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]

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

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]

2009 (2)

2008 (3)

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

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

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

2007 (1)

2006 (1)

2005 (2)

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]

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]

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)

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

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

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

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