Abstract

A slab-waveguide-based configuration for efficient frequency conversion is proposed. In the proposed structure, frequency conversion is induced through cascaded multistep nonreciprocal interband photonic transitions activated by external refractive-index modulations. The advantages of interband photonic transition over intraband photonic transition for frequency conversion are analyzed with the coupled-mode theory.

© 2010 Optical Society of America

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References

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  1. Z. Yu and S. Fan, Nat. Photon. 3, 91 (2009).
    [CrossRef]
  2. Z. Yu and S. Fan, Appl. Phys. Lett. 94, 171116 (2009).
    [CrossRef]
  3. C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, Nature Phys. 6, 192 (2010).
    [CrossRef]
  4. X. Zang and C. Jiang, J. Opt. Soc. Am. B 26, 2275 (2009).
    [CrossRef]
  5. V. V. Konotop and V. Kuzmiak, Phys. Rev. B 66, 235208 (2002).
    [CrossRef]
  6. S. F. Preble, Q. Xu, and M. Lipson, Nat. Photon. 1, 293 (2007).
    [CrossRef]
  7. Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, Nature 435, 325 (2005).
    [CrossRef] [PubMed]
  8. M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, Nature 462, 78 (2009).
    [CrossRef] [PubMed]

2010 (1)

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, Nature Phys. 6, 192 (2010).
[CrossRef]

2009 (4)

Z. Yu and S. Fan, Nat. Photon. 3, 91 (2009).
[CrossRef]

Z. Yu and S. Fan, Appl. Phys. Lett. 94, 171116 (2009).
[CrossRef]

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, Nature 462, 78 (2009).
[CrossRef] [PubMed]

X. Zang and C. Jiang, J. Opt. Soc. Am. B 26, 2275 (2009).
[CrossRef]

2007 (1)

S. F. Preble, Q. Xu, and M. Lipson, Nat. Photon. 1, 293 (2007).
[CrossRef]

2005 (1)

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, Nature 435, 325 (2005).
[CrossRef] [PubMed]

2002 (1)

V. V. Konotop and V. Kuzmiak, Phys. Rev. B 66, 235208 (2002).
[CrossRef]

Camacho, R. M.

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, Nature 462, 78 (2009).
[CrossRef] [PubMed]

Chan, J.

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, Nature 462, 78 (2009).
[CrossRef] [PubMed]

Christodoulides, D. N.

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, Nature Phys. 6, 192 (2010).
[CrossRef]

Eichenfield, M.

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, Nature 462, 78 (2009).
[CrossRef] [PubMed]

El-Ganainy, R.

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, Nature Phys. 6, 192 (2010).
[CrossRef]

Fan, S.

Z. Yu and S. Fan, Nat. Photon. 3, 91 (2009).
[CrossRef]

Z. Yu and S. Fan, Appl. Phys. Lett. 94, 171116 (2009).
[CrossRef]

Jiang, C.

Kip, D.

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, Nature Phys. 6, 192 (2010).
[CrossRef]

Konotop, V. V.

V. V. Konotop and V. Kuzmiak, Phys. Rev. B 66, 235208 (2002).
[CrossRef]

Kuzmiak, V.

V. V. Konotop and V. Kuzmiak, Phys. Rev. B 66, 235208 (2002).
[CrossRef]

Lipson, M.

S. F. Preble, Q. Xu, and M. Lipson, Nat. Photon. 1, 293 (2007).
[CrossRef]

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, Nature 435, 325 (2005).
[CrossRef] [PubMed]

Makris, K. G.

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, Nature Phys. 6, 192 (2010).
[CrossRef]

Painter, O.

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, Nature 462, 78 (2009).
[CrossRef] [PubMed]

Pradhan, S.

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, Nature 435, 325 (2005).
[CrossRef] [PubMed]

Preble, S. F.

S. F. Preble, Q. Xu, and M. Lipson, Nat. Photon. 1, 293 (2007).
[CrossRef]

Rüter, C. E.

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, Nature Phys. 6, 192 (2010).
[CrossRef]

Schmidt, B.

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, Nature 435, 325 (2005).
[CrossRef] [PubMed]

Segev, M.

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, Nature Phys. 6, 192 (2010).
[CrossRef]

Vahala, K. J.

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, Nature 462, 78 (2009).
[CrossRef] [PubMed]

Xu, Q.

S. F. Preble, Q. Xu, and M. Lipson, Nat. Photon. 1, 293 (2007).
[CrossRef]

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, Nature 435, 325 (2005).
[CrossRef] [PubMed]

Yu, Z.

Z. Yu and S. Fan, Nat. Photon. 3, 91 (2009).
[CrossRef]

Z. Yu and S. Fan, Appl. Phys. Lett. 94, 171116 (2009).
[CrossRef]

Zang, X.

Appl. Phys. Lett. (1)

Z. Yu and S. Fan, Appl. Phys. Lett. 94, 171116 (2009).
[CrossRef]

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

Nat. Photon. (2)

Z. Yu and S. Fan, Nat. Photon. 3, 91 (2009).
[CrossRef]

S. F. Preble, Q. Xu, and M. Lipson, Nat. Photon. 1, 293 (2007).
[CrossRef]

Nature (2)

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, Nature 435, 325 (2005).
[CrossRef] [PubMed]

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, Nature 462, 78 (2009).
[CrossRef] [PubMed]

Nature Phys. (1)

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, Nature Phys. 6, 192 (2010).
[CrossRef]

Phys. Rev. B (1)

V. V. Konotop and V. Kuzmiak, Phys. Rev. B 66, 235208 (2002).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

(a) Interband photonic transition in a slab waveguide between symmetric mode p 1 ( ω 1 , β 1 ) and asymmetric mode p 2 ( ω 2 , β 2 ) . (b) y-directional electric field distribution | E y | .

Fig. 2
Fig. 2

Cascaded multistep interband photonic transitions: (a) four-step interband photonic transitions ( p 1 p 2 p 3 p 4 p 5 ); (b) optical power exchange along the z axis and y-directional electric field distribution | E y | .

Fig. 3
Fig. 3

Single-steps intraband photonic transitions: (a) single-step intraband photonic transition ( p 1 p 5 and p 1 p 5 ); (b) optical power exchange along the z axis and y-directional electric field distribution | E y | .

Equations (2)

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E ( r , t ) = a i ( z ) E i ( x ) e j ( β i z ω i t ) + a f ( z ) E f ( x ) e j ( β f z ω f t ) + a n ( z ) E n ( x ) e j ( β n z ω n t ) ,
( d a i ( z ) / d z d a f ( z ) / d z d a n ( z ) / d z ) = ( 0 j C i , f e j Δ β i , f z j C i , n e j Δ β i , n z j C f , i e j Δ β i , f z 0 j C n , i e j Δ β i , n z 0 ) ( a i ( z ) a f ( z ) a n ( z ) ) ,

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