## Wavelength conversion of incoherent light by sum-frequency generation |

Optics Express, Vol. 22, Issue 11, pp. 12944-12961 (2014)

http://dx.doi.org/10.1364/OE.22.012944

Acrobat PDF (1277 KB)

### Abstract

In this paper, we reveal that some kinds of optical nonlinearities are further enhanced when incoherent light, instead of a laser, is used as a pump light. This idea was confirmed both theoretically and experimentally in the case of sum-frequency generation (SFG) using the optical second nonlinearity. The conversion efficiency of the SFG with incoherent light pumping increased as the bandwidth of the incoherent pump light decreased, finally reaching twice the conversion efficiency of conventional second harmonic generation (SHG) by laser pumping. This method dramatically relaxes the severe requirements of phase matching in the nonlinear optical process. The conversion efficiency became less sensitive to misalignment of the wavelength of pump light and also of device operation temperature when the bandwidth of the incoherent pump light was sufficiently broad, although the improvement of the conversion efficiency had an inverse relationship with the insensitivity to the phase-matching condition. The temperature tuning range was enhanced by more than two orders of magnitude in comparison with the conventional SHG method. As an example of a promising application of this new idea, we performed the generation of quantum entangled photon-pairs using cascaded optical nonlinearities (SFG and the subsequent spontaneous parametric down conversion) in a single periodically poled LiNbO_{3} waveguide device, in which the incoherent light was used as the pump source for both the parametric processes. We have achieved high fidelity exceeding 99% in quantum-state tomography experiments.

© 2014 Optical Society of America

## 1. Introduction

1. J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. **127**(6), 1918–1939 (1962). [CrossRef]

2. M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quansi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. **28**(11), 2631–2654 (1992). [CrossRef]

3. S. J. B. Yoo, “Wavelength conversion technologies for WDM network applications,” J. Lightwave Technol. **14**(6), 955–966 (1996). [CrossRef]

5. M. H. Chou, I. Brener, M. M. Fejer, E. E. Chaban, and S. B. Christman, “1.5-μm-band wavelength conversion based on cascaded second-order nonlinearity in LiNbO_{3} waveguide,” IEEE Photon. Technol. Lett. **11**(6), 653–655 (1999). [CrossRef]

6. A. W. Smith and N. Braslau, “Optical mixing of coherent and incoherent light,” IBM J. Res. Develop. **6**(3), 361–362 (1962). [CrossRef]

10. J. S. Dam, P. Tidemand-Lichtenberg, and C. Pedersen, “Room-temperature mid-infrared single-photon spectral imaging,” Nat. Photonics **6**(11), 788–793 (2012). [CrossRef]

^{(2)}) device [Fig. 1]. The best conversion efficiency that could be obtained using this approach is twice the conversion efficiency of conventional second-harmonic generation (SHG) by laser pumping. The experimental results agreed well with the theoretical predictions given in this study. Moreover, this new method relaxes the severe requirements of phase matching in the nonlinear optical process, which is often very sensitive and severe in the case of the conventional SHG method. The temperature tuning range was enhanced by more than two orders of magnitude in comparison with the conventional SHG method. As an example of a promising application of this new approach, we also discuss the generation of quantum-entangled photon pairs using cascaded optical nonlinearities (the SFG and subsequent spontaneous parametric down conversion (SPDC)) with incoherent light pumping. The quantum state achieved here was highly efficient, pure and coherent even though the nonlinear processes were driven by an incoherent light source with poor temporal coherence. High fidelity exceeding 99% in quantum-state tomography experiments was obtained in this work.

## 2. Theoretical studies

*f*generated from incoherent light, the electric fields of which are given as the dashed curve in Fig. 2.Here, we assume that the spectrum of the incoherent pump light is

_{0}*continuous*, rather than discrete as that of a laser. This is generally expected in an incoherent light source. We also assume that they are spread over an optical frequency of

*f*. The 3-dB bandwidth in the intensity profile is defined as

_{0}/2*Δf*.

_{pump}*f*is generated only from a frequency component at

_{0}*f*. Therefore, it can be neglected because this frequency component occupies a negligibly small portion in the whole spectrum. On the other hand, the SFG at the frequency

_{0}/2*f*can be generated from numerous combinations of symmetric frequency components at

_{0}*N*sections every Δ

*f*frequency. Each combination of

*f*, where

_{0}*l*-th frequency mode per unit frequency. Nonlinear polarization at

*f*per unit frequency,

_{0}*l-th*frequency mode (

1. J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. **127**(6), 1918–1939 (1962). [CrossRef]

2. M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quansi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. **28**(11), 2631–2654 (1992). [CrossRef]

*f*per unit frequency. In this equation, losses and pump depletion are neglected for simplicity. The phase mismatching parameter for the

_{0}*l*-th mode is given bywhere

*K*is a parameter corresponding to the quasi phase-matching (QPM) structure, and

*n*is the refractive index of the SFG light).

_{SFG}*i e.,*

*L*is the device length.

*f*per unit frequency,

_{0}*l = m*. Consequently,

*C*is a coefficient that includes

*A, B, L*, and so on.

*f*and the 3-dB bandwidth is

_{0}/2*Δf*where

_{pump}, i.e.,*I*is the peak spectral intensity per unit frequency.

_{pump}*Δf*is sufficiently small

*Δf*. When we compare Eq. (13) with Eq. (14), it is clear that the SFG power in this case finally exceeds the SHG power of conventional laser pumping when the spectral bandwidth is sufficiently narrow (less than 1.5 times that of the SHG bandwidth,

_{pump}*Δf*) in the case of Eq. (13). Such general tendencies are still valid in the more accurate model discussed below.

_{SHG}*f*should be given bywhereis the phase-mismatching parameter among frequency modes at frequencies

*f*(SFG).

*Δ*, which is, in general, a function of

*x*and

*f*, and it varies when the frequencies of the two pump lights and SFG light change. However, when the refractive-index profile within the spectrum of the pump light yields a linear relationship,

*i.e.*, the refractive index

*n*is simply given by

*Δ*can be expressed as,

*Δ*is

*x*-independent and has a constant value when the SFG frequency (

*f*) is fixed (here, we used the energy conservation law of the SFG process,

*Δ*as(here, we used the relationship

*Δ*is also equal to the phase mismatching of the SHG process in the case of conventional laser pumping.

*sinc*-function in Eq. (20) is equal to that of the SHG curve of conventional laser pumping.

^{2}*Δ*. According to previous reports, including our report [3

3. S. J. B. Yoo, “Wavelength conversion technologies for WDM network applications,” J. Lightwave Technol. **14**(6), 955–966 (1996). [CrossRef]

5. M. H. Chou, I. Brener, M. M. Fejer, E. E. Chaban, and S. B. Christman, “1.5-μm-band wavelength conversion based on cascaded second-order nonlinearity in LiNbO_{3} waveguide,” IEEE Photon. Technol. Lett. **11**(6), 653–655 (1999). [CrossRef]

11. T. Kishimoto and K. Nakamura, “Periodically poled MgO-doped stoichiometric LiNbO_{3} wavelength convertor with ridge-type annealed proton-exchanged waveguide,” IEEE Photon. Technol. Lett. **23**(3), 161–163 (2011). [CrossRef]

12. S. Arahira, N. Namekata, T. Kishimoto, H. Yaegashi, and S. Inoue, “Generation of polarization entangled photon pairs at telecommunication wavelength using cascaded χ^{(2)} processes in a periodically poled LiNbO_{3} ridge waveguide,” Opt. Express **19**(17), 16032–16043 (2011). [CrossRef] [PubMed]

_{3}(PPLN) waveguide device. Therefore, when the bandwidth of the input incoherent light is several tens of nanometers at most, the assumption above is valid. In this case, all the spectral components of the input incoherent light, rather than only a part of it, can contribute to the generation of the SFG. As a result, the intensity of the generated SFG light can be very high, even though optical nonlinearity is induced by the incoherent light.

*sinc*function in Eq. (20) can be expressed using the 3-dB bandwidth of the SHG curve with conventional laser pumping,

^{2}*Δf*, as follows:

_{SHG}*δ*is the deviation of the center frequency of input light’s spectrum from the optimized (phase-matching) condition

_{p}*f*.

_{0}/2*P*) and the bandwidth of the SFG spectrum (

_{SFG}*Δf*) as functions of the bandwidth of the pump light (

_{SFG}*Δf*). In these calculations, we consider the ideal case of

_{pump}*δ*= 0.

_{p}*P*and

_{SFG}*Δf*are normalized to the SHG power (

_{SFG}*P*) and the SHG bandwidth (

_{SHG}*Δf*), respectively, in the case of conventional SHG wih laser pumping at the same pump power. The bandwidth of the pump light is also normalized to

_{SHG}*Δf*.

_{SHG}*P*increased and

_{SFG}*Δf*decreased as

_{SFG}*Δf*decreased.

_{pump}*P*exceeded

_{SFG}*P*when

_{SHG}*Δf*was approximately 1.2 times that of

_{pump}*Δf*in this calculation. This value was slightly less than the value obtained through a rough estimation using Eq. (13), most likely because of spectral narrowing in the SFG spectrum.

_{SHG}*P*finally reached twice the

_{SFG}*P*when

_{SHG}*Δf*was further narrowed. This can be confirmed as follows.

_{pump}*Δf*becomes much less than

_{pump}*Δf*, the

_{SHG}*sinc*function can be treated as 1, and Eq. (22) is therefore approximately

^{2}*Δf*, as the bandwidth of pump light at which

_{cri}*P*is equal to

_{SFG}*P*, this value depends on the spectral shape of the pump light. In Fig. 3, we also showed the calculated results when the spectral shape of the pump light was rectangular (dashed) and Lorentzian (dotted). We estimated

_{SHG}*Δf*to be approximately 1.6x, 1.2x, and 0.45x

_{cri}*Δf*for rectangular, Gaussian, and Lorentzian shapes, respectively.

_{SHG}*δ*is permitted to suppress the degradation of the SFG power well. Large tolerance to the

_{p}*δ*implies that the SFG power is less sensitive to changes in operation temperature of a nonlinear device because the change in operation temperature generally changes the phase-matching wavelength (

_{p}*f*) owing to the changes in refractive indices, which gives the

_{0}/2*δ*.

_{p}*δ*as the frequency offset in which the degradation of SFG power is less than 3 dB of the best (phase-matched) case,

_{p,max}*δ*can be roughly estimated from Eq. (22) as

_{p,max}*δ*for the conventional SHG with laser pumping is

_{p,max}*N*times if we use

^{2}*N*light sources with no special consideration of interference among the light sources due to the incoherent nature of such light sources.

## 3. Experimental results

_{3}waveguide (PPLN-WG) devices with ridge waveguide structures. Details of the device structure and fabrication process are available in [11

11. T. Kishimoto and K. Nakamura, “Periodically poled MgO-doped stoichiometric LiNbO_{3} wavelength convertor with ridge-type annealed proton-exchanged waveguide,” IEEE Photon. Technol. Lett. **23**(3), 161–163 (2011). [CrossRef]

*Δf*) was approximately 50 GHz, corresponding to 0.1 nm in the wavelength domain (the measured SHG curve was plotted as red open symbols in Fig. 7). This value is typical for a 6-cm-long PPLN device [11

_{SHG}11. T. Kishimoto and K. Nakamura, “Periodically poled MgO-doped stoichiometric LiNbO_{3} wavelength convertor with ridge-type annealed proton-exchanged waveguide,” IEEE Photon. Technol. Lett. **23**(3), 161–163 (2011). [CrossRef]

12. S. Arahira, N. Namekata, T. Kishimoto, H. Yaegashi, and S. Inoue, “Generation of polarization entangled photon pairs at telecommunication wavelength using cascaded χ^{(2)} processes in a periodically poled LiNbO_{3} ridge waveguide,” Opt. Express **19**(17), 16032–16043 (2011). [CrossRef] [PubMed]

*Δf*were approximately 1548.54 nm (at 25.0°C) and 150 GHz (0.3 nm), respectively.

_{SHG}*Δf*) was experimentally estimated to be 1.3 nm (163 GHz). This value was approximately 1.1 times that of the SHG bandwidth of the 2-cm-long device (150 GHz) and also agreed well with the theoretical value.

_{cri}*i*) and

_{SFG}*Δf*. This can be understood as follows.

_{pump}*I*), the peak SFG intensity,

_{pump}*δT*, defined as the temperature range in which the degradation in the SFG (and SHG) power is less than 3 dB of the best (phase-matched) case, was estimated to be approximately 1.6 °C for the conventional SHG case. Because the temperature dependence of the QPM wavelength was approximately 0.13 nm/°C in our devices, this temperature range corresponded to approximately 26 GHz of the frequency offset. This value was half of the bandwidth of the SHG curve (

*Δf*), as predicted theoretically.

_{SHG}*δT*increased as the bandwidth of the pump light increased. When the bandwidth was 10.8 nm, the SFG power exhibited no significant degradation, even though the operation temperature changed by over 30 °C.

*Δf*satisfies the following condition:

_{pump}*δT*, and therefore the tolerance to phase mismatching, can be similarly increased even in the case of laser pumping when a laser with a broad spectral bandwidth is used as the pump light. However, this is not correct. Figure 11 shows the temperature tuning characteristics of the SHG power when we used a multi-longitudinal-mode Fabry-Perot laser diode as the pump light. The results showed periodic behavior of the SHG power. The period almost corresponded to half the mode spacing of the Fabry-Perot laser used here (approximately 1.26 nm). This indicates that the SHG power in this case was enhanced only when one of the lasing modes corresponded to the phase-matching wavelength in the SHG, or when the lasing modes were located symmetric to the phase-matching wavelength to satisfy the phase-matching condition in the SFG. These results were quite different from the method in this work, verifying the advantages of our method.

## 4. Generation of quantum entanglement by cascading χ^{(2)} processes

12. S. Arahira, N. Namekata, T. Kishimoto, H. Yaegashi, and S. Inoue, “Generation of polarization entangled photon pairs at telecommunication wavelength using cascaded χ^{(2)} processes in a periodically poled LiNbO_{3} ridge waveguide,” Opt. Express **19**(17), 16032–16043 (2011). [CrossRef] [PubMed]

14. S. Arahira and H. Murai, “Nearly degenerate wavelength-multiplexed polarization entanglement by cascaded optical nonlinearities in a PPLN ridge waveguide device,” Opt. Express **21**(6), 7841–7850 (2013). [CrossRef] [PubMed]

^{−6}per gate for both detectors. The single count rate of each single photon detector and the coincidence counts between the two detectors were measured using a time-interval analyzer.

*R*) from the coincidence counts at the matched time slot (

_{um}*R*) in the time-interval analyzer. This subtraction was performed because the accidental counts due to residual pump photons ceased to be negligible when the

_{m}*Δf*became large and the HPFs could not suppress the residual pump photons satisfactorily. Theoretically, the

_{pump}*R*value was simply proportional to the mean number of photon pairs [15

_{m}-R_{um}15. H. Takesue, H. Fukuda, T. Tsuchizawa, T. Watanabe, K. Yamada, Y. Tokura, and S. Itabashi, “Generation of polarization entangled photon pairs using silicon wire waveguide,” Opt. Express **16**(8), 5721–5727 (2008). [CrossRef] [PubMed]

^{(2)} processes in a periodically poled LiNbO_{3} ridge waveguide,” Opt. Express **19**(17), 16032–16043 (2011). [CrossRef] [PubMed]

13. M. Hunault, H. Takesue, O. Tadanaga, Y. Nishida, and M. Asobe, “Generation of time-bin entangled photon pairs by cascaded second-order nonlinearity in a single periodically poled LiNbO_{3} waveguide,” Opt. Lett. **35**(8), 1239–1241 (2010). [CrossRef] [PubMed]

^{(2)} processes in a periodically poled LiNbO_{3} ridge waveguide,” Opt. Express **19**(17), 16032–16043 (2011). [CrossRef] [PubMed]

16. H. C. Lim, A. Yoshizawa, H. Tsuchida, and K. Kikuchi, “Stable source of high quality telecom-band polarization-entangled photon-pairs based on a single, pulse-pumped, short PPLN waveguide,” Opt. Express **16**(17), 12460–12468 (2008). [CrossRef] [PubMed]

^{(2)} processes in a periodically poled LiNbO_{3} ridge waveguide,” Opt. Express **19**(17), 16032–16043 (2011). [CrossRef] [PubMed]

16. H. C. Lim, A. Yoshizawa, H. Tsuchida, and K. Kikuchi, “Stable source of high quality telecom-band polarization-entangled photon-pairs based on a single, pulse-pumped, short PPLN waveguide,” Opt. Express **16**(17), 12460–12468 (2008). [CrossRef] [PubMed]

17. D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White, “Measurement of qubits,” Phys. Rev. A **64**(5), 052312 (2001). [CrossRef]

*i.e*., increasing mean number of photon pairs, the diagonal elements and the offdiagonal elements became smaller while the

18. K. Edamatsu, “Entangled photons: generation, observation, and characterization,” Jpn. J. Appl. Phys. **46**(11), 7175–7187 (2007). [CrossRef]

*ρ*, of a

_{W}18. K. Edamatsu, “Entangled photons: generation, observation, and characterization,” Jpn. J. Appl. Phys. **46**(11), 7175–7187 (2007). [CrossRef]

*V, P*, and

*F*in the quantum-state tomography experiments. The solid curves in the figure are the calculated curves from Eq. (31) and Eq. (32). The experimental values agreed very well with the theoretical values. In the figure, we also show the fidelity of the Werner state (

*F*), defined as

_{W}18. K. Edamatsu, “Entangled photons: generation, observation, and characterization,” Jpn. J. Appl. Phys. **46**(11), 7175–7187 (2007). [CrossRef]

*F*was almost unchanged and showed values higher than 99%, even when

_{W}*V*changed, while the

*F*of the Bell state was monotonically decreased as

*V*decreased. This experimentally verified that our photon-pair source was actually close to the Werner state, similar to the case with conventional laser pumping [19

19. S. Arahira, T. Kishimoto, and H. Murai, “1.5-μm band polarization entangled photon-pair source with variable Bell states,” Opt. Express **20**(9), 9862–9875 (2012). [CrossRef] [PubMed]

## 5. Conclusion

## References and links

1. | J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. |

2. | M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quansi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. |

3. | S. J. B. Yoo, “Wavelength conversion technologies for WDM network applications,” J. Lightwave Technol. |

4. | C. Q. Xu, H. Okayama, and M. Kawahara, “Optical frequency conversions in nonlinear medium with periodically modulated linear and nonlinear optical parameters,” IEEE J. Quantum Electron. |

5. | M. H. Chou, I. Brener, M. M. Fejer, E. E. Chaban, and S. B. Christman, “1.5-μm-band wavelength conversion based on cascaded second-order nonlinearity in LiNbO |

6. | A. W. Smith and N. Braslau, “Optical mixing of coherent and incoherent light,” IBM J. Res. Develop. |

7. | P. Chmela, Z. Ficek, and S. Kielich, “Enhanced incoherent sum-frequency generation by group velocity difference,” Opt. Commun. |

8. | J. Shah, “Ultrafast luminescence spectroscopy using sum frequency generation,” IEEE J. Quantum Electron. |

9. | D. M. Hoffmann, K. Kuhnke, and K. Kern, “Sum-frequency generation microscope for opaque and reflecting samples,” Rev. Sci. Instrum. |

10. | J. S. Dam, P. Tidemand-Lichtenberg, and C. Pedersen, “Room-temperature mid-infrared single-photon spectral imaging,” Nat. Photonics |

11. | T. Kishimoto and K. Nakamura, “Periodically poled MgO-doped stoichiometric LiNbO |

12. | S. Arahira, N. Namekata, T. Kishimoto, H. Yaegashi, and S. Inoue, “Generation of polarization entangled photon pairs at telecommunication wavelength using cascaded χ |

13. | M. Hunault, H. Takesue, O. Tadanaga, Y. Nishida, and M. Asobe, “Generation of time-bin entangled photon pairs by cascaded second-order nonlinearity in a single periodically poled LiNbO |

14. | S. Arahira and H. Murai, “Nearly degenerate wavelength-multiplexed polarization entanglement by cascaded optical nonlinearities in a PPLN ridge waveguide device,” Opt. Express |

15. | H. Takesue, H. Fukuda, T. Tsuchizawa, T. Watanabe, K. Yamada, Y. Tokura, and S. Itabashi, “Generation of polarization entangled photon pairs using silicon wire waveguide,” Opt. Express |

16. | H. C. Lim, A. Yoshizawa, H. Tsuchida, and K. Kikuchi, “Stable source of high quality telecom-band polarization-entangled photon-pairs based on a single, pulse-pumped, short PPLN waveguide,” Opt. Express |

17. | D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White, “Measurement of qubits,” Phys. Rev. A |

18. | K. Edamatsu, “Entangled photons: generation, observation, and characterization,” Jpn. J. Appl. Phys. |

19. | S. Arahira, T. Kishimoto, and H. Murai, “1.5-μm band polarization entangled photon-pair source with variable Bell states,” Opt. Express |

**OCIS Codes**

(190.2620) Nonlinear optics : Harmonic generation and mixing

(230.4320) Optical devices : Nonlinear optical devices

(270.4180) Quantum optics : Multiphoton processes

(190.4975) Nonlinear optics : Parametric processes

(270.5565) Quantum optics : Quantum communications

**ToC Category:**

Nonlinear Optics

**History**

Original Manuscript: March 11, 2014

Revised Manuscript: April 20, 2014

Manuscript Accepted: May 13, 2014

Published: May 21, 2014

**Citation**

Shin Arahira and Hitoshi Murai, "Wavelength conversion of incoherent light by sum-frequency generation," Opt. Express **22**, 12944-12961 (2014)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-11-12944

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### References

- J. A. Armstrong, N. Bloembergen, J. Ducuing, P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127(6), 1918–1939 (1962). [CrossRef]
- M. M. Fejer, G. A. Magel, D. H. Jundt, R. L. Byer, “Quansi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28(11), 2631–2654 (1992). [CrossRef]
- S. J. B. Yoo, “Wavelength conversion technologies for WDM network applications,” J. Lightwave Technol. 14(6), 955–966 (1996). [CrossRef]
- C. Q. Xu, H. Okayama, M. Kawahara, “Optical frequency conversions in nonlinear medium with periodically modulated linear and nonlinear optical parameters,” IEEE J. Quantum Electron. 31(6), 981–987 (1995). [CrossRef]
- M. H. Chou, I. Brener, M. M. Fejer, E. E. Chaban, S. B. Christman, “1.5-μm-band wavelength conversion based on cascaded second-order nonlinearity in LiNbO3 waveguide,” IEEE Photon. Technol. Lett. 11(6), 653–655 (1999). [CrossRef]
- A. W. Smith, N. Braslau, “Optical mixing of coherent and incoherent light,” IBM J. Res. Develop. 6(3), 361–362 (1962). [CrossRef]
- P. Chmela, Z. Ficek, S. Kielich, “Enhanced incoherent sum-frequency generation by group velocity difference,” Opt. Commun. 62(6), 403–408 (1987). [CrossRef]
- J. Shah, “Ultrafast luminescence spectroscopy using sum frequency generation,” IEEE J. Quantum Electron. 24(2), 276–288 (1988). [CrossRef]
- D. M. Hoffmann, K. Kuhnke, K. Kern, “Sum-frequency generation microscope for opaque and reflecting samples,” Rev. Sci. Instrum. 73(9), 3221–3226 (2002). [CrossRef]
- J. S. Dam, P. Tidemand-Lichtenberg, C. Pedersen, “Room-temperature mid-infrared single-photon spectral imaging,” Nat. Photonics 6(11), 788–793 (2012). [CrossRef]
- T. Kishimoto, K. Nakamura, “Periodically poled MgO-doped stoichiometric LiNbO3 wavelength convertor with ridge-type annealed proton-exchanged waveguide,” IEEE Photon. Technol. Lett. 23(3), 161–163 (2011). [CrossRef]
- S. Arahira, N. Namekata, T. Kishimoto, H. Yaegashi, S. Inoue, “Generation of polarization entangled photon pairs at telecommunication wavelength using cascaded χ(2) processes in a periodically poled LiNbO3 ridge waveguide,” Opt. Express 19(17), 16032–16043 (2011). [CrossRef] [PubMed]
- M. Hunault, H. Takesue, O. Tadanaga, Y. Nishida, M. Asobe, “Generation of time-bin entangled photon pairs by cascaded second-order nonlinearity in a single periodically poled LiNbO3 waveguide,” Opt. Lett. 35(8), 1239–1241 (2010). [CrossRef] [PubMed]
- S. Arahira, H. Murai, “Nearly degenerate wavelength-multiplexed polarization entanglement by cascaded optical nonlinearities in a PPLN ridge waveguide device,” Opt. Express 21(6), 7841–7850 (2013). [CrossRef] [PubMed]
- H. Takesue, H. Fukuda, T. Tsuchizawa, T. Watanabe, K. Yamada, Y. Tokura, S. Itabashi, “Generation of polarization entangled photon pairs using silicon wire waveguide,” Opt. Express 16(8), 5721–5727 (2008). [CrossRef] [PubMed]
- H. C. Lim, A. Yoshizawa, H. Tsuchida, K. Kikuchi, “Stable source of high quality telecom-band polarization-entangled photon-pairs based on a single, pulse-pumped, short PPLN waveguide,” Opt. Express 16(17), 12460–12468 (2008). [CrossRef] [PubMed]
- D. F. V. James, P. G. Kwiat, W. J. Munro, A. G. White, “Measurement of qubits,” Phys. Rev. A 64(5), 052312 (2001). [CrossRef]
- K. Edamatsu, “Entangled photons: generation, observation, and characterization,” Jpn. J. Appl. Phys. 46(11), 7175–7187 (2007). [CrossRef]
- S. Arahira, T. Kishimoto, H. Murai, “1.5-μm band polarization entangled photon-pair source with variable Bell states,” Opt. Express 20(9), 9862–9875 (2012). [CrossRef] [PubMed]

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