Abstract

A parabolic tapered structure based on general interference has been proposed and studied theoretically with silica waveguides of silicon oxinitride (SiON) core by using a mathematical model based on sinusoidal modes for the reduction of coupling length of a 2×2 multimode interference (MMI) coupler. The coupling behaviors of the proposed structure are compared with those of other MMI structures. It is seen that the beat length for the proposed tapered MMI coupler is approximately half of that of a conventional MMI coupler. The effect of power imbalance on the fabrication tolerance of a 3dB coupler using the proposed tapered structure is also studied and compared with that of other MMI structures.

© 2009 Optical Society of America

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    [CrossRef]
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    [CrossRef]
  4. A. K. Das and P. P. Sahu, “Compact integrated optical devices using high index contrast waveguides,” in Proceedings of the IEEE Wireless and Optical Communication Network Conference (IEEE, 2006), paper 01666673.
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  9. P. P. Sahu, “Compact multimode interference coupler with tapered waveguide geometry,” Opt. Commun. 277, 295-301(2007).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  14. H. C. Lu and W. S. Wang, “Analysis of multimode interference coupler with a width of arbitrary exponent binomial function,” J. Lightwave Technol. 25, 2874-2878 (2007).
    [CrossRef]
  15. H. Nishihara, M. Haruna, and T. Suhara, Optical Integrated Circuits (McGraw-Hill, 1989).

2008

P. P. Sahu, “Silicon oxinitride: a material for compact waveguide device,” Indian J. Phys. 82, 265-272 (2008).

2007

2005

2000

Y. Ma, S. Park, L. Wang, and S. T. Ho, “Ultra compact multimode interference 3 dB coupler with strong lateral confinement by deep dry etching,” IEEE Photonics Technol. Lett. 12, 492-494 (2000).
[CrossRef]

1999

M. Rajarajan, B. M. A. Rahman, and K. T. V. Grattan, “A rigorous comparison of the performance of directional coupler with multimode interference devices,” J. Lightwave Technol. 17, 243-248 (1999).
[CrossRef]

D. S. Levy, K. H. Park, R. Scarmozzino, and R. M. Osgood, “Fabrication of ultracompact 3 dB2×2 MMI power splitters,” IEEE Photonics Technol. Lett. 11, 1009-1011 (1999).
[CrossRef]

1998

12. David S. Levy, Robert Scarmozzino, York M. Li, and R. M. Osgood, “A new design of ultracompact multimode interference-based 2×2 couplers,” IEEE Photonics Technol. Lett. 10, 96-98 (1998).
[CrossRef]

1997

M. R. Paiam and R. I. MacDonald, “Polarization insensitive 980/1550 nm wavelength demultiplexer using MMI couplers,” Electron. Lett. 33, 1219-1220 (1997).
[CrossRef]

1996

P. A. Besse, E. Gini, M. Bachmann, and H. Melchion, “New 2×2 and 1×3 multimode interference couplers with free selection of power splitting ratios,” J. Lightwave Technol. 14, 2286-2293 (1996).
[CrossRef]

1995

L. B. Soldano and E. C. M. Pennings, “Optical multimode interference devices on self imaging: principle and applications,” J. Lightwave Technol. 13, 615-627 (1995).
[CrossRef]

1994

Bachmann, M.

P. A. Besse, E. Gini, M. Bachmann, and H. Melchion, “New 2×2 and 1×3 multimode interference couplers with free selection of power splitting ratios,” J. Lightwave Technol. 14, 2286-2293 (1996).
[CrossRef]

M. Bachmann, P. A. Besse, and H. Melchior, “General self imaging properties in N×N multimode interference couplers including phase relations,” Appl. Opt. 33, 3905-3911 (1994).
[CrossRef] [PubMed]

Besse, P. A.

P. A. Besse, E. Gini, M. Bachmann, and H. Melchion, “New 2×2 and 1×3 multimode interference couplers with free selection of power splitting ratios,” J. Lightwave Technol. 14, 2286-2293 (1996).
[CrossRef]

M. Bachmann, P. A. Besse, and H. Melchior, “General self imaging properties in N×N multimode interference couplers including phase relations,” Appl. Opt. 33, 3905-3911 (1994).
[CrossRef] [PubMed]

Chin, M. K.

Darmawan, S.

Das, A. K.

A. K. Das and P. P. Sahu, “Compact integrated optical devices using high index contrast waveguides,” in Proceedings of the IEEE Wireless and Optical Communication Network Conference (IEEE, 2006), paper 01666673.

Gini, E.

P. A. Besse, E. Gini, M. Bachmann, and H. Melchion, “New 2×2 and 1×3 multimode interference couplers with free selection of power splitting ratios,” J. Lightwave Technol. 14, 2286-2293 (1996).
[CrossRef]

Grattan, K. T. V.

Haruna, M.

H. Nishihara, M. Haruna, and T. Suhara, Optical Integrated Circuits (McGraw-Hill, 1989).

Ho, S. T.

Y. Ma, S. Park, L. Wang, and S. T. Ho, “Ultra compact multimode interference 3 dB coupler with strong lateral confinement by deep dry etching,” IEEE Photonics Technol. Lett. 12, 492-494 (2000).
[CrossRef]

Lee, C. W.

Lee, S. Y.

Levy, D. S.

D. S. Levy, K. H. Park, R. Scarmozzino, and R. M. Osgood, “Fabrication of ultracompact 3 dB2×2 MMI power splitters,” IEEE Photonics Technol. Lett. 11, 1009-1011 (1999).
[CrossRef]

Levy, David S.

12. David S. Levy, Robert Scarmozzino, York M. Li, and R. M. Osgood, “A new design of ultracompact multimode interference-based 2×2 couplers,” IEEE Photonics Technol. Lett. 10, 96-98 (1998).
[CrossRef]

Li, York M.

12. David S. Levy, Robert Scarmozzino, York M. Li, and R. M. Osgood, “A new design of ultracompact multimode interference-based 2×2 couplers,” IEEE Photonics Technol. Lett. 10, 96-98 (1998).
[CrossRef]

Lu, H. C.

Ma, Y.

Y. Ma, S. Park, L. Wang, and S. T. Ho, “Ultra compact multimode interference 3 dB coupler with strong lateral confinement by deep dry etching,” IEEE Photonics Technol. Lett. 12, 492-494 (2000).
[CrossRef]

MacDonald, R. I.

M. R. Paiam and R. I. MacDonald, “Polarization insensitive 980/1550 nm wavelength demultiplexer using MMI couplers,” Electron. Lett. 33, 1219-1220 (1997).
[CrossRef]

Melchion, H.

P. A. Besse, E. Gini, M. Bachmann, and H. Melchion, “New 2×2 and 1×3 multimode interference couplers with free selection of power splitting ratios,” J. Lightwave Technol. 14, 2286-2293 (1996).
[CrossRef]

Melchior, H.

Nishihara, H.

H. Nishihara, M. Haruna, and T. Suhara, Optical Integrated Circuits (McGraw-Hill, 1989).

Osgood, R. M.

D. S. Levy, K. H. Park, R. Scarmozzino, and R. M. Osgood, “Fabrication of ultracompact 3 dB2×2 MMI power splitters,” IEEE Photonics Technol. Lett. 11, 1009-1011 (1999).
[CrossRef]

12. David S. Levy, Robert Scarmozzino, York M. Li, and R. M. Osgood, “A new design of ultracompact multimode interference-based 2×2 couplers,” IEEE Photonics Technol. Lett. 10, 96-98 (1998).
[CrossRef]

Paiam, M. R.

M. R. Paiam and R. I. MacDonald, “Polarization insensitive 980/1550 nm wavelength demultiplexer using MMI couplers,” Electron. Lett. 33, 1219-1220 (1997).
[CrossRef]

Park, K. H.

D. S. Levy, K. H. Park, R. Scarmozzino, and R. M. Osgood, “Fabrication of ultracompact 3 dB2×2 MMI power splitters,” IEEE Photonics Technol. Lett. 11, 1009-1011 (1999).
[CrossRef]

Park, S.

Y. Ma, S. Park, L. Wang, and S. T. Ho, “Ultra compact multimode interference 3 dB coupler with strong lateral confinement by deep dry etching,” IEEE Photonics Technol. Lett. 12, 492-494 (2000).
[CrossRef]

Pennings, E. C. M.

L. B. Soldano and E. C. M. Pennings, “Optical multimode interference devices on self imaging: principle and applications,” J. Lightwave Technol. 13, 615-627 (1995).
[CrossRef]

Rahman, B. M. A.

Rajarajan, M.

Rooks, M.

Sahu, P. P.

P. P. Sahu, “Silicon oxinitride: a material for compact waveguide device,” Indian J. Phys. 82, 265-272 (2008).

P. P. Sahu, “Compact multimode interference coupler with tapered waveguide geometry,” Opt. Commun. 277, 295-301(2007).
[CrossRef]

A. K. Das and P. P. Sahu, “Compact integrated optical devices using high index contrast waveguides,” in Proceedings of the IEEE Wireless and Optical Communication Network Conference (IEEE, 2006), paper 01666673.

Scarmozzino, R.

D. S. Levy, K. H. Park, R. Scarmozzino, and R. M. Osgood, “Fabrication of ultracompact 3 dB2×2 MMI power splitters,” IEEE Photonics Technol. Lett. 11, 1009-1011 (1999).
[CrossRef]

Scarmozzino, Robert

12. David S. Levy, Robert Scarmozzino, York M. Li, and R. M. Osgood, “A new design of ultracompact multimode interference-based 2×2 couplers,” IEEE Photonics Technol. Lett. 10, 96-98 (1998).
[CrossRef]

Sekaric, L.

Soldano, L. B.

L. B. Soldano and E. C. M. Pennings, “Optical multimode interference devices on self imaging: principle and applications,” J. Lightwave Technol. 13, 615-627 (1995).
[CrossRef]

Suhara, T.

H. Nishihara, M. Haruna, and T. Suhara, Optical Integrated Circuits (McGraw-Hill, 1989).

Vlasov, Y. A.

Wang, L.

Y. Ma, S. Park, L. Wang, and S. T. Ho, “Ultra compact multimode interference 3 dB coupler with strong lateral confinement by deep dry etching,” IEEE Photonics Technol. Lett. 12, 492-494 (2000).
[CrossRef]

Wang, W. S.

Xia, F.

Appl. Opt.

Electron. Lett.

M. R. Paiam and R. I. MacDonald, “Polarization insensitive 980/1550 nm wavelength demultiplexer using MMI couplers,” Electron. Lett. 33, 1219-1220 (1997).
[CrossRef]

IEEE Photonics Technol. Lett.

Y. Ma, S. Park, L. Wang, and S. T. Ho, “Ultra compact multimode interference 3 dB coupler with strong lateral confinement by deep dry etching,” IEEE Photonics Technol. Lett. 12, 492-494 (2000).
[CrossRef]

D. S. Levy, K. H. Park, R. Scarmozzino, and R. M. Osgood, “Fabrication of ultracompact 3 dB2×2 MMI power splitters,” IEEE Photonics Technol. Lett. 11, 1009-1011 (1999).
[CrossRef]

12. David S. Levy, Robert Scarmozzino, York M. Li, and R. M. Osgood, “A new design of ultracompact multimode interference-based 2×2 couplers,” IEEE Photonics Technol. Lett. 10, 96-98 (1998).
[CrossRef]

Indian J. Phys.

P. P. Sahu, “Silicon oxinitride: a material for compact waveguide device,” Indian J. Phys. 82, 265-272 (2008).

J. Lightwave Technol.

L. B. Soldano and E. C. M. Pennings, “Optical multimode interference devices on self imaging: principle and applications,” J. Lightwave Technol. 13, 615-627 (1995).
[CrossRef]

M. Rajarajan, B. M. A. Rahman, and K. T. V. Grattan, “A rigorous comparison of the performance of directional coupler with multimode interference devices,” J. Lightwave Technol. 17, 243-248 (1999).
[CrossRef]

P. A. Besse, E. Gini, M. Bachmann, and H. Melchion, “New 2×2 and 1×3 multimode interference couplers with free selection of power splitting ratios,” J. Lightwave Technol. 14, 2286-2293 (1996).
[CrossRef]

H. C. Lu and W. S. Wang, “Analysis of multimode interference coupler with a width of arbitrary exponent binomial function,” J. Lightwave Technol. 25, 2874-2878 (2007).
[CrossRef]

Opt. Commun.

P. P. Sahu, “Compact multimode interference coupler with tapered waveguide geometry,” Opt. Commun. 277, 295-301(2007).
[CrossRef]

Opt. Express

Other

A. K. Das and P. P. Sahu, “Compact integrated optical devices using high index contrast waveguides,” in Proceedings of the IEEE Wireless and Optical Communication Network Conference (IEEE, 2006), paper 01666673.

H. Nishihara, M. Haruna, and T. Suhara, Optical Integrated Circuits (McGraw-Hill, 1989).

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Figures (4)

Fig. 1
Fig. 1

Tapered 2 × 2 MMI coupler of coupling length L with width 2 w + h at the input end and 2 w + Δ w at the output end: (a) 3D view and (b) 2D tapered structure containing y and z axes.

Fig. 2
Fig. 2

Coupling power distribution of proposed tapered and previously reported parabolic MMI coupler [11] with w mmi 6 μm , w = 1.5 μm , cladding  index 1.45 , Δ n 5 % , wavelength 1.55 μm , and p 0.53 [solid curves, simple model-based sinusoidal modes for the proposed tapered MMI; dashed curves, simple model-based sinusoidal modes for the previously reported parabolic MMI; and dotted curves, BPM CAD tool (optiBPM)].

Fig. 3
Fig. 3

(a) Normalized cross-state power of conventional ( p = 1 ) and tapered MMI coupler with p = 0.8 , 0.67, 0.53, and 0.5 for w m 5 μm , w = 1.5 μm , cladding index 1.45 , Δ n 5 % , and wavelength 1.55 μm . (b) Variation of number of modes propagated and refracted out along the z axis of a conventional ( p = 1 ) and the proposed MMI structure ( p = 0.53 ).

Fig. 4
Fig. 4

Power imbalance characteristics versus MMI width tolerance ( w ) for the conventional, the proposed parabolic tapered ( p = 0.53 ), the linearly tapered (at the middle) [13] and the parabolic tapered (at the middle ) [11] 3 dB coupler with cladding index 1.45 , h 3 μm , index contrast 5 % power, w 1.5 μm , wavelength 1.55 μm , and w 0 = 32 μm .

Tables (1)

Tables Icon

Table 1 Power of Different Modes of TM Polarization Excited in Proposed Tapered MMI Structure and MMI Structure Reported Previously [11] with n = 5 % and w mmi = 6 μm ( h = 3 μm ), p = 0.53

Equations (11)

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

w ( z ) = w mmi [ 1 2 ( 1 p ) z L ( 1 z 2 L ) ] ,
Ψ ( x , 0 ) = i = 0 m 1 b i T Ψ i ( x , 0 ) ,
Ψ 1 ( x , L ) = i = 0 m 1 c 1 , i T Ψ i ( x ) exp [ j ( β 0 β i ) L ] ,
Ψ 2 ( x , L ) = i = 0 m 1 c 2 , i T Ψ i ( x ) exp [ j ( β 0 β i ) L ] ,
Ψ i ( x ) sin [ π ( i + 1 ) { x w mmi ( 1 + p ) / 2 Δ w ) / 2 } 2 w + Δ w ] .
Ψ ( x , 0 ) = sin [ π ( x ) / w ] , where     0 < x < w , = 0 , otherwise .
c 1 , i T = ( 2 / w ) 0 w sin [ π ( i + 1 ) { x w mmi ( 1 + p ) / 2 Δ w / 2 } 2 w + Δ w ] sin [ π x w ] d x .
c 2 , i T = ( 2 / w ) 0 w sin [ π ( i + 1 ) { x + w w mmi ( 1 p ) / 2 + Δ w / 2 } 2 w + Δ w ] sin [ π ( x + w + Δ w ) w ] d x .
P 3 P 1 = | Ψ 1 ( x , L ) Ψ ( x , 0 ) | 2 P 4 P 1 = | Ψ 2 ( x , L ) Ψ ( x , 0 ) | 2 } .
tan 1 ( ( h Δ w ) / 2 L T ) 0.8 ° .
Power Imbalance ( dB ) = 10 log 10 ( P 3 / P 4 ) .

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