Abstract

A design of all-optical diode in L-shaped photonic crystal waveguide is proposed that uses the multistability of single nonlinear Kerr microcavity with two dipole modes. Asymmetry of the waveguide is achieved through different couplings of the dipole modes with the left and right legs of the waveguide. Using coupled mode theory we demonstrate an extremely high transmission contrast. The direction of optical diode transmission can be controlled by power or frequency of injected light. The theory agrees with the numerical solution of the Maxwell equations.

© 2014 Optical Society of America

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2012

W. Ding, B. Lukyanchuk, and C.-W. Qiu, Phys. Rev. A 85, 025806 (2012).
[CrossRef]

E. N. Bulgakov and A. F. Sadreev, Phys. Rev. B 85, 165305 (2012).
[CrossRef]

E. N. Bulgakov and A. F. Sadreev, Phys. Rev. B 86, 075125 (2012).
[CrossRef]

E. N. Bulgakov and A. F. Sadreev, J. Opt. Soc. Am. B 29, 2924 (2012).
[CrossRef]

2008

2006

2004

W. Suh, Z. Wang, and S. Fan, IEEE J. Quantum Electron. 40, 1511 (2004).
[CrossRef]

2003

2002

2001

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

1999

H.-W. Lee, Phys. Rev. Lett. 82, 2358 (1999).
[CrossRef]

1998

1994

M. Scalora, J. R. Dowling, C. M. Bowden, and M. J. Bloemer, J. Appl. Phys. 76, 2023 (1994).
[CrossRef]

Assanto, G.

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

Bloemer, M. J.

M. Scalora, J. R. Dowling, C. M. Bowden, and M. J. Bloemer, J. Appl. Phys. 76, 2023 (1994).
[CrossRef]

Bowden, C. M.

M. Scalora, J. R. Dowling, C. M. Bowden, and M. J. Bloemer, J. Appl. Phys. 76, 2023 (1994).
[CrossRef]

Bulgakov, E. N.

E. N. Bulgakov and A. F. Sadreev, J. Opt. Soc. Am. B 29, 2924 (2012).
[CrossRef]

E. N. Bulgakov and A. F. Sadreev, Phys. Rev. B 86, 075125 (2012).
[CrossRef]

E. N. Bulgakov and A. F. Sadreev, Phys. Rev. B 85, 165305 (2012).
[CrossRef]

Ding, W.

W. Ding, B. Lukyanchuk, and C.-W. Qiu, Phys. Rev. A 85, 025806 (2012).
[CrossRef]

Dowling, J. R.

M. Scalora, J. R. Dowling, C. M. Bowden, and M. J. Bloemer, J. Appl. Phys. 76, 2023 (1994).
[CrossRef]

Fan, S.

Fejer, M. M.

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

Gallo, K.

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

Guo, Q.

Haus, H. A.

Hu, W.

Joannopoulos, J.

J. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light (Princeton University, 2008).

Joannopoulos, J. D.

Johnson, S. G.

S. G. Johnson, C. Manolatou, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, Opt. Lett. 23, 1855 (1998).
[CrossRef]

J. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light (Princeton University, 2008).

Kivshar, Y. S.

Lan, S.

Lee, H.-W.

H.-W. Lee, Phys. Rev. Lett. 82, 2358 (1999).
[CrossRef]

Lin, X.-S.

Lukyanchuk, B.

W. Ding, B. Lukyanchuk, and C.-W. Qiu, Phys. Rev. A 85, 025806 (2012).
[CrossRef]

Manolatou, C.

Meade, R. D.

J. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light (Princeton University, 2008).

Mingaleev, S. F.

Parameswaran, K. R.

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

Qiu, C.-W.

W. Ding, B. Lukyanchuk, and C.-W. Qiu, Phys. Rev. A 85, 025806 (2012).
[CrossRef]

Sadreev, A. F.

E. N. Bulgakov and A. F. Sadreev, Phys. Rev. B 86, 075125 (2012).
[CrossRef]

E. N. Bulgakov and A. F. Sadreev, Phys. Rev. B 85, 165305 (2012).
[CrossRef]

E. N. Bulgakov and A. F. Sadreev, J. Opt. Soc. Am. B 29, 2924 (2012).
[CrossRef]

Scalora, M.

M. Scalora, J. R. Dowling, C. M. Bowden, and M. J. Bloemer, J. Appl. Phys. 76, 2023 (1994).
[CrossRef]

Soljacic, M.

Suh, W.

W. Suh, Z. Wang, and S. Fan, IEEE J. Quantum Electron. 40, 1511 (2004).
[CrossRef]

Villeneuve, P. R.

Wang, Z.

W. Suh, Z. Wang, and S. Fan, IEEE J. Quantum Electron. 40, 1511 (2004).
[CrossRef]

Winn, J. N.

J. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light (Princeton University, 2008).

Wu, L.-J.

Yan, J.-H.

Yang, X.-B.

Yanik, M. F.

Zhao, N.-S.

Zhou, H.

Appl. Phys. Lett.

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

IEEE J. Quantum Electron.

W. Suh, Z. Wang, and S. Fan, IEEE J. Quantum Electron. 40, 1511 (2004).
[CrossRef]

J. Appl. Phys.

M. Scalora, J. R. Dowling, C. M. Bowden, and M. J. Bloemer, J. Appl. Phys. 76, 2023 (1994).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Express

Opt. Lett.

Phys. Rev. A

W. Ding, B. Lukyanchuk, and C.-W. Qiu, Phys. Rev. A 85, 025806 (2012).
[CrossRef]

Phys. Rev. B

E. N. Bulgakov and A. F. Sadreev, Phys. Rev. B 85, 165305 (2012).
[CrossRef]

E. N. Bulgakov and A. F. Sadreev, Phys. Rev. B 86, 075125 (2012).
[CrossRef]

Phys. Rev. Lett.

H.-W. Lee, Phys. Rev. Lett. 82, 2358 (1999).
[CrossRef]

Other

J. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light (Princeton University, 2008).

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Figures (5)

Fig. 1.
Fig. 1.

PhC lattice consisting of GaAs dielectric rods with radius 0.18a and dielectric constant ϵ=11.56, where a=0.5μm is the lattice unit. The nonlinear defect rod shown by the open pink larger circle has the radius 0.4a, ϵ0=n02=6.5, and the nonlinear refractive index n2=2×1012cm2/W. The additional two nearest rods (green in color) have radius 0.18a and ϵ=11.56, and the third additional rod (brown in color) has radius 0.18a, with ϵ=5 substituted into the right leg of the waveguide in order to provide coupling asymmetry. (a) The bifurcated solution with both dipole modes excited. (b) The ordinary solution with the only dipole excited, which inherits the linear case.

Fig. 2.
Fig. 2.

Intensities of dipole mode excitations versus light amplitude injected from (a) the left EL, and (b) right ER for ω=0.3618. Open circles mark unstable solutions of Eq. (5). The ordinary solution inherited from the linear case that does not permit transmission is colored by black (I1) and green (I2). The bifurcated new solution intrinsic for the nonlinear case opens transmissions colored by blue (I1) and red (I2). Transmittances corresponded to this bifurcated solution are shown in Figs. 2(c) and 2(d).

Fig. 3.
Fig. 3.

Domains of AOD. The domains of AOD from the left to the right are colored by blue, while the domains of AOD from the right to the left are colored by red.

Fig. 4.
Fig. 4.

Time dependence of outputs to right leg (solid red line) and to left leg (dashed blue line), which follow the alternating injected impulses. Below, the impulse launched from the left is marked by blue color and impulse launched from the right is marked by red color.

Fig. 5.
Fig. 5.

Transmittances versus frequency for EL=ER=0.035. The CMT-based transmittance with degenerated dipole modes is shown by solid lines where the red line shows transmission from the right to the left, and the blue line shows transmission from the left to the right. The case ω1a/2πc=0.3658, ω2a/2πc=0.3650 is presented by blue closed circles. Green open circles show transmittance in the PhC structure shown in Fig. 1 with P=0.7W/a.

Equations (9)

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iA˙1=[ω1+V11iγ1/2]A1+V12A2+iγ1ELeiωt,iA˙2=[ω2+V22iγ2/2]A2+V21A1+iγ2EReiωt,
Vmn=ω02Nmd2r⃗δϵ(r⃗)Em(r⃗)En(r⃗);
δϵ(r⃗)=n0cn2|E(r⃗)|24πn0cn2|A1E1(r⃗)+A2E2(r⃗)|24π
Nm=d2r⃗ϵ(r⃗)Em2(r⃗)=a2cn2
[ωω1+λ11I1+λ12I2+iγ1/2]A1+2λ12Re(A1*A2)A2=iγ1EL,2λ12Re(A1A2*)A1+[ωω2+λ22I2+λ12I1+iγ2/2]A2=iγ2ER,
λmn=ω0n0c2n228πa2σEm2(x,y)En2(x,y)d2r⃗,
tL=γ1A1EL,tR=γ2A2ER.
γ1|ELc|2=I1c[(ωω0+λ11I1c)2+γ12/4],γ2|ERc|2=I2c[(ωω0+λ11I2c)2+γ22/4],
I1c=2(ω0ω)±(ω0ω)23γ22/43λ12,I2c=2(ω0ω)±(ω0ω)23γ12/43λ12.

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