fujiwara, Y. Kawabe, R. Okamoto, S. Takeuchi, and K. Sasaki, “Quantum lithography under imperfect conditions effects of loss and dephasing on two-photon interference fringes,” J. Opt. Soc. Am. B28(3), 422–431 (2011). [CrossRef]
- M. Atatüre, A. V. Sergienko, B. E. A. Saleh, and M. C. Teich, “Entanglement in cascaded-crystal parametric down-conversion,” Phys. Rev. Lett.86(18), 4013–4016 (2002). [CrossRef]
- A. Steinberg, P. Kwiat, and R. Chiao, “Dispersion cancellation and high-resolution time measurements in a fourth-order optical interferometer,” Phys. Rev. A45(9), 6659–6665 (1992). [CrossRef] [PubMed]
- A. Pe’er, Y. Bromberg, B. Dayan, Y. Silberberg, and A. A. Friesem, “Broadband sum-frequency generation as an efficient two-photon detector for optical tomography,” Opt. Express15(14), 8760–8769 (2007). [CrossRef]
- R. Kaltenbaek, J. Lavoie, D. N. Biggerstaff, and K. J. Resch, “Quantum-inspired interferometry with chirped laser pulses,” Nat. Phys.4(11), 864–868 (2008). [CrossRef]

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