Abstract

Power transfer in grating-assisted couplers is governed by the excitation of the Floquet modes. This excitation not only is determined by the grating period but is also related to the amplitudes and phases of the uniform normal modes incident upon the grating as well as to the initial phase angle of the corrugation. The details of the junction are thus essential to the description of power flow. Under many practical circumstances it will be necessary to detune the grating period away the from the conventional phase-matching value to maximize coupled power. Higher-order effects that modify the uniform propagation constants, known as loading, are also considered. Coupled-mode theory is used to predict these features, including a simple expression for the detuning that maximizes power transfer.

© 1996 Optical Society of America

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References

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    [CrossRef]
  8. B. E. Little, J. Lightwave Technol. 14, 188 (1996).
    [CrossRef]

1996

B. E. Little, J. Lightwave Technol. 14, 188 (1996).
[CrossRef]

1995

S. Zhang, T. Tamir, Opt. Lett. 20, 803 (1995).
[CrossRef] [PubMed]

Y. M. N. Passaro, M. N. Armenise, IEEE J. Quantum Electron. 31, 1691 (1995).
[CrossRef]

1992

W. P. Huang, B. E. Little, C. L. Xu, IEEE Photon. Technol. Lett. 4, 151 (1992).
[CrossRef]

1991

1990

D. G. Hall, Opt. Lett. 15, 819 (1990).
[CrossRef]

1989

R. C. Alferness, T. L. Koch, L. L. Buhl, F. Storz, F. Heismann, M. J. R. Martyak, Appl. Phys. Lett. 55, 2011 (1989).
[CrossRef]

1987

D. Marcuse, J. Lightwave Technol. LT-5, 268 (1987).
[CrossRef]

Alferness, R. C.

R. C. Alferness, T. L. Koch, L. L. Buhl, F. Storz, F. Heismann, M. J. R. Martyak, Appl. Phys. Lett. 55, 2011 (1989).
[CrossRef]

Armenise, M. N.

Y. M. N. Passaro, M. N. Armenise, IEEE J. Quantum Electron. 31, 1691 (1995).
[CrossRef]

Buhl, L. L.

R. C. Alferness, T. L. Koch, L. L. Buhl, F. Storz, F. Heismann, M. J. R. Martyak, Appl. Phys. Lett. 55, 2011 (1989).
[CrossRef]

Hall, D. G.

D. G. Hall, Opt. Lett. 15, 819 (1990).
[CrossRef]

Heismann, F.

R. C. Alferness, T. L. Koch, L. L. Buhl, F. Storz, F. Heismann, M. J. R. Martyak, Appl. Phys. Lett. 55, 2011 (1989).
[CrossRef]

Huang, W. P.

W. P. Huang, B. E. Little, C. L. Xu, IEEE Photon. Technol. Lett. 4, 151 (1992).
[CrossRef]

Koch, T. L.

R. C. Alferness, T. L. Koch, L. L. Buhl, F. Storz, F. Heismann, M. J. R. Martyak, Appl. Phys. Lett. 55, 2011 (1989).
[CrossRef]

Little, B. E.

B. E. Little, J. Lightwave Technol. 14, 188 (1996).
[CrossRef]

W. P. Huang, B. E. Little, C. L. Xu, IEEE Photon. Technol. Lett. 4, 151 (1992).
[CrossRef]

Marcuse, D.

D. Marcuse, J. Lightwave Technol. LT-5, 268 (1987).
[CrossRef]

Martyak, M. J. R.

R. C. Alferness, T. L. Koch, L. L. Buhl, F. Storz, F. Heismann, M. J. R. Martyak, Appl. Phys. Lett. 55, 2011 (1989).
[CrossRef]

Matsumoto, M.

Passaro, Y. M. N.

Y. M. N. Passaro, M. N. Armenise, IEEE J. Quantum Electron. 31, 1691 (1995).
[CrossRef]

Storz, F.

R. C. Alferness, T. L. Koch, L. L. Buhl, F. Storz, F. Heismann, M. J. R. Martyak, Appl. Phys. Lett. 55, 2011 (1989).
[CrossRef]

Tamir, T.

Xu, C. L.

W. P. Huang, B. E. Little, C. L. Xu, IEEE Photon. Technol. Lett. 4, 151 (1992).
[CrossRef]

Zhang, S.

Appl. Phys. Lett.

R. C. Alferness, T. L. Koch, L. L. Buhl, F. Storz, F. Heismann, M. J. R. Martyak, Appl. Phys. Lett. 55, 2011 (1989).
[CrossRef]

IEEE J. Quantum Electron.

Y. M. N. Passaro, M. N. Armenise, IEEE J. Quantum Electron. 31, 1691 (1995).
[CrossRef]

IEEE Photon. Technol. Lett.

W. P. Huang, B. E. Little, C. L. Xu, IEEE Photon. Technol. Lett. 4, 151 (1992).
[CrossRef]

J. Lightwave Technol.

B. E. Little, J. Lightwave Technol. 14, 188 (1996).
[CrossRef]

D. Marcuse, J. Lightwave Technol. LT-5, 268 (1987).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Lett.

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Figures (3)

Fig. 1
Fig. 1

Structure of a grating-assisted coupler. ϕg is the phase angle of the grating at the beginning of the corrugation section, and ϕo, e are the phase delays accumulated by the even and the odd normal modes by propagation from the array reference plane, respectively.

Fig. 2
Fig. 2

Loading effect, or the change in phase matching that is due to the presence of a corrugation. Λo is the conventional grating period that phase matches the array modes on a z-averaged reference structure. Λ is the grating period considering higher-order effects. Loading is a small effect that is manifest only over long device lengths.

Fig. 3
Fig. 3

Power coupled into waveguide 2 (solid curves, or fast-scale oscillations) and into the even mode (dashed curves) of the structure in Fig. 1. Λo is the conventional grating period, and Λ′ is a detuned value that maximizes power transfer.

Equations (12)

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[ A e ( z ) A o ( z ) ] = exp ( j γ z / 2 ) [ t 11 t 12 t 21 t 22 ] [ A e ( 0 ) A o ( 0 ) ] .
t 11 = t 22 * = cos S z j Δ β 2 S sin S z ,
t 12 = t 21 * = j κ exp ( j ϕ g ) S sin S z ,
S = [ κ 2 + ( Δ β / 2 ) 2 ] 1 / 2 , κ = κ e κ o ,
Δ β = ( β e + γ e ) ( β o + γ o + Ω ) ,
γ = ( β e + γ e ) ( β o + γ o + Ω ) ,
γ e , o = ω 0 P e , o n Δ n 2 n G n e , o . e e , o * ,
κ e , o = ω 0 P e , o n Δ n 2 n 1 , n + 1 G n o , e · e e , o * ,
P e , o = ( e e , o × h e , o * + e e , o * × h e , o ) · z ˆ .
t 2 G n e , o + [ k 2 n 2 ( x ) ( β e , o + n Ω ) 2 ] G n e , o = k 2 Δ n 2 n δ ( x o ) h e e , o .
Λ = R [ 2 π ( β e + γ e ) ( β o + γ o ) ] · ( μ m )
δ = ± 2 κ cos ( ϕ e ϕ o ϕ g ) min [ | A e ( 0 ) | | A o ( 0 ) | , | A o ( 0 ) | | A e ( 0 ) | ] ,

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