Abstract

Spatial mode-locking in three dimensions can be achieved in a slab waveguide array architecture. This study focuses on using the resulting robust and self-starting light bullet formation for photonics applications. Specifically, light bullets can be manipulated through a simple electronically addressable spatial gain dynamics. By applying gain ramps in time and/or space via electronics technology, complete control and manipulation of the light bullets can be achieved, thus allowing for the construction of the master logic gates of NAND and NOR. Its robustness, self-starting behavior and easy addressability suggest that the slab waveguide array mode-locking merits serious consideration as a next generation photonics device.

© 2010 Optical Society of America

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B. Bale, J. Kutz, and B. Sandstede, "OptimizingWaveguide Array Mode-Locking for High-Power Fiber Lasers," IEEE J. Sel. Top. Quantum 15(1), 220-231 (2009).
[CrossRef]

M. O. Williams and J. N. Kutz, "Spatial Mode-Locking of Light Bullets in Planar Waveguide Arrays," Opt. Express 17(20), 18,320-18,329 (2009).
[CrossRef]

2008

2006

2005

J. Meier, G. I. Stegeman, D. N. Christodoulides, Y. Silberberg, R. Morandotti, H. Yang, G. Salamo,M. Sorel, and J. S. Aitchison, "Beam interactions with a blocker soliton in one-dimensional arrays," Opt. Lett. 30(9), 1027-1029 (2005).
[CrossRef] [PubMed]

Y. V. Kartashov, L. Torner, and D. N. Christodoulides, "Soliton dragging by dynamic optical lattices," Opt. Lett. 30(11), 1378-1380 (2005).
[CrossRef] [PubMed]

J. Proctor and J. N. Kutz, "Theory and Simulation of Passive Mode-locking with Waveguide Arrays," Opt. Lett. 13, 2013-1015 (2005).
[CrossRef]

X. Hachair, L. Furfaro, J. Javaloyes, M. Giudici, S. Balle and J. Tredicce, "Cavity-solitons switching in semiconductor microcavities," Phys. Rev. A 72, 013815 (2005).
[CrossRef]

2002

S. Barland, J. Tredicce, M. Brambilla, L. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knodl, M. Miller and R. Jager, "Cavity solitons as pixels in semiconductor microcavities," Nature 419, 699-702 (2002).
[CrossRef] [PubMed]

H. S. Eisenberg, R. Morandotti, Y. Silberberg, J. M. Arnold, G. Pennelli, and J. S. Aitchison, "Optical discrete solitons in waveguide arrays. 1. Soliton formation," J. Opt. Soc. Am. B 19, 2938-2944 (2002).
[CrossRef]

U. Peschel, R. Morandotti, J.M. Arnold, J. S. Aitchison, H. S. Eisenberg, Y. Silberberg, T. Pertsch, and F. Lederer, "Optical discrete solitons in waveguide arrays. 2. Dynamics properties," J. Opt. Soc. Am. B 19, 2637-2644 (2002).
[CrossRef]

S. Chi, B. Luo, and H.-Y. Tseng, "Ultrashort bragg soliton in a fiber bragg grating," Opt. Commun. 206(1-3), 115- 121 (2002).
[CrossRef]

2001

V. B. Taranenko and C. O. Weiss, "Incoherent optical switching of semiconductor resonator solitons", Appl. Phys. B 72, 893-895 (2001).

1998

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, "Discrete spatial optical solitons in waveguide arrays," Phys. Rev. Lett. 81(3383-3386) (1998).
[CrossRef]

1996

A. B. Aceves, C. D. Angelis, T. Peschel, R. Muschall, F. Lederer, S. Trillo, and S. Wabnitz, "Discrete self-trapping soliton interactions, and beam steering in nonlinear waveguide arrays," Phys. Rev. E 53, 1172-1189 (1996).
[CrossRef]

1994

W. Krolikowski, U. Trutschel, M. Cronin-Golomb, and C. Schmidt-Hattenberger, "Solitonlike optical switching in a circular fiber array," Opt. Lett. 19(5), 320-322 (1994).
[CrossRef] [PubMed]

L. Rahman and H. Winful, "Nonlinear dynamics of semiconductor laser arrays: a mean field model," IEEE J. Quantum Electron. 30(6), 1405-1416 (1994).
[CrossRef]

1992

R. H. Enns and S. S. Rangnekar, "Bistable spheroidal optical solitons," Phys. Rev. A 45(5), 3354-3357 (1992).
[CrossRef] [PubMed]

1991

A. B. Blagoeva, S. G. Dinev, A. A. Dreischuh, and A. Naidenov, "Light bullets formation in a bulk media," IEEE J. Quantum Electron. 27(8), 2060-2065 (1991).
[CrossRef]

1990

1988

Aceves, A. B.

A. B. Aceves, C. D. Angelis, T. Peschel, R. Muschall, F. Lederer, S. Trillo, and S. Wabnitz, "Discrete self-trapping soliton interactions, and beam steering in nonlinear waveguide arrays," Phys. Rev. E 53, 1172-1189 (1996).
[CrossRef]

Ackemann, T.

Y. Tanguy, T. Ackemann, W. J. Firth, and R. Jager, "Realization of a Semiconductor-Based Cavity Soliton Laser," Phys. Rev. Lett. 100, 013907 (2008).
[CrossRef] [PubMed]

Aitchison, J. S.

Angelis, C. D.

A. B. Aceves, C. D. Angelis, T. Peschel, R. Muschall, F. Lederer, S. Trillo, and S. Wabnitz, "Discrete self-trapping soliton interactions, and beam steering in nonlinear waveguide arrays," Phys. Rev. E 53, 1172-1189 (1996).
[CrossRef]

Arnold, J. M.

Arnold, J.M.

Bale, B.

B. Bale, J. Kutz, and B. Sandstede, "OptimizingWaveguide Array Mode-Locking for High-Power Fiber Lasers," IEEE J. Sel. Top. Quantum 15(1), 220-231 (2009).
[CrossRef]

Balle, S.

X. Hachair, L. Furfaro, J. Javaloyes, M. Giudici, S. Balle and J. Tredicce, "Cavity-solitons switching in semiconductor microcavities," Phys. Rev. A 72, 013815 (2005).
[CrossRef]

S. Barland, J. Tredicce, M. Brambilla, L. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knodl, M. Miller and R. Jager, "Cavity solitons as pixels in semiconductor microcavities," Nature 419, 699-702 (2002).
[CrossRef] [PubMed]

Barbay, S.

Barland, S.

S. Barland, J. Tredicce, M. Brambilla, L. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knodl, M. Miller and R. Jager, "Cavity solitons as pixels in semiconductor microcavities," Nature 419, 699-702 (2002).
[CrossRef] [PubMed]

Blagoeva, A. B.

A. B. Blagoeva, S. G. Dinev, A. A. Dreischuh, and A. Naidenov, "Light bullets formation in a bulk media," IEEE J. Quantum Electron. 27(8), 2060-2065 (1991).
[CrossRef]

Boyd, A. R.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, "Discrete spatial optical solitons in waveguide arrays," Phys. Rev. Lett. 81(3383-3386) (1998).
[CrossRef]

Brambilla, M.

S. Barland, J. Tredicce, M. Brambilla, L. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knodl, M. Miller and R. Jager, "Cavity solitons as pixels in semiconductor microcavities," Nature 419, 699-702 (2002).
[CrossRef] [PubMed]

Chi, S.

S. Chi, B. Luo, and H.-Y. Tseng, "Ultrashort bragg soliton in a fiber bragg grating," Opt. Commun. 206(1-3), 115- 121 (2002).
[CrossRef]

Christodoulides, D.

Christodoulides, D. N.

Cronin-Golomb, M.

de Sterke, C. M.

J. T. Mok, C. M. de Sterke, I. C. M. Liter, and B. J. Eggleton, "Dispersionless slow light using gap solitons," Nat. Physics 2, 775-780 (2006).
[CrossRef]

Dinev, S. G.

A. B. Blagoeva, S. G. Dinev, A. A. Dreischuh, and A. Naidenov, "Light bullets formation in a bulk media," IEEE J. Quantum Electron. 27(8), 2060-2065 (1991).
[CrossRef]

Dreischuh, A. A.

A. B. Blagoeva, S. G. Dinev, A. A. Dreischuh, and A. Naidenov, "Light bullets formation in a bulk media," IEEE J. Quantum Electron. 27(8), 2060-2065 (1991).
[CrossRef]

Eggleton, B. J.

J. T. Mok, C. M. de Sterke, I. C. M. Liter, and B. J. Eggleton, "Dispersionless slow light using gap solitons," Nat. Physics 2, 775-780 (2006).
[CrossRef]

Eisenberg, H. S.

Enns, R. H.

R. H. Enns and S. S. Rangnekar, "Bistable spheroidal optical solitons," Phys. Rev. A 45(5), 3354-3357 (1992).
[CrossRef] [PubMed]

Firth, W. J.

Y. Tanguy, T. Ackemann, W. J. Firth, and R. Jager, "Realization of a Semiconductor-Based Cavity Soliton Laser," Phys. Rev. Lett. 100, 013907 (2008).
[CrossRef] [PubMed]

Furfaro, L.

X. Hachair, L. Furfaro, J. Javaloyes, M. Giudici, S. Balle and J. Tredicce, "Cavity-solitons switching in semiconductor microcavities," Phys. Rev. A 72, 013815 (2005).
[CrossRef]

Giudici, M.

X. Hachair, L. Furfaro, J. Javaloyes, M. Giudici, S. Balle and J. Tredicce, "Cavity-solitons switching in semiconductor microcavities," Phys. Rev. A 72, 013815 (2005).
[CrossRef]

S. Barland, J. Tredicce, M. Brambilla, L. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knodl, M. Miller and R. Jager, "Cavity solitons as pixels in semiconductor microcavities," Nature 419, 699-702 (2002).
[CrossRef] [PubMed]

Hachair, X.

X. Hachair, L. Furfaro, J. Javaloyes, M. Giudici, S. Balle and J. Tredicce, "Cavity-solitons switching in semiconductor microcavities," Phys. Rev. A 72, 013815 (2005).
[CrossRef]

Jager, R.

Y. Tanguy, T. Ackemann, W. J. Firth, and R. Jager, "Realization of a Semiconductor-Based Cavity Soliton Laser," Phys. Rev. Lett. 100, 013907 (2008).
[CrossRef] [PubMed]

S. Barland, J. Tredicce, M. Brambilla, L. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knodl, M. Miller and R. Jager, "Cavity solitons as pixels in semiconductor microcavities," Nature 419, 699-702 (2002).
[CrossRef] [PubMed]

Javaloyes, J.

X. Hachair, L. Furfaro, J. Javaloyes, M. Giudici, S. Balle and J. Tredicce, "Cavity-solitons switching in semiconductor microcavities," Phys. Rev. A 72, 013815 (2005).
[CrossRef]

Joseph, R. I.

Kartashov, Y. V.

Knodl, T.

S. Barland, J. Tredicce, M. Brambilla, L. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knodl, M. Miller and R. Jager, "Cavity solitons as pixels in semiconductor microcavities," Nature 419, 699-702 (2002).
[CrossRef] [PubMed]

Krolikowski, W.

Kutz, J.

B. Bale, J. Kutz, and B. Sandstede, "OptimizingWaveguide Array Mode-Locking for High-Power Fiber Lasers," IEEE J. Sel. Top. Quantum 15(1), 220-231 (2009).
[CrossRef]

Kutz, J. N.

M. O. Williams and J. N. Kutz, "Spatial Mode-Locking of Light Bullets in Planar Waveguide Arrays," Opt. Express 17(20), 18,320-18,329 (2009).
[CrossRef]

J. N. Kutz and B. Sandstede, "Theory of passive harmonic mode-locking using waveguide arrays", Opt. Express 16, 636-650 (2008).
[CrossRef] [PubMed]

J. N. Kutz and B. Sandstede, "Theory of passive harmonicmode-locking using waveguide arrays," Opt. Express 16(2), 636-650 (2008).
[CrossRef] [PubMed]

J. Proctor and J. N. Kutz, "Theory and Simulation of Passive Mode-locking with Waveguide Arrays," Opt. Lett. 13, 2013-1015 (2005).
[CrossRef]

Lederer, F.

U. Peschel, R. Morandotti, J.M. Arnold, J. S. Aitchison, H. S. Eisenberg, Y. Silberberg, T. Pertsch, and F. Lederer, "Optical discrete solitons in waveguide arrays. 2. Dynamics properties," J. Opt. Soc. Am. B 19, 2637-2644 (2002).
[CrossRef]

A. B. Aceves, C. D. Angelis, T. Peschel, R. Muschall, F. Lederer, S. Trillo, and S. Wabnitz, "Discrete self-trapping soliton interactions, and beam steering in nonlinear waveguide arrays," Phys. Rev. E 53, 1172-1189 (1996).
[CrossRef]

Liter, I. C. M.

J. T. Mok, C. M. de Sterke, I. C. M. Liter, and B. J. Eggleton, "Dispersionless slow light using gap solitons," Nat. Physics 2, 775-780 (2006).
[CrossRef]

Lugiato, L.

S. Barland, J. Tredicce, M. Brambilla, L. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knodl, M. Miller and R. Jager, "Cavity solitons as pixels in semiconductor microcavities," Nature 419, 699-702 (2002).
[CrossRef] [PubMed]

Luo, B.

S. Chi, B. Luo, and H.-Y. Tseng, "Ultrashort bragg soliton in a fiber bragg grating," Opt. Commun. 206(1-3), 115- 121 (2002).
[CrossRef]

Maggipinto, T.

S. Barland, J. Tredicce, M. Brambilla, L. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knodl, M. Miller and R. Jager, "Cavity solitons as pixels in semiconductor microcavities," Nature 419, 699-702 (2002).
[CrossRef] [PubMed]

Meier, J.

Miller, M.

S. Barland, J. Tredicce, M. Brambilla, L. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knodl, M. Miller and R. Jager, "Cavity solitons as pixels in semiconductor microcavities," Nature 419, 699-702 (2002).
[CrossRef] [PubMed]

Mok, J. T.

J. T. Mok, C. M. de Sterke, I. C. M. Liter, and B. J. Eggleton, "Dispersionless slow light using gap solitons," Nat. Physics 2, 775-780 (2006).
[CrossRef]

Morandotti, R.

Muschall, R.

A. B. Aceves, C. D. Angelis, T. Peschel, R. Muschall, F. Lederer, S. Trillo, and S. Wabnitz, "Discrete self-trapping soliton interactions, and beam steering in nonlinear waveguide arrays," Phys. Rev. E 53, 1172-1189 (1996).
[CrossRef]

Naidenov, A.

A. B. Blagoeva, S. G. Dinev, A. A. Dreischuh, and A. Naidenov, "Light bullets formation in a bulk media," IEEE J. Quantum Electron. 27(8), 2060-2065 (1991).
[CrossRef]

Pennelli, G.

Pertsch, T.

Peschel, T.

A. B. Aceves, C. D. Angelis, T. Peschel, R. Muschall, F. Lederer, S. Trillo, and S. Wabnitz, "Discrete self-trapping soliton interactions, and beam steering in nonlinear waveguide arrays," Phys. Rev. E 53, 1172-1189 (1996).
[CrossRef]

Peschel, U.

Proctor, J.

J. Proctor and J. N. Kutz, "Theory and Simulation of Passive Mode-locking with Waveguide Arrays," Opt. Lett. 13, 2013-1015 (2005).
[CrossRef]

Rahman, L.

L. Rahman and H. Winful, "Nonlinear dynamics of semiconductor laser arrays: a mean field model," IEEE J. Quantum Electron. 30(6), 1405-1416 (1994).
[CrossRef]

Rangnekar, S. S.

R. H. Enns and S. S. Rangnekar, "Bistable spheroidal optical solitons," Phys. Rev. A 45(5), 3354-3357 (1992).
[CrossRef] [PubMed]

Salamo, G.

Sandstede, B.

Schmidt-Hattenberger, C.

Silberberg, Y.

Sorel, M.

Spinelli, L.

S. Barland, J. Tredicce, M. Brambilla, L. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knodl, M. Miller and R. Jager, "Cavity solitons as pixels in semiconductor microcavities," Nature 419, 699-702 (2002).
[CrossRef] [PubMed]

Stegeman, G. I.

Tanguy, Y.

Y. Tanguy, T. Ackemann, W. J. Firth, and R. Jager, "Realization of a Semiconductor-Based Cavity Soliton Laser," Phys. Rev. Lett. 100, 013907 (2008).
[CrossRef] [PubMed]

Taranenko, V. B.

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Supplementary Material (3)

» Media 1: MOV (941 KB)     
» Media 2: MOV (1568 KB)     
» Media 3: MOV (1301 KB)     

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Figures (8)

Fig. 1.
Fig. 1.

Schematic of the planar waveguide array. The guiding regions, shown in red, are coupled via evanescent coupling. A gold layer deposited on the 0th waveguide allows for current injection into that waveguide [28]. The gold layer is partitioned into regions. This allows for current to be injected in a non-uniform fashion to different regions of the plane.

Fig. 2.
Fig. 2.

Coordinate directions for a waveguide. In this VCSEL-like structure, the phase velocity is in the z direction, but the energy is trapped in the planar waveguides parallel to the x-y plane.

Fig. 3.
Fig. 3.

On the left, a plot of pulse height as a function of g 0. Linearly stable regions are shown in blue and linearly unstable regions in red. The three plots on the right show the spectrum of the linearized operators for three labeled points. Points in red are in the right half plane while points in blue are either in the left half plane or are known to be exactly zero.

Fig. 4.
Fig. 4.

Plot of bullet velocity with a linearly sloped gain profile. Qualitatively, the bullet translates towards regions of larger gain. Shown on the left is the amplitude of the 0th waveguide with a slope of 0.02. The speed of the bullet is directly related to the slope of the gain with larger slopes generating pulses of greater speeds.

Fig. 5.
Fig. 5.

Plot of sloped gain being used for pulse routing. From the same initial condition, shown on the left, the pulse is navigated to one of three potential outputs in a cross shape pattern. The dotted white line shows the path of the moment of the pulse as it travels through the system. (Media 1)

Fig. 6.
Fig. 6.

Plot of light bullet movement with a time-dependent gain. The movement of the gain envelope, shown by the solid red line, is copied by the movement of the pulse tracing out the circle, shown in dashed lines above. Note that the lines depict the exact route taken by the bullet and are not simply a guide for the eye. (Media 2)

Fig. 7.
Fig. 7.

All four possible inputs for the WGA acting as a NOR gate, the initial condition is shown on top and the result after pulse interaction is shown on the bottom. The bullet in the region labeled clock acts as a clock signal. If the clock bullet reaches the right hand of the domain, the result is considered “high” otherwise it is considered “low”. All four potential logic inputs are tested and the resulting outputs are consistent with a NOR gate.

Fig. 8.
Fig. 8.

All four possible logic inputs for the WGA configured as a NAND gate. The initial condition is a clock and auxiliary pulse along with the different inputs to the system. The output of the system is determined solely by whether or not the clock pulse translates to the right hand side without being destroyed. (Media 3)

Equations (10)

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i A 0 t + D 2 2 A 0 + β A 0 2 A 0 + C A 1 + i γ 0 A 0 ig ( x , y , t ) ( 1 + τ 2 ) A 0 + A 0 4 A 0 = 0
i A 1 t + C ( A 0 + A 2 ) + i γ 1 A 1 = 0
i A 2 t + C A 1 + i γ 2 A 2 = 0
g ( x , y , t ) = 2 g 0 1 + A 0 2 / e 0 f ( x , y , t ) .
A n = a n e i Θ t
( D , β , C , γ 0 , γ 1 , γ 2 , ρ ) = ( 1,8,10,0,0,10,1 ) f ( x , y , t ) = 1 ,
f ( x , y , t ) = 1 + mx
f ( x , y , t ) = { ( 1 + mx + ny ) 0 x < 8 or y < 8 otherwise
f ( x , y , t ) = exp ( α ( [ x 10 cos ( ωt ) ] 2 + [ y 10 sin ( ωt ) ] 2 ) )
pulse center = x A 0 2 dxdy A 0 2 x ̂ + y A 0 2 dxdy A 0 2 y ̂ .

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