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Optics Express

  • Editor: J. H. Eberly
  • Vol. 3, Iss. 11 — Nov. 23, 1998
  • pp: 411–417
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High-repetition-rate soliton-train generation using fiber Bragg gratings

N. M. Litchinitser, G. P. Agrawal, B. J. Eggleton, and G. Lenz  »View Author Affiliations


Optics Express, Vol. 3, Issue 11, pp. 411-417 (1998)
http://dx.doi.org/10.1364/OE.3.000411


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Abstract

We propose a high-repetition-rate soliton-train source based on adiabatic compression of a dual-frequency optical signal in nonuniform fiber Bragg gratings. As the signal propagates through the grating, it is reshaped into a train of Bragg solitons whose repetition rate is predetermined by the frequency of initial sinusoidal modulation. We develop an approximate analytical model to predict the width of compressed soliton-like pulses and to provide conditions for adiabatic compression. We demonstrate numerically the formation of a 40-GHz train of 2.6-ps pulses and find that the numerical results are in good agreement with the predictions of our analytical model. The scheme relies on the dispersion provided by the grating, which can be up to six orders of magnitude larger than of fiber and makes it possible to reduce the fiber length significantly.

© Optical Society of America

1. Introduction

High-repetition-rate optical pulse sources are key components in designing high-speed fiberoptic communication systems. Recently, several soliton-pulse sources based on lithium niobate modulators have been proposed, and nearly transform-limited pulses at repetition rates of up to 15 GHz have been generated [1

1. J. J. Veselka and S. K. Korotky, “Pulse generation for soliton systems using lithium niobate modulators,” IEEE J. Sel. Top. Quantum Electron. 2, 300–310 (1996). [CrossRef]

]. However, it is difficult to achieve repetition rates > 20 GHz by this electronic technique. An all-optical method, capable of generating soliton-like pulse trains at high repetition rates, makes use of modulational instability in optical fibers [2

2. A. Hasegawa, “Generation of a train of soliton pulses by induced modulational instability in optical fibers,” Opt. Lett. 9, 288–290 (1984). [CrossRef] [PubMed]

]. Pulse trains at repetition rates of up to 300 GHz have been generated by using such a method [3

3. K. Tai, A. Tomita, J. L. Jewell, and A. Hasegawa, “Generation of subpicosecond solitonlike optical pulses at 0.3 THz repetition rate by induced modulational instability,” Appl. Phys. Lett. 49, 236–238 (1986). [CrossRef]

]. However, individual pulses contain a significant pedestal, leading to nonlinear interactions between neighboring solitons.

A novel all-optical technique which was proposed a few years ago makes use of adiabatic compression of a dual-frequency signal inside an optical fiber and has been used to generate a stable train of pedestal-free, non-interacting solitons [4–11

4. E. M. Dianov, P. V. Mamyshev, A. M. Prokhorov, and S. V. Chernikov, “Generation of a train of fundamental solitons at a high repetition rate in optical fibers,” Opt. Lett. 14, 1008–1010 (1989). [CrossRef] [PubMed]

]. It has been shown that a dispersion-decreasing fiber (DDF) can be used for adiabatic pulse compression and, in fact, is mathematically equivalent to a uniform fiber with distributed gain [5

5. V. A. Bogatyrev, M. M. Bubnov, E. M. Dianov, A. S. Kurkov, P. V. Mamyshev, A. M. Prokhorov, S. D. Rumyantsev, V. A. Semenov, S. L. Semenov, A. A. Sysoliatin, S. V. Chernikov, A. N. Gur’yanov, G. G. Devyatykh, and S. I. Miroshnichenko, “A single-mode fiber with chromatic dispersion varying along the length,” J. Lightwave Technol. 9, 561–566 (1991). [CrossRef]

,6

6. P. V. Mamyshev, S. V. Chernikov, and E. M. Dianov, “Generation of fundamental soliton trains for high-bit-rate optical fiber communication lines,” IEEE J. Quantum Electron. 27, 2347–2355 (1991). [CrossRef]

]. If the group-velocity dispersion (GVD) inside a DDF decreases adiabatically, the soliton self-adjusts to preserve the balance between dispersion and nonlinearity, resulting in pulse compression and enhancement of peak power. Soliton pulse trains with a repetition rate of up to 200 GHz have been generated by using a DDF [6

6. P. V. Mamyshev, S. V. Chernikov, and E. M. Dianov, “Generation of fundamental soliton trains for high-bit-rate optical fiber communication lines,” IEEE J. Quantum Electron. 27, 2347–2355 (1991). [CrossRef]

]. However, because of the relatively small GVD of optical fibers, this technique requires long fiber lengths (> 1 km). Moreover, fabrication of fibers with complex dispersion profiles usually involves splicing of several different fibers or drawing the fiber with an axially varying core diameter.

A more attractive solution consists of adiabatic compression of pulses in a highly dispersive nonlinear medium such as a fiber Bragg grating. Grating dispersion just outside the stop band is up to six orders of magnitude larger than that of silica fiber [12

12. B. J. Eggleton, T. Stephens, P. A. Krug, G. Dhozi, Z. Brodzeli, and F. Ouellette, “Dispersion compensation over 100 km at 10 Gbit/s using a fiber grating in transmission,” Electron. Lett. 32, 1610–1611 (1996). [CrossRef]

,13

13. N. M. Litchinitser, B. J. Eggleton, and D. B. Patterson, “Fiber Bragg gratings for dispersion compensation in transmission: Theoretical model and design criterion for nearly ideal pulse compression,” J. Lightwave Technol. 15, 1303–1313 (1997). [CrossRef]

] and can be tailored simply by changing the grating profile. Indeed, a pulse-compression scheme based on a fiber grating with slowly decreasing dispersion was recently proposed [14

14. G. Lenz and B. J. Eggleton, “Adiabatic Bragg soliton compression in nonuniform grating structures,” J. Opt. Soc. Am. B, in press.

]. Moreover, almost any grating profile can be manufactured using the state-of-the-art grating-writing techniques [15

15. A. Asseh, H. Storay, B. E. Sahlgren, S. Sandgren, and R. A. H. Stubbe, “A writing technique for long fiber Bragg gratings with complex reflectivity profiles,” J. Lightwave Technol. 15, 1419–1423 (1997). [CrossRef]

,16

16. L. Dong, M. J. Cole, M. Durkin, M. Ibsen, and R. I. Laming, “40Gbit/s 1.55um transmission over 109km of non-dispersion-shifted fiber with long continuously chirped fiber gratings,” in 1996Opt. Fiber Commun. Conf. (OFC'96), postdeadline paper PD6.

]. To change the dispersion along the grating length one can vary the average refractive index, the period of the grating (chirped grating), or the index modulation depth. Experimental results on adiabatic soliton evolution in chirped fiber Bragg grating are reported in Ref. [17

17. R. E. Slusher, B. J. Eggleton, C. M. de Sterke, and T. A. Strasser, “Nonlinear pulse reflections from chirped fiber gratings,” Opt. Express 3, (1998). http://epubs.osa.org/oearchive/source/6996.htm [CrossRef] [PubMed]

] elsewhere in this issue. In this paper we consider only changes in the index modulation depth but the theory is general.

We propose a high-repetition-rate soliton source based on adiabatic compression of a dual-frequency signal in a nonuniform fiber Bragg grating operating in transmission. As the signal propagates through the grating whose index modulation depth decreases along its length, it is reshaped into a train of solitons through adiabatic compression, as shown in Fig. 1. In Section II we develop a simple analytical model based on the nonlinear Schrödinger equation (NLSE) for optimization of the grating parameters required for generating high-quality, soliton-like, pulse trains. In Section III we demonstrate numerically that a soliton train at a 40-GHz repetition rate can be generated by this technique and find that the numerical results are in good agreement with the predictions of our analytical model. Finally, in Section IV we summarize our results.

Fig. 1. Generation of a high-repetition-rate soliton train based on adiabatic compression in a nonuniform fiber Bragg grating. The stop-band width varies along the grating because of changes in the index modulation depth.

2. Analytical model

High-intensity pulse propagation through a fiber Bragg grating is governed by the nonlinear coupled-mode equations of the form [18

19. A. B. Aceves and S. Wabnitz, “Self-induced transparency solitons in nonlinear refractive periodic media,” Phys. Lett. A 141, 37–42 (1989). [CrossRef]

]

iE+z+i1VE+t+κE+ΓsE+2E++2Γ×E2E+=0,
(1)
iEz+i1VEt+κE++ΓsE2E+2Γ×E+2E=0.
(2)

Here E + and E - are the slowly varying amplitudes of forward and backward propagating waves, respectively, V = c/n is the velocity of light in fiber, n is the average refractive index, κ = πηΔn/λ B is the coupling coefficient, Δn is the index modulation depth, η is the fraction of the energy in the fiber core, λ B is the Bragg wavelength. Γs and Γ× are the nonlinear parameters responsible for self- and cross-phase modulation such that Γs = Γ× ≡ Γ0 = 2 π n 2/λ, n 2 is the nonlinear refractive index, and λ is the signal wavelength. The nonlinear coupled mode equations have solitary-wave solutions, called Bragg solitons [19

20. B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, “Bragg grating solitons,” Phys. Rev. Lett. 76, 1627–1630 (1996). [CrossRef] [PubMed]

], that have been observed in recent experiments [20–22

20. B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, “Bragg grating solitons,” Phys. Rev. Lett. 76, 1627–1630 (1996). [CrossRef] [PubMed]

].

If the grating parameters are nearly constant over the spectral bandwidth of the pulse and the central frequency of the incident pulse is close to but outside the grating stop band, the nonlinear coupled-mode equations can be reduced to a simple NLSE having the form [23–25

23. C. M. de Sterke and J. E. Sipe, “Coupled modes and the nonlinear Schrödinger equation,” Phys. Rev. A 42, 550–555 (1990). [CrossRef]

]

iAz12β22At2+ΓA2A=0.
(3)

β2=1V21γ2v3δ,Γ=Γ03v22v,
(4)

where δ = n/c(ω - ω B) represents detuning of the incident signal from the Bragg frequency, v = [1-(κ/δ)2]1/2, and γ = (1-v 2)-1/2. We note that if the grating parameters κ or δ vary with z, both β2 and Γ also vary along the grating length.

The fundamental soliton, by definition, obeys the following relation [26

26. G. P. Agrawal, Nonlinear Fiber Optics, (Academic, New York, 1995).

]

N2=LDLNL=ΓIinT2β2=ESΓ2σeffT|β2=1,
(5)

where LD = T 2/|β2| is the dispersion length, LNL = (ΓIin )-1 is the nonlinear length, Iin = |A|2 is the peak intensity of the pulse inside the grating, and T is a measure of the pulse width. For a pulse of the form sech(t/T), T = T FWHM/1.763, where T FWHM is the intensity full width at half maximum. The soliton energy E S = 2Iin eff, where σeff is the effective core area. Note that the intensity inside the uniform fiber grating is enhanced with respect to that outside the grating by a factor 1/v, i.e. Iin = Iout /v [25

25. B. J. Eggleton, C. M. de Sterke, A. Aceves, J. E. Sipe, T. A. Strasser, and R. E. Slusher, “Modulational instabilities and tunable multiple soliton generation in apodized fiber gratings,” Opt. Commun. 149, 267–271 (1998). [CrossRef]

].

We now consider soliton propagation in an axially nonuniform grating for which both β2 and Γ are z dependent. Combining equations (4

4. E. M. Dianov, P. V. Mamyshev, A. M. Prokhorov, and S. V. Chernikov, “Generation of a train of fundamental solitons at a high repetition rate in optical fibers,” Opt. Lett. 14, 1008–1010 (1989). [CrossRef] [PubMed]

) and (5) we obtain the following condition for maintaining N=1 soliton in a nonuniform grating:

ESπn2σeffλT(z)β2eff(z)=1,
(6)

where β2eff is an effective GVD parameter defined to include the frequency dependence of both β2 and Γ (see Eq. (4

4. E. M. Dianov, P. V. Mamyshev, A. M. Prokhorov, and S. V. Chernikov, “Generation of a train of fundamental solitons at a high repetition rate in optical fibers,” Opt. Lett. 14, 1008–1010 (1989). [CrossRef] [PubMed]

)) and is given by

β2eff=2V2(3v2)γ2v2δ.
(7)

From Eq. (6) we find that if β2eff decreases adiabatically with z such that the soliton energy Es remains constant, T must follow changes in β2eff to maintain the condition (5), while the peak intensity must increase. Note also that as β2eff decreases, the soliton accelerates, i.e. v increases with z. The soliton width at the end of the grating is given by

T(L)=T(0)β2eff(L)β2eff(0).
(8)

ξ=1T2(0)0zβ2(z)dz,F=T(0)Γ(z)β2(z)A(z),

Eq. (3) becomes

iFξ+122Fτ2+F2F=ig(ξ)F,
(9)

where τ = t/T(0) and assume β2 is negative,

g(ξ)=12ΓΓξ12β2β2ξ=12β2effβ2effξ.
(10)

The effective gain coefficient g(ξ) takes into account axial variations of both β2 and Γ.

Following Ref. [6], we define the total effective gain as

Geff(ξ)=exp(20ξg(ξ)).
(11)

Using Eq. (11) it can be reduced to

Geff(z)=β2(0)β2(z)Γ(z)Γ(0)=β2eff(0)β2eff(z).
(12)

With the help of Eq. (8) and (12) the pulse width at the grating output can be written as

T(L)=T(0)Geff(L),
(13)

where Geff represents the factor by which the input pulse is compressed. Equations (12) and (13) show that the compression factor is determined by the ratio of the effective dispersion at the end points of the grating.

To ensure that the compression remains adiabatic, we impose the condition that the gain coefficient g is small enough that little amplification occurs over one dispersion length, i.e.

gLD1.
(14)

If g(ξ) varies slowly with ξ, it can be averaged over the grating length. From Eq. (11), Geff (L) = exp(2gL) for z = L. The condition (14) can thus be written as ln(Geff ) ≪ L/LD or, using Eq.(12), as

LD2Lln(β2eff(0)β2eff(z))1.
(15)

We note that the simple theory developed in this Section is based on the assumption that the second-order dispersion of the grating is dominant, i.e. the impact of higher-order dispersion terms is negligible. This assumption is valid only for input signals whose wavelength is tuned close to a stop-band edge but remains far enough from the edges so that the third- and higher-order dispersion terms are small [13

13. N. M. Litchinitser, B. J. Eggleton, and D. B. Patterson, “Fiber Bragg gratings for dispersion compensation in transmission: Theoretical model and design criterion for nearly ideal pulse compression,” J. Lightwave Technol. 15, 1303–1313 (1997). [CrossRef]

].

3. Numerical simulations

A(t,0)=A0sin(πtTS),
(16)

where TS = (Δv)-1 is the modulation period for a mode spacing of Δν. We consider a fiber grating whose coupling coefficient is nonuniform with a functional form

κ(z)=κ0(1Cz),
(17)

where κ 0 is maximum coupling coefficient, and C is a constant. The effective dispersion parameter corresponding to this profile is given by

β2eff(z)=2κ2(z)δV2[2δ2+κ2(z)][δ2κ2(z)].
(18)

Figure 2 shows the axial variations of the coupling coefficient and the effective GVD as functions of z. Note that a linear variation of κ in Eq. (17) was chosen only for simplicity. In principle, κ can have any functional form as long as the conditions (6) and (15) are satisfied.

Fig. 2. Axial variations of κ(z) (black line) and |β2eff(z)| (red line) inside the grating.

Fig. 3. Input sinusoidal signal (upper plot), and soliton train generated at the grating output (lower plot).
Fig. 4. Input dual-frequency signal spectrum (upper plot) and output spectrum of the soliton train (lower plot).

4. Conclusions

In this paper we have proposed a high-repetition-rate soliton-train source based on a nonuniform fiber Bragg grating. In our scheme, a dual-frequency signal is reshaped into a train of soliton-like pulses as it is compressed adiabatically during its propagation in a fiber grating with a nonuniform coupling coefficient. We develop an simple analytical model to predict the width of compressed soliton-like pulses and to provide conditions for adiabatic compression. We demonstrate numerically that a 40-GHz train of 2.6 ps solitons can be generated using a fiber grating with linearly decreasing coupling coefficient. Higher repetition rates can be achieved using stronger and longer gratings or other types of photonic crystals. Since the proposed scheme relies on the dispersion provided by the grating, which is many orders of magnitude larger than that of silica fibers, the device length can be reduced significantly, compared to fiber-based devices. However, note that the intensities required when silica-fiber gratings are used are very large (~10 GW/cm2). The required intensity can be scaled down using a medium with high nonlinearity. For example, the nonlinear coefficient of As2S3 chalcogenide fibers is 100 times larger than that of standard silica fibers [28

28. M. Asobe, “Nonlinear optical properties of chalcogenide glass fibers and their application to all-optical switching,” Opt. Fiber Technol. 3, 142–148 (1997). [CrossRef]

] and, therefore, the peak intensity of 7 GW/cm2 used in our numerical example in Section III will scale down to 70 MW/cm2 (peak power ~ 10 W) if such fibers are used.

Acknowledgments

N.M. Litchinitser thanks the Aileen S. Andrew Foundation for postdoctoral fellowship grant.

References and links

1.

J. J. Veselka and S. K. Korotky, “Pulse generation for soliton systems using lithium niobate modulators,” IEEE J. Sel. Top. Quantum Electron. 2, 300–310 (1996). [CrossRef]

2.

A. Hasegawa, “Generation of a train of soliton pulses by induced modulational instability in optical fibers,” Opt. Lett. 9, 288–290 (1984). [CrossRef] [PubMed]

3.

K. Tai, A. Tomita, J. L. Jewell, and A. Hasegawa, “Generation of subpicosecond solitonlike optical pulses at 0.3 THz repetition rate by induced modulational instability,” Appl. Phys. Lett. 49, 236–238 (1986). [CrossRef]

4.

E. M. Dianov, P. V. Mamyshev, A. M. Prokhorov, and S. V. Chernikov, “Generation of a train of fundamental solitons at a high repetition rate in optical fibers,” Opt. Lett. 14, 1008–1010 (1989). [CrossRef] [PubMed]

5.

V. A. Bogatyrev, M. M. Bubnov, E. M. Dianov, A. S. Kurkov, P. V. Mamyshev, A. M. Prokhorov, S. D. Rumyantsev, V. A. Semenov, S. L. Semenov, A. A. Sysoliatin, S. V. Chernikov, A. N. Gur’yanov, G. G. Devyatykh, and S. I. Miroshnichenko, “A single-mode fiber with chromatic dispersion varying along the length,” J. Lightwave Technol. 9, 561–566 (1991). [CrossRef]

6.

P. V. Mamyshev, S. V. Chernikov, and E. M. Dianov, “Generation of fundamental soliton trains for high-bit-rate optical fiber communication lines,” IEEE J. Quantum Electron. 27, 2347–2355 (1991). [CrossRef]

7.

S.V. Chernikov, D.J. Richardson, R.I. Laming, E.M. Dianov, and D.N. Payne, “70 Gbit/s fiber based source of fundamental solitons at 1550nm,” Electron. Lett. 28, 1210–1212 (1992). [CrossRef]

8.

M. Romagnoli, S. Trillo, and S. Wabnitz, “Soliton switching in nonlinear couplers,” Optical and Quantum Electon. 24, S1237–S1267 (1992). [CrossRef]

9.

S. V. Chernikov, J. R. Taylor, and R. Kashyap, “Comblike dispersion-profiled fiber for soliton pulse train generation,” Opt. Lett. 19, 539–541 (1994). [CrossRef] [PubMed]

10.

E. A. Swanson and S. R. Chinn, “23-GHz and 123-GHz soliton pulse generation using two cw lasers and standard single-mode fiber,” IEEE Photon. Technol. Lett. 6, 796–799 (1994). [CrossRef]

11.

N. Akhmediev and A. Ankiewicz, “Generation of a train of solitons with arbitrary phase difference between neighboring solitons,” Opt. Lett. 19, 545–547 (1994). [CrossRef] [PubMed]

12.

B. J. Eggleton, T. Stephens, P. A. Krug, G. Dhozi, Z. Brodzeli, and F. Ouellette, “Dispersion compensation over 100 km at 10 Gbit/s using a fiber grating in transmission,” Electron. Lett. 32, 1610–1611 (1996). [CrossRef]

13.

N. M. Litchinitser, B. J. Eggleton, and D. B. Patterson, “Fiber Bragg gratings for dispersion compensation in transmission: Theoretical model and design criterion for nearly ideal pulse compression,” J. Lightwave Technol. 15, 1303–1313 (1997). [CrossRef]

14.

G. Lenz and B. J. Eggleton, “Adiabatic Bragg soliton compression in nonuniform grating structures,” J. Opt. Soc. Am. B, in press.

15.

A. Asseh, H. Storay, B. E. Sahlgren, S. Sandgren, and R. A. H. Stubbe, “A writing technique for long fiber Bragg gratings with complex reflectivity profiles,” J. Lightwave Technol. 15, 1419–1423 (1997). [CrossRef]

16.

L. Dong, M. J. Cole, M. Durkin, M. Ibsen, and R. I. Laming, “40Gbit/s 1.55um transmission over 109km of non-dispersion-shifted fiber with long continuously chirped fiber gratings,” in 1996Opt. Fiber Commun. Conf. (OFC'96), postdeadline paper PD6.

17.

R. E. Slusher, B. J. Eggleton, C. M. de Sterke, and T. A. Strasser, “Nonlinear pulse reflections from chirped fiber gratings,” Opt. Express 3, (1998). http://epubs.osa.org/oearchive/source/6996.htm [CrossRef] [PubMed]

18.

C. M. de Sterke and J. E. Sipe, in Progress in Optics XXXIII, ed. by E. Wolf (North-Holand, Amsterdam, 1994), pp. 203-260.

19.

A. B. Aceves and S. Wabnitz, “Self-induced transparency solitons in nonlinear refractive periodic media,” Phys. Lett. A 141, 37–42 (1989). [CrossRef]

20.

B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, “Bragg grating solitons,” Phys. Rev. Lett. 76, 1627–1630 (1996). [CrossRef] [PubMed]

21.

D. Taverner, N.G.R. Broderick, D.T. Richardson, R.I. Laming, and M. Ibsen, “Nonlinear self-switching and multiple gap-soliton formation in a fiber Bragg grating,” Opt. Lett. 23, 328–330 (1998). [CrossRef]

22.

B. J. Eggleton, C. M. de Sterke, and R. E. Slusher, “Bragg solitons in the nonlinear Schrödinger limit: theory and experiment,” submitted to J. Opt. Soc. Am. B (1998).

23.

C. M. de Sterke and J. E. Sipe, “Coupled modes and the nonlinear Schrödinger equation,” Phys. Rev. A 42, 550–555 (1990). [CrossRef]

24.

C. M. de Sterke and B. J. Eggleton, “Bragg solitons and the nonlinear Schrödinger equation,” Phys. Rev. E. , in press.

25.

B. J. Eggleton, C. M. de Sterke, A. Aceves, J. E. Sipe, T. A. Strasser, and R. E. Slusher, “Modulational instabilities and tunable multiple soliton generation in apodized fiber gratings,” Opt. Commun. 149, 267–271 (1998). [CrossRef]

26.

G. P. Agrawal, Nonlinear Fiber Optics, (Academic, New York, 1995).

27.

J. P. Gordon, “Interaction forces among solitons in optical fibers,” Opt. Lett. 8, 596–598 (1983). [CrossRef] [PubMed]

28.

M. Asobe, “Nonlinear optical properties of chalcogenide glass fibers and their application to all-optical switching,” Opt. Fiber Technol. 3, 142–148 (1997). [CrossRef]

OCIS Codes
(060.4370) Fiber optics and optical communications : Nonlinear optics, fibers
(230.6080) Optical devices : Sources
(270.5530) Quantum optics : Pulse propagation and temporal solitons
(320.5520) Ultrafast optics : Pulse compression
(350.2770) Other areas of optics : Gratings

ToC Category:
Focus Issue: Bragg solitons and nonlinear optics of periodic structures

History
Published: November 23, 1998

Citation
Natalia Litchinitser, Govind Agrawal, Benjamin Eggleton, and Gadi Lenz, "High-repetition-rate soliton-train generation using fiber Bragg gratings," Opt. Express 3, 411-417 (1998)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-3-11-411


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References

  1. J. J. Veselka and S. K. Korotky, "Pulse generation for soliton systems using lithium niobate modulators," IEEE J. Sel. Top. Quantum Electron. 2, 300-310 (1996). [CrossRef]
  2. A. Hasegawa, "Generation of a train of soliton pulses by induced modulational instability in optical fibers," Opt. Lett. 9, 288-290 (1984). [CrossRef] [PubMed]
  3. K. Tai, A. Tomita, J. L. Jewell and A. Hasegawa, "Generation of subpicosecond solitonlike optical pulses at 0.3 THz repetition rate by induced modulational instability," Appl. Phys. Lett. 49, 236-238 (1986). [CrossRef]
  4. E. M. Dianov, P. V. Mamyshev, A. M. Prokhorov and S. V. Chernikov, "Generation of a train of fundamental solitons at a high repetition rate in optical fibers," Opt. Lett. 14, 1008-1010 (1989). [CrossRef] [PubMed]
  5. V. A. Bogatyrev, M. M. Bubnov, E. M. Dianov, A. S. Kurkov, P. V. Mamyshev, A. M. Prokhorov, S. D. Rumyantsev, V. A. Semenov, S. L. Semenov, A. A. Sysoliatin, S. V. Chernikov, A. N. Guryanov, G. G. Devyatykh and S. I. Miroshnichenko, "A single-mode fiber with chromatic dispersion varying along the length," J. Lightwave Technol. 9, 561-566 (1991). [CrossRef]
  6. P. V. Mamyshev, S. V. Chernikov and E. M. Dianov, "Generation of fundamental soliton trains for high-bit- rate optical fiber communication lines," IEEE J. Quantum Electron. 27, 2347-2355 (1991). [CrossRef]
  7. S.V. Chernikov, D.J. Richardson, R.I. Laming, E.M. Dianov and D.N. Payne, "70 Gbit/s fiber based source of fundamental solitons at 1550nm," Electron. Lett. 28, 1210-1212 (1992). [CrossRef]
  8. M. Romagnoli, S. Trillo and S. Wabnitz, "Soliton switching in nonlinear couplers," Optical and Quantum Electon. 24, S1237-S1267 (1992). [CrossRef]
  9. S. V. Chernikov, J. R. Taylor and R. Kashyap, "Comblike dispersion-profiled fiber for soliton pulse train generation," Opt. Lett. 19, 539-541 (1994). [CrossRef] [PubMed]
  10. E. A. Swanson and S. R. Chinn, "23-GHz and 123-GHz soliton pulse generation using two cw lasers and standard single-mode fiber," IEEE Photon. Technol. Lett. 6, 796-799 (1994). [CrossRef]
  11. N. Akhmediev and A. Ankiewicz, "Generation of a train of solitons with arbitrary phase difference between neighboring solitons," Opt. Lett. 19, 545-547 (1994). [CrossRef] [PubMed]
  12. B. J. Eggleton, T. Stephens, P. A. Krug, G. Dhozi, Z. Brodzeli and F. Ouellette, "Dispersion compensation over 100 km at 10 Gbit/s using a fiber grating in transmission," Electron. Lett. 32, 1610-1611 (1996). [CrossRef]
  13. N. M. Litchinitser, B. J. Eggleton and D. B. Patterson, "Fiber Bragg gratings for dispersion compensation in transmission: Theoretical model and design criterion for nearly ideal pulse compression," J. Lightwave Technol. 15, 1303-1313 (1997). [CrossRef]
  14. G. Lenz and B. J. Eggleton, "Adiabatic Bragg soliton compression in nonuniform grating structures," J. Opt. Soc. Am. B, in press.
  15. A. Asseh, H. Storoy, B. E. Sahlgren, S. Sandgren and R. A. H. Stubbe, "A writing technique for long fiber Bragg gratings with complex reflectivity profiles," J. Lightwave Technol. 15, 1419-1423 (1997). [CrossRef]
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