Abstract

A novel iterative projection-type optimal design algorithm of arrayed waveguide gratings (AWGs) with a flat spectral response is proposed based on the Fourier optics model of AWG. The enhancement of the spectral-response flatness of the AWG is demonstrated, with an analysis on the trade-off relationship between band flatness and crosstalk.

© 2013 Optical Society of America

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References

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  1. C. Brackett, “Dense wavelength division multiplexing networks: principles and applications,” IEEE J. Sel. Areas Commun. 8, 948–964 (1990).
    [CrossRef]
  2. A. S. Manouri and R. Faraji-Dana, “Arrayed waveguide grating multiplexers with flat spectral response using non-uniform arrays,” Proceedings of the 12th International Conference on Microelectronics, Teheran (2000), pp. 307–310.
  3. F. Xiao, G. Li, and A. Xu, “Modeling and design of irregularly arrayed waveguide gratings,” Opt. Express 15, 3888–3901 (2007).
    [CrossRef]
  4. I. Molina-Fernandez and J. G. Wanguemert-Perez, “Improved AWG Fourier optics model,” Opt. Express 12, 4804–4821 (2004).
    [CrossRef]
  5. P. Munoz and S. D. Walker, “Design of arrayed-waveguide gratings using hybrid Fourier–Fresnel transform techniques,” IEEE J. Sel. Top. Quantum Electron. 5, 1379–1384 (1999).
    [CrossRef]
  6. M. R. Amersfoort, C. R. de Boer, F. P. G. M. van Ham, M. K. Smit, P. Demeester, J. J. G. M. van der Tol, and A. Kuntze, “Phased-array wavelength demultiplexer with flattened wavelength response,” Electron. Lett. 30, 300–302 (1994).
    [CrossRef]
  7. M. R. Amersfoort, J. B. D. Soole, H. P. LeBlance, N. C. Andreadakis, A. Rajhel, and C. Caneau, “Passband broadening of integrated arrayed waveguide filters using multimode interference couplers,” Electron. Lett. 32, 449–451 (1996).
    [CrossRef]
  8. Y. P. Ho, H. Li, and Y. J. Chen, “Flat channel-passband-wavelength multiplexing and demultiplexing devices by multiple-Rowland-circle design,” IEEE Photon. Technol. Lett. 9, 342–344 (1997).
    [CrossRef]
  9. A. Rigny, A. Bruno, and H. Sik, “Multigrating method for flattened spectral response wavelength multi/demultiplexer,” Electron. Lett. 33, 1701–1702 (1997).
    [CrossRef]
  10. H. Kim and B. Lee, “Optimal non-monotonic convergence of iterative Fourier transform algorithm,” Opt. Lett. 30, 296–298 (2005).
    [CrossRef]
  11. H. Kim, B. Yang, and B. Lee, “Iterative Fourier transform algorithm with regularization for the optimal design of diffractive optical elements,” J. Opt. Soc. Am. A 21, 2353–2365 (2004).
    [CrossRef]

2007 (1)

2005 (1)

2004 (2)

1999 (1)

P. Munoz and S. D. Walker, “Design of arrayed-waveguide gratings using hybrid Fourier–Fresnel transform techniques,” IEEE J. Sel. Top. Quantum Electron. 5, 1379–1384 (1999).
[CrossRef]

1997 (2)

Y. P. Ho, H. Li, and Y. J. Chen, “Flat channel-passband-wavelength multiplexing and demultiplexing devices by multiple-Rowland-circle design,” IEEE Photon. Technol. Lett. 9, 342–344 (1997).
[CrossRef]

A. Rigny, A. Bruno, and H. Sik, “Multigrating method for flattened spectral response wavelength multi/demultiplexer,” Electron. Lett. 33, 1701–1702 (1997).
[CrossRef]

1996 (1)

M. R. Amersfoort, J. B. D. Soole, H. P. LeBlance, N. C. Andreadakis, A. Rajhel, and C. Caneau, “Passband broadening of integrated arrayed waveguide filters using multimode interference couplers,” Electron. Lett. 32, 449–451 (1996).
[CrossRef]

1994 (1)

M. R. Amersfoort, C. R. de Boer, F. P. G. M. van Ham, M. K. Smit, P. Demeester, J. J. G. M. van der Tol, and A. Kuntze, “Phased-array wavelength demultiplexer with flattened wavelength response,” Electron. Lett. 30, 300–302 (1994).
[CrossRef]

1990 (1)

C. Brackett, “Dense wavelength division multiplexing networks: principles and applications,” IEEE J. Sel. Areas Commun. 8, 948–964 (1990).
[CrossRef]

Amersfoort, M. R.

M. R. Amersfoort, J. B. D. Soole, H. P. LeBlance, N. C. Andreadakis, A. Rajhel, and C. Caneau, “Passband broadening of integrated arrayed waveguide filters using multimode interference couplers,” Electron. Lett. 32, 449–451 (1996).
[CrossRef]

M. R. Amersfoort, C. R. de Boer, F. P. G. M. van Ham, M. K. Smit, P. Demeester, J. J. G. M. van der Tol, and A. Kuntze, “Phased-array wavelength demultiplexer with flattened wavelength response,” Electron. Lett. 30, 300–302 (1994).
[CrossRef]

Andreadakis, N. C.

M. R. Amersfoort, J. B. D. Soole, H. P. LeBlance, N. C. Andreadakis, A. Rajhel, and C. Caneau, “Passband broadening of integrated arrayed waveguide filters using multimode interference couplers,” Electron. Lett. 32, 449–451 (1996).
[CrossRef]

Brackett, C.

C. Brackett, “Dense wavelength division multiplexing networks: principles and applications,” IEEE J. Sel. Areas Commun. 8, 948–964 (1990).
[CrossRef]

Bruno, A.

A. Rigny, A. Bruno, and H. Sik, “Multigrating method for flattened spectral response wavelength multi/demultiplexer,” Electron. Lett. 33, 1701–1702 (1997).
[CrossRef]

Caneau, C.

M. R. Amersfoort, J. B. D. Soole, H. P. LeBlance, N. C. Andreadakis, A. Rajhel, and C. Caneau, “Passband broadening of integrated arrayed waveguide filters using multimode interference couplers,” Electron. Lett. 32, 449–451 (1996).
[CrossRef]

Chen, Y. J.

Y. P. Ho, H. Li, and Y. J. Chen, “Flat channel-passband-wavelength multiplexing and demultiplexing devices by multiple-Rowland-circle design,” IEEE Photon. Technol. Lett. 9, 342–344 (1997).
[CrossRef]

de Boer, C. R.

M. R. Amersfoort, C. R. de Boer, F. P. G. M. van Ham, M. K. Smit, P. Demeester, J. J. G. M. van der Tol, and A. Kuntze, “Phased-array wavelength demultiplexer with flattened wavelength response,” Electron. Lett. 30, 300–302 (1994).
[CrossRef]

Demeester, P.

M. R. Amersfoort, C. R. de Boer, F. P. G. M. van Ham, M. K. Smit, P. Demeester, J. J. G. M. van der Tol, and A. Kuntze, “Phased-array wavelength demultiplexer with flattened wavelength response,” Electron. Lett. 30, 300–302 (1994).
[CrossRef]

Faraji-Dana, R.

A. S. Manouri and R. Faraji-Dana, “Arrayed waveguide grating multiplexers with flat spectral response using non-uniform arrays,” Proceedings of the 12th International Conference on Microelectronics, Teheran (2000), pp. 307–310.

Ho, Y. P.

Y. P. Ho, H. Li, and Y. J. Chen, “Flat channel-passband-wavelength multiplexing and demultiplexing devices by multiple-Rowland-circle design,” IEEE Photon. Technol. Lett. 9, 342–344 (1997).
[CrossRef]

Kim, H.

Kuntze, A.

M. R. Amersfoort, C. R. de Boer, F. P. G. M. van Ham, M. K. Smit, P. Demeester, J. J. G. M. van der Tol, and A. Kuntze, “Phased-array wavelength demultiplexer with flattened wavelength response,” Electron. Lett. 30, 300–302 (1994).
[CrossRef]

LeBlance, H. P.

M. R. Amersfoort, J. B. D. Soole, H. P. LeBlance, N. C. Andreadakis, A. Rajhel, and C. Caneau, “Passband broadening of integrated arrayed waveguide filters using multimode interference couplers,” Electron. Lett. 32, 449–451 (1996).
[CrossRef]

Lee, B.

Li, G.

Li, H.

Y. P. Ho, H. Li, and Y. J. Chen, “Flat channel-passband-wavelength multiplexing and demultiplexing devices by multiple-Rowland-circle design,” IEEE Photon. Technol. Lett. 9, 342–344 (1997).
[CrossRef]

Manouri, A. S.

A. S. Manouri and R. Faraji-Dana, “Arrayed waveguide grating multiplexers with flat spectral response using non-uniform arrays,” Proceedings of the 12th International Conference on Microelectronics, Teheran (2000), pp. 307–310.

Molina-Fernandez, I.

Munoz, P.

P. Munoz and S. D. Walker, “Design of arrayed-waveguide gratings using hybrid Fourier–Fresnel transform techniques,” IEEE J. Sel. Top. Quantum Electron. 5, 1379–1384 (1999).
[CrossRef]

Rajhel, A.

M. R. Amersfoort, J. B. D. Soole, H. P. LeBlance, N. C. Andreadakis, A. Rajhel, and C. Caneau, “Passband broadening of integrated arrayed waveguide filters using multimode interference couplers,” Electron. Lett. 32, 449–451 (1996).
[CrossRef]

Rigny, A.

A. Rigny, A. Bruno, and H. Sik, “Multigrating method for flattened spectral response wavelength multi/demultiplexer,” Electron. Lett. 33, 1701–1702 (1997).
[CrossRef]

Sik, H.

A. Rigny, A. Bruno, and H. Sik, “Multigrating method for flattened spectral response wavelength multi/demultiplexer,” Electron. Lett. 33, 1701–1702 (1997).
[CrossRef]

Smit, M. K.

M. R. Amersfoort, C. R. de Boer, F. P. G. M. van Ham, M. K. Smit, P. Demeester, J. J. G. M. van der Tol, and A. Kuntze, “Phased-array wavelength demultiplexer with flattened wavelength response,” Electron. Lett. 30, 300–302 (1994).
[CrossRef]

Soole, J. B. D.

M. R. Amersfoort, J. B. D. Soole, H. P. LeBlance, N. C. Andreadakis, A. Rajhel, and C. Caneau, “Passband broadening of integrated arrayed waveguide filters using multimode interference couplers,” Electron. Lett. 32, 449–451 (1996).
[CrossRef]

van der Tol, J. J. G. M.

M. R. Amersfoort, C. R. de Boer, F. P. G. M. van Ham, M. K. Smit, P. Demeester, J. J. G. M. van der Tol, and A. Kuntze, “Phased-array wavelength demultiplexer with flattened wavelength response,” Electron. Lett. 30, 300–302 (1994).
[CrossRef]

van Ham, F. P. G. M.

M. R. Amersfoort, C. R. de Boer, F. P. G. M. van Ham, M. K. Smit, P. Demeester, J. J. G. M. van der Tol, and A. Kuntze, “Phased-array wavelength demultiplexer with flattened wavelength response,” Electron. Lett. 30, 300–302 (1994).
[CrossRef]

Walker, S. D.

P. Munoz and S. D. Walker, “Design of arrayed-waveguide gratings using hybrid Fourier–Fresnel transform techniques,” IEEE J. Sel. Top. Quantum Electron. 5, 1379–1384 (1999).
[CrossRef]

Wanguemert-Perez, J. G.

Xiao, F.

Xu, A.

Yang, B.

Electron. Lett. (3)

M. R. Amersfoort, C. R. de Boer, F. P. G. M. van Ham, M. K. Smit, P. Demeester, J. J. G. M. van der Tol, and A. Kuntze, “Phased-array wavelength demultiplexer with flattened wavelength response,” Electron. Lett. 30, 300–302 (1994).
[CrossRef]

M. R. Amersfoort, J. B. D. Soole, H. P. LeBlance, N. C. Andreadakis, A. Rajhel, and C. Caneau, “Passband broadening of integrated arrayed waveguide filters using multimode interference couplers,” Electron. Lett. 32, 449–451 (1996).
[CrossRef]

A. Rigny, A. Bruno, and H. Sik, “Multigrating method for flattened spectral response wavelength multi/demultiplexer,” Electron. Lett. 33, 1701–1702 (1997).
[CrossRef]

IEEE J. Sel. Areas Commun. (1)

C. Brackett, “Dense wavelength division multiplexing networks: principles and applications,” IEEE J. Sel. Areas Commun. 8, 948–964 (1990).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

P. Munoz and S. D. Walker, “Design of arrayed-waveguide gratings using hybrid Fourier–Fresnel transform techniques,” IEEE J. Sel. Top. Quantum Electron. 5, 1379–1384 (1999).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

Y. P. Ho, H. Li, and Y. J. Chen, “Flat channel-passband-wavelength multiplexing and demultiplexing devices by multiple-Rowland-circle design,” IEEE Photon. Technol. Lett. 9, 342–344 (1997).
[CrossRef]

J. Opt. Soc. Am. A (1)

Opt. Express (2)

Opt. Lett. (1)

Other (1)

A. S. Manouri and R. Faraji-Dana, “Arrayed waveguide grating multiplexers with flat spectral response using non-uniform arrays,” Proceedings of the 12th International Conference on Microelectronics, Teheran (2000), pp. 307–310.

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Figures (9)

Fig. 1.
Fig. 1.

Schematic of a two-dimensional AWG.

Fig. 2.
Fig. 2.

Diffraction field profile V(x;λs): (a) λs=1550nm, Δλs=0nm and (b) λs=1550nm, Δλs=9×0.8nm.

Fig. 3.
Fig. 3.

Transmission spectra of all 33 channels with the wavelength ranging from 1520 to 1580 nm and the channel spacing of 0.8 nm.

Fig. 4.
Fig. 4.

Schematic of crosstalk and flatness level in optimized AWG.

Fig. 5.
Fig. 5.

Iterative projection algorithm.

Fig. 6.
Fig. 6.

Target amplitude profile for iterative projection algorithm with two variables: spot ratio and spot depth.

Fig. 7.
Fig. 7.

(a) Convergence feature of the proposed iterative projection algorithm. (b) Optimal profile of the extra-phase freedom over 165 waveguide array.

Fig. 8.
Fig. 8.

(a) Comparison of the field profiles obtained by the conventional method and the proposed method. (b) Simulated spectral response of the designed AWG (crosstalk=2.5dB, flatness=0.05dB).

Fig. 9.
Fig. 9.

Tolerance analysis: (a) ΔLk profile with the deviation factor η and (b) spectral response variation with the deviation factor η.

Equations (21)

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F(x;λs)=rect[xawin],
V(u;λs)=ej2πfin/λsjλsfinF(x)exp(j2πλsfinxu)dx=ej2πfin/λsjλsfinwin/2win/2exp(j2πλsfinxu)exp(j2πλsfinau)dx=ej2πfin/λsjλsfinwinsinc(winufinλs)exp(j2πλsfinau),
Tin=2finλswinq,
d¯=2finλsqwin(2N+1),
F(u;λs)=k=NNAkrect[ukd¯w¯]exp(j2πλsfinkd¯a),
V(x;λs)=ej2πfout/λsjλsfout{k=1NAkexp[j2πλsfoutx(kd¯)]w¯sinc(w¯xfoutλs)exp(j2πλsfinkd¯a)+A0w¯sinc(w¯xfoutλs)+k=N1Akexp[j2πλsfoutx(kd¯)]w¯sinc(w¯xfoutλs)exp(j2πλsfinkd¯a)}=ej2πfout/λsjλsfoutw¯sinc(w¯xfoutλs)[k=NNAkexp[j2πλsfoutx(kd¯)]exp(j2πλsfinkd¯a)]=ej2πfout/λsjλsfoutw¯sinc(w¯xfoutλs)[k=NNAkexp[j2πλsfout(x+foutfina)(kd¯)]].
Tout=λsfoutd¯.
Tout=(2M+1)dout=λsfoutwin(2N+1)2finλsq,
win=2fin(2M+1)fout(2N+1)dout.
Ak(λw)=ηk(λw)exp(jϕk(λw)),
exp(jϕk(λ))=exp(j2πLλwk)exp(j2πλwLk).
V(x;λs)=ej2πfout/λsjλsfoutw¯sinc(w¯xfoutλs)[k=NNAkexp[j2πλsfoutx(kd¯)]exp(j2πλsfinkd¯a)]=ej2πfout/λsjλsfoutw¯sinc(w¯xfoutλs)[k=NNηkexp(j2πLλwk)exp[j2πλsfout(x+foutfina)(kd¯)]]=ej2πfout/λsjλsfoutw¯sinc(w¯xfoutλs)[k=NNηkexp(j2πλ¯wmλwk)exp[j2πλsfout(x+foutfina)(kd¯)]]=ej2πfout/λsjλsfoutw¯sinc(w¯xfoutλs)[k=NNηkexp[j2πλsfout(x+foutfinaλ¯wmλsfoutλwd¯)(kd¯)]].
V(x;λs)=ej2πfout/λsjλsfoutw¯sinc(w¯xfoutλs)[k=NNηkexp[j2πλsfout(xλ¯wmλsfoutλwd¯)(kd¯)]].
2πλsfout(xλ¯wmλsfoutλwd¯)d¯=2πp,
x=pλsfoutd¯+λ¯wmλsfoutλwd¯=λsfoutd¯(p+λ¯wmλw)=λsfoutd¯(p+mΔλwmλ¯w+Δλw)=λsfoutd¯(p+mΔλwmλw)=λsfoutd¯(p+m)foutnwΔλwmd¯=λsfoutd¯(p+m)foutΔλsmd¯,
Ck(λs)=V(x;λs)Wk(x)dx.
V(x)=k=NNGk(x)ηkexp(j2πΔLkλw),
Gk(x)=ej2πfout/λsjλsfoutw¯sinc(w¯xfoutλs)exp[j2πλsfout(xλ¯wmλsfoutλwd¯)(kd¯)].
[VNV0VN]=[GN,NG0,NGN,NGN,NG0,NGN,NGN,NG0,NGN,N][ηNexp(jϕN)η0exp(jϕ0)ηNexp(jϕN)],
V¯(x)={ηV(x)forI(x)=0I(x)exp(jV(x))forI(x)0.
η(u)exp(jϕ(u))=G1(V¯(x)),

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