Abstract

We develop, to the best of our knowledge, the first model for an array waveguide grating (AWG) device subject to quantum inputs and analyze its basic transformation functionalities for single-photon states. A commercial, cyclic AWG is experimentally characterized with weak input coherent states as a means of exploring its behaviour under realistic quantum detection. In particular it is shown the existence of a cutoff value of the average photon number below which quantum crosstalk between AWG ports is negligible with respect to dark counts. These results can be useful when considering the application of AWG devices to integrated quantum photonic systems.

© 2013 OSA

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [PubMed]
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    [CrossRef]
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    [CrossRef]
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2013 (2)

2012 (3)

M. K. Smit, J. van der Tol, and M. Hill, “Moore laws in photonics,” Lasers & Photon. Rev.6(1), 1–13 (2012).
[CrossRef]

J. C. F. Matthews and M. G. Thompson, “Quantum optics: An entangled walk of photons,” Nature484(7392), 47–48 (2012).
[PubMed]

M. Davanco, J. R. Ong, A. B. Shehata, A. Tosi, I. Agha, S. Assefa, F. Xia, W. M. J. Green, S. Mookherjea, and K. Srinivasan, “Telecommunications-band heralded single photons from a silicon nanophotonic chip,” Appl. Phys. Lett.100(26), 261104 (2012).
[CrossRef]

2011 (2)

M. G. Thompson, A. Politi, J. C. F. Matthews, and J. L. O’Brien, “Integrated waveguide circuits for optical quantum computing,” IET Circuits Devices Syst.5(2), 94–102 (2011).
[CrossRef]

S. Kalliakos, I. Farrer, J. P. Griffiths, G. A. C. Jones, D. A. Ritchie, and A. J. Shields, “On-chip single photon emission from an integrated semiconductor quantum dot into a photonic crystal waveguide,” Appl. Phys. Lett.99(26), 261108 (2011).
[CrossRef]

2010 (2)

2009 (2)

J. L. O’Brien, A. Furusawa, and J. Vučković, “Photonic quantum technologies,” Nat. Photonics3(12), 687–695 (2009).
[CrossRef]

A. Politi, J. C. F. Matthews, M. G. Thompson, and J. L. O’Brien, “Integrated quantum photonics,” IEEE J. Sel. Top. Quantum Electron.15(6), 1673–1684 (2009).
[CrossRef]

2003 (1)

U. Leonhardt, “Quantum physics of simple optical instruments,” Rep. Prog. Phys.66(7), 1207–1249 (2003).
[CrossRef]

2002 (1)

1996 (1)

M. K. Smit and C. van Dam, “PHASAR-based WDM-devices: Principles, design and applications,” J. Sel. Top. Quant. Electron.2(2), 236–250 (1996).
[CrossRef]

Agha, I.

M. Davanco, J. R. Ong, A. B. Shehata, A. Tosi, I. Agha, S. Assefa, F. Xia, W. M. J. Green, S. Mookherjea, and K. Srinivasan, “Telecommunications-band heralded single photons from a silicon nanophotonic chip,” Appl. Phys. Lett.100(26), 261104 (2012).
[CrossRef]

Assefa, S.

M. Davanco, J. R. Ong, A. B. Shehata, A. Tosi, I. Agha, S. Assefa, F. Xia, W. M. J. Green, S. Mookherjea, and K. Srinivasan, “Telecommunications-band heralded single photons from a silicon nanophotonic chip,” Appl. Phys. Lett.100(26), 261104 (2012).
[CrossRef]

Broome, M. A.

Capmany, J.

Davanco, M.

M. Davanco, J. R. Ong, A. B. Shehata, A. Tosi, I. Agha, S. Assefa, F. Xia, W. M. J. Green, S. Mookherjea, and K. Srinivasan, “Telecommunications-band heralded single photons from a silicon nanophotonic chip,” Appl. Phys. Lett.100(26), 261104 (2012).
[CrossRef]

Farrer, I.

S. Kalliakos, I. Farrer, J. P. Griffiths, G. A. C. Jones, D. A. Ritchie, and A. J. Shields, “On-chip single photon emission from an integrated semiconductor quantum dot into a photonic crystal waveguide,” Appl. Phys. Lett.99(26), 261108 (2011).
[CrossRef]

Fedrizzi, A.

Fernández-Pousa, C. R.

Fickler, R.

Furusawa, A.

J. L. O’Brien, A. Furusawa, and J. Vučković, “Photonic quantum technologies,” Nat. Photonics3(12), 687–695 (2009).
[CrossRef]

Green, W. M. J.

M. Davanco, J. R. Ong, A. B. Shehata, A. Tosi, I. Agha, S. Assefa, F. Xia, W. M. J. Green, S. Mookherjea, and K. Srinivasan, “Telecommunications-band heralded single photons from a silicon nanophotonic chip,” Appl. Phys. Lett.100(26), 261104 (2012).
[CrossRef]

Griffiths, J. P.

S. Kalliakos, I. Farrer, J. P. Griffiths, G. A. C. Jones, D. A. Ritchie, and A. J. Shields, “On-chip single photon emission from an integrated semiconductor quantum dot into a photonic crystal waveguide,” Appl. Phys. Lett.99(26), 261108 (2011).
[CrossRef]

Hill, M.

M. K. Smit, J. van der Tol, and M. Hill, “Moore laws in photonics,” Lasers & Photon. Rev.6(1), 1–13 (2012).
[CrossRef]

Jones, G. A. C.

S. Kalliakos, I. Farrer, J. P. Griffiths, G. A. C. Jones, D. A. Ritchie, and A. J. Shields, “On-chip single photon emission from an integrated semiconductor quantum dot into a photonic crystal waveguide,” Appl. Phys. Lett.99(26), 261108 (2011).
[CrossRef]

Kalliakos, S.

S. Kalliakos, I. Farrer, J. P. Griffiths, G. A. C. Jones, D. A. Ritchie, and A. J. Shields, “On-chip single photon emission from an integrated semiconductor quantum dot into a photonic crystal waveguide,” Appl. Phys. Lett.99(26), 261108 (2011).
[CrossRef]

Leonhardt, U.

U. Leonhardt, “Quantum physics of simple optical instruments,” Rep. Prog. Phys.66(7), 1207–1249 (2003).
[CrossRef]

Matthews, J. C. F.

J. C. F. Matthews and M. G. Thompson, “Quantum optics: An entangled walk of photons,” Nature484(7392), 47–48 (2012).
[PubMed]

M. G. Thompson, A. Politi, J. C. F. Matthews, and J. L. O’Brien, “Integrated waveguide circuits for optical quantum computing,” IET Circuits Devices Syst.5(2), 94–102 (2011).
[CrossRef]

A. Politi, J. C. F. Matthews, M. G. Thompson, and J. L. O’Brien, “Integrated quantum photonics,” IEEE J. Sel. Top. Quantum Electron.15(6), 1673–1684 (2009).
[CrossRef]

Mookherjea, S.

J. R. Ong and S. Mookherjea, “Quantum light generation on a silicon chip using waveguides and resonators,” Opt. Express21(4), 5171–5181 (2013).
[CrossRef] [PubMed]

M. Davanco, J. R. Ong, A. B. Shehata, A. Tosi, I. Agha, S. Assefa, F. Xia, W. M. J. Green, S. Mookherjea, and K. Srinivasan, “Telecommunications-band heralded single photons from a silicon nanophotonic chip,” Appl. Phys. Lett.100(26), 261104 (2012).
[CrossRef]

Munoz, P.

O’Brien, J. L.

M. G. Thompson, A. Politi, J. C. F. Matthews, and J. L. O’Brien, “Integrated waveguide circuits for optical quantum computing,” IET Circuits Devices Syst.5(2), 94–102 (2011).
[CrossRef]

A. Politi, J. C. F. Matthews, M. G. Thompson, and J. L. O’Brien, “Integrated quantum photonics,” IEEE J. Sel. Top. Quantum Electron.15(6), 1673–1684 (2009).
[CrossRef]

J. L. O’Brien, A. Furusawa, and J. Vučković, “Photonic quantum technologies,” Nat. Photonics3(12), 687–695 (2009).
[CrossRef]

Ong, J. R.

J. R. Ong and S. Mookherjea, “Quantum light generation on a silicon chip using waveguides and resonators,” Opt. Express21(4), 5171–5181 (2013).
[CrossRef] [PubMed]

M. Davanco, J. R. Ong, A. B. Shehata, A. Tosi, I. Agha, S. Assefa, F. Xia, W. M. J. Green, S. Mookherjea, and K. Srinivasan, “Telecommunications-band heralded single photons from a silicon nanophotonic chip,” Appl. Phys. Lett.100(26), 261104 (2012).
[CrossRef]

Pastor, D.

Politi, A.

M. G. Thompson, A. Politi, J. C. F. Matthews, and J. L. O’Brien, “Integrated waveguide circuits for optical quantum computing,” IET Circuits Devices Syst.5(2), 94–102 (2011).
[CrossRef]

A. Politi, J. C. F. Matthews, M. G. Thompson, and J. L. O’Brien, “Integrated quantum photonics,” IEEE J. Sel. Top. Quantum Electron.15(6), 1673–1684 (2009).
[CrossRef]

Rahimi-Keshari, S.

Ralph, T. C.

Ritchie, D. A.

S. Kalliakos, I. Farrer, J. P. Griffiths, G. A. C. Jones, D. A. Ritchie, and A. J. Shields, “On-chip single photon emission from an integrated semiconductor quantum dot into a photonic crystal waveguide,” Appl. Phys. Lett.99(26), 261108 (2011).
[CrossRef]

Shehata, A. B.

M. Davanco, J. R. Ong, A. B. Shehata, A. Tosi, I. Agha, S. Assefa, F. Xia, W. M. J. Green, S. Mookherjea, and K. Srinivasan, “Telecommunications-band heralded single photons from a silicon nanophotonic chip,” Appl. Phys. Lett.100(26), 261104 (2012).
[CrossRef]

Shields, A. J.

S. Kalliakos, I. Farrer, J. P. Griffiths, G. A. C. Jones, D. A. Ritchie, and A. J. Shields, “On-chip single photon emission from an integrated semiconductor quantum dot into a photonic crystal waveguide,” Appl. Phys. Lett.99(26), 261108 (2011).
[CrossRef]

Smit, M. K.

M. K. Smit, J. van der Tol, and M. Hill, “Moore laws in photonics,” Lasers & Photon. Rev.6(1), 1–13 (2012).
[CrossRef]

M. K. Smit and C. van Dam, “PHASAR-based WDM-devices: Principles, design and applications,” J. Sel. Top. Quant. Electron.2(2), 236–250 (1996).
[CrossRef]

Srinivasan, K.

M. Davanco, J. R. Ong, A. B. Shehata, A. Tosi, I. Agha, S. Assefa, F. Xia, W. M. J. Green, S. Mookherjea, and K. Srinivasan, “Telecommunications-band heralded single photons from a silicon nanophotonic chip,” Appl. Phys. Lett.100(26), 261104 (2012).
[CrossRef]

Thompson, M. G.

J. C. F. Matthews and M. G. Thompson, “Quantum optics: An entangled walk of photons,” Nature484(7392), 47–48 (2012).
[PubMed]

M. G. Thompson, A. Politi, J. C. F. Matthews, and J. L. O’Brien, “Integrated waveguide circuits for optical quantum computing,” IET Circuits Devices Syst.5(2), 94–102 (2011).
[CrossRef]

A. Politi, J. C. F. Matthews, M. G. Thompson, and J. L. O’Brien, “Integrated quantum photonics,” IEEE J. Sel. Top. Quantum Electron.15(6), 1673–1684 (2009).
[CrossRef]

Tosi, A.

M. Davanco, J. R. Ong, A. B. Shehata, A. Tosi, I. Agha, S. Assefa, F. Xia, W. M. J. Green, S. Mookherjea, and K. Srinivasan, “Telecommunications-band heralded single photons from a silicon nanophotonic chip,” Appl. Phys. Lett.100(26), 261104 (2012).
[CrossRef]

van Dam, C.

M. K. Smit and C. van Dam, “PHASAR-based WDM-devices: Principles, design and applications,” J. Sel. Top. Quant. Electron.2(2), 236–250 (1996).
[CrossRef]

van der Tol, J.

M. K. Smit, J. van der Tol, and M. Hill, “Moore laws in photonics,” Lasers & Photon. Rev.6(1), 1–13 (2012).
[CrossRef]

Vuckovic, J.

J. L. O’Brien, A. Furusawa, and J. Vučković, “Photonic quantum technologies,” Nat. Photonics3(12), 687–695 (2009).
[CrossRef]

White, A. G.

Xia, F.

M. Davanco, J. R. Ong, A. B. Shehata, A. Tosi, I. Agha, S. Assefa, F. Xia, W. M. J. Green, S. Mookherjea, and K. Srinivasan, “Telecommunications-band heralded single photons from a silicon nanophotonic chip,” Appl. Phys. Lett.100(26), 261104 (2012).
[CrossRef]

Appl. Phys. Lett. (2)

S. Kalliakos, I. Farrer, J. P. Griffiths, G. A. C. Jones, D. A. Ritchie, and A. J. Shields, “On-chip single photon emission from an integrated semiconductor quantum dot into a photonic crystal waveguide,” Appl. Phys. Lett.99(26), 261108 (2011).
[CrossRef]

M. Davanco, J. R. Ong, A. B. Shehata, A. Tosi, I. Agha, S. Assefa, F. Xia, W. M. J. Green, S. Mookherjea, and K. Srinivasan, “Telecommunications-band heralded single photons from a silicon nanophotonic chip,” Appl. Phys. Lett.100(26), 261104 (2012).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

A. Politi, J. C. F. Matthews, M. G. Thompson, and J. L. O’Brien, “Integrated quantum photonics,” IEEE J. Sel. Top. Quantum Electron.15(6), 1673–1684 (2009).
[CrossRef]

IET Circuits Devices Syst. (1)

M. G. Thompson, A. Politi, J. C. F. Matthews, and J. L. O’Brien, “Integrated waveguide circuits for optical quantum computing,” IET Circuits Devices Syst.5(2), 94–102 (2011).
[CrossRef]

J. Lightwave Technol. (1)

J. Opt. Soc. Am. B (1)

J. Sel. Top. Quant. Electron. (1)

M. K. Smit and C. van Dam, “PHASAR-based WDM-devices: Principles, design and applications,” J. Sel. Top. Quant. Electron.2(2), 236–250 (1996).
[CrossRef]

Lasers & Photon. Rev. (1)

M. K. Smit, J. van der Tol, and M. Hill, “Moore laws in photonics,” Lasers & Photon. Rev.6(1), 1–13 (2012).
[CrossRef]

Nat. Photonics (1)

J. L. O’Brien, A. Furusawa, and J. Vučković, “Photonic quantum technologies,” Nat. Photonics3(12), 687–695 (2009).
[CrossRef]

Nature (1)

J. C. F. Matthews and M. G. Thompson, “Quantum optics: An entangled walk of photons,” Nature484(7392), 47–48 (2012).
[PubMed]

Opt. Express (3)

Rep. Prog. Phys. (1)

U. Leonhardt, “Quantum physics of simple optical instruments,” Rep. Prog. Phys.66(7), 1207–1249 (2003).
[CrossRef]

Other (3)

R. Loudon, The Quantum Theory of Light (Oxford Univ. Press, 2000).

C. C. Gerry and P. L. Knight, Introductory Quantum Optics (Cambridge Univ. Press, 2005).

J. C. Garrison and R. Y. Chiao, Quantum Optics (Oxford Univ. Press, 2008).

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Figures (7)

Fig. 1
Fig. 1

(Upper) Artistic top view of an AWG device. (Lower) detailed layout of the AWG device showing the relevant input/output and intermediate array waveguides, the free propagation regions (FPRs) and the curvilinear coordinate axes. The inset shows the construction of the circular regions that define (x0, x1) coordinate axes for which an exact Fourier transform is achieved by means of Fresnel diffraction.

Fig. 2
Fig. 2

Spectral measurements for the 18 × 18 AWG employed in the measurements. Left: detail of the transfer function for the j = 9, i = 9 input/output waveguide configuration. Right: detail of the transfer functions keeping j = 9 as the input waveguide ant taking i = 8, 9 and 10 as output waveguides respectively. The wavelength separation between adjacent maxima is Δλc.

Fig. 3
Fig. 3

Experimental configuration employed to measure the behavior of the 18 × 18 AWG under illumination by coherent states. The left part shows a typical single pass AWG configuration. In the fold-back measurements it was replaced by the configuration shown in the right part of the figure where feedback from output to input waveguides is provided.

Fig. 4
Fig. 4

(a) Experimental measurements (points) for the photon count of the CH9 (▲, i = 9) and the adjacent channels (⬛, i = 7; ⚫, i = 8; ▼, i = 10; ◆, i = 11) introducing coherent states by port j = 9. (b) Experimental measurement (points) for the photon count of the output port i = 8 (⬛), i = 9 (⚫) and i = 10 (▲) when coherent states are introduced by port j = 8, 9 and 10, respectively. The solid curves represent the theoretical predictions.

Fig. 5
Fig. 5

Optical transfer function Tij(ν) for the input and output ports j = 9 and i = 9, respectively, for different cyclical bands centered at (a) 1530.75, (b) 1544.95 and (c) 1559.44 nm. Experimental (points) and theoretical (solid curve) photon counts are plotted in (d) by selecting the corresponding center wavelength for each coherent state.

Fig. 6
Fig. 6

(a) Optical transfer function for different fold-back configurations and the (b) experimental (points) photon counts and the corresponding theoretical predictions (curve) for a coherent state at wavelength 1544.95 nm.

Fig. 7
Fig. 7

Photocount transfer function in (a) simple and (b) fold-back AWG configuration introducing different coherent states with μ from 0.1 to 100.

Tables (1)

Tables Icon

Table 1 Input, fold-back and output ports for three fold-back configurations

Equations (13)

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( E ˜ 1 out (ν) E ˜ 2 out (ν) E ˜ N out (ν) )=( t 11 (ν) t 12 (ν) t 1N (ν) t 21 (ν) t 22 (ν) t 2N (ν) t N1 (ν) t N2 (ν) t NN (ν) )( E ˜ 1 in (ν) E ˜ 2 in (ν) E ˜ N in (ν) )
t ij (ν)=ψ(ν) d x 3 d x 0 b out [ x 3 (i(N/2)1) d out ]K( x 3 , x 0 |ν) b in [ x 0 (j(N/2)1) d in ]
K( x 3 , x 0 |ν)= r= e jrβ(ν)Δl N d w /2 N d w /2 d x 2 α ν d x 1 α ν b g ( x 2 r d w ) e j2π x 3 x 2 / α ν b g ( x 1 r d w ) e j2π x 1 x 0 / α ν
s(ν)=( t(ν) ±j 1 t + (ν)t(ν) ±j 1 t + (ν)t(ν) t + (ν) )
S ^ AWG a ^ j in+ (ν) S ^ AWG + = i=1 2N s ij (ν) a ^ i out+ (ν)
ρ in ρ out =t r 2 ( S ^ AWG ( ρ in | vac 2 vac |) S ^ AWG + )
S ^ AWG | 1 j ,φ = S ^ AWG 0 dνφ(ν) a ^ j in+ (ν) | vac 1 = i=1 N 0 dνφ(ν) t ij (ν) a ^ i out+ (ν) | vac 1 + |Ψ 2
Prob ji = P ^ i S ^ AWG | 1 j ,φ 2 = 0 dν φ ij (ν) a ^ i out+ (ν) | vac 1 2 = 0 dν|φ(ν) t ij (ν) | 2
Prob ji | t ij ( ν 0 ) | 2 0 dν|φ(ν) | 2 = | t ij ( ν 0 ) | 2 = T ij ( ν 0 )
Prob ji | k φ( ν ij +kΔ ν FSR ) | 2 0 dν| t ij (ν) | 2 = T ¯ ij δν | k φ( ν ij +kΔ ν FSR ) | 2
N cps = f 0 [ p ij (ν)+ p d p ij (ν) p d ] f 0 [ p ij (ν)+ p d ]= f 0 [1exp(ρ μ j T ij (ν))+ p d ]
Xtal k i±n,j PC = 1exp(ρ μ j T ij ( ν ij )) 1exp(ρ μ j T i±n,j ( ν ij )) T ij ( ν ij ) T i±n,j ( ν ij ) MSLR
T ij PC (ν)= p ij (ν) p j (ν) = 1exp(ρ μ j T ij (ν)) 1exp(ρ μ j ) = T ij (ν) 1 2 ρ μ j T ij (ν)( T ij (ν)1)+...

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