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Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 24 — Nov. 19, 2012
  • pp: 27441–27446
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Photon-pair generation in arrays of cubic nonlinear waveguides

Alexander S. Solntsev, Andrey A. Sukhorukov, Dragomir N. Neshev, and Yuri S. Kivshar  »View Author Affiliations


Optics Express, Vol. 20, Issue 24, pp. 27441-27446 (2012)
http://dx.doi.org/10.1364/OE.20.027441


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Abstract

We study photon-pair generation in arrays of cubic nonlinear waveguides through spontaneous four-wave mixing. We analyze numerically the quantum statistics of photon pairs at the array output as a function of waveguide dispersion and pump beam power. We show flexible spatial quantum state control such as pump-power-controlled transition between bunching and anti-bunching correlations due to nonlinear self-focusing.

© 2012 OSA

1. Introduction

With the development of quantum optics it is now feasible to realize complex quantum logic algorithms, however an increasing number of optical elements is required for multi-step quantum simulations. Integrated photonic circuits have been considered as the solution to this challenge, as they are intrinsically scalable and interferometrically stable [1

1. J. C. F. Matthews, A. Politi, A. Stefanov, and J. L. O’Brien, “Manipulation of multiphoton entanglement in waveguide quantum circuits,” Nature Photonics 3, 346–350 (2009). [CrossRef]

]. Integrated realization of multi-photon entanglement [1

1. J. C. F. Matthews, A. Politi, A. Stefanov, and J. L. O’Brien, “Manipulation of multiphoton entanglement in waveguide quantum circuits,” Nature Photonics 3, 346–350 (2009). [CrossRef]

], quantum factoring algorithms [2

2. A. Politi, J. C. F. Matthews, and J. L. O’Brien, “Shor’s quantum factoring algorithm on a photonic chip,” Science 325, 1221–1221 (2009). [CrossRef] [PubMed]

], and polarization entanglement [3

3. L. Sansoni, F. Sciarrino, G. Vallone, P. Mataloni, A. Crespi, R. Ramponi, and R. Osellame, “Polarization entangled state measurement on a chip,” Phys. Rev. Lett. 105, 200503 (2010). [CrossRef]

] have already been demonstrated experimentally.

One of particularly interesting devices in integrated photonics is a waveguide array (WGA). Recently WGAs have been shown to generate unusual and strongly non-classical correlations of photon pairs propagating in the regime of quantum walks [4

4. A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X. Q. Zhou, Y. Lahini, N. Ismail, K. Worhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, and J. L. O’Brien, “Quantum walks of correlated photons,” Science 329, 1500–1503 (2010). [CrossRef] [PubMed]

]. Combining quantum walks with photon pair generation in nonlinear waveguide arrays further opens the possibility for enhanced spatial quantum state control and improved clarity of spatial correlations [5

5. A. S. Solntsev, A. A. Sukhorukov, D. N. Neshev, and Y. S. Kivshar, “Spontaneous parametric down-conversion and quantum walks in arrays of quadratic nonlinear waveguides,” Phys. Rev. Lett. 108, 023601 (2012). [CrossRef] [PubMed]

]. While WGAs with quadratic nonlinearity have been recently studied [5

5. A. S. Solntsev, A. A. Sukhorukov, D. N. Neshev, and Y. S. Kivshar, “Spontaneous parametric down-conversion and quantum walks in arrays of quadratic nonlinear waveguides,” Phys. Rev. Lett. 108, 023601 (2012). [CrossRef] [PubMed]

, 6

6. A. Rai and D. G. Angelakis, “Dynamics of nonclassical light in integrated nonlinear waveguide arrays and generation of robust continuous-variable entanglement,” Phys. Rev. A 85, 052330 (2012). [CrossRef]

], we expect that WGAs with cubic nonlinearity can provide an entirely new realm of all-optical control of the quantum photon statistics. With on-chip photon-pair sources based on spontaneous four-wave mixing (SFWM) being readily available [7

7. J. E. Sharping, K. F. Lee, M. A. Foster, A. C. Turner, B. S. Schmidt, M. Lipson, A. L. Gaeta, and P. Kumar, “Generation of correlated photons in nanoscale silicon waveguides,” Opt. Express 14, 12388–12393 (2006). [CrossRef] [PubMed]

, 8

8. H. Takesue, Y. Tokura, H. Fukuda, T. Tsuchizawa, T. Watanabe, K. Yamada, and S. ichi Itabashi, “Entanglement generation using silicon wire waveguide,” Appl. Phys. Lett. 91, 201108 (2007). [CrossRef]

], it becomes of much interest to study the quantum state dynamics in WGAs with cubic nonlinear response.

In this work, we describe the generation of correlated photon pairs through SFWM in a cubic nonlinear WGA and analyze the interplay between SFWM phase-matching and WGA dispersion for the generation of complex entangled quantum states. We also demonstrate the potential of Kerr-based self-phase modulation (SPM) and cross-phase modulation (XPM) for quantum state control by investigating a case of stronger pump with special spectral filtering.

2. SFWM in WGAs at low pump powers

We consider lossless near-degenerate SFWM with signal and idler frequencies being close to the pump frequency, with the rest of photon-pairs being filtered out. In this case the mode profiles and coupling between waveguides remain approximately the same for pump, signal and idler photons. It has been demonstrated that even with less than 0.5% difference between these frequencies, the pump can be effectively filtered at the output of the system, and photon pair correlations can be measured with high signal-to-noise ratio [7

7. J. E. Sharping, K. F. Lee, M. A. Foster, A. C. Turner, B. S. Schmidt, M. Lipson, A. L. Gaeta, and P. Kumar, “Generation of correlated photons in nanoscale silicon waveguides,” Opt. Express 14, 12388–12393 (2006). [CrossRef] [PubMed]

, 8

8. H. Takesue, Y. Tokura, H. Fukuda, T. Tsuchizawa, T. Watanabe, K. Yamada, and S. ichi Itabashi, “Entanglement generation using silicon wire waveguide,” Appl. Phys. Lett. 91, 201108 (2007). [CrossRef]

]. The main difference between spontaneous four-wave mixing in bulk or single waveguides in comparison to WGAs [Fig. 1(a)] is a different spatial dispersion leading to modified phase-matching. We begin the analysis of SFWM in WGA by studying the four-wave-mixing phase-matching for plane waves, Δβ = 2βpβsβi. Here βp,s,i are the propagation constants for pump, signal and idler. In a WGA they depend on normalized transverse momenta kp,s,i as βp,s,i=βp,s,i(0)+2Ccos(πkp,s,i), where C is the coupling coefficient between the waveguides [9

9. D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424, 817–823 (2003). [CrossRef] [PubMed]

]. Meanwhile the overlap between interacting Bloch waves [5

5. A. S. Solntsev, A. A. Sukhorukov, D. N. Neshev, and Y. S. Kivshar, “Spontaneous parametric down-conversion and quantum walks in arrays of quadratic nonlinear waveguides,” Phys. Rev. Lett. 108, 023601 (2012). [CrossRef] [PubMed]

, 9

9. D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424, 817–823 (2003). [CrossRef] [PubMed]

] can be written as nexp[iπ(2kpkski)n], where n is a waveguide number. Since nexp(2iπkpniπksniπkin)=2πNδ(2πkpπksπki2πN), where N ∈ 𝕑, then the transverse momenta kp,s,i for periodical solutions will satisfy the condition 2kp=ks+ki. Therefore we can write an analytical expression for plane-wave four-wave mixing phase-mismatch in a WGA:
Δβ=Δβ(0)+4Ccos(π(ks+ki)/2)2Ccos(πks)2Ccos(πki).
(1)
The spatial dispersion and therefore the phase-matching conditions for SFWM in WGAs are qualitatively different from that in bulk, opening new possibilities for generating photon pairs with unusual quantum statistics.

Fig. 1 (a) Schematic and (b) power profile of linear pump propagation in a WGA for input pump amplitude Enp=0(p)(0)=105. (c–f) Photon-pair correlations in (c,e,g) real-space and (d,f,h) k-space for different group-velocity dispersion: (c,d) anomalous Δβ(0) = −18, (e,f) zero Δβ(0) = 0 and (g,h) normal Δβ(0) = 18.

If pump is no longer a plane wave, but instead it is initially coupled to a finite number of waveguides, it then propagates in the regime of discrete diffraction [9

9. D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424, 817–823 (2003). [CrossRef] [PubMed]

] as illustrated in Fig. 1(b). For developing a model describing SFWM based photon-pair generation with a negligible number of higher multiphoton events in a cubic WGA, we first consider low pump powers that do not lead to pump spatial reshaping or nonlinear phase modulation. In the absence of SPM, XPM and losses, the system Hamiltonian consists of linear [4

4. A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X. Q. Zhou, Y. Lahini, N. Ismail, K. Worhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, and J. L. O’Brien, “Quantum walks of correlated photons,” Science 329, 1500–1503 (2010). [CrossRef] [PubMed]

] and nonlinear [10

10. L. G. Helt, M. Liscidini, and J. E. Sipe, “How does it scale? comparing quantum and classical nonlinear optical processes in integrated devices,” J. Opt. Soc. Am. B 29, 2199–2212 (2012). [CrossRef]

] parts Ĥ = Ĥ (lin) + Ĥ (nonlin), H^(lin)=h¯ns[Δβ(0)a^nsa^ns+Ca^ns1a^ns+Ca^ns+1a^ns]+h¯ni[Δβ(0)a^nia^ni+Ca^ni1a^ni+Ca^ni+1a^ni], H^(nonlin)=ih¯γnp[Enp(p)Enp(p)a^nsa^niδns,npδni,npEnp(p)*Enp(p)*a^nsa^niδns,npδni,np]. Here ns and ni are the waveguide numbers describing the positions of the signal, and the idler photons, and Enp(p)(z) is the pump amplitude in waveguide number np. Δβ(0) is the linear four-wave mixing phase-mismatch in a single waveguide, γ is a nonlinear coefficient. The normalized pump field profile evolution along the propagation distance z is defined through the classical coupled-mode equations [9

9. D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424, 817–823 (2003). [CrossRef] [PubMed]

]:
dEnp(p)(z)/dz=iC[Enp1(p)(z)+Enp+1(p)(z)].
(2)
Generation of photon pairs in cubic nonlinear WGAs through SFWM in the absence of multiple photon pairs can be characterized by the evolution of a bi-photon wave function ψns,ni (z) in a Schrodinger-type equation. The equation is obtained from the Hamiltonian, and it has a form ¨ similar to that of quadratic media [11

11. M. Grafe, A. S. Solntsev, R. Keil, A. A. Sukhorukov, M. Heinrich, A. Tunnermann, S. Nolte, A. Szameit, and Y. S. Kivshar, “Biphoton generation in quadratic waveguide arrays: A classical optical simulation,” Sci. Rep. 2, 562 (2012). [CrossRef] [PubMed]

]:
dψns,ni(z)/dz=iC[ψns1,ni(z)+ψns,ni1(z)+ψns+1,ni(z)+ψns,ni+1(z)]+iΔβ(0)ψns,ni+γEns(p)(z)Ens(p)(z)δns,ni.
(3)
We notice that the spatial dispersion described by Eqs. (2) and (3) exactly agrees with Eq. (1).

After calculating the wave function, we obtain two-photon correlations in real-space as Γns,ni = |ψns,ni (L)|2, where L is the propagation length. In order to find correlations for the signal and idler photons in k-space we apply the two-dimensional Fourier-transform, Γks,ki=|nsniexp(iπksns)exp(iπkini)ψns,ni(L)|2. For the examples presented below, we normalize all parameters to the WGA length L = 1 and nonlinearity γ = 1. The physical value of the nonlinear coefficient can be determined following the approach of Ref. [10

10. L. G. Helt, M. Liscidini, and J. E. Sipe, “How does it scale? comparing quantum and classical nonlinear optical processes in integrated devices,” J. Opt. Soc. Am. B 29, 2199–2212 (2012). [CrossRef]

]. We use the coupling coefficient C = 5, and consider a pump beam coupled only to the central waveguide (n = 0).

We study the case of low pump amplitude Enp=0(p)(0)=105 when the input beam exhibits linear discrete diffraction [9

9. D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424, 817–823 (2003). [CrossRef] [PubMed]

], see Fig. 1(b). We analyze three different types of group velocity dispersion (GVD): anomalous Δβ(0) = −18, zero Δβ(0) = 0 and normal Δβ(0) = 18. In the case of anomalous GVD, photons in a pair tend to end up mostly away from the central waveguide, with higher probability to be at either the same or the opposite waveguides, see photon-pair probability correlation in Fig. 1(c). This behavior corresponds to weakly pronounced simultaneous spatial bunching and antibunching. The quantum statistics in this case is quasi-anyonic, which can be interesting for quantum simulations [12

12. J. C. F. Matthews, K. Poulios, J. D. A. Meinecke, A. Politi, A. Peruzzo, N. Ismail, K. Wrhoff, M. G. Thompson, and J. L. O’Brien, “Simulating quantum statistics with entangled photons: a continuous transition from bosons to fermions,” http://arxiv.org/abs/1106.1166 (2011).

]. The k-space correlations show an elliptical shape centered at ks=ki=0 [Fig. 1(d)]. This shape corresponds to the wavenumbers with the most efficient phase-matched interactions, i.e. Δβ = 0. For zero GVD the signal and idler photons mostly leave the structure from the same waveguides, thus demonstrating strong spatial bunching behavior [Fig. 1(e)]. Figure 1(f) shows that the transverse wavenumbers for photon pairs satisfy the relations ks+ks±1. We note that for zero dispersion photon pairs have much higher probability to arrive to the center of the WGA, because phase matching can now be achieved for a broader range of transverse momenta. In the case of normal GVD, the real-space correlations [Fig. 1(g)] are the same as for anomalous GVD [Fig. 1(c)]. Indeed for low pump powers with negligible SPM and XPM, the system is symmetrical with respect to the GVD sign. In k-space the correlations form an elliptical shape centered around ks=ki=±1 [Fig. 1(h)]. We note that there is a gradual transition from ellipses centered at 0 [Fig. 1(d)] through linear shapes [Fig. 1(f)] to ellipses centered at ks=ki=±1 [Fig. 1(h)] when tuning the GVD from anomalous to normal. GVD tuning can achieved by changing the pump wavelength [13

13. J. Zhang, Q. Lin, G. Piredda, R. W. Boyd, G. P. Agrawal, and P. M. Fauchet, “Optical solitons in a silicon waveguide,” Opt. Express 15, 7682–7688 (2007). [CrossRef] [PubMed]

], however such tuning can be complicated due to the required corresponding spectral shift of output filters for signal and idler photons.

3. SFWM and pump self-focusing at high pump powers

Fig. 2 (a) Output pump power profile vs. input pump amplitude (single waveguide excitation). (b) Normalized pump spectrum (green solid line), normalized signal (red dashed line) and idler (blue dotted line) spectral filters. Gray shading marks a part of the pump spectrum contributing to the filtered photon-pair generation.

Since high pump peak powers lead to the pump beam focusing [Fig. 2(a)], generated photon pairs will have different spatial distributions depending on the pump power. The pump power will also effectively change the SFWM phase-matching conditions due to XPM. We incorporate these effects by adding the terms responsible for XPM and SPM into the Eqs. (2) and (3):
dEnp(p)(z)/dz=iC[Enp1(p)(z)+Enp+1(p)(z)]+iγ|Enp(p)(z)|2Enp(p)(z).
(4)
dψns,ni(z)/dz=iC[ψns1,ni(z)+ψns,ni1(z)+ψns+1,ni(z)+ψns,ni+1(z)]+γEns(p)(z)Ens(p)(z)δns,ni+i[Δβ(0)+2γ|Ens(p)(z)|2+2γ|Eni(p)(z)|2]ψns,ni(z),
(5)
We acknowledge that this model is only the first-order approximation and that simulations designed to give precise quantitative results should incorporate full dispersion curves both for propagation and coupling constants, as well as spatio-temporal dynamics. However, we believe that the simplified model that we present here is useful to obtain a qualitative insight into the quantum statistics control that can be achieved in cubic WGAs.

When the pump power is increased, the pump beam distribution collapses to a single waveguide, as illustrated in Fig. 3(a) for Enp=0(p)(0)=4.5[Enp=0(p)(0)/C=0.9]. This self-focusing dramatically changes the spatial photon-pair correlations. The real space correlations in anomalous GVD regime collapse to a single waveguide, following the pump [Fig. 3(b)]. This can be explained by the phenomenon of forward-propagation dispersion compensation. Anomalous GVD allows to phase-match four-wave mixing in a single waveguide, which corresponds to a broad k-space phase matching in the array [Fig. 3(c)]. For zero GVD, the XPM leads to a phase-matching of angled SFWM, corresponding to a small-scale antibunching in real space correlations [Fig. 3(d)] and more pronounced selectivity of phase-matched signal and idler transverse momenta [Fig. 3(e)]. In the normal GVD case the real space correlations now demonstrate very pronounced antibunching [Fig. 3(f)], which corresponds to k-space phase matching mostly for transverse momenta far away from zero [Fig. 3(g)]. This makes it possible for photon pairs to escape from the localized pump beam. In this case the generated photon pairs become spatially filtered from the pump beam and show strongly pronounced anti-bunching. This demonstrates that by tuning the pump wavelength and power we can get a great degree of control on the spatial photon-pair correlations, which is useful for applications in quantum information.

Fig. 3 (a) Pump spatial soliton formation with input pump amplitude Enp=0(p)(0)=4.5. (b–g) Photon-pair correlations in (b,d,f) real space and (c,e,g) k-space for different group-velocity dispersion: (b,c) anomalous Δβ(0) = −18, (d,e) zero Δβ(0) = 0 and (f,g) normal Δβ(0) = 18.

To further illustrate this flexibility, we focus on two particulary interesting regimes, namely bunching and antibunching. We introduce a bunching to antibunching ratio, R = (∑ni=ns Γns,ni)/(∑ni=−ns Γns,ni) and study the dynamics of this ratio with respect to pump power [Fig. 4(a) ( Media 1)], while also tracking the spatial photon-pair correlations for anomalous [Fig. 4(b) ( Media 1)] and normal GVD [Fig. 4(c) ( Media 1)] and the pump propagation [Fig. 4(d) ( Media 1)]. We observe that the pump power tuning provides access to a wide range of photon-pair quantum statistics. We also see that in general, normal dispersion can lead to stronger spatial antibunching, as in this case only angled phase-matching can be satisfied.

Fig. 4 ( Media 1) (a) Photon-pair bunching to antibunching ratio R vs. the input pump amplitude Enp=0(p)(0) for the anomalous GVD Δβ(0) = −18 (red solid line) and the normal GVD Δβ(0) = 18 (blue dashed line). Red and blue circles correspond to the the input pump amplitude Enp=0(p)(0)=2.850 for the plots (b–d). (b,c) Real-space photon-pair correlations at (b) anomalous and (c) normal dispersion. (d) Pump power distribution in the array.

4. Conclusion

We have demonstrated that waveguide arrays with cubic nonlinearity can be employed as a a flexible platform for all-optical manipulation of the generated bi-photon quantum statistics. We have shown that interplay between spatial dispersion and four-wave mixing phase-matching in waveguide arrays leads to the generation of complex spatial quantum states, which can be controlled by tuning the pump power and wavelength. We anticipate that our results will open new opportunities for integrated quantum photonics with all-optical controls.

Acknowledgments

We acknowledge useful discussions with Sergey Kruk and Luke Helt. The work was supported by the Australian Research Council.

References and links

1.

J. C. F. Matthews, A. Politi, A. Stefanov, and J. L. O’Brien, “Manipulation of multiphoton entanglement in waveguide quantum circuits,” Nature Photonics 3, 346–350 (2009). [CrossRef]

2.

A. Politi, J. C. F. Matthews, and J. L. O’Brien, “Shor’s quantum factoring algorithm on a photonic chip,” Science 325, 1221–1221 (2009). [CrossRef] [PubMed]

3.

L. Sansoni, F. Sciarrino, G. Vallone, P. Mataloni, A. Crespi, R. Ramponi, and R. Osellame, “Polarization entangled state measurement on a chip,” Phys. Rev. Lett. 105, 200503 (2010). [CrossRef]

4.

A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X. Q. Zhou, Y. Lahini, N. Ismail, K. Worhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, and J. L. O’Brien, “Quantum walks of correlated photons,” Science 329, 1500–1503 (2010). [CrossRef] [PubMed]

5.

A. S. Solntsev, A. A. Sukhorukov, D. N. Neshev, and Y. S. Kivshar, “Spontaneous parametric down-conversion and quantum walks in arrays of quadratic nonlinear waveguides,” Phys. Rev. Lett. 108, 023601 (2012). [CrossRef] [PubMed]

6.

A. Rai and D. G. Angelakis, “Dynamics of nonclassical light in integrated nonlinear waveguide arrays and generation of robust continuous-variable entanglement,” Phys. Rev. A 85, 052330 (2012). [CrossRef]

7.

J. E. Sharping, K. F. Lee, M. A. Foster, A. C. Turner, B. S. Schmidt, M. Lipson, A. L. Gaeta, and P. Kumar, “Generation of correlated photons in nanoscale silicon waveguides,” Opt. Express 14, 12388–12393 (2006). [CrossRef] [PubMed]

8.

H. Takesue, Y. Tokura, H. Fukuda, T. Tsuchizawa, T. Watanabe, K. Yamada, and S. ichi Itabashi, “Entanglement generation using silicon wire waveguide,” Appl. Phys. Lett. 91, 201108 (2007). [CrossRef]

9.

D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424, 817–823 (2003). [CrossRef] [PubMed]

10.

L. G. Helt, M. Liscidini, and J. E. Sipe, “How does it scale? comparing quantum and classical nonlinear optical processes in integrated devices,” J. Opt. Soc. Am. B 29, 2199–2212 (2012). [CrossRef]

11.

M. Grafe, A. S. Solntsev, R. Keil, A. A. Sukhorukov, M. Heinrich, A. Tunnermann, S. Nolte, A. Szameit, and Y. S. Kivshar, “Biphoton generation in quadratic waveguide arrays: A classical optical simulation,” Sci. Rep. 2, 562 (2012). [CrossRef] [PubMed]

12.

J. C. F. Matthews, K. Poulios, J. D. A. Meinecke, A. Politi, A. Peruzzo, N. Ismail, K. Wrhoff, M. G. Thompson, and J. L. O’Brien, “Simulating quantum statistics with entangled photons: a continuous transition from bosons to fermions,” http://arxiv.org/abs/1106.1166 (2011).

13.

J. Zhang, Q. Lin, G. Piredda, R. W. Boyd, G. P. Agrawal, and P. M. Fauchet, “Optical solitons in a silicon waveguide,” Opt. Express 15, 7682–7688 (2007). [CrossRef] [PubMed]

14.

A. V. Gorbach, W. Ding, O. K. Staines, C. E. de Nobriga, G. D. Hobbs, W. J. Wadsworth, J. C. Knight, D. V. Skryabin, A. Samarelli, M. Sorel, and R. M. De La Rue, “Spatiotemporal nonlinear optics in arrays of subwavelength waveguides,” Phys. Rev. A 82, 041802 (2010). [CrossRef]

15.

C. J. Benton and D. V. Skryabin, “Coupling induced anomalous group velocity dispersion in nonlinear arrays of silicon photonic wires,” Opt. Express 17, 5879–5884 (2009). [CrossRef] [PubMed]

OCIS Codes
(190.4380) Nonlinear optics : Nonlinear optics, four-wave mixing
(270.0270) Quantum optics : Quantum optics
(080.1238) Geometric optics : Array waveguide devices

ToC Category:
Four-Wave Mixing in Waveguides and Fibers

History
Original Manuscript: September 5, 2012
Revised Manuscript: October 19, 2012
Manuscript Accepted: October 20, 2012
Published: November 19, 2012

Virtual Issues
Nonlinear Photonics (2012) Optics Express

Citation
Alexander S. Solntsev, Andrey A. Sukhorukov, Dragomir N. Neshev, and Yuri S. Kivshar, "Photon-pair generation in arrays of cubic nonlinear waveguides," Opt. Express 20, 27441-27446 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-24-27441


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References

  1. J. C. F. Matthews, A. Politi, A. Stefanov, and J. L. O’Brien, “Manipulation of multiphoton entanglement in waveguide quantum circuits,” Nature Photonics3, 346–350 (2009). [CrossRef]
  2. A. Politi, J. C. F. Matthews, and J. L. O’Brien, “Shor’s quantum factoring algorithm on a photonic chip,” Science325, 1221–1221 (2009). [CrossRef] [PubMed]
  3. L. Sansoni, F. Sciarrino, G. Vallone, P. Mataloni, A. Crespi, R. Ramponi, and R. Osellame, “Polarization entangled state measurement on a chip,” Phys. Rev. Lett.105, 200503 (2010). [CrossRef]
  4. A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X. Q. Zhou, Y. Lahini, N. Ismail, K. Worhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, and J. L. O’Brien, “Quantum walks of correlated photons,” Science329, 1500–1503 (2010). [CrossRef] [PubMed]
  5. A. S. Solntsev, A. A. Sukhorukov, D. N. Neshev, and Y. S. Kivshar, “Spontaneous parametric down-conversion and quantum walks in arrays of quadratic nonlinear waveguides,” Phys. Rev. Lett.108, 023601 (2012). [CrossRef] [PubMed]
  6. A. Rai and D. G. Angelakis, “Dynamics of nonclassical light in integrated nonlinear waveguide arrays and generation of robust continuous-variable entanglement,” Phys. Rev. A85, 052330 (2012). [CrossRef]
  7. J. E. Sharping, K. F. Lee, M. A. Foster, A. C. Turner, B. S. Schmidt, M. Lipson, A. L. Gaeta, and P. Kumar, “Generation of correlated photons in nanoscale silicon waveguides,” Opt. Express14, 12388–12393 (2006). [CrossRef] [PubMed]
  8. H. Takesue, Y. Tokura, H. Fukuda, T. Tsuchizawa, T. Watanabe, K. Yamada, and S. ichi Itabashi, “Entanglement generation using silicon wire waveguide,” Appl. Phys. Lett.91, 201108 (2007). [CrossRef]
  9. D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature424, 817–823 (2003). [CrossRef] [PubMed]
  10. L. G. Helt, M. Liscidini, and J. E. Sipe, “How does it scale? comparing quantum and classical nonlinear optical processes in integrated devices,” J. Opt. Soc. Am. B29, 2199–2212 (2012). [CrossRef]
  11. M. Grafe, A. S. Solntsev, R. Keil, A. A. Sukhorukov, M. Heinrich, A. Tunnermann, S. Nolte, A. Szameit, and Y. S. Kivshar, “Biphoton generation in quadratic waveguide arrays: A classical optical simulation,” Sci. Rep.2, 562 (2012). [CrossRef] [PubMed]
  12. J. C. F. Matthews, K. Poulios, J. D. A. Meinecke, A. Politi, A. Peruzzo, N. Ismail, K. Wrhoff, M. G. Thompson, and J. L. O’Brien, “Simulating quantum statistics with entangled photons: a continuous transition from bosons to fermions,” http://arxiv.org/abs/1106.1166 (2011).
  13. J. Zhang, Q. Lin, G. Piredda, R. W. Boyd, G. P. Agrawal, and P. M. Fauchet, “Optical solitons in a silicon waveguide,” Opt. Express15, 7682–7688 (2007). [CrossRef] [PubMed]
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