Abstract

A two-mode optical combiner–splitter device is designed based on all straight waveguides that maintains the integrity of the two modes during propagation and allows for an analytic analysis. The design analysis has the potential to improve the precision of the device fabrication. The design is used in an analytic optical gate based on a nonlinear Mach–Zehnder interferometer. The design reduces the size of a previously proposed device and simplifies its analysis.

© 2007 Optical Society of America

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References

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  1. S. Medhekar and R. K. Sarkar, "All-optical passive transistor," Opt. Lett. 30, 887-889 (2005).
    [CrossRef] [PubMed]
  2. Y. Silberberg and P. W. Smith, "Integrated all-optical switching devices," U.S. patent 4,856,860 (15 August 1989).
  3. T. Yabu, M. Geshiro, T. Kitamura, K. Nishida, and S. Sawa, "All-optical logic gates containing a two-mode nonlinear waveguide," IEEE J. Quantum Electron. 38, 37-46 (2002).
    [CrossRef]
  4. H. Yajima, "Dielectric thin-film optical branching waveguide," Appl. Phys. Lett. 22, 647-649 (1973).
    [CrossRef]
  5. M. Mirkov, B. G. Bagley, and R. T. Deck, "Design of multichannel optical splitter without bends," Fiber Integr. Opt. 20, 241-254 (2001).
  6. Y. Silberberg and G. I. Stegeman, "Nonlinear coupling of waveguide modes," Appl. Phys. Lett. 50, 801-803 (1987).
    [CrossRef]

2005

2002

T. Yabu, M. Geshiro, T. Kitamura, K. Nishida, and S. Sawa, "All-optical logic gates containing a two-mode nonlinear waveguide," IEEE J. Quantum Electron. 38, 37-46 (2002).
[CrossRef]

2001

M. Mirkov, B. G. Bagley, and R. T. Deck, "Design of multichannel optical splitter without bends," Fiber Integr. Opt. 20, 241-254 (2001).

1989

Y. Silberberg and P. W. Smith, "Integrated all-optical switching devices," U.S. patent 4,856,860 (15 August 1989).

1987

Y. Silberberg and G. I. Stegeman, "Nonlinear coupling of waveguide modes," Appl. Phys. Lett. 50, 801-803 (1987).
[CrossRef]

1973

H. Yajima, "Dielectric thin-film optical branching waveguide," Appl. Phys. Lett. 22, 647-649 (1973).
[CrossRef]

Bagley, B. G.

M. Mirkov, B. G. Bagley, and R. T. Deck, "Design of multichannel optical splitter without bends," Fiber Integr. Opt. 20, 241-254 (2001).

Deck, R. T.

M. Mirkov, B. G. Bagley, and R. T. Deck, "Design of multichannel optical splitter without bends," Fiber Integr. Opt. 20, 241-254 (2001).

Geshiro, M.

T. Yabu, M. Geshiro, T. Kitamura, K. Nishida, and S. Sawa, "All-optical logic gates containing a two-mode nonlinear waveguide," IEEE J. Quantum Electron. 38, 37-46 (2002).
[CrossRef]

Kitamura, T.

T. Yabu, M. Geshiro, T. Kitamura, K. Nishida, and S. Sawa, "All-optical logic gates containing a two-mode nonlinear waveguide," IEEE J. Quantum Electron. 38, 37-46 (2002).
[CrossRef]

Medhekar, S.

Mirkov, M.

M. Mirkov, B. G. Bagley, and R. T. Deck, "Design of multichannel optical splitter without bends," Fiber Integr. Opt. 20, 241-254 (2001).

Nishida, K.

T. Yabu, M. Geshiro, T. Kitamura, K. Nishida, and S. Sawa, "All-optical logic gates containing a two-mode nonlinear waveguide," IEEE J. Quantum Electron. 38, 37-46 (2002).
[CrossRef]

Sarkar, R. K.

Sawa, S.

T. Yabu, M. Geshiro, T. Kitamura, K. Nishida, and S. Sawa, "All-optical logic gates containing a two-mode nonlinear waveguide," IEEE J. Quantum Electron. 38, 37-46 (2002).
[CrossRef]

Silberberg, Y.

Y. Silberberg and P. W. Smith, "Integrated all-optical switching devices," U.S. patent 4,856,860 (15 August 1989).

Y. Silberberg and G. I. Stegeman, "Nonlinear coupling of waveguide modes," Appl. Phys. Lett. 50, 801-803 (1987).
[CrossRef]

Smith, P. W.

Y. Silberberg and P. W. Smith, "Integrated all-optical switching devices," U.S. patent 4,856,860 (15 August 1989).

Stegeman, G. I.

Y. Silberberg and G. I. Stegeman, "Nonlinear coupling of waveguide modes," Appl. Phys. Lett. 50, 801-803 (1987).
[CrossRef]

Yabu, T.

T. Yabu, M. Geshiro, T. Kitamura, K. Nishida, and S. Sawa, "All-optical logic gates containing a two-mode nonlinear waveguide," IEEE J. Quantum Electron. 38, 37-46 (2002).
[CrossRef]

Yajima, H.

H. Yajima, "Dielectric thin-film optical branching waveguide," Appl. Phys. Lett. 22, 647-649 (1973).
[CrossRef]

Appl. Phys. Lett.

H. Yajima, "Dielectric thin-film optical branching waveguide," Appl. Phys. Lett. 22, 647-649 (1973).
[CrossRef]

Y. Silberberg and G. I. Stegeman, "Nonlinear coupling of waveguide modes," Appl. Phys. Lett. 50, 801-803 (1987).
[CrossRef]

Fiber Integr. Opt.

M. Mirkov, B. G. Bagley, and R. T. Deck, "Design of multichannel optical splitter without bends," Fiber Integr. Opt. 20, 241-254 (2001).

IEEE J. Quantum Electron.

T. Yabu, M. Geshiro, T. Kitamura, K. Nishida, and S. Sawa, "All-optical logic gates containing a two-mode nonlinear waveguide," IEEE J. Quantum Electron. 38, 37-46 (2002).
[CrossRef]

Opt. Lett.

Other

Y. Silberberg and P. W. Smith, "Integrated all-optical switching devices," U.S. patent 4,856,860 (15 August 1989).

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Figures (7)

Fig. 1
Fig. 1

Diagram of the signal combiner∕splitter device based on straight waveguides.

Fig. 2
Fig. 2

Numerical evaluation of the field intensity versus z in channels of widths w 1 and w 3 , for the case that the field initiates in the channel of width w 1 . Designed parameter values in Fig. 1 are: λ = 1.55   μm , w 1 = 3.0   μm , w 3 = 4.0   μm , d 1 = 3.0   μm , index of refraction of cladding, n o = 1.444 , index of channels B 1 and B 2 , n 1 = 1.4589 , index of channels C and D, n 2 = n 3 = 1.4754 . Plot shows transfer of symmetric mode in right-hand channel into and out of antisymmetric mode in left-hand channel.

Fig. 3
Fig. 3

Diagram of the optical gating device designed in Ref. 3.

Fig. 4
Fig. 4

Diagram of optical gate proposed here. Lengths along the transverse x direction are expanded by a factor of 100 compared with lengths along the z direction. The index of refraction is n 1 in channels A, B 1 , B 2 , B 1 , B 2 , and X, n 2 in channels C, D, E, F, C , D , E , F′, and n 3 2 + α | E | 2 in channels N and N . The index of the channel claddings is n o .

Fig. 5
Fig. 5

Graphs of the powers (per unit width in the y direction) in the symmetric and antisymmetric modes of the nonlinear channel N in Fig. 4 as a function of propagation distance z, derived from the solution of Eqs. (15). Graphs show power exchanges between the modes resulting from the nonlinearity of the channel.

Fig. 6
Fig. 6

Graphs of phase θ 2 ( z ) of the antisymmetric mode in channel N in Fig. 4 as a function of z in the separate cases in which the control signal is (a) present (-----) or (b) absent (-...-...). Numerical difference between the graphs is represented by the solid curve that intersects the line corresponding to the phase change of π after a propagation distance in the nonlinear channel equal to 2293 μm.

Fig. 7
Fig. 7

Graph of output power in channel X in Fig. 4 versus the control power in channel C. Both powers are scaled to their maximum values.

Equations (28)

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[ 2 x 2 + 2 z 2 + ω 2 c 2 ε N ( x , z ) ] E N ( x , z ) = 0 ,
ε III ( x , z ) = ε III ( x ) + α | E III ( x , z ) | 2 ,
E N ( x , z ) = j a N j ( z ) E N j ( x ) exp ( i β N j z ) ,
[ d 2 d x 2 + ω 2 c 2 ε N ( x ) β N j ] E N j ( x ) = 0 .
d x E N j ( x ) E N j ( x ) = δ j j .
a N j ( z N o ) = d x E N j ( x ) E ( x , z N o ) exp ( i β N j z N o ) .
ε III ( x , z ) = ε III ( x ) + α { | a 1 ( z ) | 2 | E 1 ( x ) | 2 + | a 2 ( z ) | 2 | E 2 ( x ) | 2 + 2 Re a 1 ( z ) a 2 * ( z ) E 1 ( x ) E 2 ( x ) exp [ i ( β 1 β 2 ) z ] } ,
E 1 e i β 1 z [ d 2 a 1 d z 2 + 2 i β 1 d a 1 d z ] + E 2 e i β 2 z [ d 2 a 2 d z 2 + 2 i β 2 d a 2 d z ] + ω 2 c 2 α [ a 1 E 1 e i β 1 z + a 2 E 2 e i β 2 z ] | E III ( x , z ) | 2 = 0.
d a j ( z ) d z β j a j ( z ) , d 2 a j ( z ) d z 2 β j d a j ( z ) d z ,
2 i β 1 E 1 ( x ) e i β 1 z d a 1 d z + 2 i β 2 E 2 ( x ) e i β 2 z d a 2 d z + ω 2 c 2 α [ a 1 E 1 ( x ) e i β 1 z + a 2 E 2 ( x ) e i β 2 z ] | E III ( x , z ) | 2 = 0.
d a 1 ( z ) d z = i β 1 Q 1 ( z ) a 1 ( z ) + i β 1 Q 12 ( z ) a 2 ( z ) e i ( β 2 β 1 ) z ,
d a 2 ( z ) d z = i β 2 Q 2 ( z ) a 2 ( z ) + i β 2 Q 12 ( z ) a 1 ( z ) e i ( β 1 β 2 ) z ,
Q j ( z ) = ω 2 c 2 α 2 d x E j 2 ( x ) | E III ( x , z ) | 2 ,
Q 12 ( z ) = ω 2 c 2 α 2 d x E 1 ( x ) E 2 ( x ) | E III ( x , z ) | 2 .
Q 1 ( z ) = ω 2 c 2 α 2 { K 1 | a 1 ( z ) | 2 + K 12 | a 2 ( z ) | 2 + 2 K 13 Re a 1 ( z ) a 2 * ( z ) e i ( β 1 β 2 ) z } ,
Q 2 ( z ) = ω 2 c 2 α 2 { K 2 | a 2 ( z ) | 2 + K 12 | a 1 ( z ) | 2 + 2 K 23 Re a 1 ( z ) a 2 * ( z ) e i ( β 1 β 2 ) z } ,
Q 12 ( z ) = ω 2 c 2 α 2 { K 13 | a 1 ( z ) | 2 + K 23 | a 2 ( z ) | 2 + 2 K 12 Re a 1 ( z ) a 2 * ( z ) e i ( β 1 β 2 ) z } ,
K 1 d x E 1 4 ( x ) , K 2 d x E 2 4 ( x ) ,
K 12 d x E 1 2 ( x ) E 2 2 ( x ) , K 13 d x E 1 3 ( x ) E 2 ( x ) ,
K 23 d x E 1 ( x ) E 2 3 ( x ) .
d a 1 d z = i β 1 ω 2 c 2 α 2 { K 1 | a 1 | 2 a 1 + K 12 | a 2 | 2 a 1 + 2 K 12 Re [ a 1 a 2 * e i ( β 1 β 2 ) z ] a 2 e i ( β 2 β 1 ) z } ,
d a 2 d z = i β 2 ω 2 c 2 α 2 { K 2 | a 2 | 2 a 2 + K 12 | a 1 | 2 a 2 + 2 K 12 Re [ a 1 a 2 * e i ( β 1 β 2 ) z ] a 1 e i ( β 1 β 2 ) z } .
a j ( z ) = a j ( z IIIo ) ρ j ( z ) exp [ i θ j ( z ) ] ,
θ j ( z ) = tan 1 [ Im a j ( z ) / Re a j ( z ) ] .
E III ( x , z ) = [ a 1 ( z IIIo ) ρ 1 ( z ) exp ( i [ β 1 z + θ 1 ( z ) ] ) ε 1 ( x ) + a 2 ( z IIIo ) ρ 2 ( z ) exp ( i [ β 2 z + θ 2 ( z ) ] ) ε 2 ( x ) ] ,
( β 1 β 2 ) z + [ θ 1 ( z ) θ 2 ( z ) ] .
w ( 2 π λ ) 2 ε g β 2 = 2 tan 1 ( β 2 ( 2 π λ ) 2 ε c ( 2 π λ ) 2 ε g β 2 ) + n π ,
P n ( z ) = c 2 8 π ω β n | a n ( z ) | 2 ,

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