Abstract

We propose nondegenerate four-wave mixing mirrorless oscillation in a multimode silicon nonlinear waveguide. Thanks to the large modal dispersion between two spatial modes caused by the high-index-contrast waveguide structure, two counterpropagating pumps of one spatial mode can generate two new optical waves of the other spatial mode at different frequencies. The phase-matching condition can be satisfied with the higher-order modes involved; therefore, frequencies of the newly generated light can be tuned by simply changing the pump frequency. The threshold power and conversion efficiency of the proposed mirrorless oscillation are investigated under different waveguide parameters.

© 2011 Optical Society of America

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  1. A. Yariv and D. M. Pepper, Opt. Lett. 1, 16 (1977).
    [CrossRef] [PubMed]
  2. S. Pitois, A. Picozzil, G. Millot, H. R. Jauslin, and M. Haelterman, Europhys. Lett. 70, 88 (2005).
    [CrossRef]
  3. D. M. Bloom, P. F. Liao, and N. P. Economou, Opt. Lett. 2, 58 (1978).
    [CrossRef] [PubMed]
  4. A. Picozzi, M. Haelterman, S. Pitois, and G. Millot, Phys. Rev. Lett. 92, 143906 (2004).
    [CrossRef] [PubMed]
  5. C. Canalias and V. Pasiskevicius, Nat. Photon. 1, 459 (2007).
    [CrossRef]
  6. A. S. Zibrov, M. D. Lukin, and M. O. Scully, Phys. Rev. Lett. 83, 4049 (1999).
    [CrossRef]
  7. R. H. Stolen, IEEE J. Quantum Electron. 11, 100 (1975).
    [CrossRef]
  8. S. Bian and M. Kuzyk, Appl. Phys. Lett. 84, 858 (2004).
    [CrossRef]
  9. I. D. Rukhlenko, M. Premaratne, and G. P. Agrawal, IEEE J. Sel. Top. Quantum Electron. 16, 200 (2010).
    [CrossRef]
  10. A. D. Bristow, N. Rotenberg, and H. M. Driel, Appl. Phys. Lett. 90, 191104 (2007).
    [CrossRef]
  11. A. V. Shahraam and T. M. Monro, Opt. Express 17, 2298 (2009).
    [CrossRef]
  12. Q. Lin, J. Zhang, G. Piredda, R. W. Boyed, P. M. Fauchet, and G. P. Agrawal, Appl. Phys. Lett. 91, 021111 (2007).
    [CrossRef]
  13. Q. Lin, O. J. Painter, and G. P. Agrawal, Opt. Express 15, 16604 (2007).
    [CrossRef] [PubMed]
  14. Y. Ja, Opt. Quantum Electron. 15, 529 (1983).
    [CrossRef]

2010 (1)

I. D. Rukhlenko, M. Premaratne, and G. P. Agrawal, IEEE J. Sel. Top. Quantum Electron. 16, 200 (2010).
[CrossRef]

2009 (1)

2007 (4)

Q. Lin, O. J. Painter, and G. P. Agrawal, Opt. Express 15, 16604 (2007).
[CrossRef] [PubMed]

A. D. Bristow, N. Rotenberg, and H. M. Driel, Appl. Phys. Lett. 90, 191104 (2007).
[CrossRef]

Q. Lin, J. Zhang, G. Piredda, R. W. Boyed, P. M. Fauchet, and G. P. Agrawal, Appl. Phys. Lett. 91, 021111 (2007).
[CrossRef]

C. Canalias and V. Pasiskevicius, Nat. Photon. 1, 459 (2007).
[CrossRef]

2005 (1)

S. Pitois, A. Picozzil, G. Millot, H. R. Jauslin, and M. Haelterman, Europhys. Lett. 70, 88 (2005).
[CrossRef]

2004 (2)

A. Picozzi, M. Haelterman, S. Pitois, and G. Millot, Phys. Rev. Lett. 92, 143906 (2004).
[CrossRef] [PubMed]

S. Bian and M. Kuzyk, Appl. Phys. Lett. 84, 858 (2004).
[CrossRef]

1999 (1)

A. S. Zibrov, M. D. Lukin, and M. O. Scully, Phys. Rev. Lett. 83, 4049 (1999).
[CrossRef]

1983 (1)

Y. Ja, Opt. Quantum Electron. 15, 529 (1983).
[CrossRef]

1978 (1)

1977 (1)

1975 (1)

R. H. Stolen, IEEE J. Quantum Electron. 11, 100 (1975).
[CrossRef]

Agrawal, G. P.

I. D. Rukhlenko, M. Premaratne, and G. P. Agrawal, IEEE J. Sel. Top. Quantum Electron. 16, 200 (2010).
[CrossRef]

Q. Lin, J. Zhang, G. Piredda, R. W. Boyed, P. M. Fauchet, and G. P. Agrawal, Appl. Phys. Lett. 91, 021111 (2007).
[CrossRef]

Q. Lin, O. J. Painter, and G. P. Agrawal, Opt. Express 15, 16604 (2007).
[CrossRef] [PubMed]

Bian, S.

S. Bian and M. Kuzyk, Appl. Phys. Lett. 84, 858 (2004).
[CrossRef]

Bloom, D. M.

Boyed, R. W.

Q. Lin, J. Zhang, G. Piredda, R. W. Boyed, P. M. Fauchet, and G. P. Agrawal, Appl. Phys. Lett. 91, 021111 (2007).
[CrossRef]

Bristow, A. D.

A. D. Bristow, N. Rotenberg, and H. M. Driel, Appl. Phys. Lett. 90, 191104 (2007).
[CrossRef]

Canalias, C.

C. Canalias and V. Pasiskevicius, Nat. Photon. 1, 459 (2007).
[CrossRef]

Driel, H. M.

A. D. Bristow, N. Rotenberg, and H. M. Driel, Appl. Phys. Lett. 90, 191104 (2007).
[CrossRef]

Economou, N. P.

Fauchet, P. M.

Q. Lin, J. Zhang, G. Piredda, R. W. Boyed, P. M. Fauchet, and G. P. Agrawal, Appl. Phys. Lett. 91, 021111 (2007).
[CrossRef]

Haelterman, M.

S. Pitois, A. Picozzil, G. Millot, H. R. Jauslin, and M. Haelterman, Europhys. Lett. 70, 88 (2005).
[CrossRef]

A. Picozzi, M. Haelterman, S. Pitois, and G. Millot, Phys. Rev. Lett. 92, 143906 (2004).
[CrossRef] [PubMed]

Ja, Y.

Y. Ja, Opt. Quantum Electron. 15, 529 (1983).
[CrossRef]

Jauslin, H. R.

S. Pitois, A. Picozzil, G. Millot, H. R. Jauslin, and M. Haelterman, Europhys. Lett. 70, 88 (2005).
[CrossRef]

Kuzyk, M.

S. Bian and M. Kuzyk, Appl. Phys. Lett. 84, 858 (2004).
[CrossRef]

Liao, P. F.

Lin, Q.

Q. Lin, O. J. Painter, and G. P. Agrawal, Opt. Express 15, 16604 (2007).
[CrossRef] [PubMed]

Q. Lin, J. Zhang, G. Piredda, R. W. Boyed, P. M. Fauchet, and G. P. Agrawal, Appl. Phys. Lett. 91, 021111 (2007).
[CrossRef]

Lukin, M. D.

A. S. Zibrov, M. D. Lukin, and M. O. Scully, Phys. Rev. Lett. 83, 4049 (1999).
[CrossRef]

Millot, G.

S. Pitois, A. Picozzil, G. Millot, H. R. Jauslin, and M. Haelterman, Europhys. Lett. 70, 88 (2005).
[CrossRef]

A. Picozzi, M. Haelterman, S. Pitois, and G. Millot, Phys. Rev. Lett. 92, 143906 (2004).
[CrossRef] [PubMed]

Monro, T. M.

Painter, O. J.

Pasiskevicius, V.

C. Canalias and V. Pasiskevicius, Nat. Photon. 1, 459 (2007).
[CrossRef]

Pepper, D. M.

Picozzi, A.

A. Picozzi, M. Haelterman, S. Pitois, and G. Millot, Phys. Rev. Lett. 92, 143906 (2004).
[CrossRef] [PubMed]

Picozzil, A.

S. Pitois, A. Picozzil, G. Millot, H. R. Jauslin, and M. Haelterman, Europhys. Lett. 70, 88 (2005).
[CrossRef]

Piredda, G.

Q. Lin, J. Zhang, G. Piredda, R. W. Boyed, P. M. Fauchet, and G. P. Agrawal, Appl. Phys. Lett. 91, 021111 (2007).
[CrossRef]

Pitois, S.

S. Pitois, A. Picozzil, G. Millot, H. R. Jauslin, and M. Haelterman, Europhys. Lett. 70, 88 (2005).
[CrossRef]

A. Picozzi, M. Haelterman, S. Pitois, and G. Millot, Phys. Rev. Lett. 92, 143906 (2004).
[CrossRef] [PubMed]

Premaratne, M.

I. D. Rukhlenko, M. Premaratne, and G. P. Agrawal, IEEE J. Sel. Top. Quantum Electron. 16, 200 (2010).
[CrossRef]

Rotenberg, N.

A. D. Bristow, N. Rotenberg, and H. M. Driel, Appl. Phys. Lett. 90, 191104 (2007).
[CrossRef]

Rukhlenko, I. D.

I. D. Rukhlenko, M. Premaratne, and G. P. Agrawal, IEEE J. Sel. Top. Quantum Electron. 16, 200 (2010).
[CrossRef]

Scully, M. O.

A. S. Zibrov, M. D. Lukin, and M. O. Scully, Phys. Rev. Lett. 83, 4049 (1999).
[CrossRef]

Shahraam, A. V.

Stolen, R. H.

R. H. Stolen, IEEE J. Quantum Electron. 11, 100 (1975).
[CrossRef]

Yariv, A.

Zhang, J.

Q. Lin, J. Zhang, G. Piredda, R. W. Boyed, P. M. Fauchet, and G. P. Agrawal, Appl. Phys. Lett. 91, 021111 (2007).
[CrossRef]

Zibrov, A. S.

A. S. Zibrov, M. D. Lukin, and M. O. Scully, Phys. Rev. Lett. 83, 4049 (1999).
[CrossRef]

Appl. Phys. Lett. (3)

S. Bian and M. Kuzyk, Appl. Phys. Lett. 84, 858 (2004).
[CrossRef]

A. D. Bristow, N. Rotenberg, and H. M. Driel, Appl. Phys. Lett. 90, 191104 (2007).
[CrossRef]

Q. Lin, J. Zhang, G. Piredda, R. W. Boyed, P. M. Fauchet, and G. P. Agrawal, Appl. Phys. Lett. 91, 021111 (2007).
[CrossRef]

Europhys. Lett. (1)

S. Pitois, A. Picozzil, G. Millot, H. R. Jauslin, and M. Haelterman, Europhys. Lett. 70, 88 (2005).
[CrossRef]

IEEE J. Quantum Electron. (1)

R. H. Stolen, IEEE J. Quantum Electron. 11, 100 (1975).
[CrossRef]

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

I. D. Rukhlenko, M. Premaratne, and G. P. Agrawal, IEEE J. Sel. Top. Quantum Electron. 16, 200 (2010).
[CrossRef]

Nat. Photon. (1)

C. Canalias and V. Pasiskevicius, Nat. Photon. 1, 459 (2007).
[CrossRef]

Opt. Express (2)

Opt. Lett. (2)

Opt. Quantum Electron. (1)

Y. Ja, Opt. Quantum Electron. 15, 529 (1983).
[CrossRef]

Phys. Rev. Lett. (2)

A. Picozzi, M. Haelterman, S. Pitois, and G. Millot, Phys. Rev. Lett. 92, 143906 (2004).
[CrossRef] [PubMed]

A. S. Zibrov, M. D. Lukin, and M. O. Scully, Phys. Rev. Lett. 83, 4049 (1999).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Concept of nondegenerate FWM mirrorless oscillation between the quasi-TE polarized fundamental mode (mode 1) and the second-order mode (mode 2) in a multimode silicon waveguide.

Fig. 2
Fig. 2

Dispersion curves of two spatial modes in the silicon waveguide and the phase-matching condition for backward FWM: fundamental spatial mode (mode 1, top line) and second-order mode (mode 2, bottom line). Δ f = f 1 f 3 = f 4 f 2 . The arrows show the waves’ propagation directions.

Fig. 3
Fig. 3

Frequency relation of four waves in backward FWM between two spatial modes. The dots show the result given by Eq. (1) from exact waveguide dispersion. The dashed line shows the result of approximated frequency relation given by Eq. (2).

Fig. 4
Fig. 4

(a) Optical power distribution of pumps P p 1 , P p 2 and generated light P s , P i in the mirrorless oscillation in the waveguide. (b) Output power of the generated light P s , out and pump P p , out as functions of input pump power P in for three values of nonlinear coefficient γ. Turning points of the curves denote the threshold power P th .

Fig. 5
Fig. 5

(a) Conversion efficiency as functions of the input pump power P in under different waveguide linear loss assumptions. (b) Threshold power as functions of waveguide length l 0 under different waveguide linear loss assumptions.

Equations (3)

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f 1 + f 2 = f 3 + f 4 ( β 3 + β 4 ) ( β 1 + β 2 ) = ( | β 3 | | β 1 | ) ( | β 4 | | β 2 | ) = 0 ,
f 4 f 3 f 2 f 1 = a 2 a 1 or Δ f f 2 f 1 = a 2 a 1 2 a 1 ,
A p 1 z = α 1 A p 1 + [ 2 i ( γ 1 | A p 2 | 2 + γ 1 , 2 | A s 3 | 2 + γ 1 , 2 | A i 4 | 2 ) + i γ 1 | A p 1 | 2 ] A p 1 + 2 i γ 1 , 2 A s 3 A i 4 A p 2 * , A p 2 z = α 1 A p 2 + [ 2 i ( γ 1 | A p 1 | 2 + γ 1 , 2 | A s 3 | 2 + γ 1 , 2 | A i 4 | 2 ) + i γ 1 | A p 2 | 2 ] A p 2 + 2 i γ 1 , 2 A s 3 A i 4 A p 1 * , A s 3 z = α 2 A s 3 + [ 2 i ( γ 1 , 2 | A p 1 | 2 + γ 1 , 2 | A p 2 | 2 + γ 2 | A i 4 | 2 ) + i γ 2 | A s 3 | 2 ] A s 3 + 2 i γ 1 , 2 A p 1 A p 2 A 4 i * , A i 4 z = α 2 A i 4 + [ 2 i ( γ 1 , 2 | A p 1 | 2 + γ 1 , 2 | A p 2 | 2 + γ 2 | A s 3 | 2 ) + i γ 2 | A i 4 | 2 ] A i 4 + 2 i γ 1 , 2 A p 1 A p 2 A s 3 * ,

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