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.

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References

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  1. P. Munoz, 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 6, 124-135 (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 x 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, Houghton, D.C., Fitzgerald, E. A., eds., Proc. SPIE 3630, 198-206, 1999.
  9. C. Dragone e.a., "Efficient N x 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 x 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]

Other (14)

P. Munoz, D. Pastor and J. Capmany, "Modeling and designing arrayed waveguide gratings," J. Light. Tech. (Submitted).

H. Takenouchi, H. Tsuda and T. Kurokawa, "Analysis of optical-signal processing using an arrayed-waveguide grating," Opt. Express 6, 124-135 (2000), http://www.opticsexpress.org/oearchive/source/19103.htm
[CrossRef] [PubMed]

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

C. Dragone, "Efficient techniques for widening the passband of a wavelength router," J. Light. Tech. 16, 1895-1906 (1998).
[CrossRef]

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]

H. Takahashi e.a., "Transmission characterisitics of arrayed waveguide N x N wavelength multiplexer," J. Light. Tech. 13, 447-455 (1995).
[CrossRef]

F. Pizzato, G. Perrone and I. Montroset, "Arrayed waveguide grating demultiplexers: a new efficient numerical analysis approach," in Silicon-based Optoelectronics, Houghton, D.C., Fitzgerald, E. A., eds., Proc. SPIE 3630, 198-206, 1999.

C. Dragone e.a., "Efficient N x 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]

C. Dragone, C. Edwards and R. Kistler, "Integrated optics N x N multiplexer on silicon," IEEE Photon. Technol. Lett. 3, 896-898 (1991).
[CrossRef]

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).

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]

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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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