Abstract

A concept for the design of nonlinear optical diodes is proposed that uses the multistability of coupled nonlinear microcavities and the dependence of switching thresholds on the direction of incidence. A typical example of such a diode can be created by combining two mirror-symmetric microcavities where modes of the opposite parity dominate. It is shown that a strong nonreciprocal behavior can be achieved together with a negligible insertion loss. To describe the dynamical properties of such systems, a model based on the coupled-mode theory is developed, and a possible implementation in the form of multilayered structures is considered.

© 2011 Optical Society of America

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2011 (2)

S. V. Zhukovsky and A. G. Smirnov, Phys. Rev. A 83, 023818(2011).
[CrossRef]

V. Grigoriev and F. Biancalana, Phys. Rev. A 83, 043816(2011).
[CrossRef]

2010 (6)

S. V. Zhukovsky, Phys. Rev. A 81, 053808 (2010).
[CrossRef]

V. Grigoriev and F. Biancalana, New J. Phys. 12, 053041(2010).
[CrossRef]

I. V. Shadrivov, K. Y. Bliokh, Y. P. Bliokh, V. Freilikher, and Y. S. Kivshar, Phys. Rev. Lett. 104, 123902 (2010).
[CrossRef] [PubMed]

Z. Y. Yu, F. Xu, X. W. Lin, X. S. Song, X. S. Qian, Q. Wang, and Y. Q. Lu, Opt. Lett. 35, 3327 (2010).
[CrossRef] [PubMed]

D. Jalas, A. Petrov, M. Krause, J. Hampe, and M. Eich, Opt. Lett. 35, 3438 (2010).
[CrossRef] [PubMed]

C. Menzel, C. Helgert, C. Rockstuhl, E. B. Kley, A. Tunnermann, T. Pertsch, and F. Lederer, Phys. Rev. Lett. 104, 253902 (2010).
[CrossRef] [PubMed]

2009 (2)

2008 (3)

H. Takeda and S. John, Phys. Rev. A 78, 023804 (2008).
[CrossRef]

A. Alberucci and G. Assanto, Opt. Lett. 33, 1641 (2008).
[CrossRef] [PubMed]

F. Biancalana, J. Appl. Phys. 104, 093113 (2008).
[CrossRef]

2007 (1)

2006 (1)

2005 (2)

J. Hwang, M. H. Song, B. Park, S. Nishimura, T. Toyooka, J. W. Wu, Y. Takanishi, K. Ishikawa, and H. Takezoe, Nat. Mater. 4, 383 (2005).
[CrossRef] [PubMed]

H. Dötsch, N. Bahlmann, O. Zhuromskyy, M. Hammer, L. Wilkens, R. Gerhardt, P. Hertel, and A. F. Popkov, J. Opt. Soc. Am. B 22, 240 (2005).
[CrossRef]

2004 (1)

R. J. Potton, Rep. Prog. Phys. 67, 717 (2004).
[CrossRef]

2003 (1)

2001 (1)

K. Gallo, G. Assanto, K. R. Parameswaran, and M. M. Fejer, Appl. Phys. Lett. 79, 314 (2001).
[CrossRef]

Alberucci, A.

Assanto, G.

A. Alberucci and G. Assanto, Opt. Lett. 33, 1641 (2008).
[CrossRef] [PubMed]

K. Gallo, G. Assanto, K. R. Parameswaran, and M. M. Fejer, Appl. Phys. Lett. 79, 314 (2001).
[CrossRef]

Bahlmann, N.

Biancalana, F.

V. Grigoriev and F. Biancalana, Phys. Rev. A 83, 043816(2011).
[CrossRef]

V. Grigoriev and F. Biancalana, New J. Phys. 12, 053041(2010).
[CrossRef]

F. Biancalana, J. Appl. Phys. 104, 093113 (2008).
[CrossRef]

Bliokh, K. Y.

I. V. Shadrivov, K. Y. Bliokh, Y. P. Bliokh, V. Freilikher, and Y. S. Kivshar, Phys. Rev. Lett. 104, 123902 (2010).
[CrossRef] [PubMed]

Bliokh, Y. P.

I. V. Shadrivov, K. Y. Bliokh, Y. P. Bliokh, V. Freilikher, and Y. S. Kivshar, Phys. Rev. Lett. 104, 123902 (2010).
[CrossRef] [PubMed]

Bravo-Abad, J.

Dötsch, H.

Eich, M.

Fan, S.

Fan, S. H.

Fejer, M. M.

K. Gallo, G. Assanto, K. R. Parameswaran, and M. M. Fejer, Appl. Phys. Lett. 79, 314 (2001).
[CrossRef]

Freilikher, V.

I. V. Shadrivov, K. Y. Bliokh, Y. P. Bliokh, V. Freilikher, and Y. S. Kivshar, Phys. Rev. Lett. 104, 123902 (2010).
[CrossRef] [PubMed]

Gallo, K.

K. Gallo, G. Assanto, K. R. Parameswaran, and M. M. Fejer, Appl. Phys. Lett. 79, 314 (2001).
[CrossRef]

Galynsky, V. M.

Gerhardt, R.

Grigoriev, V.

V. Grigoriev and F. Biancalana, Phys. Rev. A 83, 043816(2011).
[CrossRef]

V. Grigoriev and F. Biancalana, New J. Phys. 12, 053041(2010).
[CrossRef]

Guo, Q.

Hammer, M.

Hampe, J.

Helgert, C.

C. Menzel, C. Helgert, C. Rockstuhl, E. B. Kley, A. Tunnermann, T. Pertsch, and F. Lederer, Phys. Rev. Lett. 104, 253902 (2010).
[CrossRef] [PubMed]

Hertel, P.

Hu, W.

Hwang, J.

J. Hwang, M. H. Song, B. Park, S. Nishimura, T. Toyooka, J. W. Wu, Y. Takanishi, K. Ishikawa, and H. Takezoe, Nat. Mater. 4, 383 (2005).
[CrossRef] [PubMed]

Ishikawa, K.

J. Hwang, M. H. Song, B. Park, S. Nishimura, T. Toyooka, J. W. Wu, Y. Takanishi, K. Ishikawa, and H. Takezoe, Nat. Mater. 4, 383 (2005).
[CrossRef] [PubMed]

Jalas, D.

Joannopoulos, J. D.

John, S.

H. Takeda and S. John, Phys. Rev. A 78, 023804 (2008).
[CrossRef]

Johnson, S. G.

Kivshar, Y. S.

I. V. Shadrivov, K. Y. Bliokh, Y. P. Bliokh, V. Freilikher, and Y. S. Kivshar, Phys. Rev. Lett. 104, 123902 (2010).
[CrossRef] [PubMed]

Kley, E. B.

C. Menzel, C. Helgert, C. Rockstuhl, E. B. Kley, A. Tunnermann, T. Pertsch, and F. Lederer, Phys. Rev. Lett. 104, 253902 (2010).
[CrossRef] [PubMed]

Krause, M.

Lan, S.

Lederer, F.

C. Menzel, C. Helgert, C. Rockstuhl, E. B. Kley, A. Tunnermann, T. Pertsch, and F. Lederer, Phys. Rev. Lett. 104, 253902 (2010).
[CrossRef] [PubMed]

Lin, X. S.

Lin, X. W.

Lu, Y. Q.

Luo, C.

Menzel, C.

C. Menzel, C. Helgert, C. Rockstuhl, E. B. Kley, A. Tunnermann, T. Pertsch, and F. Lederer, Phys. Rev. Lett. 104, 253902 (2010).
[CrossRef] [PubMed]

Nishimura, S.

J. Hwang, M. H. Song, B. Park, S. Nishimura, T. Toyooka, J. W. Wu, Y. Takanishi, K. Ishikawa, and H. Takezoe, Nat. Mater. 4, 383 (2005).
[CrossRef] [PubMed]

Novitsky, A. V.

Parameswaran, K. R.

K. Gallo, G. Assanto, K. R. Parameswaran, and M. M. Fejer, Appl. Phys. Lett. 79, 314 (2001).
[CrossRef]

Park, B.

J. Hwang, M. H. Song, B. Park, S. Nishimura, T. Toyooka, J. W. Wu, Y. Takanishi, K. Ishikawa, and H. Takezoe, Nat. Mater. 4, 383 (2005).
[CrossRef] [PubMed]

Pertsch, T.

C. Menzel, C. Helgert, C. Rockstuhl, E. B. Kley, A. Tunnermann, T. Pertsch, and F. Lederer, Phys. Rev. Lett. 104, 253902 (2010).
[CrossRef] [PubMed]

Petrov, A.

Popkov, A. F.

Potton, R. J.

R. J. Potton, Rep. Prog. Phys. 67, 717 (2004).
[CrossRef]

Qian, X. S.

Rockstuhl, C.

C. Menzel, C. Helgert, C. Rockstuhl, E. B. Kley, A. Tunnermann, T. Pertsch, and F. Lederer, Phys. Rev. Lett. 104, 253902 (2010).
[CrossRef] [PubMed]

Shadrivov, I. V.

I. V. Shadrivov, K. Y. Bliokh, Y. P. Bliokh, V. Freilikher, and Y. S. Kivshar, Phys. Rev. Lett. 104, 123902 (2010).
[CrossRef] [PubMed]

Smirnov, A. G.

S. V. Zhukovsky and A. G. Smirnov, Phys. Rev. A 83, 023818(2011).
[CrossRef]

Soljacic, M.

Song, M. H.

J. Hwang, M. H. Song, B. Park, S. Nishimura, T. Toyooka, J. W. Wu, Y. Takanishi, K. Ishikawa, and H. Takezoe, Nat. Mater. 4, 383 (2005).
[CrossRef] [PubMed]

Song, X. S.

Takanishi, Y.

J. Hwang, M. H. Song, B. Park, S. Nishimura, T. Toyooka, J. W. Wu, Y. Takanishi, K. Ishikawa, and H. Takezoe, Nat. Mater. 4, 383 (2005).
[CrossRef] [PubMed]

Takeda, H.

H. Takeda and S. John, Phys. Rev. A 78, 023804 (2008).
[CrossRef]

Takezoe, H.

J. Hwang, M. H. Song, B. Park, S. Nishimura, T. Toyooka, J. W. Wu, Y. Takanishi, K. Ishikawa, and H. Takezoe, Nat. Mater. 4, 383 (2005).
[CrossRef] [PubMed]

Toyooka, T.

J. Hwang, M. H. Song, B. Park, S. Nishimura, T. Toyooka, J. W. Wu, Y. Takanishi, K. Ishikawa, and H. Takezoe, Nat. Mater. 4, 383 (2005).
[CrossRef] [PubMed]

Tunnermann, A.

C. Menzel, C. Helgert, C. Rockstuhl, E. B. Kley, A. Tunnermann, T. Pertsch, and F. Lederer, Phys. Rev. Lett. 104, 253902 (2010).
[CrossRef] [PubMed]

Wang, Q.

Wilkens, L.

Wu, J. W.

J. Hwang, M. H. Song, B. Park, S. Nishimura, T. Toyooka, J. W. Wu, Y. Takanishi, K. Ishikawa, and H. Takezoe, Nat. Mater. 4, 383 (2005).
[CrossRef] [PubMed]

Xu, F.

Yang, X. B.

Yu, Z. F.

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

Yu, Z. Y.

Zhao, N. S.

Zhou, H.

Zhukovsky, S. V.

S. V. Zhukovsky and A. G. Smirnov, Phys. Rev. A 83, 023818(2011).
[CrossRef]

S. V. Zhukovsky, Phys. Rev. A 81, 053808 (2010).
[CrossRef]

S. V. Zhukovsky, A. V. Novitsky, and V. M. Galynsky, Opt. Lett. 34, 1988 (2009).
[CrossRef] [PubMed]

Zhuromskyy, O.

Appl. Phys. Lett. (1)

K. Gallo, G. Assanto, K. R. Parameswaran, and M. M. Fejer, Appl. Phys. Lett. 79, 314 (2001).
[CrossRef]

J. Appl. Phys. (1)

F. Biancalana, J. Appl. Phys. 104, 093113 (2008).
[CrossRef]

J. Lightwave Technol. (1)

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

Nat. Mater. (1)

J. Hwang, M. H. Song, B. Park, S. Nishimura, T. Toyooka, J. W. Wu, Y. Takanishi, K. Ishikawa, and H. Takezoe, Nat. Mater. 4, 383 (2005).
[CrossRef] [PubMed]

Nat. Photon. (1)

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

New J. Phys. (1)

V. Grigoriev and F. Biancalana, New J. Phys. 12, 053041(2010).
[CrossRef]

Opt. Lett. (5)

Phys. Rev. A (4)

H. Takeda and S. John, Phys. Rev. A 78, 023804 (2008).
[CrossRef]

V. Grigoriev and F. Biancalana, Phys. Rev. A 83, 043816(2011).
[CrossRef]

S. V. Zhukovsky and A. G. Smirnov, Phys. Rev. A 83, 023818(2011).
[CrossRef]

S. V. Zhukovsky, Phys. Rev. A 81, 053808 (2010).
[CrossRef]

Phys. Rev. Lett. (2)

C. Menzel, C. Helgert, C. Rockstuhl, E. B. Kley, A. Tunnermann, T. Pertsch, and F. Lederer, Phys. Rev. Lett. 104, 253902 (2010).
[CrossRef] [PubMed]

I. V. Shadrivov, K. Y. Bliokh, Y. P. Bliokh, V. Freilikher, and Y. S. Kivshar, Phys. Rev. Lett. 104, 123902 (2010).
[CrossRef] [PubMed]

Rep. Prog. Phys. (1)

R. J. Potton, Rep. Prog. Phys. 67, 717 (2004).
[CrossRef]

Other (1)

I.Chremmos, O.Schwelb, and N.Uzunoglu, Photonic Microresonator Research and Applications, Springer Series in Optical Sciences (Springer, 2010).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

(a) Schematic representation of the proposed OD in the form of multilayered structure. It consists of two mirror-symmetric MCs filled with a Kerr nonlinear material. (b) Sketch of the model used to describe the transient dynamics.

Fig. 2
Fig. 2

(a) Hysteresis of transmission for single MCs “A” and “B.” Their quality factors Q B = Q A / f and characteristic intensities I B = f I A are related by the parameter f = 2.1 . (b) Hysteresis of transmission for coupled MCs “A” and “B” when signals are propagating in the “AB” and “BA” directions.

Fig. 3
Fig. 3

(a) Transient dynamics of the OD for a CW signal with the carrier frequency ω = ω 0 2.1 γ A and a staircase envelope. The intensities of the input and transmitted signals for the opposite directions of incidence are shown as a function of time. (b) Amplitudes of the MCs during the switching to a high transmission state. (c) When the input intensity is increased for the reversed direction of incidence, the amplitudes of the MCs move away from the resonance condition | A ( t ) | 2 / I A = | B ( t ) | 2 / I A = Δ ω / γ A .

Equations (6)

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

d A d t = [ i ( ω 0 γ A | A | 2 I A ) + γ A ] A + γ A ( u + ± s ) ,
( u s + ) = ( u + s ) + A ( ± 1 1 ) ,
M A = I i ( ω ω 0 γ A + | s + ± s | 2 I A ) [ 1 ± 1 1 1 ]
T A = I out I in = [ 1 + ( ω ω 0 γ A + I out I A ) 2 ] 1 .
Q A I A = Q B I B .
( H L ) p A D 2 m A ( L H ) p A + p B D 2 m B ( H L ) p B ,

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