Abstract

We present the design of an all-optical router based on the properties of both propagation and interaction of Gaussian beams in lenslike planar guides. Variational results of single co- and counterpropagation are derived and used to design three integrated optical devices, that is, a header extraction device, an optical bistable device and a data routing device, which perform an ultrafast, phase-insensitive and fiber compatible routing operation in the optical domain.

© 2005 Optical Society of America

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References

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App. Opt.

J. Liñares, G. C. Righini, and J. E. Alvarellos,�??Modal coupling analysis for integrated optical components in glass and lithium niobate,�?? App. Opt. 31, 5292 (1992).
[CrossRef]

Fiber and Int. Optics

E. F. Mateo, and J. Liñares, �??Third order nonlinear integrated device based on an effective graded-index waveguide for all-optical multistability,�?? Fiber and Int. Optics. To be published (2005).
[CrossRef]

IEEE Photon. Technol. Lett.

B. Olsson, L. Rau, and J. Blumenthal,�??WDM to OTDM multiplexing using an ultrafast all-optical wavelength converter,�?? IEEE Photon. Technol. Lett. 13, 1905 (2001).
[CrossRef]

H. J. Lee, J. B. Yoo, V. K. Tsui, and K. H. Fong, �??A simple all-optical label detection and swapping technique incorporating a fiber Bragg grating filter,�?? IEEE Photon. Technol. Lett. 13, 635 (2001).
[CrossRef]

J. Lightwave Technol.

J. Opt. A: Pure Appl. Opt.

E. F. Mateo, J. Liñares, and C. Montero, �??Intrinsic bistability achieved by transverse modal coupling in a nonlinear integrated device,�?? J. Opt. A: Pure Appl. Opt. 4, 562 (2002).
[CrossRef]

J. Opt. Soc. Am. B

Jpn. J. Appl. Phys.

J. Liñares, M. C. Nistal, �??Single local mode propagation though ion-exchanged waveguide elements with quasi-abrupt transitions,�?? Jpn. J. Appl. Phys. 35, L1596 (1996).
[CrossRef]

Opt. Commun.

J. Liñares, C. Montero, and D. Sotelo, �??Theory and design of an integrated optical sensor based on planar waveguiding lenses,�?? Opt. Commun. 180, 29 (2000).
[CrossRef]

Opt. Eng.

K. H. Park, and T. Mizumoto, �??All-optical address extraction for optical routing,�?? Opt. Eng., 38, 1848 (1999).
[CrossRef]

Opt. Express

Opt. Lett.

Opt. Quantum Electron.

E. F. Mateo, and J. Liñares, �??All-optical integrated logic gates based on intensity-dependent transverse modal coupling,�?? Opt. Quantum Electron. 35, 1221 (2003).
[CrossRef]

F. Garzia, C. Sibilia, and M. Bertolotti, �??All-optical serial switcher,�?? Opt. Quantum Electron. 32, 781 (2000).
[CrossRef]

Opt. Soc. Am. B

M. Desaix, D. Anderson, M. J. and Lisak, �??Variational approach to collapse of optical pulses,�?? Opt. Soc. Am. B 8, 2082 (1991).
[CrossRef]

Phys. Rev. A

J. H. Marburger, and F. S. Felber, �??Theory of a lossless nonlinear Fabry-Perot interferometer,�?? Phys. Rev. A 17, 335 (1978).
[CrossRef]

D. Anderson, and M. Lisak, �??Bandwidth limits due to incoherent soliton interaction in optical-fiber communication systems,�?? Phys. Rev. A 32, 2270 (1985).
[CrossRef] [PubMed]

Phys.Rev. A

D. Anderson, �??Variational approach to nonlinear pulse propagation in optical fibers,�?? Phys.Rev. A 27, 3135 (1983).
[CrossRef]

Scientific American

G. Stix, �??The triumph of light,�?? Scientific American, January (1998)

Other

R. G. Hunsperger, Integrated optics: Theory and technology (Springer-Verlag, Berlin, 1991).

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Figures (10)

Fig. 1.
Fig. 1.

Sketch of the intensity-dependent routing operation where HE-D represents the Header Extraction Device, OB-D is the Optical Bistable Device and DR-D is the Data Routing Device. In figure (A) is represented the operation under the presence of a 1-valued header bit whereas in figure (B) is represented the operation for a 0-valued header bit.

Fig. 2.
Fig. 2.

Transverse view of the waveguide.

Fig. 3.
Fig. 3.

Top view of the header extraction device where the variational evolution of the header (solid) and data (dashed) Gaussian beam widths are shown.

Fig. 4.
Fig. 4.

Variational results for the data (A) and header (B) beam propagation.

Fig. 5.
Fig. 5.

Sketch of the bistable device showing the propagation behaviour of the counterpropagating beams in cases of low (A) and high (B) transmission output.

Fig. 6.
Fig. 6.

Optical bistability plot showing the bi-valued points for routing operation at pin =0.55, where A is the output power value for a header bit “0”, and B is for the header value “1”.

Fig. 7.
Fig. 7.

Integrated device performing the data routing under the absence (A) and presence (B) of the pump wave. The variational evolution of the pump (dashed) and data (solid) are shown for each case.

Fig. 8.
Fig. 8.

Propagation plots (top view) for the data routing operation. (A) Data wave propagation under the absence of pump (header bit “0”); (B) Data and pump wave propagation under the presence of pump (header bit “1”).

Fig. 9.
Fig. 9.

Scheme of the cascaded configuration for multi-bit header routing where a [0,1] header routes the data packet onto its correspondent output channel.

Fig. 10.
Fig. 10.

Sketch of a multilens with two EFT modules.

Tables (1)

Tables Icon

Table 1. Transverse coupling efficiencies of the data and pump beams onto the output optical fibers.

Equations (48)

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2 ( r , t ) = μ 0 2 t 2 [ ε 0 n l 2 ( x , y ) + 3 ε 0 χ Re ( 3 ) ( x , y ) 2 ] .
( x , y , z , t ) = 1 2 φ ( y ) [ ψ 1 ( x , z ) exp ( i β 1 z ) + ψ 2 ( x , z ) exp ( i β 2 z ) ] exp ( i ω 0 t ) + c c .
2 i β α ψ α z + 2 ψ α x 2 + k 2 [ Δ n ( x , y ) φ 2 d y ] ψ α +
3 4 k 2 [ χ Re ( 3 ) ( x , y ) φ 4 d y ] ( ψ α 2 + J ψ 3 α 2 ) ψ α = 0 ,
2 i β α ψ α z + 2 ψ α x 2 G 2 x 2 ψ α + k 2 n ˜ k 0 ( 1 + Q 2 x 2 ) ( ψ α 2 + J ψ 3 α 2 ) ψ α = 0 ,
ψ α ( x , z ) = E 0 α exp [ ( x x α ) 2 a 2 w α 2 ] exp [ i β α ρ α ( x x α ) 2 + i V α ( x x α ) ] .
d 2 w α d τ 2 1 w α 3 + g w α + 1 2 p α 1 w α 2 ( 1 q w α 2 + Q 2 x α 2 ) + 2 J p 3 α 1 w α 2 ×
( 1 + w 3 α 2 w α 2 ) 3 2 ( K 0 α q K 1 α + Q 2 K 2 α ) exp [ 2 ( x α x 3 α ) 2 a 2 w α 2 + a 2 w 3 α 2 ] = 0 ,
d 2 x α d τ 2 + g x α 2 p α q x α 1 w α + J 2 p 3 α ( D 0 α q D 1 α ) exp [ 2 ( x α x 3 α ) 2 a 2 w α 2 + a 2 w 3 α 2 ] = 0 ,
V α = β α d x α d τ ,
K 0 α = 1 4 ( x α x 3 α ) 2 a 2 w α 2 + a 2 w 3 α 2 , K 1 α = 2 w 3 α 2 3 w α 2 w 3 α 2 w α 2 + w 3 α 2 ,
K 2 α = 4 x 3 α ( w α 2 x 3 α + w 3 α 2 x α ) w α 2 + w 3 α 2 + 4 ( w α 2 x 3 α + w 3 α 2 x α ) 2 ( x α x 3 α ) 2 a 2 ( w α 2 + w 3 α 2 ) 3
+ 5 ( w α 2 x 3 α + w 3 α 2 x α ) + w α 2 w 3 α 2 ( x α x 3 α ) 2 ( w α 2 + w 3 α 2 ) 2 .
D 0 α = ( x α x 3 α ) ( w α 2 + w 3 α 2 ) 3 2 , D 1 α = 8 w 3 α 2 ( w α 2 x 3 α + w 3 α 2 x α ) ( w α 2 + w 3 α 2 ) 5 2
4 ( x α x 3 α ) ( w α 2 + w 3 α 2 ) 5 2 4 ( w α 2 x 3 α + w 3 α 2 x α ) 2 ( x α x 3 α ) a 2 ( w α 2 + w 3 α 2 ) 7 2 .
d 2 w h d τ 2 1 w h 3 + g w h + 1 2 p h 1 w h 2 ( 1 q w h 2 + Q 2 x h 2 ) = 0 ,
d 2 x h d τ 2 + g x h 2 p q x h 1 w h = 0 .
d 2 w d d τ 2 1 w d 3 + g w d = 0 ,
d 2 x d d τ 2 + g x d = 0 .
p st = 2 ( 1 g ) 1 q = 16 4 G 2 α 4 8 Q 2 α 2 .
Λ l = 2 π g 1 2 = 4 π G a 2 .
d 2 w + 1 d τ 2 1 w + 1 3 + 1 2 p + 1 1 w + 1 2 + 2 2 p 1 1 w + 1 2 ( 1 + w 1 2 w + 1 2 ) 3 2 = 0 ,
d 2 w 1 d τ 2 1 w 1 3 + 1 2 p 1 1 w 1 2 + 2 2 p + 1 1 w 1 2 ( 1 + w + 1 2 w 1 2 ) 3 2 = 0 .
η 3 ( p + 1 , p 1 ) = 2 w + 1 ( z 2 , p + 1 , p 1 ) 1 + w + 1 2 ( z 2 , p + 1 , p 1 ) ,
p 1 = η 3 ( p + 1 , p 1 ) R p + 1 .
η 0 ( p 1 , p + 1 ) = 2 w 1 ( z 1 , p 1 , p + 1 ) 1 + w 1 2 ( z 1 , p 1 , p + 1 ) ,
p out = p 1 η 0 ( p + 1 , p 1 ) .
d 2 w d 0 d τ 2 1 w d 0 3 + g w d 0 = 0 , d 2 x d 0 d τ 2 + g x d 0 = 0 , V d 0 = β 0 d x d 0 d τ .
d 2 w p 1 d τ 2 1 w p 1 3 + g w p 1 + 1 2 p p 1 1 w p 1 2 ( 1 q w p 1 2 + Q 2 x p 1 2 ) ,
d 2 x p 1 d τ 2 + g x p 1 2 p p 1 q x p 1 1 w p 1 = 0 , V p 1 = β 0 d x p 1 d τ .
d 2 w d 1 d τ 2 1 w d 1 3 + g w d 1 +
+ 2 p p 1 1 w d 1 2 ( 1 + w p 1 2 w d 1 2 ) 3 2 ( K 0 + q K 1 Q K 2 ) exp [ 2 ( x d 1 x p 1 ) 2 a 2 w d 1 2 + a 2 w p 1 2 ] = 0 ,
d 2 x d 1 d τ 2 + g x d 1 + 1 2 p p 1 ( D 0 q D 1 ) exp [ 2 ( x d 1 x p 1 ) 2 a 2 w d 1 2 + a 2 w p 1 2 ] = 0 ,
V d 1 = β 0 d x d 1 d τ ,
a w d 1 ( z 3 ) = w g , x d 1 ( z 3 ) = δ .
a w d 1 ( z 2 ) = 2 B k 1 w g , V d 1 ( z 2 ) = k δ B .
a w d 1 ( z 2 ) V d 1 ( z 2 ) = 2 δ w g = 10 , B / k = 1 2 a w d 1 ( z 2 ) w g .
a w d 0 ( z 3 ) = 2 B k 1 a w d 0 ( z 2 ) = w d 1 ( z 2 ) w g w d 0 ( z 2 ) , x d 0 ( z 3 ) = 0 , V d 0 ( z 3 ) = 0 ,
a w p 1 ( z 3 ) = 2 B k 1 a w p 1 ( z 2 ) = w d 1 ( z 2 ) w g w p 1 ( z 2 ) , x p 1 ( z 3 ) = B k x p 1 ( z 2 ) = 1 2 a w d 1 ( z 2 ) w g V p 1 ( z 2 ) ,
V p 1 ( z 3 ) = k B x p 1 ( z 2 ) = 2 a w d 1 ( z 2 ) w g x p 1 ( z 2 ) .
ψ σ ( x ) = 2 1 4 ( π a 2 w σ 2 ) 1 4 exp [ ( x x σ ) 2 a 2 w σ 2 ] exp [ i V σ ( x x σ ) ] ,
φ g ( x ) = 2 1 4 ( π w g 2 ) 1 4 exp [ ( x Δ ) 2 w g 2 ] .
η σ = ψ σ ( x ) φ g ( x ) d x 2 = 2 a w σ w g a 2 w σ 2 + w g 2 exp [ 1 2 a 2 w σ 2 w g 2 V σ 2 + 4 ( x σ Δ ) 2 a 2 w σ 2 + w g 2 ] ,
N o t j = N i l j , m j cos 1 ( 1 t j N i f j ) = π 2 ,
f j = N o N i N o 1 t j [ t j 2 + ( A j 2 ) 2 ] .
a w j = 2 B j k 1 a w j 1 , x j = B j k V j 1 and V j = k B j x j 1 ,
B j = [ 2 t j f j N i t j 2 N o 2 ] .
a w 2 = B 2 B 1 a w 0 , x 2 = B 2 B 1 x 0 and V 2 = B 1 B 2 V 0 .

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