Abstract

We present an extension of the AWG model and design procedure described in [1] to incorporate multimode interference, MMI, couplers. For the first time to our knowledge, a closed formula for the passing bands bandwidth and crosstalk estimation plots are derived.

© 2001 Optical Society of America

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References

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  1. P. Muñoz, D. Pastor, and J. Capmany, “Modeling and designing arrayed waveguide gratings,” J. Light. Tech. (Submitted)
  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/oearchive/source/19103.htm
    [Crossref] [PubMed]
  3. K. Okamoto and A. Sugita, “Flat spectral response arrayed-waveguide grating multiplexer with parabolic waveguide horns,” Electron. Lett. 32, 1661–1662 (1996).
    [Crossref]
  4. C. Dragone, “Efficient techniques for widening the passband of a wavelength router,” J. Light. Tech. 16, 1895–1906 (1998).
    [Crossref]
  5. M.K. Smit and C. van Dam, “PHASAR-based WDM-devices: Principles, design and applications,” J. Sel. Top. Quant. Electron. 2, 236–250 (1996).
    [Crossref]
  6. J. Soole e.a., “Use of multimode interference couplers to broaden the passband of wavelength-dispersive integrated WDM filters,” IEEE Photon. Technol. Lett. 8, 1340–1342 (1996).
    [Crossref]
  7. H. Takahashi e.a., “Transmission characterisitics of arrayed waveguide N×N wavelength multiplexer,” J. Light. Tech. 13, 447–455 (1995).
    [Crossref]
  8. F. Pizzato, G. Perrone, and I. Montroset, “Arrayed waveguide grating demultiplexers: a new efficient numerical analysis approach,” in Silicon-based Optoelectronics, D.C. Houghton and E. A. Fitzgerald, eds., Proc. SPIE3630, 198–206, 1999.
  9. C. Dragone e.a., “Efficient N×N star couplers using Fourier optics,” J. Light. Technol. 7, 479–489 (1989).
    [Crossref]
  10. C. Dragone e.a., “Efficient multichannel integrated optics star coupler on silicon,” IEEE Photon. Technol. Lett. 1, 241–243 (1989).
    [Crossref]
  11. C. Dragone, C. Edwards, and R. Kistler, “Integrated optics N×N multiplexer on silicon,” IEEE Photon. Technol. Lett. 3, 896–898 (1991).
    [Crossref]
  12. G.P. Agrawal,Fiber-Optic Communications Systems, (John Wiley and Sons, New York, 1997).
  13. A.W. Snyder and J.D. Love,Optical Waveguide Theory, (Chapman& Hall, New York, 1983).
  14. L.B. Soldano and E.C. Pennings, “Optical multi-mode interference devices based on self-imaging: Principles and applications,” J. Light. Technol. 13, 615–627 (1995).
    [Crossref]

2000 (1)

1998 (1)

C. Dragone, “Efficient techniques for widening the passband of a wavelength router,” J. Light. Tech. 16, 1895–1906 (1998).
[Crossref]

1996 (3)

M.K. Smit and C. van Dam, “PHASAR-based WDM-devices: Principles, design and applications,” J. Sel. Top. Quant. Electron. 2, 236–250 (1996).
[Crossref]

J. Soole e.a., “Use of multimode interference couplers to broaden the passband of wavelength-dispersive integrated WDM filters,” IEEE Photon. Technol. 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]

1995 (2)

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

H. Takahashi e.a., “Transmission characterisitics of arrayed waveguide N×N wavelength multiplexer,” J. Light. Tech. 13, 447–455 (1995).
[Crossref]

1991 (1)

C. Dragone, C. Edwards, and R. Kistler, “Integrated optics N×N multiplexer on silicon,” IEEE Photon. Technol. Lett. 3, 896–898 (1991).
[Crossref]

1989 (2)

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

C. Dragone e.a., “Efficient multichannel integrated optics star coupler on silicon,” IEEE Photon. Technol. Lett. 1, 241–243 (1989).
[Crossref]

Agrawal, G.P.

G.P. Agrawal,Fiber-Optic Communications Systems, (John Wiley and Sons, New York, 1997).

Capmany, J.

P. Muñoz, D. Pastor, and J. Capmany, “Modeling and designing arrayed waveguide gratings,” J. Light. Tech. (Submitted)

Dragone, C.

C. Dragone, “Efficient techniques for widening the passband of a wavelength router,” J. Light. Tech. 16, 1895–1906 (1998).
[Crossref]

C. Dragone, C. Edwards, and R. Kistler, “Integrated optics N×N multiplexer on silicon,” IEEE Photon. Technol. Lett. 3, 896–898 (1991).
[Crossref]

Dragone e.a., C.

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

C. Dragone e.a., “Efficient multichannel integrated optics star coupler on silicon,” IEEE Photon. Technol. Lett. 1, 241–243 (1989).
[Crossref]

Edwards, C.

C. Dragone, C. Edwards, and R. Kistler, “Integrated optics N×N multiplexer on silicon,” IEEE Photon. Technol. Lett. 3, 896–898 (1991).
[Crossref]

Kistler, R.

C. Dragone, C. Edwards, and R. Kistler, “Integrated optics N×N multiplexer on silicon,” IEEE Photon. Technol. Lett. 3, 896–898 (1991).
[Crossref]

Kurokawa, T.

Love, J.D.

A.W. Snyder and J.D. Love,Optical Waveguide Theory, (Chapman& Hall, New York, 1983).

Montroset, I.

F. Pizzato, G. Perrone, and I. Montroset, “Arrayed waveguide grating demultiplexers: a new efficient numerical analysis approach,” in Silicon-based Optoelectronics, D.C. Houghton and E. A. Fitzgerald, eds., Proc. SPIE3630, 198–206, 1999.

Muñoz, P.

P. Muñoz, D. Pastor, and J. Capmany, “Modeling and designing arrayed waveguide gratings,” J. Light. Tech. (Submitted)

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.

P. Muñoz, D. Pastor, and J. Capmany, “Modeling and designing arrayed waveguide gratings,” J. Light. Tech. (Submitted)

Pennings, E.C.

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

Perrone, G.

F. Pizzato, G. Perrone, and I. Montroset, “Arrayed waveguide grating demultiplexers: a new efficient numerical analysis approach,” in Silicon-based Optoelectronics, D.C. Houghton and E. A. Fitzgerald, eds., Proc. SPIE3630, 198–206, 1999.

Pizzato, F.

F. Pizzato, G. Perrone, and I. Montroset, “Arrayed waveguide grating demultiplexers: a new efficient numerical analysis approach,” in Silicon-based Optoelectronics, D.C. Houghton and E. A. Fitzgerald, eds., Proc. SPIE3630, 198–206, 1999.

Smit, M.K.

M.K. Smit and C. van Dam, “PHASAR-based WDM-devices: Principles, design and applications,” J. Sel. Top. Quant. Electron. 2, 236–250 (1996).
[Crossref]

Snyder, A.W.

A.W. Snyder and J.D. Love,Optical Waveguide Theory, (Chapman& Hall, New York, 1983).

Soldano, L.B.

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

Soole e.a., J.

J. Soole e.a., “Use of multimode interference couplers to broaden the passband of wavelength-dispersive integrated WDM filters,” IEEE Photon. Technol. 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]

Takahashi e.a., H.

H. Takahashi e.a., “Transmission characterisitics of arrayed waveguide N×N wavelength multiplexer,” J. Light. Tech. 13, 447–455 (1995).
[Crossref]

Takenouchi, H.

Tsuda, H.

van Dam, C.

M.K. Smit and C. van Dam, “PHASAR-based WDM-devices: Principles, design and applications,” J. Sel. Top. Quant. Electron. 2, 236–250 (1996).
[Crossref]

Electron. Lett. (1)

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

IEEE Photon. Technol. Lett. (3)

C. Dragone e.a., “Efficient multichannel integrated optics star coupler on silicon,” IEEE Photon. Technol. Lett. 1, 241–243 (1989).
[Crossref]

C. Dragone, C. Edwards, and R. Kistler, “Integrated optics N×N multiplexer on silicon,” IEEE Photon. Technol. Lett. 3, 896–898 (1991).
[Crossref]

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

J. Light. Tech. (2)

H. Takahashi e.a., “Transmission characterisitics of arrayed waveguide N×N wavelength multiplexer,” J. Light. Tech. 13, 447–455 (1995).
[Crossref]

C. Dragone, “Efficient techniques for widening the passband of a wavelength router,” J. Light. Tech. 16, 1895–1906 (1998).
[Crossref]

J. Light. Technol. (2)

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

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

J. Sel. Top. Quant. Electron. (1)

M.K. Smit and C. van Dam, “PHASAR-based WDM-devices: Principles, design and applications,” J. Sel. Top. Quant. Electron. 2, 236–250 (1996).
[Crossref]

Opt. Express (1)

Other (4)

P. Muñoz, D. Pastor, and J. Capmany, “Modeling and designing arrayed waveguide gratings,” J. Light. Tech. (Submitted)

G.P. Agrawal,Fiber-Optic Communications Systems, (John Wiley and Sons, New York, 1997).

A.W. Snyder and J.D. Love,Optical Waveguide Theory, (Chapman& Hall, New York, 1983).

F. Pizzato, G. Perrone, and I. Montroset, “Arrayed waveguide grating demultiplexers: a new efficient numerical analysis approach,” in Silicon-based Optoelectronics, D.C. Houghton and E. A. Fitzgerald, eds., Proc. SPIE3630, 198–206, 1999.

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Figures (7)

Fig. 1.
Fig. 1.

AWG physical layout. Insets, waveguide parameters (left) and FPR coupler layout (right)

Fig. 2.
Fig. 2.

MMI coupler layout

Fig. 3.
Fig. 3.

Cross talk level @ Δνc with MMI at the IW’s

Fig. 4.
Fig. 4.

Cross talk level @ Δνc with MMI at the IW’s

Fig. 5.
Fig. 5.

MMI-based 1×16 frequency cyclic AWG module response versus detunning from the design frequency

Fig. 6.
Fig. 6.

MMI-based AWG module (blue) and delay (green) response versus detunning from the design frequency

Fig. 7.
Fig. 7.

MMI-based (red) and ordinary (blue) AWG module responses

Tables (1)

Tables Icon

Table 1. High Level Requirements for the designed AWG’s

Equations (35)

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β i ( x 0 ) = 2 π ω i 2 4 e ( x 0 ω i ) 2
B i ( x 1 ) = 2 π ω i 2 α 2 4 e ( π ω i x 1 α ) 2
α = c L f n s ν 0
β g ( x 1 ) = 2 π ω g 2 4 e ( x 1 ω g ) 2
f 1 ( x 1 ) = [ Π ( x 1 N d w ) B i ( x 1 ) δ ω ( x 1 ) ] 2 π ω g 2 4 β g ( x 1 )
Π ( x 1 N d ω ) = { 1 x 1 N d ω 2 0 otherwise
δ w ( x 1 ) = r = + δ ( x 1 r d w )
Δ l = m λ 0 n c = m c n c ν 0
f 2 ( x 2 , ν ) = [ B i ( x 2 ) Π ( x 2 N d w ) δ w ( x 2 ) ϕ ( x 2 , ν ) ] 2 π ω g 2 4 β g ( x 2 )
ϕ ( x 2 , ν ) = ψ ( ν ) e j 2 π m ν ν 0 x 2 d w
ψ ( ν ) = e i 2 π ν ( n c l 0 c + m N ν 0 2 )
f 3 ( x 3 , ν ) = 2 π ω g 2 α 2 4 B g ( x 3 ) ψ ( ν ) r = f M ( x 3 r α d w + ν γ )
γ = d ω ν 0 α m
B g ( x 3 ) = F { β g ( x 2 ) } u = x 3 α = 2 π ω g 2 4 e ( π ω g x 3 α ) 2
f M ( x 3 ) = ( α 2 8 π ω i 2 ) 1 4 e ( x 3 ω i ) 2 [ er f ( π ω i N d w 2 α + i x 3 α ) + er f ( π ω i N d w 2 α i x 3 α ) ]
Δ x 3 , FSR = α d w
Δ ν FSR = ν m
f 3 ( x 3 , ν ) = 2 π ω g 2 α 2 4 B g ( x 3 ) ψ ( ν ) r = f M ( x 3 Δ x 3 , FSR [ r ν Δ ν FSR , 0 ] )
t 0 , q ( ν ) = + f 3 ( x 3 , ν ) β o ( x 3 q d o ) x 3
L m = 3 π 8 ( ζ 0 ζ 1 )
β i ( x 0 ) = [ 2 ω i π 2 ( 1 + e Δ x m 2 2 ω i 2 ) ] 1 2 [ e ( x 0 1 2 Δ x m ω i ) 2 + e ( x 0 + 1 2 Δ x m ω i ) 2 ]
B i ( x 1 ) = [ 2 α 2 π ω i ( 1 + e Δ x m 2 2 ω i 2 ) ] 1 4 [ e i π Δ x m x 1 α + e i π Δ x m x 1 α ] e ( π ω i x 1 α ) 2
f 3 ( x 3 , ν ) = π ω g 2 2 α 2 ( 1 + e Δ x m 2 2 ω i 2 ) 4 B g ( x 3 ) ψ ( ν ) r = [ f M ( x 3 r α d w + ν γ + Δ x m 2 ) ]
+ f M ( x 3 r α d w + ν γ Δ x m 2 ) ]
t 0,0 ( Δ ν ) + β i ( x 3 Δ ν γ ) β o ( x 3 ) x 3
t 0,0 , n ( Δ ν ) = t 0,0 ( Δ ν ) t 0,0 ( 0 ) = e 1 2 ( Δ ν ω o γ ) 2 cosh ( Δ x m Δ ν 2 ω o 2 γ )
Δ x m = 2 ω i
t 0,0 , n ( x ) = e 1 2 x 2 cosh ( x ) = 10 3 20
Δ ν b ω = 2 γ ω o 1.6173
Δ ν b ω = 2 γ ω o 0.8311
t 0,1 ( σ , σ o ) = + β i ( u n ) β o ( u n ) u n
σ = α π N d w ω o
σ o = d o ω o
B i ( x 1 n ) = e ( x 1 n σ ) 2 ( e i 2 x 1 n σ + e i 2 x 1 n σ )
β o ( u n ) = e ( π σ u n σ o ) 2

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