Abstract

An effective method for analyzing the effect of point defects (e.g., dust grains and air bubbles) on an etched diffraction grating demultiplexer is presented by using the method of moments. This method leads to a deep insight into the influence of point defects on the loss of the demultiplexer. Numerical results show that strong resonance losses can be produced at some special point defects and incident light.

© 2005 Optical Society of America

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References

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  1. M. K. Smit, 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, 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, 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, K. A. McGreer, “Polarization dependence of diffraction gratings that have total internal reflection facets,” J. Opt. Soc. Am. A 17, 1590–1594 (2002).
    [CrossRef]
  5. C. Cremer, N. Emeis, M. Schier, G. Heise, G. Ebbinghaus, L. Stoll, “Grating spectrograph integrated with photodiode array in InGaAsP∕InGaAs∕InP,” IEEE Photonics Technol. Lett. 4, 108–110 (1992).
    [CrossRef]
  6. J.-J. He, E. S. Koteles, B. Lamontagne, L. Erickson, A. Delage, M. Davies, “Integrated polarization compensator for WDM waveguide demultiplexers,” IEEE Photonics Technol. Lett. 11, 224–226 (1999).
    [CrossRef]
  7. V. I. Tolstikhin, A. Demsmore, K. Pimonov, Y. Logvin, F. Wu, S. Laframboise, S. Grabtchak, “Monolithically integrated optical channel monitor for DWDM transmission systems,” J. Lightwave Technol. 22, 146–153 (2004).
    [CrossRef]
  8. T. H. Teng, L. Carin, “FDTD analysis of plane-wave diffraction from microwave devices on an infinite dielectric slab,” IEEE Microw. Guid. Wave Lett. 6, 16–18 (1996).
    [CrossRef]
  9. J. Song, D. Q. Pang, S. He, “A MoM-based design and simulation method for an etched diffraction grating demultiplexer,” Opt. Commun. 233, 363–371 (2004).
    [CrossRef]
  10. J. Song, 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]
  11. J.-J. He, B. Lamontagne, A. Delage, L. Erickson, M. Davies, E. S. Koteles, “Monolithic integrated wavelength demultiplexer based on a waveguide Rowland circle grating in InGaAsP∕InP,” J. Lightwave Technol. 16, 631–638 (1998).
    [CrossRef]
  12. J. Song, D. Q. Pang, S. He, “A planar waveguide demultiplexer with a flat passband, sharp transitions and a low chromatic dispersion,” Opt. Commun. 227, 89–97 (2003).
    [CrossRef]
  13. J. J. He, “Phase-dithered waveguide grating with flat passband and sharp transitions,” IEEE J. Sel. Top. Quantum Electron. 8, 1186–1193 (2002).
    [CrossRef]
  14. Z. M. Shi, S. He, “A three-focal-point method for the optimal design of a flat-top planar waveguide demultiplexer,” IEEE J. Sel. Top. Quantum Electron. 8, 1179–1185 (2002).
    [CrossRef]
  15. Z. M. Shi, J.-J. He, S. He, “An analytic method for designing passband flattened DWDM demultiplexers using spatial phase modulation,” J. Lightwave Technol. 21, 2314–2321 (2003).
    [CrossRef]
  16. G. H. Goedecke, S. O. Brien, “Scattering by irregular inhomogeneous particles via the digitized Green’s function algorithm,” Appl. Opt. 27, 2431–2438 (1998).
    [CrossRef]
  17. R. F. Harrington, ed., Field Computation by Moment Methods (IEEE Press, 1993).
    [CrossRef]

2004 (4)

Z. Shi, J.-J. He, 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]

V. I. Tolstikhin, A. Demsmore, K. Pimonov, Y. Logvin, F. Wu, S. Laframboise, S. Grabtchak, “Monolithically integrated optical channel monitor for DWDM transmission systems,” J. Lightwave Technol. 22, 146–153 (2004).
[CrossRef]

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

J. Song, 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]

2003 (2)

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

Z. M. Shi, J.-J. He, S. He, “An analytic method for designing passband flattened DWDM demultiplexers using spatial phase modulation,” J. Lightwave Technol. 21, 2314–2321 (2003).
[CrossRef]

2002 (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]

Z. M. Shi, S. He, “A three-focal-point method for the optimal design of a flat-top planar waveguide demultiplexer,” IEEE J. Sel. Top. Quantum Electron. 8, 1179–1185 (2002).
[CrossRef]

S. Y. Sadov, K. A. McGreer, “Polarization dependence of diffraction gratings that have total internal reflection facets,” J. Opt. Soc. Am. A 17, 1590–1594 (2002).
[CrossRef]

1999 (1)

J.-J. He, E. S. Koteles, B. Lamontagne, L. Erickson, A. Delage, M. Davies, “Integrated polarization compensator for WDM waveguide demultiplexers,” IEEE Photonics Technol. Lett. 11, 224–226 (1999).
[CrossRef]

1998 (2)

1996 (2)

T. H. Teng, L. Carin, “FDTD analysis of plane-wave diffraction from microwave devices on an infinite dielectric slab,” IEEE Microw. Guid. Wave Lett. 6, 16–18 (1996).
[CrossRef]

M. K. Smit, C. Van Dam, “PHASAR-based WDM-devices: principles, design and applications,” IEEE J. Sel. Top. Quantum Electron. 2, 236–250 (1996).
[CrossRef]

1992 (1)

C. Cremer, N. Emeis, M. Schier, G. Heise, G. Ebbinghaus, L. Stoll, “Grating spectrograph integrated with photodiode array in InGaAsP∕InGaAs∕InP,” IEEE Photonics Technol. Lett. 4, 108–110 (1992).
[CrossRef]

1991 (1)

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

Brien, S. O.

Carin, L.

T. H. Teng, L. Carin, “FDTD analysis of plane-wave diffraction from microwave devices on an infinite dielectric slab,” IEEE Microw. Guid. Wave Lett. 6, 16–18 (1996).
[CrossRef]

Cremer, C.

C. Cremer, N. Emeis, M. Schier, G. Heise, G. Ebbinghaus, L. Stoll, “Grating spectrograph integrated with photodiode array in InGaAsP∕InGaAs∕InP,” IEEE Photonics Technol. Lett. 4, 108–110 (1992).
[CrossRef]

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

Davies, M.

J.-J. He, E. S. Koteles, B. Lamontagne, L. Erickson, A. Delage, M. Davies, “Integrated polarization compensator for WDM waveguide demultiplexers,” IEEE Photonics Technol. Lett. 11, 224–226 (1999).
[CrossRef]

J.-J. He, B. Lamontagne, A. Delage, L. Erickson, M. Davies, E. S. Koteles, “Monolithic integrated wavelength demultiplexer based on a waveguide Rowland circle grating in InGaAsP∕InP,” J. Lightwave Technol. 16, 631–638 (1998).
[CrossRef]

Delage, A.

J.-J. He, E. S. Koteles, B. Lamontagne, L. Erickson, A. Delage, M. Davies, “Integrated polarization compensator for WDM waveguide demultiplexers,” IEEE Photonics Technol. Lett. 11, 224–226 (1999).
[CrossRef]

J.-J. He, B. Lamontagne, A. Delage, L. Erickson, M. Davies, E. S. Koteles, “Monolithic integrated wavelength demultiplexer based on a waveguide Rowland circle grating in InGaAsP∕InP,” J. Lightwave Technol. 16, 631–638 (1998).
[CrossRef]

Demsmore, A.

Ebbinghaus, G.

C. Cremer, N. Emeis, M. Schier, G. Heise, G. Ebbinghaus, L. Stoll, “Grating spectrograph integrated with photodiode array in InGaAsP∕InGaAs∕InP,” IEEE Photonics Technol. Lett. 4, 108–110 (1992).
[CrossRef]

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

Emeis, N.

C. Cremer, N. Emeis, M. Schier, G. Heise, G. Ebbinghaus, L. Stoll, “Grating spectrograph integrated with photodiode array in InGaAsP∕InGaAs∕InP,” IEEE Photonics Technol. Lett. 4, 108–110 (1992).
[CrossRef]

Erickson, L.

J.-J. He, E. S. Koteles, B. Lamontagne, L. Erickson, A. Delage, M. Davies, “Integrated polarization compensator for WDM waveguide demultiplexers,” IEEE Photonics Technol. Lett. 11, 224–226 (1999).
[CrossRef]

J.-J. He, B. Lamontagne, A. Delage, L. Erickson, M. Davies, E. S. Koteles, “Monolithic integrated wavelength demultiplexer based on a waveguide Rowland circle grating in InGaAsP∕InP,” J. Lightwave Technol. 16, 631–638 (1998).
[CrossRef]

Goedecke, G. H.

Grabtchak, S.

He, J. J.

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

J. Song, 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, 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]

Z. M. Shi, J.-J. He, S. He, “An analytic method for designing passband flattened DWDM demultiplexers using spatial phase modulation,” J. Lightwave Technol. 21, 2314–2321 (2003).
[CrossRef]

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

Z. M. Shi, S. He, “A three-focal-point method for the optimal design of a flat-top planar waveguide demultiplexer,” IEEE J. Sel. Top. Quantum Electron. 8, 1179–1185 (2002).
[CrossRef]

Heise, G.

C. Cremer, N. Emeis, M. Schier, G. Heise, G. Ebbinghaus, L. Stoll, “Grating spectrograph integrated with photodiode array in InGaAsP∕InGaAs∕InP,” IEEE Photonics Technol. Lett. 4, 108–110 (1992).
[CrossRef]

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

Koteles, E. S.

J.-J. He, E. S. Koteles, B. Lamontagne, L. Erickson, A. Delage, M. Davies, “Integrated polarization compensator for WDM waveguide demultiplexers,” IEEE Photonics Technol. Lett. 11, 224–226 (1999).
[CrossRef]

J.-J. He, B. Lamontagne, A. Delage, L. Erickson, M. Davies, E. S. Koteles, “Monolithic integrated wavelength demultiplexer based on a waveguide Rowland circle grating in InGaAsP∕InP,” J. Lightwave Technol. 16, 631–638 (1998).
[CrossRef]

Laframboise, S.

Lamontagne, B.

J.-J. He, E. S. Koteles, B. Lamontagne, L. Erickson, A. Delage, M. Davies, “Integrated polarization compensator for WDM waveguide demultiplexers,” IEEE Photonics Technol. Lett. 11, 224–226 (1999).
[CrossRef]

J.-J. He, B. Lamontagne, A. Delage, L. Erickson, M. Davies, E. S. Koteles, “Monolithic integrated wavelength demultiplexer based on a waveguide Rowland circle grating in InGaAsP∕InP,” J. Lightwave Technol. 16, 631–638 (1998).
[CrossRef]

Logvin, Y.

McGreer, K. A.

Muller-Nawrath, R.

C. Cremer, G. Ebbinghaus, G. Heise, R. Muller-Nawrath, M. Schienle, 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, 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, S. He, “A planar waveguide demultiplexer with a flat passband, sharp transitions and a low chromatic dispersion,” Opt. Commun. 227, 89–97 (2003).
[CrossRef]

Pimonov, K.

Sadov, S. Y.

Schienle, M.

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

Schier, M.

C. Cremer, N. Emeis, M. Schier, G. Heise, G. Ebbinghaus, L. Stoll, “Grating spectrograph integrated with photodiode array in InGaAsP∕InGaAs∕InP,” IEEE Photonics Technol. Lett. 4, 108–110 (1992).
[CrossRef]

Shi, Z.

Shi, Z. M.

Z. M. Shi, J.-J. He, S. He, “An analytic method for designing passband flattened DWDM demultiplexers using spatial phase modulation,” J. Lightwave Technol. 21, 2314–2321 (2003).
[CrossRef]

Z. M. Shi, S. He, “A three-focal-point method for the optimal design of a flat-top planar waveguide demultiplexer,” IEEE J. Sel. Top. Quantum Electron. 8, 1179–1185 (2002).
[CrossRef]

Smit, M. K.

M. K. Smit, 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, D. Q. Pang, S. He, “A MoM-based design and simulation method for an etched diffraction grating demultiplexer,” Opt. Commun. 233, 363–371 (2004).
[CrossRef]

J. Song, 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, 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, N. Emeis, M. Schier, G. Heise, G. Ebbinghaus, L. Stoll, “Grating spectrograph integrated with photodiode array in InGaAsP∕InGaAs∕InP,” IEEE Photonics Technol. Lett. 4, 108–110 (1992).
[CrossRef]

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

Teng, T. H.

T. H. Teng, L. Carin, “FDTD analysis of plane-wave diffraction from microwave devices on an infinite dielectric slab,” IEEE Microw. Guid. Wave Lett. 6, 16–18 (1996).
[CrossRef]

Tolstikhin, V. I.

Van Dam, C.

M. K. Smit, C. Van Dam, “PHASAR-based WDM-devices: principles, design and applications,” IEEE J. Sel. Top. Quantum Electron. 2, 236–250 (1996).
[CrossRef]

Wu, F.

Appl. Opt. (1)

Appl. Phys. Lett. (1)

C. Cremer, G. Ebbinghaus, G. Heise, R. Muller-Nawrath, M. Schienle, 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)

M. K. Smit, C. Van Dam, “PHASAR-based WDM-devices: principles, design and applications,” IEEE J. Sel. Top. Quantum Electron. 2, 236–250 (1996).
[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]

Z. M. Shi, S. He, “A three-focal-point method for the optimal design of a flat-top planar waveguide demultiplexer,” IEEE J. Sel. Top. Quantum Electron. 8, 1179–1185 (2002).
[CrossRef]

IEEE Microw. Guid. Wave Lett. (1)

T. H. Teng, L. Carin, “FDTD analysis of plane-wave diffraction from microwave devices on an infinite dielectric slab,” IEEE Microw. Guid. Wave Lett. 6, 16–18 (1996).
[CrossRef]

IEEE Photonics Technol. Lett. (2)

C. Cremer, N. Emeis, M. Schier, G. Heise, G. Ebbinghaus, L. Stoll, “Grating spectrograph integrated with photodiode array in InGaAsP∕InGaAs∕InP,” IEEE Photonics Technol. Lett. 4, 108–110 (1992).
[CrossRef]

J.-J. He, E. S. Koteles, B. Lamontagne, L. Erickson, A. Delage, M. Davies, “Integrated polarization compensator for WDM waveguide demultiplexers,” IEEE Photonics Technol. Lett. 11, 224–226 (1999).
[CrossRef]

J. Lightwave Technol. (3)

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

J. Song, 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 (2)

Opt. Commun. (2)

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

Other (1)

R. F. Harrington, ed., Field Computation by Moment Methods (IEEE Press, 1993).
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

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

Fig. 2
Fig. 2

Schematic diagram of a point defect in the FPR.

Fig. 3
Fig. 3

Loss as the wavelength increases.

Fig. 4
Fig. 4

Field distribution near the air bubble at the wavelengths of (a) 1.24 μ m and (b) 1.55 μ m .

Fig. 5
Fig. 5

Loss at different positions for different radii of an air bubble.

Fig. 6
Fig. 6

Loss at different positions for different radii of a dust grain.

Equations (10)

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

E 0 ( x , z ) = 1 2 ( n eff λ ) 1 2 input E in ( x , z ) P in P ( 1 + cos θ d ) exp ( j k P in P ) d l ,
2 E 0 ( x , z ) k 0 2 ϵ w ( x , z ) E 0 ( x , z ) = 0 ,
2 E ( x , z ) k 0 2 ϵ w ( x , z ) E ( x , z ) = k 0 2 Δ ϵ ( x , z ) E ( x , z ) .
2 G ( r , r p ) k 0 2 ϵ w ( r , r p ) G ( r , r p ) = δ ( r r p ) ,
E ( r ) = E 0 ( r ) L Δ ϵ ( r ) ϵ w ( r ) E ( r ) + lim δ V 0 V δ V G ( r , r p ) k 0 2 Δ ϵ ( r p ) E ( r p ) d r p ,
E i = E i 0 + q = 1 , q i N G i , q k 0 2 Δ ϵ q E q V q + M i k 0 2 Δ ϵ i E i ,
M i = k 0 2 [ π Δ x i Δ z i 2 k H 1 ( 1 ) ( k Δ x i Δ z i π ) + ( i k ) 2 ] ,
G ( r i , r q ) = i 4 k 0 2 H 0 ( 1 ) ( k ( x i x q ) 2 + ( z i z q ) 2 ) ,
[ 1 M i 1 Δ ϵ i 1 G i 1 , i Δ ϵ i G i 1 , i + 1 Δ ϵ i + 1 G i , i 1 Δ ϵ i 1 1 M i Δ ϵ i G i , i + 1 Δ ϵ i + 1 G i + 1 , i 1 Δ ϵ i 1 G i + 1 , i Δ ϵ i 1 M i + 1 Δ ϵ i + 1 ] N 1 × N 1 ( E i 1 E i E i + 1 ) N 1 = ( E i 1 0 E i 0 E i + 1 0 ) ,
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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