Abstract

We present a novel concept which enables the realization of unidirectional and irreversible grating assisted couplers by using gain-loss modulated medium to eliminate the reversibility. Employing a matched periodic modulation of both refractive index and loss (gain) we achieve a unidirectional energy transfer between the modes of the coupler which translates to light transmission from one waveguide to another while disabling the inverse transmission. The importance of self coupling coefficients is explored as well and a feasible implementation, where the real and imaginary perturbations are implemented in different waveguides is presented.

© 2004 Optical Society of America

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References

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  1. T.L. Koch, E.G. Burkhard, F.G. Stortz, T.J. Bridges and T. Sizer, II, Vertically grating-coupled ARROW structures for III-V integrated optics,�?? IEEE J. Quantum Electron. QE-23, 889-897, (1987).
    [CrossRef]
  2. B.Little and T.Murphy, "Design rules for maximally flat wavelength-insensitive optical power dividers using Mach-Zehnder structures," IEEE Photon. Technol. Lett. 9, 1607-1609, (1997).
    [CrossRef]
  3. R.C. Alferness, T.L. Koch, L.L.Buhl, F.Storz, F.Heismann and M.J.R. Martyak, "Grating-assisted InGaAs/InP verstical codirectional coupler filter," Appl. Phys. Lett. 55, 2011-2013, (1989)
    [CrossRef]
  4. G.R. Hill, "Wavelength domain optical network techniques," in Proc. IEEE 77, 121-132, (1989).
  5. L.Poladian, "Resonanse mode expansions and exact solutions for nonuniform gratings," Phys. Rev. E 54, 2963-2975, (1996).
    [CrossRef]
  6. D.Marcuse, Theory of Dielectric Optical Waveguides Sec. Ed., Academic Press, Boston San Diego, New York, (1974).
  7. M.Greenberg, M.Orenstein, "Irreversible coupling by use of dissipative optics," Opt. Lett. 29, 451-453, (2004).
    [CrossRef] [PubMed]
  8. W. P. Huang, C. L. Xu "Simulation of Three-Dimensional Optical Waveguides by a Full-Vector Beam Propagation Metod," IEEE J. Quantum Electron. 29, 2639-2649 (1993).
    [CrossRef]

Appl. Phys. Lett.

R.C. Alferness, T.L. Koch, L.L.Buhl, F.Storz, F.Heismann and M.J.R. Martyak, "Grating-assisted InGaAs/InP verstical codirectional coupler filter," Appl. Phys. Lett. 55, 2011-2013, (1989)
[CrossRef]

IEEE J. Quantum Electron.

T.L. Koch, E.G. Burkhard, F.G. Stortz, T.J. Bridges and T. Sizer, II, Vertically grating-coupled ARROW structures for III-V integrated optics,�?? IEEE J. Quantum Electron. QE-23, 889-897, (1987).
[CrossRef]

W. P. Huang, C. L. Xu "Simulation of Three-Dimensional Optical Waveguides by a Full-Vector Beam Propagation Metod," IEEE J. Quantum Electron. 29, 2639-2649 (1993).
[CrossRef]

IEEE Photon. Technol. Lett.

B.Little and T.Murphy, "Design rules for maximally flat wavelength-insensitive optical power dividers using Mach-Zehnder structures," IEEE Photon. Technol. Lett. 9, 1607-1609, (1997).
[CrossRef]

Opt. Lett.

Phys. Rev. E

L.Poladian, "Resonanse mode expansions and exact solutions for nonuniform gratings," Phys. Rev. E 54, 2963-2975, (1996).
[CrossRef]

Proc. IEEE

G.R. Hill, "Wavelength domain optical network techniques," in Proc. IEEE 77, 121-132, (1989).

Other

D.Marcuse, Theory of Dielectric Optical Waveguides Sec. Ed., Academic Press, Boston San Diego, New York, (1974).

Supplementary Material (2)

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Figures (4)

Fig. 1.
Fig. 1.

Influence of the self-coupling coefficients in the case of conversion. In each simulation the inter-modal coupling was K12=K21=K=1.15·10-3µm-1. and the self-coupling coefficients were 1. K11=K22=0; 2. K11=K, K22=0; 3. K11=0, K22=K; and 4. K11=K22=K. Calculations were performed by numerical integration of Eqs.(2) and (3).

Fig. 2.
Fig. 2.

(a) Fundamental mode of the single waveguide w=6µm, (b) fundamental mode of the single waveguide w=3µm. (c) and (d) first and second compound modes of the coupler structure 6µm×6µm×3µm. The overlap integrals between the powers of the corresponding single and compound modes are 99.8% and 98.4%.

Fig. 3.
Fig. 3.

(Movies 834 KB and 157 KB) Modal power for 6µm×6µm×3µm coupler with the complex perturbation f(z)=exp{iΔβz} located in w=6µm waveguide, perturbation strength Δ=0.001. (a) Initial conditions c1 (0)=1, c2 (0)=0 and (b) Initial conditions c1 (0)=0, c2 (0)=1. Maximum relative power of the first mode does not exceed -26dB.

Fig. 4.
Fig. 4.

Modal power for the 6µm×6µm×3µm coupler with the complex gratings f(z)=exp{iΔβz}, gratings depth Δ=0.001. Real and imaginary perturbations are located in different waveguides. (a) Initial conditions c1 (0)=1, c2 (0)=0. The power of the second mode exhibits significant oscillations. (b) Initial conditions c1 (0)=0, c2 (0)=1. Maximum relative power of the first mode does not exceed -30[dB]. Calculations were performed by SBPM.

Equations (10)

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P m , n ( z ) 0 z f ( z ) exp { i ( β m β n ) z } dz
c ˙ 1 = i exp { i Δ β z } K 11 c 1 i exp { i Δ β z } K 12 c 2 exp { i Δ β z }
c ˙ 2 = i exp { i Δ β z } K 21 c 1 exp { i Δ β z } i exp { i Δ β z } K 22 c 2
K mn = ω ε 0 4 P + + Δ ( x , y ) E mt * E nt dxdy
c ˙ 1 = 0
c ˙ 2 = i K 21 c 1
c 1 ( z ) = C 01
c 2 ( z ) = i K 21 C 01 z + C 02
c ˙ 1 = i [ K 11 r cos ( Δ β z ) + i K 11 i sin ( Δ β z ) ] c 1 i [ K 12 r cos ( Δ β z ) + i K 12 i sin ( Δ β z ) ] c 2 exp { i Δ β z }
c ˙ 2 = i [ K 21 r cos ( Δ β z ) + i K 21 i sin ( Δ β z ) ] c 1 exp { i Δ β z } i [ K 22 r cos ( Δ β z ) + i K 22 i sin ( Δ β z ) ] c 2

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