Abstract

In this paper, the procedure to optimize flat-top Arrayed Waveguide Grating (AWG) devices in terms of transmission and dispersion properties is presented. The systematic procedure consists on the stigmatization and minimization of the Light Path Function (LPF) used in classic planar spectrograph theory. The resulting geometry arrangement for the Arrayed Waveguides (AW) and the Output Waveguides (OW) is not the classical Rowland mounting, but an arbitrary geometry arrangement. Simulation using previous published enhanced modeling show how this geometry reduces the passband ripple, asymmetry and dispersion, in a design example.

© 2003 Optical Society of America

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  1. M.K. Smit and C. van Dam, “PHASAR-Based WDM-Devices: Principles, Design and Applications,” J. Sel. Top. Quantum Electron. 2, 236–250 (1996).
    [Crossref]
  2. H. Takenouchi, H. Tsuda, and T. Kurokawa, “Analysis of optical-signal processing using an arrayed-waveguide grating,” Opt. Express 6124–135 (2000), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-6-6-124
    [Crossref] [PubMed]
  3. Y. Yoshikuni, “Semiconductor ArrayedWaveguide Gratings for Photonic Integrated Devices,” J. Sel. Top. Quantum Electron. 8, 1102–1114 (2002).
    [Crossref]
  4. H. Takahashi, S. Suzuki, and I. Nishi, “Wavelength multiplexer based on SiO2-Ta2O5 arrayed-waveguide grating,” J. Lightwave Technol. 12, 989–995 (1994).
    [Crossref]
  5. H. Takahashi, H. Toba, and Y. Inoue, “Multiwavelength ring laser composed of EDFAs and an arrayed-waveguide wavelength multiplexer,” Electron. Lett. 30, 44–45 (1994).
    [Crossref]
  6. D. Huang, T. Chin, and Y. Lai, “Arrayed waveguide grating DWDM interleaver,” Proc. OFC,  3 WDD80 1–3 (2001).
  7. H. Takahashi, K. Oda, H. Toba, and Y. Inoue, “Transmission characteristics of arrayed waveguide N×N wavelength multiplexer,” J. Lightwave Technol. 13447–455 (1995).
    [Crossref]
  8. C. Dragone, “Efficient N×N star couplers using Fourier Optics,” J. Lightwave Technol. 7, 479–489 (1989).
    [Crossref]
  9. R. März, Integrated optics: design & modeling, (Artech House, 1995), Chap. 8.
  10. B. Soole e.a., “Use of multimode interference couplers to broaden the passband of wavelength-dispersive integrated WDM filters,” Phot. Tech. Lett. 8, 1340–1342 (1996).
    [Crossref]
  11. L.B. Soldano and E.C.M. Pennings, “Optical multi-mode interference devices based on self-imaging: principles and applications,” J. Lightwave Technol. 13, 615–627 (1995).
    [Crossref]
  12. K. Okamoto and A. Sugita, “Flat spectral response arrayed-waveguide grating multiplexer with parabolic waveguide horns,” Electron. Lett. 32, 1661–1662 (1996).
    [Crossref]
  13. D. Wang, G. Jin, Y. Yan, and M. Wu, “Aberration theory of arrayed waveguide grating,” J. Lightwave Technol. 19, 279–284 (2001).
    [Crossref]
  14. P. Mũnoz, D. Pastor, and J. Capmany, “Modeling and design of arrayed waveguide gratings,”, J. Lightwave Technol. 20, 661–674 (2002).
    [Crossref]
  15. P. Mũnoz, D. Pastor, and J. Capmany, “Analysis and design of arrayed waveguide gratings with MMI couplers,” Opt. Express 9, 328–338 (2001), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-9-7-328
    [Crossref]
  16. ITU-T G.692 Rec. “Optical interfaces for multichannel systems with optical amplifiers,” (1998).
  17. M. Hammer, “WMM mode solver. Numerical simulation of rectangular integrated optical waveguides,” University of Twente, Faculty of Mathematical Sciences. http://www.physik.uni-osnabrueck.de/theophys/
  18. C.D. Lee e.a., “The role of photomask resolution on the performance of arrayed-waveguide grating devices,” J. Lightwave Technol. 19, 1726–1733 (2001).
    [Crossref]
  19. P. Mũnoz, D. Pastor, J. Capmany, and S. Sales, “Analytical and Numerical Analysis of Phase and Amplitude Errors in the Performance of Arrayed Waveguide Gratings,” J. Sel. Top. Quantum Electron. 8, 1130–1141 (2002).
    [Crossref]
  20. J.W. Goodman, Introduction to Fourier Optics, (McGraw-Hill, 1994), Chaps. 4 and 5.

2002 (3)

Y. Yoshikuni, “Semiconductor ArrayedWaveguide Gratings for Photonic Integrated Devices,” J. Sel. Top. Quantum Electron. 8, 1102–1114 (2002).
[Crossref]

P. Mũnoz, D. Pastor, J. Capmany, and S. Sales, “Analytical and Numerical Analysis of Phase and Amplitude Errors in the Performance of Arrayed Waveguide Gratings,” J. Sel. Top. Quantum Electron. 8, 1130–1141 (2002).
[Crossref]

P. Mũnoz, D. Pastor, and J. Capmany, “Modeling and design of arrayed waveguide gratings,”, J. Lightwave Technol. 20, 661–674 (2002).
[Crossref]

2001 (4)

2000 (1)

1996 (3)

B. Soole e.a., “Use of multimode interference couplers to broaden the passband of wavelength-dispersive integrated WDM filters,” Phot. Tech. Lett. 8, 1340–1342 (1996).
[Crossref]

K. Okamoto and A. Sugita, “Flat spectral response arrayed-waveguide grating multiplexer with parabolic waveguide horns,” Electron. Lett. 32, 1661–1662 (1996).
[Crossref]

M.K. Smit and C. van Dam, “PHASAR-Based WDM-Devices: Principles, Design and Applications,” J. Sel. Top. Quantum Electron. 2, 236–250 (1996).
[Crossref]

1995 (2)

L.B. Soldano and E.C.M. Pennings, “Optical multi-mode interference devices based on self-imaging: principles and applications,” J. Lightwave Technol. 13, 615–627 (1995).
[Crossref]

H. Takahashi, K. Oda, H. Toba, and Y. Inoue, “Transmission characteristics of arrayed waveguide N×N wavelength multiplexer,” J. Lightwave Technol. 13447–455 (1995).
[Crossref]

1994 (2)

H. Takahashi, S. Suzuki, and I. Nishi, “Wavelength multiplexer based on SiO2-Ta2O5 arrayed-waveguide grating,” J. Lightwave Technol. 12, 989–995 (1994).
[Crossref]

H. Takahashi, H. Toba, and Y. Inoue, “Multiwavelength ring laser composed of EDFAs and an arrayed-waveguide wavelength multiplexer,” Electron. Lett. 30, 44–45 (1994).
[Crossref]

1989 (1)

C. Dragone, “Efficient N×N star couplers using Fourier Optics,” J. Lightwave Technol. 7, 479–489 (1989).
[Crossref]

Capmany, J.

Chin, T.

D. Huang, T. Chin, and Y. Lai, “Arrayed waveguide grating DWDM interleaver,” Proc. OFC,  3 WDD80 1–3 (2001).

Dragone, C.

C. Dragone, “Efficient N×N star couplers using Fourier Optics,” J. Lightwave Technol. 7, 479–489 (1989).
[Crossref]

Goodman, J.W.

J.W. Goodman, Introduction to Fourier Optics, (McGraw-Hill, 1994), Chaps. 4 and 5.

Hammer, M.

M. Hammer, “WMM mode solver. Numerical simulation of rectangular integrated optical waveguides,” University of Twente, Faculty of Mathematical Sciences. http://www.physik.uni-osnabrueck.de/theophys/

Huang, D.

D. Huang, T. Chin, and Y. Lai, “Arrayed waveguide grating DWDM interleaver,” Proc. OFC,  3 WDD80 1–3 (2001).

Inoue, Y.

H. Takahashi, K. Oda, H. Toba, and Y. Inoue, “Transmission characteristics of arrayed waveguide N×N wavelength multiplexer,” J. Lightwave Technol. 13447–455 (1995).
[Crossref]

H. Takahashi, H. Toba, and Y. Inoue, “Multiwavelength ring laser composed of EDFAs and an arrayed-waveguide wavelength multiplexer,” Electron. Lett. 30, 44–45 (1994).
[Crossref]

Jin, G.

Kurokawa, T.

Lai, Y.

D. Huang, T. Chin, and Y. Lai, “Arrayed waveguide grating DWDM interleaver,” Proc. OFC,  3 WDD80 1–3 (2001).

Lee, C.D.

März, R.

R. März, Integrated optics: design & modeling, (Artech House, 1995), Chap. 8.

Munoz, P.

Nishi, I.

H. Takahashi, S. Suzuki, and I. Nishi, “Wavelength multiplexer based on SiO2-Ta2O5 arrayed-waveguide grating,” J. Lightwave Technol. 12, 989–995 (1994).
[Crossref]

Oda, K.

H. Takahashi, K. Oda, H. Toba, and Y. Inoue, “Transmission characteristics of arrayed waveguide N×N wavelength multiplexer,” J. Lightwave Technol. 13447–455 (1995).
[Crossref]

Okamoto, K.

K. Okamoto and A. Sugita, “Flat spectral response arrayed-waveguide grating multiplexer with parabolic waveguide horns,” Electron. Lett. 32, 1661–1662 (1996).
[Crossref]

Pastor, D.

Pennings, E.C.M.

L.B. Soldano and E.C.M. Pennings, “Optical multi-mode interference devices based on self-imaging: principles and applications,” J. Lightwave Technol. 13, 615–627 (1995).
[Crossref]

Sales, S.

P. Mũnoz, D. Pastor, J. Capmany, and S. Sales, “Analytical and Numerical Analysis of Phase and Amplitude Errors in the Performance of Arrayed Waveguide Gratings,” J. Sel. Top. Quantum Electron. 8, 1130–1141 (2002).
[Crossref]

Smit, M.K.

M.K. Smit and C. van Dam, “PHASAR-Based WDM-Devices: Principles, Design and Applications,” J. Sel. Top. Quantum Electron. 2, 236–250 (1996).
[Crossref]

Soldano, L.B.

L.B. Soldano and E.C.M. Pennings, “Optical multi-mode interference devices based on self-imaging: principles and applications,” J. Lightwave Technol. 13, 615–627 (1995).
[Crossref]

Soole, B.

B. Soole e.a., “Use of multimode interference couplers to broaden the passband of wavelength-dispersive integrated WDM filters,” Phot. Tech. Lett. 8, 1340–1342 (1996).
[Crossref]

Sugita, A.

K. Okamoto and A. Sugita, “Flat spectral response arrayed-waveguide grating multiplexer with parabolic waveguide horns,” Electron. Lett. 32, 1661–1662 (1996).
[Crossref]

Suzuki, S.

H. Takahashi, S. Suzuki, and I. Nishi, “Wavelength multiplexer based on SiO2-Ta2O5 arrayed-waveguide grating,” J. Lightwave Technol. 12, 989–995 (1994).
[Crossref]

Takahashi, H.

H. Takahashi, K. Oda, H. Toba, and Y. Inoue, “Transmission characteristics of arrayed waveguide N×N wavelength multiplexer,” J. Lightwave Technol. 13447–455 (1995).
[Crossref]

H. Takahashi, H. Toba, and Y. Inoue, “Multiwavelength ring laser composed of EDFAs and an arrayed-waveguide wavelength multiplexer,” Electron. Lett. 30, 44–45 (1994).
[Crossref]

H. Takahashi, S. Suzuki, and I. Nishi, “Wavelength multiplexer based on SiO2-Ta2O5 arrayed-waveguide grating,” J. Lightwave Technol. 12, 989–995 (1994).
[Crossref]

Takenouchi, H.

Toba, H.

H. Takahashi, K. Oda, H. Toba, and Y. Inoue, “Transmission characteristics of arrayed waveguide N×N wavelength multiplexer,” J. Lightwave Technol. 13447–455 (1995).
[Crossref]

H. Takahashi, H. Toba, and Y. Inoue, “Multiwavelength ring laser composed of EDFAs and an arrayed-waveguide wavelength multiplexer,” Electron. Lett. 30, 44–45 (1994).
[Crossref]

Tsuda, H.

van Dam, C.

M.K. Smit and C. van Dam, “PHASAR-Based WDM-Devices: Principles, Design and Applications,” J. Sel. Top. Quantum Electron. 2, 236–250 (1996).
[Crossref]

Wang, D.

Wu, M.

Yan, Y.

Yoshikuni, Y.

Y. Yoshikuni, “Semiconductor ArrayedWaveguide Gratings for Photonic Integrated Devices,” J. Sel. Top. Quantum Electron. 8, 1102–1114 (2002).
[Crossref]

Electron. Lett. (2)

H. Takahashi, H. Toba, and Y. Inoue, “Multiwavelength ring laser composed of EDFAs and an arrayed-waveguide wavelength multiplexer,” Electron. Lett. 30, 44–45 (1994).
[Crossref]

K. Okamoto and A. Sugita, “Flat spectral response arrayed-waveguide grating multiplexer with parabolic waveguide horns,” Electron. Lett. 32, 1661–1662 (1996).
[Crossref]

J. Lightwave Technol. (7)

D. Wang, G. Jin, Y. Yan, and M. Wu, “Aberration theory of arrayed waveguide grating,” J. Lightwave Technol. 19, 279–284 (2001).
[Crossref]

P. Mũnoz, D. Pastor, and J. Capmany, “Modeling and design of arrayed waveguide gratings,”, J. Lightwave Technol. 20, 661–674 (2002).
[Crossref]

L.B. Soldano and E.C.M. Pennings, “Optical multi-mode interference devices based on self-imaging: principles and applications,” J. Lightwave Technol. 13, 615–627 (1995).
[Crossref]

C.D. Lee e.a., “The role of photomask resolution on the performance of arrayed-waveguide grating devices,” J. Lightwave Technol. 19, 1726–1733 (2001).
[Crossref]

H. Takahashi, K. Oda, H. Toba, and Y. Inoue, “Transmission characteristics of arrayed waveguide N×N wavelength multiplexer,” J. Lightwave Technol. 13447–455 (1995).
[Crossref]

C. Dragone, “Efficient N×N star couplers using Fourier Optics,” J. Lightwave Technol. 7, 479–489 (1989).
[Crossref]

H. Takahashi, S. Suzuki, and I. Nishi, “Wavelength multiplexer based on SiO2-Ta2O5 arrayed-waveguide grating,” J. Lightwave Technol. 12, 989–995 (1994).
[Crossref]

J. Sel. Top. Quantum Electron. (3)

Y. Yoshikuni, “Semiconductor ArrayedWaveguide Gratings for Photonic Integrated Devices,” J. Sel. Top. Quantum Electron. 8, 1102–1114 (2002).
[Crossref]

M.K. Smit and C. van Dam, “PHASAR-Based WDM-Devices: Principles, Design and Applications,” J. Sel. Top. Quantum Electron. 2, 236–250 (1996).
[Crossref]

P. Mũnoz, D. Pastor, J. Capmany, and S. Sales, “Analytical and Numerical Analysis of Phase and Amplitude Errors in the Performance of Arrayed Waveguide Gratings,” J. Sel. Top. Quantum Electron. 8, 1130–1141 (2002).
[Crossref]

Opt. Express (2)

Phot. Tech. Lett. (1)

B. Soole e.a., “Use of multimode interference couplers to broaden the passband of wavelength-dispersive integrated WDM filters,” Phot. Tech. Lett. 8, 1340–1342 (1996).
[Crossref]

Proc. OFC (1)

D. Huang, T. Chin, and Y. Lai, “Arrayed waveguide grating DWDM interleaver,” Proc. OFC,  3 WDD80 1–3 (2001).

Other (4)

R. März, Integrated optics: design & modeling, (Artech House, 1995), Chap. 8.

J.W. Goodman, Introduction to Fourier Optics, (McGraw-Hill, 1994), Chaps. 4 and 5.

ITU-T G.692 Rec. “Optical interfaces for multichannel systems with optical amplifiers,” (1998).

M. Hammer, “WMM mode solver. Numerical simulation of rectangular integrated optical waveguides,” University of Twente, Faculty of Mathematical Sciences. http://www.physik.uni-osnabrueck.de/theophys/

Supplementary Material (4)

» Media 1: GIF (1087 KB)     
» Media 2: GIF (1115 KB)     
» Media 3: GIF (1129 KB)     
» Media 4: GIF (1135 KB)     

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Figures (6)

Fig. 1.
Fig. 1.

Light path function definition.

Fig. 2.
Fig. 2.

(Movie 1.1 MB) Grating line side geometry, Rowland circle (red) and AW layout (green squares) -upper plot-, x displacement -center plot- and z displacement -lower plot-from the ideal grating line.

Fig. 3.
Fig. 3.

(Movie 1.1 MB) Focal line side geometry, Rowland mounting (red), OW poisitions (blue circles) and stigmatic points positions (green triangles).

Fig. 4.
Fig. 4.

(Movies 1.2 MB) Tranmssion [dB] and dispersion [ps/nm] for the optimized geometry (blue) and Rowland mounting based (red) AWG. [Media 4]

Fig. 5.
Fig. 5.

Bandwidth [nm] evolution (left) and percent reduction (right) along the optimization steps, for 0.5 dB, 1 dB, 3 dB and 20 dB bandwidth values

Fig. 6.
Fig. 6.

Ripple (left) and asymmetry (right) evolution, both in [dB], along the optimization steps.

Equations (9)

Equations on this page are rendered with MathJax. Learn more.

F ( x ) n s ( λ ) ( I P I ¯ I O I ¯ ) + n c ( λ ) ( P I P O I O ) + n s ( λ ) ( PD ¯ OD ¯ ) G ( x )
F ( x ) n s ( λ ) F i ( x ) + n c ( λ ) Δ L ( x ) + n s ( λ ) F d ( x ) G ( x )
F ( x ) n s ( λ ) F i ( x , z G ( x ) ) + n c ( λ ) Δ L ( x ) + n s ( λ ) F d ( x , z G ( x ) ) G ( x )
n s ( λ 1 ) F i ( x , z G ( x ) ) + n c ( λ 1 ) Δ L ( x ) + n s ( λ 1 ) F d , 1 ( x , z G ( x ) ) m λ 1 G ( x ) = 0
n s ( λ 2 ) F i ( x , z G ( x ) ) + n c ( λ 2 ) Δ L ( x ) + n s ( λ 2 ) F d , 2 ( x , z G ( x ) ) m λ 2 G ( x ) = 0
x 0 = G ( x ) d w
z G ( x 0 ) = R 2 R 2 x 0 2
Δ L ( x 0 ) = m λ 0 n c G ( x )
n s ( λ k ) F i ( x , z G ( x ) ) + n c ( λ k ) Δ L ( x ) + n s ( λ k ) F d , k ( x , z G ( x ) ) m λ k G ( x ) = 0

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