Abstract

We discuss the optimization of photonic crystal waveguides for four-wave mixing (FWM) applications, taking into account linear loss and free-carrier effects. Suitable figures of merit are introduced in order to guide us through the choice of practical, high-efficiency designs requiring relatively low pump power and small waveguide length. In order to realistically perform the waveguide optimization process, we propose and validate an approximate expression for the FWM efficiency, which significantly alleviates our numerical calculations. Promising waveguide designs are identified by means of an exhaustive search, altering some structural parameters. Our approach aims to optimize the waveguides for nonlinear signal-processing applications based on the FWM.

© 2014 Optical Society of America

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2010 (3)

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R. Salem, M. A. Foster, A. C. Turner, D. F. Geragthy, M. Lipson, and A. L. Gaeta, Nat. Photonics 2, 35 (2008).
[CrossRef]

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K. O. Hill, D. C. Johnson, B. S. Kawasaki, and R. I. MacDonald, J. Appl. Phys. 49, 5098 (1978).
[CrossRef]

Beggs, D. M.

Cao, L.

Chen, T.

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S. Rawal, R. K. Sinha, and R. M. De La Rue, J. Nanophoton. 6, 063504 (2012).
[CrossRef]

Duan, T.

Ebnali-Heidari, M.

Eggleton, B. J.

Foster, M. A.

A. C. Turner-Foster, M. A. Foster, J. S. Levy, C. B. Poitras, R. Salem, and A. L. Gaeta, Opt. Express 18, 3582 (2010).
[CrossRef]

R. Salem, M. A. Foster, A. C. Turner, D. F. Geragthy, M. Lipson, and A. L. Gaeta, Nat. Photonics 2, 35 (2008).
[CrossRef]

Gaeta, A. L.

A. C. Turner-Foster, M. A. Foster, J. S. Levy, C. B. Poitras, R. Salem, and A. L. Gaeta, Opt. Express 18, 3582 (2010).
[CrossRef]

R. Salem, M. A. Foster, A. C. Turner, D. F. Geragthy, M. Lipson, and A. L. Gaeta, Nat. Photonics 2, 35 (2008).
[CrossRef]

Gao, S.

Geragthy, D. F.

R. Salem, M. A. Foster, A. C. Turner, D. F. Geragthy, M. Lipson, and A. L. Gaeta, Nat. Photonics 2, 35 (2008).
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Gordon, M. K.

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Grillet, C.

He, S.

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Huang, J.

Hugonin, J. P.

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[CrossRef]

Kamalakis, T.

Kanakis, P.

Kawasaki, B. S.

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[CrossRef]

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Kuipers, L.

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Li, L.

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Mazoyer, S.

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Pelusi, M. D.

Poitras, C. B.

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S. Rawal, R. K. Sinha, and R. M. De La Rue, J. Nanophoton. 6, 063504 (2012).
[CrossRef]

Salem, R.

A. C. Turner-Foster, M. A. Foster, J. S. Levy, C. B. Poitras, R. Salem, and A. L. Gaeta, Opt. Express 18, 3582 (2010).
[CrossRef]

R. Salem, M. A. Foster, A. C. Turner, D. F. Geragthy, M. Lipson, and A. L. Gaeta, Nat. Photonics 2, 35 (2008).
[CrossRef]

Schulz, S. A.

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S. Rawal, R. K. Sinha, and R. M. De La Rue, J. Nanophoton. 6, 063504 (2012).
[CrossRef]

Spasenovic, M.

Sphicopoulos, T.

Sun, J.

Turner, A. C.

R. Salem, M. A. Foster, A. C. Turner, D. F. Geragthy, M. Lipson, and A. L. Gaeta, Nat. Photonics 2, 35 (2008).
[CrossRef]

Turner-Foster, A. C.

Wang, L.

White, T. P.

Xu, D.-X.

Zhang, W.

J. Appl. Phys. (1)

K. O. Hill, D. C. Johnson, B. S. Kawasaki, and R. I. MacDonald, J. Appl. Phys. 49, 5098 (1978).
[CrossRef]

J. Nanophoton. (1)

S. Rawal, R. K. Sinha, and R. M. De La Rue, J. Nanophoton. 6, 063504 (2012).
[CrossRef]

J. Opt. Soc. Am. B (2)

Nat. Photonics (1)

R. Salem, M. A. Foster, A. C. Turner, D. F. Geragthy, M. Lipson, and A. L. Gaeta, Nat. Photonics 2, 35 (2008).
[CrossRef]

Opt. Express (7)

Opt. Lett. (1)

Other (1)

L. F. Shampine and M. K. Gordon, Computer Solution of Ordinary Differential Equations: The Initial Value Problem, W. H. Freeman, ed. (W. H. Freeman & Co Ltd., 1975).

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Figures (5)

Fig. 1.
Fig. 1.

PCW formed by embedding air holes in a thin layer of silicon. The numbers indicate the hole class according to their proximity to the waveguide defect, while arrows indicate the structural perturbation.

Fig. 2.
Fig. 2.

FWM conversion efficiency with respect to the wavelength of the idler (λi) and the signal (λs) waves obtained (a) numerically solving the ODEs and (b) using Eq. (11).

Fig. 3.
Fig. 3.

(a) EBT and (b) EBTPL values with respect to the design parameters Δy1 and Δy2.

Fig. 4.
Fig. 4.

(a) EBT and (b) EBTPL values with respect to the design parameters Δy1 and r1.

Fig. 5.
Fig. 5.

FWM conversion efficiency with respect to the signal and idler wavelengths for designs (a) A and (b) B in Table 1.

Tables (2)

Tables Icon

Table 1. Waveguide Designs

Tables Icon

Table 2. FWM Efficiency Dependence on the Loss Mechanism

Equations (13)

Equations on this page are rendered with MathJax. Learn more.

ηPi(L)/Ps(0),
EBT=max{P0,L}{η0×Δλ×δλ},
EBTPL=max{P0,L}{η0×Δλ×δλP0×L}.
dPp/dz(ap+2FpPp2)Pp,
FμNCPp2(j2πλμC1C22)(λμλ0)2.
Aρκψ=V|Eρ|2dV(V|Eκ|2dVV|Eψ|2dV)1/2aVEρ*Eρ*EκEψdV,
Pp(z)=P0eapz(1+δ(1e2apz))1/2,
P¯P=P0apLδ{sin1(eapLδ1+1)sin1(1δ1+1)},
P¯p2=1L0LPp2(z)dz=P022apδln(1+δ(1e2apL)).
li=Pi(L)/Pi(0)=exp(aiL+2LRe{Fi}P¯p2),
η=liλsλi(1+κtot24g2)sinh2(gL).
κ=Δk+4πn2P¯p(Apss1λs1+Apii1λi1Appp1λp1),
g=(n22Sp2SiSsωiωsP¯pc2Apsi2κ2/4)1/2,

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