Abstract

Ultrashort pulse propagation through grating-assisted codirectional couplers (GACCs) operating in the linear regime is theoretically investigated. For this purpose, the temporal responses of uniform GACCs to ultrashort optical pulses are calculated and the effects of varying the different physical grating parameters (e.g., length and coupling strength) on these temporal responses are evaluated. We will show that the most interesting pulse re-shaping operations occur typically for the “energy receptor” mode and that depending on the length and coupling strength of the uniform perturbation one can achieve very different temporal shapes at the output of the device, including triangular pulses, square temporal waveforms as well as sequences of equalized multiple pulses. Moreover, the temporal scales of the pulses generated from a GACC are generally much shorter (in more than one order of magnitude) than those that can be generated from an equivalent Bragg grating (with the same grating length).

© 2004 Optical Society of America

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2004 (1)

M. Gioannini and I. Montrosset, “Time domain numerical model for linear and nonlinear grating assisted co-directional coupler,” Opt. Quantum Electron. 36, 119–131 (2004).
[Crossref]

2003 (2)

N. K. Berger, B. Levit, S. Atkins, and B. Fischer, “Repetition-rate multiplication of optical pulses using uniform fiber Bragg gratings,” Opt. Commun. 221, 331–335 (2003).
[Crossref]

J. Azaña, R. Slavík, P. Kockaert, L.R. Chen, and S. LaRochelle, “Generation of customized ultrahigh repetition rate pulse sequences using superimposed fiber Bragg gratings,” IEEE J. Lightwave Technol. 21, 1490–1498 (2003).
[Crossref]

2002 (1)

J. E. Sipe, C. Martijn de Sterke, and B. J. Eggleton, “Rigorous derivation of coupled mode equations for short, high-intensity grating-coupled, co-propagating pulses,” J. Mod. Opt. 49, 1437–1452 (2002).
[Crossref]

2001 (2)

2000 (1)

1997 (4)

J. N. Kutz, B. J. Eggleton, J. B. Stark, and R. E. Slusher, “Nonlinear pulse propagation in long-period fiber gratings: Theory and experiment,” IEEE J. Select. Topics in Quantum Electron. 3, 1232–1245 (1997).
[Crossref]

L. R. Chen, S. D. Benjamin, P. W. E. Smith, J. E. Sipe, and S. Juma, “Ultrashort pulse propagation in multiple-grating fiber structures,” Opt. Lett. 22, 402–405 (1997).
[Crossref] [PubMed]

L. R. Chen, S. D. Benjamin, H. Jung, P.W.E. Smith, and J. E. Sipe, “Dynamics of Ultrashort Pulse Propagation Through Fiber Gratings,” Opt. Express 1, 242–249 (1997), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-1-9-242.
[Crossref] [PubMed]

Ph. Emplit, M. Haelterman, R. Kashyap, and M. De Lathouwer, “Fiber Bragg grating for optical dark soliton generation,” IEEE Photon. Technol. Lett. 9, 1122–1124 (1997)
[Crossref]

1996 (1)

1995 (1)

1994 (1)

K. Rottwitt, M. J. Guy, A. Boskovic, D. U. Noske, J. R. Taylor, and R. Kashyap, “Interaction of uniform phase picosecond pulses with chirped and unchirped photosensitive fibre Bragg gratings,” Electron. Lett. 30, 995–996 (1994).
[Crossref]

1993 (1)

1992 (1)

1991 (3)

Agogliati, B.

Archambault, J.-L.

Atkins, S.

N. K. Berger, B. Levit, S. Atkins, and B. Fischer, “Repetition-rate multiplication of optical pulses using uniform fiber Bragg gratings,” Opt. Commun. 221, 331–335 (2003).
[Crossref]

Azaña, J.

J. Azaña, R. Slavík, P. Kockaert, L.R. Chen, and S. LaRochelle, “Generation of customized ultrahigh repetition rate pulse sequences using superimposed fiber Bragg gratings,” IEEE J. Lightwave Technol. 21, 1490–1498 (2003).
[Crossref]

Belmonte, M.

Benjamin, S. D.

Bergano, N. S.

Berger, N. K.

N. K. Berger, B. Levit, S. Atkins, and B. Fischer, “Repetition-rate multiplication of optical pulses using uniform fiber Bragg gratings,” Opt. Commun. 221, 331–335 (2003).
[Crossref]

Boskovic, A.

K. Rottwitt, M. J. Guy, A. Boskovic, D. U. Noske, J. R. Taylor, and R. Kashyap, “Interaction of uniform phase picosecond pulses with chirped and unchirped photosensitive fibre Bragg gratings,” Electron. Lett. 30, 995–996 (1994).
[Crossref]

Brady, D. J.

Chaudhuri, S. K.

W. Huang, B. E. Little, and S. K. Chaudhuri, “A new approach to grating-assisted couplers,” J. Lightwave Technol. 9, 721–727 (1991).
[Crossref]

Chen, L. R.

Chen, L.R.

J. Azaña, R. Slavík, P. Kockaert, L.R. Chen, and S. LaRochelle, “Generation of customized ultrahigh repetition rate pulse sequences using superimposed fiber Bragg gratings,” IEEE J. Lightwave Technol. 21, 1490–1498 (2003).
[Crossref]

Chen, Y.

Davidson, C. R.

De Lathouwer, M.

Ph. Emplit, M. Haelterman, R. Kashyap, and M. De Lathouwer, “Fiber Bragg grating for optical dark soliton generation,” IEEE Photon. Technol. Lett. 9, 1122–1124 (1997)
[Crossref]

Eggleton, B. J.

J. E. Sipe, C. Martijn de Sterke, and B. J. Eggleton, “Rigorous derivation of coupled mode equations for short, high-intensity grating-coupled, co-propagating pulses,” J. Mod. Opt. 49, 1437–1452 (2002).
[Crossref]

J. N. Kutz, B. J. Eggleton, J. B. Stark, and R. E. Slusher, “Nonlinear pulse propagation in long-period fiber gratings: Theory and experiment,” IEEE J. Select. Topics in Quantum Electron. 3, 1232–1245 (1997).
[Crossref]

Ellis, A. D.

Emplit, Ph.

Ph. Emplit, M. Haelterman, R. Kashyap, and M. De Lathouwer, “Fiber Bragg grating for optical dark soliton generation,” IEEE Photon. Technol. Lett. 9, 1122–1124 (1997)
[Crossref]

Feced, R.

Fischer, B.

N. K. Berger, B. Levit, S. Atkins, and B. Fischer, “Repetition-rate multiplication of optical pulses using uniform fiber Bragg gratings,” Opt. Commun. 221, 331–335 (2003).
[Crossref]

Gioannini, M.

M. Gioannini and I. Montrosset, “Time domain numerical model for linear and nonlinear grating assisted co-directional coupler,” Opt. Quantum Electron. 36, 119–131 (2004).
[Crossref]

Guy, M. J.

K. Rottwitt, M. J. Guy, A. Boskovic, D. U. Noske, J. R. Taylor, and R. Kashyap, “Interaction of uniform phase picosecond pulses with chirped and unchirped photosensitive fibre Bragg gratings,” Electron. Lett. 30, 995–996 (1994).
[Crossref]

Haelterman, M.

Ph. Emplit, M. Haelterman, R. Kashyap, and M. De Lathouwer, “Fiber Bragg grating for optical dark soliton generation,” IEEE Photon. Technol. Lett. 9, 1122–1124 (1997)
[Crossref]

Hill, K. B.

Holmes, A. S.

Huang, W.

W. Huang, B. E. Little, and S. K. Chaudhuri, “A new approach to grating-assisted couplers,” J. Lightwave Technol. 9, 721–727 (1991).
[Crossref]

Ibsen, M.

Judkins, J. B.

Juma, S.

Jung, H.

Kashyap, R.

Ph. Emplit, M. Haelterman, R. Kashyap, and M. De Lathouwer, “Fiber Bragg grating for optical dark soliton generation,” IEEE Photon. Technol. Lett. 9, 1122–1124 (1997)
[Crossref]

K. Rottwitt, M. J. Guy, A. Boskovic, D. U. Noske, J. R. Taylor, and R. Kashyap, “Interaction of uniform phase picosecond pulses with chirped and unchirped photosensitive fibre Bragg gratings,” Electron. Lett. 30, 995–996 (1994).
[Crossref]

R. Kashyap, Fiber Bragg Gratings, Academic Press, San Diego, (1999).

Kockaert, P.

J. Azaña, R. Slavík, P. Kockaert, L.R. Chen, and S. LaRochelle, “Generation of customized ultrahigh repetition rate pulse sequences using superimposed fiber Bragg gratings,” IEEE J. Lightwave Technol. 21, 1490–1498 (2003).
[Crossref]

Kutz, J. N.

J. N. Kutz, B. J. Eggleton, J. B. Stark, and R. E. Slusher, “Nonlinear pulse propagation in long-period fiber gratings: Theory and experiment,” IEEE J. Select. Topics in Quantum Electron. 3, 1232–1245 (1997).
[Crossref]

Laporta, P.

LaRochelle, S.

J. Azaña, R. Slavík, P. Kockaert, L.R. Chen, and S. LaRochelle, “Generation of customized ultrahigh repetition rate pulse sequences using superimposed fiber Bragg gratings,” IEEE J. Lightwave Technol. 21, 1490–1498 (2003).
[Crossref]

Lemaire, P. J.

Levit, B.

N. K. Berger, B. Levit, S. Atkins, and B. Fischer, “Repetition-rate multiplication of optical pulses using uniform fiber Bragg gratings,” Opt. Commun. 221, 331–335 (2003).
[Crossref]

Little, B. E.

W. Huang, B. E. Little, and S. K. Chaudhuri, “A new approach to grating-assisted couplers,” J. Lightwave Technol. 9, 721–727 (1991).
[Crossref]

Longhi, S.

Makrimichalou, S.

Marano, M.

Martijn de Sterke, C.

J. E. Sipe, C. Martijn de Sterke, and B. J. Eggleton, “Rigorous derivation of coupled mode equations for short, high-intensity grating-coupled, co-propagating pulses,” J. Mod. Opt. 49, 1437–1452 (2002).
[Crossref]

Montrosset, I.

M. Gioannini and I. Montrosset, “Time domain numerical model for linear and nonlinear grating assisted co-directional coupler,” Opt. Quantum Electron. 36, 119–131 (2004).
[Crossref]

Noske, D. U.

K. Rottwitt, M. J. Guy, A. Boskovic, D. U. Noske, J. R. Taylor, and R. Kashyap, “Interaction of uniform phase picosecond pulses with chirped and unchirped photosensitive fibre Bragg gratings,” Electron. Lett. 30, 995–996 (1994).
[Crossref]

Payne, D. N.

Pedrazzani, J. R.

Petropoulos, P.

Reekie, L.

Richardson, D. J.

Rottwitt, K.

K. Rottwitt, M. J. Guy, A. Boskovic, D. U. Noske, J. R. Taylor, and R. Kashyap, “Interaction of uniform phase picosecond pulses with chirped and unchirped photosensitive fibre Bragg gratings,” Electron. Lett. 30, 995–996 (1994).
[Crossref]

Russell, P. St. J.

Sipe, J. E.

Slavík, R.

J. Azaña, R. Slavík, P. Kockaert, L.R. Chen, and S. LaRochelle, “Generation of customized ultrahigh repetition rate pulse sequences using superimposed fiber Bragg gratings,” IEEE J. Lightwave Technol. 21, 1490–1498 (2003).
[Crossref]

Slusher, R. E.

J. N. Kutz, B. J. Eggleton, J. B. Stark, and R. E. Slusher, “Nonlinear pulse propagation in long-period fiber gratings: Theory and experiment,” IEEE J. Select. Topics in Quantum Electron. 3, 1232–1245 (1997).
[Crossref]

Smith, P. W. E.

Smith, P.W.E.

Snyder, A. W.

Stark, J. B.

J. N. Kutz, B. J. Eggleton, J. B. Stark, and R. E. Slusher, “Nonlinear pulse propagation in long-period fiber gratings: Theory and experiment,” IEEE J. Select. Topics in Quantum Electron. 3, 1232–1245 (1997).
[Crossref]

Syms, R. R. A.

Taverner, D.

Taylor, J. R.

K. Rottwitt, M. J. Guy, A. Boskovic, D. U. Noske, J. R. Taylor, and R. Kashyap, “Interaction of uniform phase picosecond pulses with chirped and unchirped photosensitive fibre Bragg gratings,” Electron. Lett. 30, 995–996 (1994).
[Crossref]

Vengsarkar, A. M.

Zervas, M. N.

Appl. Opt. (3)

Electron. Lett. (1)

K. Rottwitt, M. J. Guy, A. Boskovic, D. U. Noske, J. R. Taylor, and R. Kashyap, “Interaction of uniform phase picosecond pulses with chirped and unchirped photosensitive fibre Bragg gratings,” Electron. Lett. 30, 995–996 (1994).
[Crossref]

IEEE J. Lightwave Technol. (1)

J. Azaña, R. Slavík, P. Kockaert, L.R. Chen, and S. LaRochelle, “Generation of customized ultrahigh repetition rate pulse sequences using superimposed fiber Bragg gratings,” IEEE J. Lightwave Technol. 21, 1490–1498 (2003).
[Crossref]

IEEE J. Select. Topics in Quantum Electron. (1)

J. N. Kutz, B. J. Eggleton, J. B. Stark, and R. E. Slusher, “Nonlinear pulse propagation in long-period fiber gratings: Theory and experiment,” IEEE J. Select. Topics in Quantum Electron. 3, 1232–1245 (1997).
[Crossref]

IEEE Photon. Technol. Lett. (1)

Ph. Emplit, M. Haelterman, R. Kashyap, and M. De Lathouwer, “Fiber Bragg grating for optical dark soliton generation,” IEEE Photon. Technol. Lett. 9, 1122–1124 (1997)
[Crossref]

J. Lightwave Technol. (2)

J. Mod. Opt. (1)

J. E. Sipe, C. Martijn de Sterke, and B. J. Eggleton, “Rigorous derivation of coupled mode equations for short, high-intensity grating-coupled, co-propagating pulses,” J. Mod. Opt. 49, 1437–1452 (2002).
[Crossref]

J. Opt. Soc. Am. A (1)

Opt. Commun. (1)

N. K. Berger, B. Levit, S. Atkins, and B. Fischer, “Repetition-rate multiplication of optical pulses using uniform fiber Bragg gratings,” Opt. Commun. 221, 331–335 (2003).
[Crossref]

Opt. Express (1)

Opt. Lett. (5)

Opt. Quantum Electron. (1)

M. Gioannini and I. Montrosset, “Time domain numerical model for linear and nonlinear grating assisted co-directional coupler,” Opt. Quantum Electron. 36, 119–131 (2004).
[Crossref]

Other (1)

R. Kashyap, Fiber Bragg Gratings, Academic Press, San Diego, (1999).

Supplementary Material (1)

» Media 1: MOV (998 KB)     

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Figures (3)

Fig. 1.
Fig. 1.

(2.1 MB) Movie showing the evolution of a Gaussian temporal pulse propagating through a GACC with a 30-mm long uniform grating and a coupling coefficient κ so that κL=π. The top (bottom) plot shows the evolution of the temporal response corresponding to the so-called “supplier” (“receptor”) mode. The input pulse to the GACC is also shown in the top plot. The label inside the figures indicates the grating distance z where the temporal responses are evaluated (z=14mm in the static figure) (14.1 MBversion).

Fig. 2.
Fig. 2.

Results corresponding to a GACC with a 14-mm long uniform grating: Temporal waveforms (left column) and spectra (right column) of the output pulses in the “receptor” mode (red curves), output pulses in the “supplier” mode (blue curves) and input pulses to the GACC (magenta curves) for different values of the grating strength (κL).

Fig.3.
Fig.3.

Results corresponding to a GACC with a 60-mm long uniform grating. Same definitions as for Fig. 2.

Equations (4)

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

h s ( t ) = 1 { H in ( ν ) H s ( ν ) }
h r ( t ) = 1 { H in ( ν ) H r ( ν ) }
H s ( ν ) = [ cos ( γ L ) + j σ γ sin ( γ L ) ] exp ( j ( β s σ ) L )
H r ( ν ) = j κ * γ sin ( γ L ) exp ( j ( β r + σ ) L )

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