## Spectral engineering by Gaussian phase-matching for quantum photonics |

Optics Express, Vol. 21, Issue 5, pp. 5879-5890 (2013)

http://dx.doi.org/10.1364/OE.21.005879

Acrobat PDF (1157 KB)

### Abstract

We demonstrate Gaussian-shaped phase matching of a periodically-poled potassium titanyl phosphate (PPKTP) crystal by imposing a custom duty-cycle pattern on its grating structure while keeping the grating period fixed. The PPKTP’s phase-matching characteristics are verified through optical difference-frequency generation measurements, showing good agreement with expected values based on our design parameters. Our theoretical analysis predicts that under extended phase-matching conditions the custom-poled PPKTP crystal is capable of generating heralded single photons with a spectral purity of 97%, and can reach as high as 99.5% with gentle spectral filtering, something that is highly desirable for photonic quantum information processing applications.

© 2013 OSA

## 1. Introduction

1. P. Kok, H. Lee, and J. P. Dowling, “Creation of large-photon-number path entanglement conditioned on photodetection,” Phys. Rev. A **65**, 052104 (2002) [CrossRef] .

3. V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum-enhanced measurements: Beating the standard quantum limit,” Science **306**, 1330–1336 (2004) [CrossRef] [PubMed] .

4. M. Halder, A. Beveratos, N. Gisin, V. Scarani, C. Simon, and H. Zbinden, “Entangling independent photons by time measurement,” Nat. Phys. **3**, 692–695 (2007) [CrossRef] .

5. R. Kaltenbaek, R. Prevedel, M. Aspelmeyer, and A. Zeilinger, “High-fidelity entanglement swapping with fully independent sources,” Phys. Rev. A **79**, 040302 (2009) [CrossRef] .

7. A. Aspuru-Guzik and P. Walther, “Photonic quantum simulators,” Nat. Phys. **8**, 285–291 (2012) [CrossRef] .

8. T. Peyronel, O. Firstenberg, Q.-Y. Liang, S. Hoffenberth, A. V. Gorshkov, T. Pohl, M. D. Lukin, and V. Vuletić, “Quantum nonlinear optics with single photons enabled by strongly interacting atoms,” Nature **488**, 57–60 (2012) [CrossRef] [PubMed] .

9. A. Muller, W. Fang, J. Lawall, and G. S. Solomon, “Creating polarization-entangled photon pairs from a semiconductor quantum dot using the optical stark effect,” Phys. Rev. Lett. **103**, 217402 (2009) [CrossRef] .

10. J. Chen, K. F. Lee, C. Liang, and P. Kumar, “Fiber-based telecom-band degenerate-frequency source of entangled photon pairs,” Opt. Lett. **31**, 2798–2800 (2006) [CrossRef] [PubMed] .

11. C. K. Hong and L. Mandel, “Theory of parametric frequency down conversion of light,” Phys. Rev. A **31**, 2409–2418 (1985) [CrossRef] [PubMed] .

12. C. Gerry and P. Knight, *Introductory Quantum Optics* (Cambridge University Press, 2004) [CrossRef] .

13. P. J. Mosley, J. S. Lundeen, B. J. Smith, P. Wasylczyk, A. B. U’Ren, C. Silberhorn, and I. A. Walmsley, “Heralded generation of ultrafast single photons in pure quantum states,” Phys. Rev. Lett. **100**, 133601 (2008) [CrossRef] [PubMed] .

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

16. R. Kaltenbaek, B. Blauensteiner, M. Żukowski, M. Aspelmeyer, and A. Zeilinger, “Experimental interference of independent photons,” Phys. Rev. Lett. **96**, 240502 (2006) [CrossRef] [PubMed] .

13. P. J. Mosley, J. S. Lundeen, B. J. Smith, P. Wasylczyk, A. B. U’Ren, C. Silberhorn, and I. A. Walmsley, “Heralded generation of ultrafast single photons in pure quantum states,” Phys. Rev. Lett. **100**, 133601 (2008) [CrossRef] [PubMed] .

17. W. P. Grice, A. B. U’Ren, and I. A. Walmsley, “Eliminating frequency and space-time correlations in multiphoton states,” Phys. Rev. A **64**, 063815 (2001) [CrossRef] .

23. E. Pomarico, B. Sanguinetti, C. I. Osorio, H. Herrmann, and R. T. Thew, “Engineering integrated pure narrow-band photon sources,” New J. Phys. **14**, 033008 (2012) [CrossRef] .

24. I. Ali Khan and J. C. Howell, “Experimental demonstration of high two-photon time-energy entanglement,” Phys. Rev. A **73**, 031801 (2006) [CrossRef] .

16. R. Kaltenbaek, B. Blauensteiner, M. Żukowski, M. Aspelmeyer, and A. Zeilinger, “Experimental interference of independent photons,” Phys. Rev. Lett. **96**, 240502 (2006) [CrossRef] [PubMed] .

25. Y.-P. Huang, J. B. Altepeter, and P. Kumar, “Heralding single photons without spectral factorability,” Phys. Rev. A **82**, 043826 (2010) [CrossRef] .

26. R. S. Bennink, “Optimal collinear Gaussian beams for spontaneous parametric down-conversion,” Phys. Rev. A **81**, 053805 (2010) [CrossRef] .

18. O. Kuzucu, F. N. C. Wong, S. Kurimura, and S. Tovstonog, “Joint temporal density measurements for two-photon state characterization,” Phys. Rev. Lett. **101**, 153602 (2008) [CrossRef] [PubMed] .

*et al.*showed that by varying the poling-order of PPKTP with near 50:50 duty cycles, it was possible to modulate the effective optical nonlinearity to produce an approximately Gaussian phase-matching function [21

21. A. M. Brańczyk, A. Fedrizzi, T. M. Stace, T. C. Ralph, and A. G. White, “Engineered optical nonlinearity for quantum light sources,” Opt. Express **19**, 55–65 (2011) [CrossRef] .

## 2. Grating structure modification

37. M. Fejer, G. Magel, D. Jundt, and R. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quant.Electron. **28**, 2631–2654 (1992) [CrossRef] .

*E*

_{1}with a fixed frequency

*ω*

_{1}and a tunable input probe

*E*

_{2}with frequency

*ω*

_{2}, the standard coupled-mode equations yield for the output signal field

*E*

_{3}with frequency

*ω*

_{3}. Here:

*d*

_{eff}is the effective nonlinear coefficient;

*L*is the crystal length;

*c*is the speed of light in vacuum;

*n*is the crystal’s index of refraction for the

_{j}*E*field with

_{j}*j*= {1, 2, 3}; Δ

*k*is the longitudinal wave-vector mismatch in the nonlinear material; and

*G*(Δ

*k*) is the phase-matching function given by with

*g*(

*z*) =

*d*(

*z*)/

*d*

_{eff}being the signed fractional nonlinear coefficient whose value is bounded by ±1, and

*k*the wave-vector inside the crystal for the

_{j}*E*field with

_{j}*j*= {1, 2, 3}. For standard quasi-phase matching

*g*(

*z*) is +1 for one polarization of the ferroelectric domains and −1 for the opposite polarization. To maximize efficiency the ideal first-order grating structure is composed of alternating equal-length segments of

*g*(

*z*) = 1 and

*g*(

*z*) = −1. Each segment length is Λ/2, where Λ is the grating period, in which case the grating has a 50:50 duty cycle.

*ε*

_{0}is the vacuum permittivity. Under conventional phase matching (Λ → ∞),

*g*(

*z*) = 1 and |

*G*(Δ

*k*)|

^{2}= sinc

^{2}(Δ

*kL*/2) yields the usual sinc-squared output as a function of the probe and signal wavelengths. The grating structure for quasi-phase matching allows the operating wavelengths to be tuned within the crystal’s transparency window by adjusting the grating period Λ and the reduced output is given by |

*G*(Δ

*k*)|

^{2}= (4/

*π*

^{2})sinc

^{2}(Δ

*kL*/2).

*G*(Δ

*k*) and

*g*(

*z*) are a Fourier transform pair and that the phase-matching function

*G*(Δ

*k*) can be tailored by modifying the grating structure

*g*(

*z*) [37

37. M. Fejer, G. Magel, D. Jundt, and R. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quant.Electron. **28**, 2631–2654 (1992) [CrossRef] .

38. M. A. Arbore, A. Galvanauskas, D. Harter, M. H. Chou, and M. M. Fejer, “Engineerable compression of ultrashort pulses by use of second-harmonic generation in chirped-period-poled lithium niobate,” Opt. Lett. **22**, 1341–1343 (1997) [CrossRef] .

39. M. B. Nasr, S. Carrasco, B. E. A. Saleh, A. V. Sergienko, M. C. Teich, J. P. Torres, L. Torner, D. S. Hum, and M. M. Fejer, “Ultrabroadband biphotons generated via chirped quasi-phase-matched optical parametric down-conversion,” Phys. Rev. Lett. **100**, 183601 (2008) [CrossRef] [PubMed] .

*g*(

*z*). However,

*d*(

*z*) is not a continuously variable function because the nonlinearity

*d*

_{eff}is fixed and the domain segments are fully aligned one way or the other so that

*g*(

*z*) must be either +1 or −1. Moreover, poling limitations restrict domain-inversion periods to no shorter than a few microns. Therefore, in practice,

*g*(

*z*) is designed with numerical modeling and evaluation. Given that

*g*(

*z*) is constant within each ferroelectric domain segment and that it changes sign across the poling boundary, one can write the spatial nonlinearity function as where

*H*(

*z*) is the unit step function and

*z*is the

_{j}*j*-th poling boundary,

*N*is the number of domain segments, with

*z*

_{0}= 0 and

*z*

_{N}_{+1}=

*L*. The mismatch function can then be evaluated with the result being Equation (7) yields the desired grating period Λ ≡ 2(

*z*

_{j}_{+1}−

*z*) = 2

_{j}*π*/Δ

*k*for standard quasi-phase matching with equal domain segment lengths, where Δ

_{c}*k*is the wave-vector mismatch at the center operating wavelengths. For example, in type-II phase-matched SPDC with degenerate output frequencies or DFG with a fixed pump frequency, we have Δ

_{c}*k*=

_{c}*k*

_{1}(

*ω*

_{1},

*n*

_{1}) −

*k*

_{2}(

*ω*

_{1}/2,

*n*

_{2}) −

*k*

_{3}(

*ω*

_{1}/2,

*n*

_{3}), in which the probe and signal refractive indices,

*n*

_{2}and

*n*

_{3}, can be different.

37. M. Fejer, G. Magel, D. Jundt, and R. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quant.Electron. **28**, 2631–2654 (1992) [CrossRef] .

*G*(Δ

*k*)|

^{2}as the signal frequency is tuned. The relationship between Δ

*k*and the operating wavelengths (frequencies) can be found using the appropriate Sellmeier equations for the nonlinear medium [40

40. T. Y. Fan, C. E. Huang, B. Q. Hu, R. C. Eckardt, Y. X. Fan, R. L. Byer, and R. S. Feigelson, “Second harmonic generation and accurate index of refraction measurements in flux-grown KTiOPO_{4},” Appl. Opt. **26**, 2390–2394 (1987) [CrossRef] [PubMed] .

43. F. König and F. N. C. Wong, “Extended phase matching of second-harmonic generation in periodically poled KTiOPO_{4} with zero group-velocity mismatch,” Appl. Phys. Lett. **84**, 1644–1646 (2004) [CrossRef] .

*G*(Δ

*k*) is to manipulate the poling boundaries {

*z*}. In Ref. [21

_{n}21. A. M. Brańczyk, A. Fedrizzi, T. M. Stace, T. C. Ralph, and A. G. White, “Engineered optical nonlinearity for quantum light sources,” Opt. Express **19**, 55–65 (2011) [CrossRef] .

*z*

_{2(j+1)}−

*z*

_{2j}between even-numbered boundaries is held constant at the grating period Λ = 2

*π*/Δ

*k*, while the odd-numbered boundaries take the form

_{c}*z*

_{2}

_{j}_{+1}= (

*j*+

*r*)Λ, with 0 <

_{j}*r*< 1 being the duty cycle. This duty-cycle variation method—illustrated conceptually in Fig. 1—affords a smooth modulation of the optical nonlinearity’s effective strength.

_{j}18. O. Kuzucu, F. N. C. Wong, S. Kurimura, and S. Tovstonog, “Joint temporal density measurements for two-photon state characterization,” Phys. Rev. Lett. **101**, 153602 (2008) [CrossRef] [PubMed] .

*μ*m.

*μ*m to allow for angle tuning, and a crystal length of

*L*= 12 mm, resulting in about 520 domain segments. We worked with PPKTP manufacturer AdvR Inc. to implement our grating design within its manufacturing capability. In particular, poling domain segments shorter than about 5

*μ*m are not advisable, because of domain fusing and poling irregularity. Using the Sellmeier equations in Ref. [43

43. F. König and F. N. C. Wong, “Extended phase matching of second-harmonic generation in periodically poled KTiOPO_{4} with zero group-velocity mismatch,” Appl. Phys. Lett. **84**, 1644–1646 (2004) [CrossRef] .

*z*=

*L*/2, and it decreases (increases) toward the beginning (end) of the crystal

*z*= 0 (

*z*=

*L*). We use our numerical model to optimize and fine tune the characteristics of the resulting phase-matching function, especially in its side lobes because they give rise to undesirable asymmetry in the biphoton’s joint spectral density. Figure 2 displays the final design for the 12-mm-long type-II quasi-phase-matched bulk KTP crystal and the duty-cycle

*r*(

*z*) can be approximated by: We obtain the discrete-domain duty cycles {

*r*} by evaluating {

_{j}*r*(

*z*

_{2}

*)} from Eq. (8) and rounding those values to the nearest 0.1*

_{j}*μ*m. The resulting model has a duty cycle of 10.2% at one end, and 89.8% at the other end. For a poling period of 46.0

*μ*m this gives a minimum domain segment width of 4.7

*μ*m, the constant offset and sub-unity magnitude of the error function in Eq. 8 are chosen to preclude domain segments shorter than this. The nearly Gaussian error-function modulation was chosen over a true Gaussian modulation to allow for a more straightforward optimization of the numerical model while incorporating manufacturing constraints. The design choice is expected to yield a nearly Gaussian phase-matching function. We note that the numerical model allows us to investigate the effects of angle tuning and possible crystal manufacturing defects such as over-poling, missed poling domains, and random boundary-location errors.

## 3. Experimental characterization

*y*-axis (

*z*-axis) with light propagation occurring along the crystal’s

*x*-axis. A horizontally-polarized pump beam at 790.9 nm was chopped at 600 Hz for lock-in detection and focused into the crystal with an average power of 150 mW at the crystal. A 2 mW, vertically-polarized probe beam was derived from a continuous-wave (cw) tunable laser operating at a 1582 nm center wavelength. The two beams were focused at the center of the crystal with a common focal parameter of

*ζ*=

*L/b*≈ 0.17, where

*b*= 2

*πn*

_{j}w^{2}/

*λ*is the confocal parameter,

_{j}*n*is the crystal’s refractive index at the vacuum wavelength

_{j}*λ*,

_{j}*w*is the beam waist,

_{j}*L*is the crystal’s length, and

*j*= {1, 2} for pump and probe, respectively. The resulting DFG signal was horizontally polarized, centered at 1582 nm wavelength, and modulated by the 600 Hz chopping of the pump input. After the crystal, we blocked the pump and probe beams using a combination of spectral and polarization filters. The transmitted DFG signal output was coupled into a multi-mode optical fiber and detected with a low-noise InGaAs photodetector (Thorlabs model PDA-255). The output of the photodetector was sent to a lock-in amplifier that was synchronized to the pump-beam chopping frequency. We recorded the synchronously-detected DFG signal as a function of probe wavelength

*λ*

_{2}between 1572 nm and 1592 nm, providing a direct measurement of |

*G*(Δ

*k*)|

^{2}for a fixed pump wavelength

*λ*

_{1}= 790.9 nm.

*G*(Δ

*k*)|

^{2}is very close to Gaussian—indicating the crystal has the desired characteristics—however, its bandwidth is 23% wider than expected. The measured DFG bandwidth, full width at half-maximum (FWHM), is 3.1 nm compared with the predicted DFG bandwidth of 2.5 nm, indicating that although the crystal exhibits a Gaussian shaped phase-matching function, there are manufacturing errors such as missed or partially-inverted domains.

*μ*m were missed, leaving a crystal with a duty cycle range of 20.4% to 79.6%. However, it only takes missed domain segments below 7.0

*μ*m (15.2% to 84.8% duty cycle range) to account for the observed 3.1 nm phase-matching bandwidth. This type of defect is not entirely unexpected, indeed, even for crystals with uniform grating periods that are large compared to our smallest domain segment, errors in phase-matching width of 3 to 4 percent are present [31

31. O. Kuzucu, M. Fiorentino, M. A. Albota, F. N. C. Wong, and F. X. Kärtner, “Two-Photon Coincident-Frequency Entanglement via Extended Phase Matching,” Phys. Rev. Lett. **94**, 083601 (2005) [CrossRef] [PubMed] .

*G*(Δ

*k*)|

^{2}predicted by our numerical model (blue curve) after scaling to match the experimentally-observed bandwidth. We plot the data on a linear scale (left panel), as well as on a logarithmic scale (right panel) to better show the fine details in the wings of the phase-matching function. The measured data agree well with predictions for the central Gaussian region, the small residual lobe near 1588 nm, and there being no other wavelengths with appreciable DFG output. The Gaussian fit closely follows the measured data, with significant deviations only occurring below −15 dB.

## 4. Implications for quantum information science

*s*) and idler (

*i*)—at ∼1582 nm. For type-II phase-matching in PPKTP the signal and idler photons are orthogonally polarized, which allows easy separation by a polarization beam-splitter. The quantum state of this biphoton is determined by the frequency spectrum of the pump field

*E*(

_{p}*ω*) and the phase-matching function of the crystal

*G*(Δ

*k*). Neglecting inconsequential normalization constants and assuming collinear plane-wave propagation (i.e., loose pump focusing), the SPDC biphoton state is given by [32

32. V. Giovannetti, L. Maccone, J. H. Shapiro, and F. N. C. Wong, “Extended phase-matching conditions for improved entanglement generation,” Phys. Rev. A **66**, 043813 (2002) [CrossRef] .

*ω*〉 (|

_{s}*ω*〉) is a single-photon state with signal (idler) frequency

_{i}*ω*(

_{s}*ω*), and the pump’s intensity spectrum |

_{i}*E*|

_{p}^{2}is centered at

*ω*with bandwidth Ω

_{p}*. Alternatively, we can express the state in terms of vacuum wavelengths: where and we have again neglected a normalization constant.*

_{p}*G*(Δ

*k*) of our 12-mm-long PPKTP crystal with its modulated duty cycle, and include a wavelength scaling to match the observed phase-matching bandwidth that is ∼23% wider than expected. This amounts to assuming that

*G*(Δ

*k*) has no extraneous phase behavior unaccounted for in Eq. (7). For comparison, we assume the usual sinc-function phase matching for an 8.1-mm-long PPKTP crystal, in which the crystal length is chosen to match the observed phase-matching bandwidth of the custom-poled crystal. Figure 4 shows the two performance metrics

*H*(left panel) and

_{ψ}*P*(right panel) for the standard uniformly-poled crystal (red curve) and custom-poled crystal (blue curve) as a function of the full-width at half-maximum (FWHM) bandwidth Δ

_{ψ}*λ*of the pump’s Gaussian-shaped intensity spectrum. For all evaluated values of the pump bandwidth the custom-poled crystal shows improved results compared with those obtained with the standard crystal. The standard uniformly-poled crystal with a 1.30 nm FWHM pump bandwidth produces a biphoton state with a minimum entropy of entanglement of 0.71 bits, corresponding to a maximum heralded state purity of ∼83%, whereas pumping our custom-poled crystal with a 1.40 nm bandwidth yields a state with a minimum entropy of entanglement of 0.16 bits and a corresponding heralded-state purity of 97%.

_{p}*P*reaches 99.5% at the expense of 10% filtering transmission loss for each beam (assuming unity peak-transmission efficiency for the filters). This capability gives flexibility to further fine tune the output state characteristics, however an important point to note is that this filtering will reduce the total flux as well as the heralding efficiency [26

_{ψ}26. R. S. Bennink, “Optimal collinear Gaussian beams for spontaneous parametric down-conversion,” Phys. Rev. A **81**, 053805 (2010) [CrossRef] .

*β*̃(

*λ*,

_{s}*λ*)

_{i}*G*(Δ

*k*)| for the minimum-entropy biphoton states obtained for the standard uniformly-poled 8.1-mm crystal (left panel) with 1.30 nm pump bandwidth and the custom-poled 12-mm crystal (right panel) with 1.40 nm pump bandwidth. Both states have nearly circular central lobes. However the side lobes, clearly present in the standard crystal’s output, are strongly suppressed in our custom-poled crystal’s output, as expected from its increased purity. The effect of a mild spectral filter, not shown in Fig. 5, is to further reduce the residual side lobes for the custom-poled source enabling its output to achieve even higher purity.

21. A. M. Brańczyk, A. Fedrizzi, T. M. Stace, T. C. Ralph, and A. G. White, “Engineered optical nonlinearity for quantum light sources,” Opt. Express **19**, 55–65 (2011) [CrossRef] .

**19**, 55–65 (2011) [CrossRef] .

**19**, 55–65 (2011) [CrossRef] .

*P*and the minimum entropy of entanglement

_{ψ}*H*. Also of interest are the relative SPDC output flux, defined as ∬ |

_{ψ}*β*̃(

*λ*,

_{s}*λ*)

_{i}*G*(Δ

*k*)|

^{2}

*dλ*for each crystal relative to that of a standard crystal, and the output SPDC FWHM bandwidth. The two methods of generating Gaussian phase-matching functions used by [21

_{s}dλ_{i}**19**, 55–65 (2011) [CrossRef] .

**19**, 55–65 (2011) [CrossRef] .

*et al.*does not have this limitation.

## 5. Conclusions

## Acknowledgments

## References and links

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32. | V. Giovannetti, L. Maccone, J. H. Shapiro, and F. N. C. Wong, “Extended phase-matching conditions for improved entanglement generation,” Phys. Rev. A |

33. | P. J. Mosley, J. S. Lundeen, B. J. Smith, and I. A. Walmsley, “Conditional preparation of single photons using parametric downconversion: a recipe for purity,” New J. Phys. |

34. | A. Christ, A. Eckstein, P. J. Mosley, and C. Silberhorn, “Pure single photon generation by type-I PDC with backward-wave amplification,” Opt. Express |

35. | M. G. Raymer, J. Noh, K. Banaszek, and I. A. Walmsley, “Pure-state single-photon wave-packet generation by parametric down-conversion in a distributed microcavity,” Phys. Rev. A |

36. | R. Boyd, |

37. | M. Fejer, G. Magel, D. Jundt, and R. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quant.Electron. |

38. | M. A. Arbore, A. Galvanauskas, D. Harter, M. H. Chou, and M. M. Fejer, “Engineerable compression of ultrashort pulses by use of second-harmonic generation in chirped-period-poled lithium niobate,” Opt. Lett. |

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

40. | T. Y. Fan, C. E. Huang, B. Q. Hu, R. C. Eckardt, Y. X. Fan, R. L. Byer, and R. S. Feigelson, “Second harmonic generation and accurate index of refraction measurements in flux-grown KTiOPO |

41. | D. H. Jundt, “Temperature-dependent Sellmeier equation for the index of refraction, 22, 1553–1555 (1997) [CrossRef] . |

42. | K. Fradkin, A. Arie, A. Skliar, and G. Rosenman, “Tunable midinfrared source by difference frequency generation in bulk periodically poled KTiOPO |

43. | F. König and F. N. C. Wong, “Extended phase matching of second-harmonic generation in periodically poled KTiOPO |

44. | S. Popescu and D. Rohrlich, “Thermodynamics and the measure of entanglement,” Phys. Rev. A |

45. | O. Kuzucu, F. N. C. Wong, S. Kurimura, and S. Tovstonog, “Time-resolved single-photon detection by femtosecond upconversion,” Opt. Lett. |

**OCIS Codes**

(190.4410) Nonlinear optics : Nonlinear optics, parametric processes

(270.5585) Quantum optics : Quantum information and processing

**ToC Category:**

Quantum Optics

**History**

Original Manuscript: December 21, 2012

Revised Manuscript: February 21, 2013

Manuscript Accepted: February 21, 2013

Published: March 1, 2013

**Citation**

P. Ben Dixon, Jeffrey H. Shapiro, and Franco N. C. Wong, "Spectral engineering by Gaussian phase-matching for quantum photonics," Opt. Express **21**, 5879-5890 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-5-5879

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