Abstract

The fabrication tolerance of surface roughness on the performance [such as the insertion loss, the polarization-dependent loss (PDL), and the chromatic dispersion] of an etched diffraction grating demultiplexer is analyzed by using an accurate method of moments. The results show that both the insertion loss and the chromatic dispersion rapidly increase as the roughness of the grating facets increases. Appropriate residual roughness of the shaded facets can reduce the PDL of the demultiplexer, and the mechanism for the existence of an optimal residual roughness is explained.

© 2006 Optical Society of America

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  1. M. K. Smit and C. van Dam, 'Phasar-based WDM-devices: principles, design and applications,' IEEE J. Sel. Top. Quantum Electron. 2, 236-250 (1996).
    [CrossRef]
  2. C. Cremer, G. Ebbinghaus, G. Heise, R. Muller-Nawrath,M. Schienle, and L. Stoll, 'Grating spectrograph in InGaAsP/InP for dense wavelength division multiplexing,' Appl. Phys. Lett. 59, 627-629 (1991).
    [CrossRef]
  3. Z. Shi, J.-J. He, and S. He, 'Analysis and design of a concave diffraction grating with total internal reflection facets using a hybrid diffraction method,' J. Opt. Soc. Am. A 21, 1198-1206 (2004).
    [CrossRef]
  4. S. Y. Sadov and K. A. McGreer, 'Polarization dependence of diffraction gratings that have total internal reflection facets,' J. Opt. Soc. Am. A 17, 1590-1594 (2000).
    [CrossRef]
  5. J. Song, N. Zhu, and S. He, 'Analysis of the loss resulting from point defects for an etched diffraction grating demultiplexer by using the method of moments,' J. Opt. Soc. Am. A 22, 1620-1623 (2005).
    [CrossRef]
  6. J. J. He, 'Phase-dithered waveguide grating with flat passband and sharp transitions,' IEEE J. Sel. Top. Quantum Electron. 8, 1186-1193 (2002).
    [CrossRef]
  7. J. Song, J. J. He, and S. He, 'Polarization performance analysis of etched diffraction grating demultiplexer using boundary element method,' IEEE J. Sel. Top. Quantum Electron. 11, 224-231 (2005).
    [CrossRef]
  8. J. Song, D. Q. Pang, and S. He, 'A MoM-based design and simulation method for an etched diffraction grating demultiplexer,' Opt. Commun. 233, 363-371 (2004).
    [CrossRef]
  9. J. Song and S. He, 'Effects of rounded corners to the performance of an echelle diffraction grating demultiplexer,' J. Opt. A, Pure Appl. Opt. 6, 769-773 (2004).
    [CrossRef]
  10. J. Song, D. Q. Pang, and S. He, 'A planar waveguide demultiplexer with a flat passband, sharp transitions and a low chromatic dispersion,' Opt. Commun. 227, 89-97 (2003).
    [CrossRef]
  11. L. Tsang, J. A. Kong, and K. H. Ding, Scattering of Electromagnetic Waves, Vol. 1 of Theories and Applications (Wiley, 2000).
    [CrossRef]

2005 (2)

J. Song, J. J. He, and S. He, 'Polarization performance analysis of etched diffraction grating demultiplexer using boundary element method,' IEEE J. Sel. Top. Quantum Electron. 11, 224-231 (2005).
[CrossRef]

J. Song, N. Zhu, and S. He, 'Analysis of the loss resulting from point defects for an etched diffraction grating demultiplexer by using the method of moments,' J. Opt. Soc. Am. A 22, 1620-1623 (2005).
[CrossRef]

2004 (3)

J. Song, D. Q. Pang, and S. He, 'A MoM-based design and simulation method for an etched diffraction grating demultiplexer,' Opt. Commun. 233, 363-371 (2004).
[CrossRef]

J. Song and S. He, 'Effects of rounded corners to the performance of an echelle diffraction grating demultiplexer,' J. Opt. A, Pure Appl. Opt. 6, 769-773 (2004).
[CrossRef]

Z. Shi, J.-J. He, and S. He, 'Analysis and design of a concave diffraction grating with total internal reflection facets using a hybrid diffraction method,' J. Opt. Soc. Am. A 21, 1198-1206 (2004).
[CrossRef]

2003 (1)

J. Song, D. Q. Pang, and S. He, 'A planar waveguide demultiplexer with a flat passband, sharp transitions and a low chromatic dispersion,' Opt. Commun. 227, 89-97 (2003).
[CrossRef]

2002 (1)

J. J. He, 'Phase-dithered waveguide grating with flat passband and sharp transitions,' IEEE J. Sel. Top. Quantum Electron. 8, 1186-1193 (2002).
[CrossRef]

2000 (1)

1996 (1)

M. K. Smit and C. van Dam, 'Phasar-based WDM-devices: principles, design and applications,' IEEE J. Sel. Top. Quantum Electron. 2, 236-250 (1996).
[CrossRef]

1991 (1)

C. Cremer, G. Ebbinghaus, G. Heise, R. Muller-Nawrath,M. Schienle, and L. Stoll, 'Grating spectrograph in InGaAsP/InP for dense wavelength division multiplexing,' Appl. Phys. Lett. 59, 627-629 (1991).
[CrossRef]

Cremer, C.

C. Cremer, G. Ebbinghaus, G. Heise, R. Muller-Nawrath,M. Schienle, and L. Stoll, 'Grating spectrograph in InGaAsP/InP for dense wavelength division multiplexing,' Appl. Phys. Lett. 59, 627-629 (1991).
[CrossRef]

Ding, K. H.

L. Tsang, J. A. Kong, and K. H. Ding, Scattering of Electromagnetic Waves, Vol. 1 of Theories and Applications (Wiley, 2000).
[CrossRef]

Ebbinghaus, G.

C. Cremer, G. Ebbinghaus, G. Heise, R. Muller-Nawrath,M. Schienle, and L. Stoll, 'Grating spectrograph in InGaAsP/InP for dense wavelength division multiplexing,' Appl. Phys. Lett. 59, 627-629 (1991).
[CrossRef]

He, J. J.

J. Song, J. J. He, and S. He, 'Polarization performance analysis of etched diffraction grating demultiplexer using boundary element method,' IEEE J. Sel. Top. Quantum Electron. 11, 224-231 (2005).
[CrossRef]

J. J. He, 'Phase-dithered waveguide grating with flat passband and sharp transitions,' IEEE J. Sel. Top. Quantum Electron. 8, 1186-1193 (2002).
[CrossRef]

He, J.-J.

He, S.

J. Song, J. J. He, and S. He, 'Polarization performance analysis of etched diffraction grating demultiplexer using boundary element method,' IEEE J. Sel. Top. Quantum Electron. 11, 224-231 (2005).
[CrossRef]

J. Song, N. Zhu, and S. He, 'Analysis of the loss resulting from point defects for an etched diffraction grating demultiplexer by using the method of moments,' J. Opt. Soc. Am. A 22, 1620-1623 (2005).
[CrossRef]

Z. Shi, J.-J. He, and S. He, 'Analysis and design of a concave diffraction grating with total internal reflection facets using a hybrid diffraction method,' J. Opt. Soc. Am. A 21, 1198-1206 (2004).
[CrossRef]

J. Song, D. Q. Pang, and S. He, 'A MoM-based design and simulation method for an etched diffraction grating demultiplexer,' Opt. Commun. 233, 363-371 (2004).
[CrossRef]

J. Song and S. He, 'Effects of rounded corners to the performance of an echelle diffraction grating demultiplexer,' J. Opt. A, Pure Appl. Opt. 6, 769-773 (2004).
[CrossRef]

J. Song, D. Q. Pang, and S. He, 'A planar waveguide demultiplexer with a flat passband, sharp transitions and a low chromatic dispersion,' Opt. Commun. 227, 89-97 (2003).
[CrossRef]

Heise, G.

C. Cremer, G. Ebbinghaus, G. Heise, R. Muller-Nawrath,M. Schienle, and L. Stoll, 'Grating spectrograph in InGaAsP/InP for dense wavelength division multiplexing,' Appl. Phys. Lett. 59, 627-629 (1991).
[CrossRef]

Kong, J. A.

L. Tsang, J. A. Kong, and K. H. Ding, Scattering of Electromagnetic Waves, Vol. 1 of Theories and Applications (Wiley, 2000).
[CrossRef]

McGreer, K. A.

Muller-Nawrath, R.

C. Cremer, G. Ebbinghaus, G. Heise, R. Muller-Nawrath,M. Schienle, and L. Stoll, 'Grating spectrograph in InGaAsP/InP for dense wavelength division multiplexing,' Appl. Phys. Lett. 59, 627-629 (1991).
[CrossRef]

Pang, D. Q.

J. Song, D. Q. Pang, and S. He, 'A MoM-based design and simulation method for an etched diffraction grating demultiplexer,' Opt. Commun. 233, 363-371 (2004).
[CrossRef]

J. Song, D. Q. Pang, and S. He, 'A planar waveguide demultiplexer with a flat passband, sharp transitions and a low chromatic dispersion,' Opt. Commun. 227, 89-97 (2003).
[CrossRef]

Sadov, S. Y.

Schienle, M.

C. Cremer, G. Ebbinghaus, G. Heise, R. Muller-Nawrath,M. Schienle, and L. Stoll, 'Grating spectrograph in InGaAsP/InP for dense wavelength division multiplexing,' Appl. Phys. Lett. 59, 627-629 (1991).
[CrossRef]

Shi, Z.

Smit, M. K.

M. K. Smit and C. van Dam, 'Phasar-based WDM-devices: principles, design and applications,' IEEE J. Sel. Top. Quantum Electron. 2, 236-250 (1996).
[CrossRef]

Song, J.

J. Song, N. Zhu, and S. He, 'Analysis of the loss resulting from point defects for an etched diffraction grating demultiplexer by using the method of moments,' J. Opt. Soc. Am. A 22, 1620-1623 (2005).
[CrossRef]

J. Song, J. J. He, and S. He, 'Polarization performance analysis of etched diffraction grating demultiplexer using boundary element method,' IEEE J. Sel. Top. Quantum Electron. 11, 224-231 (2005).
[CrossRef]

J. Song, D. Q. Pang, and S. He, 'A MoM-based design and simulation method for an etched diffraction grating demultiplexer,' Opt. Commun. 233, 363-371 (2004).
[CrossRef]

J. Song and S. He, 'Effects of rounded corners to the performance of an echelle diffraction grating demultiplexer,' J. Opt. A, Pure Appl. Opt. 6, 769-773 (2004).
[CrossRef]

J. Song, D. Q. Pang, and S. He, 'A planar waveguide demultiplexer with a flat passband, sharp transitions and a low chromatic dispersion,' Opt. Commun. 227, 89-97 (2003).
[CrossRef]

Stoll, L.

C. Cremer, G. Ebbinghaus, G. Heise, R. Muller-Nawrath,M. Schienle, and L. Stoll, 'Grating spectrograph in InGaAsP/InP for dense wavelength division multiplexing,' Appl. Phys. Lett. 59, 627-629 (1991).
[CrossRef]

Tsang, L.

L. Tsang, J. A. Kong, and K. H. Ding, Scattering of Electromagnetic Waves, Vol. 1 of Theories and Applications (Wiley, 2000).
[CrossRef]

van Dam, C.

M. K. Smit and C. van Dam, 'Phasar-based WDM-devices: principles, design and applications,' IEEE J. Sel. Top. Quantum Electron. 2, 236-250 (1996).
[CrossRef]

Zhu, N.

Appl. Phys. Lett. (1)

C. Cremer, G. Ebbinghaus, G. Heise, R. Muller-Nawrath,M. Schienle, and L. Stoll, 'Grating spectrograph in InGaAsP/InP for dense wavelength division multiplexing,' Appl. Phys. Lett. 59, 627-629 (1991).
[CrossRef]

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

J. J. He, 'Phase-dithered waveguide grating with flat passband and sharp transitions,' IEEE J. Sel. Top. Quantum Electron. 8, 1186-1193 (2002).
[CrossRef]

J. Song, J. J. He, and S. He, 'Polarization performance analysis of etched diffraction grating demultiplexer using boundary element method,' IEEE J. Sel. Top. Quantum Electron. 11, 224-231 (2005).
[CrossRef]

M. K. Smit and C. van Dam, 'Phasar-based WDM-devices: principles, design and applications,' IEEE J. Sel. Top. Quantum Electron. 2, 236-250 (1996).
[CrossRef]

J. Opt. A, Pure Appl. Opt. (1)

J. Song and S. He, 'Effects of rounded corners to the performance of an echelle diffraction grating demultiplexer,' J. Opt. A, Pure Appl. Opt. 6, 769-773 (2004).
[CrossRef]

J. Opt. Soc. Am. A (3)

Opt. Commun. (2)

J. Song, D. Q. Pang, and S. He, 'A planar waveguide demultiplexer with a flat passband, sharp transitions and a low chromatic dispersion,' Opt. Commun. 227, 89-97 (2003).
[CrossRef]

J. Song, D. Q. Pang, and S. He, 'A MoM-based design and simulation method for an etched diffraction grating demultiplexer,' Opt. Commun. 233, 363-371 (2004).
[CrossRef]

Other (1)

L. Tsang, J. A. Kong, and K. H. Ding, Scattering of Electromagnetic Waves, Vol. 1 of Theories and Applications (Wiley, 2000).
[CrossRef]

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Figures (9)

Fig. 1
Fig. 1

Schematic diagram of an EDG demultiplexer based on a Rowland circle (Rc) mounting.

Fig. 2
Fig. 2

Contour plot of the loss as k δ and λ vary for an EDG demultiplexer for (a) TE and (b) TM polarizations when all the grating facets are rough.

Fig. 3
Fig. 3

Contour plot of the PDL as k δ and λ vary for an EDG demultiplexer when all the grating facets are rough.

Fig. 4
Fig. 4

Contour plot of the chromatic dispersion as k δ and λ vary for an EDG demultiplexer for (a) TE and (b) TM polarizations when all the grating facets are rough.

Fig. 5
Fig. 5

Contour plot of the loss as k δ and λ vary for an EDG demultiplexer for (a) TE and (b) TM polarizations when only the shaded facets are rough.

Fig. 6
Fig. 6

Contour plot of the PDL as k δ and λ vary for an EDG demultiplexer when only the shaded facets are rough.

Fig. 7
Fig. 7

Loss of the EDG demultiplexer at different wavelengths.

Fig. 8
Fig. 8

Contour plot of the chromatic dispersion as k δ and λ vary for an EDG demultiplexer for (a) TE and (b) TM polarizations when only the shaded facets are rough.

Fig. 9
Fig. 9

Excess cross talk at the central channel at different k δ .

Equations (4)

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W m n J = H ,
where W m n = { j k 4 n = 1 N cos Φ m n H 1 ( 2 ) ( k r m r n ) S n m n 1 2 m = n } ,
J n = J ( r n ) , H n = H g ( r n ) .
I ( f ) = E image ( f , x ) E outwg * ( f , x ) d x 2 E image ( f , x ) 2 d x E outwg ( f , x ) 2 d x ,

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