Abstract

Configuration of a novel compact dispersive and focusing device based on a Curved Waveguide Grating (CWG) is presented, which is essentially an integrated optic wavelength demultiplexer consisting of a curved stripe waveguide with tilted grating, a slab waveguide adjacent to it, and a set of output waveguides locate on focal line of the curved waveguide. Underlying wavelength demultiplexing mechanism of CWG is theoretically illustrated by employing the Fourier optics approach. Analysis shows that device based on CWG possesses fine wavelength resolution, compact configuration, and potentially low cost as well, which make it a promising wavelength demultiplexer, or a network performance monitor, in DWDM optical networks.

©2006 Optical Society of America

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References

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  1. M. K. Smit and C. van Dam, “PHASAR-based WDM-devices: Principles, design and application,” IEEE J. Sel. Top Quantum. Electron. 2, 236–250 (1996).
    [Crossref]
  2. E. Gini, W. Hunziker, and H. Melchior, “Polarization independent InP WDM multiplexer/demultiplexer module,” IEEE J. Lightwave Technol. 16, 625–630 (1998).
    [Crossref]
  3. C. K. Madsen, J. Wagener, T. A. Strasser, D. Muehlner, M. A. Milbrodt, E. J. Laskowski, and J. DeMarco, “Planar waveguide optical spectrum analyzer using a UV-induced grating,” IEEE J. Sel. Top Quantum. Electron. 4, 925–929 (1998).
    [Crossref]
  4. A. Yariv and M. Nakamura, “Periodic structures for integrated optics,” IEEE J. Quantum. Electron. 13, 233–252 (1977).
    [Crossref]
  5. H. Takenouchi, H. Tsuda, and T. Kurokawa, “Analysis of optical signal processing using an arrayed waveguide grating,” Opt. Express 6, 124–135 (2000).
    [Crossref] [PubMed]
  6. P. Munoz, D. Pastor, and J. Capmany, “Analysis and design of arrayed waveguide gratings with MMI coupler,” Opt. Express 9, 328–338 (2001).
    [Crossref] [PubMed]
  7. P. Munoz, D. Pastor, and J. Capmany, “Modeling and design of arrayed waveguide gratings,” IEEE J. Lightwave. Technol. 20, 661–674 (2002).
    [Crossref]

2002 (1)

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

2001 (1)

2000 (1)

1998 (2)

E. Gini, W. Hunziker, and H. Melchior, “Polarization independent InP WDM multiplexer/demultiplexer module,” IEEE J. Lightwave Technol. 16, 625–630 (1998).
[Crossref]

C. K. Madsen, J. Wagener, T. A. Strasser, D. Muehlner, M. A. Milbrodt, E. J. Laskowski, and J. DeMarco, “Planar waveguide optical spectrum analyzer using a UV-induced grating,” IEEE J. Sel. Top Quantum. Electron. 4, 925–929 (1998).
[Crossref]

1996 (1)

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

1977 (1)

A. Yariv and M. Nakamura, “Periodic structures for integrated optics,” IEEE J. Quantum. Electron. 13, 233–252 (1977).
[Crossref]

Capmany, J.

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

P. Munoz, D. Pastor, and J. Capmany, “Analysis and design of arrayed waveguide gratings with MMI coupler,” Opt. Express 9, 328–338 (2001).
[Crossref] [PubMed]

DeMarco, J.

C. K. Madsen, J. Wagener, T. A. Strasser, D. Muehlner, M. A. Milbrodt, E. J. Laskowski, and J. DeMarco, “Planar waveguide optical spectrum analyzer using a UV-induced grating,” IEEE J. Sel. Top Quantum. Electron. 4, 925–929 (1998).
[Crossref]

Gini, E.

E. Gini, W. Hunziker, and H. Melchior, “Polarization independent InP WDM multiplexer/demultiplexer module,” IEEE J. Lightwave Technol. 16, 625–630 (1998).
[Crossref]

Hunziker, W.

E. Gini, W. Hunziker, and H. Melchior, “Polarization independent InP WDM multiplexer/demultiplexer module,” IEEE J. Lightwave Technol. 16, 625–630 (1998).
[Crossref]

Kurokawa, T.

Laskowski, E. J.

C. K. Madsen, J. Wagener, T. A. Strasser, D. Muehlner, M. A. Milbrodt, E. J. Laskowski, and J. DeMarco, “Planar waveguide optical spectrum analyzer using a UV-induced grating,” IEEE J. Sel. Top Quantum. Electron. 4, 925–929 (1998).
[Crossref]

Madsen, C. K.

C. K. Madsen, J. Wagener, T. A. Strasser, D. Muehlner, M. A. Milbrodt, E. J. Laskowski, and J. DeMarco, “Planar waveguide optical spectrum analyzer using a UV-induced grating,” IEEE J. Sel. Top Quantum. Electron. 4, 925–929 (1998).
[Crossref]

Melchior, H.

E. Gini, W. Hunziker, and H. Melchior, “Polarization independent InP WDM multiplexer/demultiplexer module,” IEEE J. Lightwave Technol. 16, 625–630 (1998).
[Crossref]

Milbrodt, M. A.

C. K. Madsen, J. Wagener, T. A. Strasser, D. Muehlner, M. A. Milbrodt, E. J. Laskowski, and J. DeMarco, “Planar waveguide optical spectrum analyzer using a UV-induced grating,” IEEE J. Sel. Top Quantum. Electron. 4, 925–929 (1998).
[Crossref]

Muehlner, D.

C. K. Madsen, J. Wagener, T. A. Strasser, D. Muehlner, M. A. Milbrodt, E. J. Laskowski, and J. DeMarco, “Planar waveguide optical spectrum analyzer using a UV-induced grating,” IEEE J. Sel. Top Quantum. Electron. 4, 925–929 (1998).
[Crossref]

Munoz, P.

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

P. Munoz, D. Pastor, and J. Capmany, “Analysis and design of arrayed waveguide gratings with MMI coupler,” Opt. Express 9, 328–338 (2001).
[Crossref] [PubMed]

Nakamura, M.

A. Yariv and M. Nakamura, “Periodic structures for integrated optics,” IEEE J. Quantum. Electron. 13, 233–252 (1977).
[Crossref]

Pastor, D.

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

P. Munoz, D. Pastor, and J. Capmany, “Analysis and design of arrayed waveguide gratings with MMI coupler,” Opt. Express 9, 328–338 (2001).
[Crossref] [PubMed]

Smit, M. K.

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

Strasser, T. A.

C. K. Madsen, J. Wagener, T. A. Strasser, D. Muehlner, M. A. Milbrodt, E. J. Laskowski, and J. DeMarco, “Planar waveguide optical spectrum analyzer using a UV-induced grating,” IEEE J. Sel. Top Quantum. Electron. 4, 925–929 (1998).
[Crossref]

Takenouchi, H.

Tsuda, H.

van Dam, C.

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

Wagener, J.

C. K. Madsen, J. Wagener, T. A. Strasser, D. Muehlner, M. A. Milbrodt, E. J. Laskowski, and J. DeMarco, “Planar waveguide optical spectrum analyzer using a UV-induced grating,” IEEE J. Sel. Top Quantum. Electron. 4, 925–929 (1998).
[Crossref]

Yariv, A.

A. Yariv and M. Nakamura, “Periodic structures for integrated optics,” IEEE J. Quantum. Electron. 13, 233–252 (1977).
[Crossref]

IEEE J. Lightwave Technol. (1)

E. Gini, W. Hunziker, and H. Melchior, “Polarization independent InP WDM multiplexer/demultiplexer module,” IEEE J. Lightwave Technol. 16, 625–630 (1998).
[Crossref]

IEEE J. Lightwave. Technol. (1)

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

IEEE J. Quantum. Electron. (1)

A. Yariv and M. Nakamura, “Periodic structures for integrated optics,” IEEE J. Quantum. Electron. 13, 233–252 (1977).
[Crossref]

IEEE J. Sel. Top Quantum. Electron. (2)

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

C. K. Madsen, J. Wagener, T. A. Strasser, D. Muehlner, M. A. Milbrodt, E. J. Laskowski, and J. DeMarco, “Planar waveguide optical spectrum analyzer using a UV-induced grating,” IEEE J. Sel. Top Quantum. Electron. 4, 925–929 (1998).
[Crossref]

Opt. Express (2)

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Figures (6)

Fig. 1.
Fig. 1. Schematic of the CWG.

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Fig. 2.
Fig. 2. Bragg diffraction for a local section of the CWG.

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Fig. 3.
Fig. 3. Schematic of amplitude factor of diffraction field.

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Fig. 4.
Fig. 4. Amplitude (left) and phase (right) factor of E1(x1).

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Fig. 5.
Fig. 5. Relationship between diffracted light field and grating structure.

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Fig. 6.
Fig. 6. Diffraction-limited and calculated focused spot size for Rowland circle configuration for grating length 10mm and 20mm.

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Equations (31)

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2 n eff π λ − 2 n c π λ cos θ = m 2 π Λ .
Λ = m λ 0 n eff = mc n eff ν 0 ,
E ( x 0 , y ) = U g ( x 0 ) f 0 ( y ) e − i β ( x 0 + N Λ ) .
β = 2 π n eff λ = 2 π n eff c ν .
f 0 ( y ) = ( 2 π ω 0 2 ) 1 ⁄ 4 e − ( y ω 0 ) 2 .
U g ( x 0 ) = U g ( − N Λ ) e − C ( x 0 + N Λ ) ,
P g ( x 0 ) = 1 2 ( ε μ 0 ) 1 ⁄ 2 U g 2 ( x 0 ) .
P g ( x 0 ) = 1 2 ( ε μ 0 ) 1 ⁄ 2 U g 2 ( − N Λ ) e − 2 C ( x 0 + N Λ ) .
P d ( x 0 ) = − d P g ( x 0 ) = − d P g ( x 0 ) d x 0 d x 0 .
P d ′ ( x 0 ) = − d P g ( x 0 ) d x 0 Λ .
P d ′ ( x 0 ) = 1 2 2 C Λ ( ε μ 0 ) 1 ⁄ 2 U 2 ( − N Λ ) e − 2 C ( x 0 + N Λ ) .
U d ( x 0 ) = ( 2 C Λ ) 1 ⁄ 2 U ( − N Λ ) e − C ( x 0 + N Λ ) ( − N Λ ≤ x 0 ≤ N Λ ) ,
φ ( x 0 , ν ) = ϕ ( ν ) e − i 2 π n eff ν c x 0 ,
ϕ ( ν ) = e − i ( 2 π n eff ν c N Λ + κ ) .
E d ( x 0 , ν ) = [ U d ( x 0 ) φ ( x 0 , ν ) δ Λ ( x 0 ) ] * g ( x 0 ) .
δ Λ ( x 0 ) = ∑ r = − ∞ + ∞ δ ( x 0 − r Λ ) .
f 1 ( x 1 , ν ) = [ E 1 ( x 1 ) * Φ ( x 1 , ν ) * Δ Λ ( x 1 ) ] G ( x 1 ) ,
E 1 ( x 1 ) = FT [ U d ( x 0 ) ] ∣ u = x 1 ⁄ α ,
E 1 ( x 1 ) = ( 2 C Λ ) 1 ⁄ 2 U ( − N Λ ) [ C 2 + ( 2 π x 1 ⁄ α ) 2 ] 1 ⁄ 2 e − i tan − 1 ( 2 π x 1 C α ) ( e CN Λ e i ( 2 π x 1 N Λ α ) − e − CN Λ e − i ( 2 π x 1 N Λ α ) ) ,
Φ ( x 1 , ν ) = FT [ φ ( x 0 , ν ) ] ∣ u = x 1 ⁄ α = c L f n s ν 0 ϕ ( ν ) δ ( x 1 + n eff L f n s ν 0 ν ) .
Δ Λ ( x 1 ) = FT [ δ Λ ( x 0 ) ] ∣ u = x 1 ⁄ α = ∑ r = − ∞ + ∞ δ ( x 1 − r n eff L f n s m ) .
G ( x 1 ) = FT [ g ( x 0 ) ] ∣ u = x 1 ⁄ α .
α ν = c L f n s ν = λ L f n s ,
α ν = α ν 0 = α .
f 1 ( x 1 , ν ) = G ( x 1 ) ∑ r = − ∞ + ∞ E 1 ( x 1 − r n eff L f n c m + ν γ ) .
γ = n s ν 0 n eff L f .
Δ x 1 , FSR = n eff L f n c m .
g ( x 0 ) = W L W T rect ( x 0 W T ) f ( x 0 ) .
rect ( x 0 W T ) = { 1 for ∣ x 0 ∣ ≤ W T 2 0 others .
g ( x 0 ) = ( 2 π ω g 2 ) 1 ⁄ 4 e − ( x 0 ω g ) 2 .
G ( x 1 ) = ( 2 π ω g 2 ) 1 ⁄ 4 e − ( π ω g x 1 α ) 2 .

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