Abstract

The ability of laser systems to emit different adjustable temporal pulse profiles and patterns is desirable for a broad range of applications. While passive mode-locking techniques have been widely employed for the realization of ultrafast laser pulses with mainly Gaussian or hyperbolic secant temporal profiles, the generation of versatile pulse shapes in a controllable way and from a single laser system remains a challenge. Here we show that a nonlinear amplifying loop mirror (NALM) laser with a bandwidth-limiting filter (in a nearly dispersion-free arrangement) and a short integrated nonlinear waveguide enables the realization and distinct control of multiple mode-locked pulsing regimes (e.g., Gaussian pulses, square waves, fast sinusoidal-like oscillations) with repetition rates that are variable from the fundamental (7.63 MHz) through its 205th harmonic (1.56 GHz). These dynamics are described by a newly developed and compact theoretical model, which well agrees with our experimental results. It attributes the control of emission regimes to the change of the NALM response function that is achieved by the adjustable interplay between the NALM amplification and the nonlinearity. In contrast to previous square wave emissions, we experimentally observed that an Ikeda instability was responsible for square wave generation. The presented approach enables laser systems that can be universally applied to various applications, e.g., spectroscopy, ultrafast signal processing and generation of non-classical light states.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
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2019 (1)

A. G. Vladimirov, A. V. Kovalev, E. A. Viktorov, N. Rebrova, and G. Huyet, “Dynamics of a class A nonlinear mirror mode-locked laser,” Phys. Rev. E 100(1), 012216 (2019).
[Crossref]

2017 (7)

A. V. Kovalev and E. A. Viktorov, “Class-A mode-locked lasers: Fundamental solutions,” Chaos 27(11), 114318 (2017).
[Crossref]

M. Kues, C. Reimer, B. Wetzel, P. Roztocki, B. E. Little, S. T. Chu, T. Hansson, E. A. Viktorov, D. J. Moss, and R. Morandotti, “Passively mode-locked laser with an ultra-narrow spectral width,” Nat. Photonics 11(3), 159–162 (2017).
[Crossref]

D. Chaparro, L. Furfaro, and S. Balle, “Subpicosecond pulses in a self-starting mode-locked semiconductor-based figure-of-eight fiber laser,” Photonics Res. 5(1), 37–40 (2017).
[Crossref]

P. Roztocki, M. Kues, C. Reimer, B. Wetzel, S. Sciara, Y. Zhang, A. Cino, B. E. Little, S. T. Chu, D. J. Moss, and R. Morandotti, “Practical system for the generation of pulsed quantum frequency combs,” Opt. Express 25(16), 18940–18949 (2017).
[Crossref]

Y. Wang, J. Li, K. Mo, Y. Wang, F. Liu, and Y. Liu, “14.5 GHz passive harmonic mode-locking in a dispersion compensated Tm-doped fiber laser,” Sci. Rep. 7(1), 7779 (2017).
[Crossref]

Y. Zhang, C. Reimer, J. Wu, P. Roztocki, B. Wetzel, B. E. Little, S. T. Chu, D. J. Moss, B. J. Eggleton, M. Kues, and R. Morandotti, “Multichannel phase-sensitive amplification in a low-loss CMOS-compatible spiral waveguide,” Opt. Lett. 42(21), 4391–4394 (2017).
[Crossref]

Z. S. Deng, G. K. Zhao, J. Q. Yuan, J. P. Lin, H. J. Chen, H. Z. Liu, A. P. Luo, H. Cui, Z. C. Luo, and W. C. Xu, “Switchable generation of rectangular noise-like pulse and dissipative soliton resonance in a fiber laser,” Opt. Lett. 42(21), 4517–4520 (2017).
[Crossref]

2016 (2)

2015 (2)

2014 (2)

W. Shi, Q. Fang, X. Zhu, R. A. Norwood, and N. Peyghambarian, “Fiber lasers and their applications,” Appl. Opt. 53(28), 6554–6568 (2014).
[Crossref]

M. Marconi, J. Javaloyes, S. Balle, and M. Giudici, “How lasing localized structures evolve out of passive mode locking,” Phys. Rev. Lett. 112(22), 223901 (2014).
[Crossref]

2013 (3)

2012 (3)

Z. B. Lin, A. P. Luo, S. K. Wang, H. Y. Wang, W. J. Cao, Z. C. Luo, and W. C. Xu, “Generation of dual-wavelength domain-wall rectangular shape pulses in HNLF-based fiber ring laser,” Opt. Laser Technol. 44(7), 2260–2264 (2012).
[Crossref]

X. Zhang, C. Gu, G. Chen, B. Sun, L. Xu, A. Wang, and H. Ming, “Square-wave pulse with ultra-wide tuning range in a passively mode-locked fiber laser,” Opt. Lett. 37(8), 1334–1336 (2012).
[Crossref]

P. Grelu and N. Akhmediev, “Dissipative solitons for mode-locked lasers,” Nat. Photonics 6(2), 84–92 (2012).
[Crossref]

2011 (2)

A. Pasquazi, M. Peccianti, Y. Park, B. E. Little, S. T. Chu, R. Morandotti, J. Azaña, and D. J. Moss, “Sub-picosecond phase-sensitive optical pulse characterization on a chip,” Nat. Photonics 5(10), 618–623 (2011).
[Crossref]

J. C. Hernandez-Garcia, O. Pottiez, R. Grajales-Coutiño, B. Ibarra-Escamilla, E. A. Kuzin, J. M. Estudillo-Ayala, and J. Gutierrez-Gutierrez, “Generation of long broadband pulses with a figure-eight fiber laser,” Laser Phys. 21(8), 1518–1524 (2011).
[Crossref]

2010 (3)

2009 (2)

2008 (1)

W. Chang, A. Ankiewicz, J. M. Soto-Crespo, and N. Akhmediev, “Dissipative soliton resonances,” Phys. Rev. A 78(2), 023830 (2008).
[Crossref]

2007 (1)

R. Kaiser and B. Hüttl, “Monolithic 40-GHz mode-locked MQW DBR lasers for high-speed optical communication systems,” IEEE J. Sel. Top. Quantum Electron. 13(1), 125–135 (2007).
[Crossref]

2004 (1)

2003 (1)

U. Keller, “Recent developments in compact ultrafast lasers,” Nature 424(6950), 831–838 (2003).
[Crossref]

2000 (1)

H. A. Haus, “Mode-locking of lasers,” IEEE J. Sel. Top. Quantum Electron. 6(6), 1173–1185 (2000).
[Crossref]

1999 (1)

T. P. Montoya and G. S. Smith, “Land mine detection using a ground-penetrating radar based on resistively loaded vee dipoles,” IEEE Trans. Antennas Propag. 47(12), 1795–1806 (1999).
[Crossref]

1998 (1)

1994 (2)

1993 (1)

X. Shan and D. M. Spirit, “Spirit “Novel method to suppress noise in harmonically mode-locked erbium fibre lasers,” Electron. Lett. 29(11), 979–981 (1993).
[Crossref]

1992 (4)

A. Takagi, K. Jinguji, and M. Kawachi, “Wavelength Characteristics of (2 ( 2) Optical Channel-Type Directional Couplers with Symmetric or Nonsymmetric Coupling Structures,” J. Lightwave Technol. 10(6), 735–746 (1992).
[Crossref]

S. M. Kelly, “Characteristic sideband instability of periodically amplified average soliton,” Electron. Lett. 28(8), 806–807 (1992).
[Crossref]

A. B. Grudinin, D. J. Richardson, and D. N. Payne, “Energy quantisation in figure eight fibre laser,” Electron. Lett. 28(1), 67–68 (1992).
[Crossref]

I. A. Young, J. K. Greason, and K. L. Wong, “A PLL clock generator with 5 to 110 MHz of lock range for microprocessors,” IEEE J. Solid-State Circuits 27(11), 1599–1607 (1992).
[Crossref]

1991 (1)

M. Nakazawa, E. Yoshida, and Y. Kimura, “Low threshold, 290 fs erbium-doped fiber laser with a nonlinear amplifying loop mirror pumped by InGaAsP laser diodes,” Appl. Phys. Lett. 59(17), 2073–2075 (1991).
[Crossref]

1990 (2)

M. E. Fermann, F. Haberl, M. Hofer, and H. Hochreiter, “Nonlinear amplifying loop mirror,” Opt. Lett. 15(13), 752–754 (1990).
[Crossref]

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26(4), 760–769 (1990).
[Crossref]

1983 (1)

M. W. Derstine, H. M. Gibbs, F. A. Hopf, and D. L. Kaplan, “Alternate paths to chaos in optical bistability,” Phys. Rev. A 27(6), 3200–3208 (1983).
[Crossref]

1982 (2)

K. Ikeda, K. Kondo, and O. Akimoto, “Successive higher-harmonic bifurcations in systems with delayed feedback,” Phys. Rev. Lett. 49(20), 1467–1470 (1982).
[Crossref]

C. Henry, “Theory of the linewidth of semiconductor lasers,” IEEE J. Quantum Electron. 18(2), 259–264 (1982).
[Crossref]

Agrawal, G. P.

A. M. Kaplan, G. P. Agrawal, and D. N. Maywar, “Optical square-wave clock generation based on an all-optical flip-flop,” IEEE Photonics Technol. Lett. 22(7), 489–491 (2010).
[Crossref]

G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2013).

Aguergaray, G.

Akhmediev, N.

P. Grelu and N. Akhmediev, “Dissipative solitons for mode-locked lasers,” Nat. Photonics 6(2), 84–92 (2012).
[Crossref]

W. Chang, A. Ankiewicz, J. M. Soto-Crespo, and N. Akhmediev, “Dissipative soliton resonances,” Phys. Rev. A 78(2), 023830 (2008).
[Crossref]

Akimoto, O.

K. Ikeda, K. Kondo, and O. Akimoto, “Successive higher-harmonic bifurcations in systems with delayed feedback,” Phys. Rev. Lett. 49(20), 1467–1470 (1982).
[Crossref]

and Hou, J.

Ankiewicz, A.

W. Chang, A. Ankiewicz, J. M. Soto-Crespo, and N. Akhmediev, “Dissipative soliton resonances,” Phys. Rev. A 78(2), 023830 (2008).
[Crossref]

Avrutin, E.

E. Avrutin and J. Javaloyes, “Mode-locked Semiconductor Lasers,” in Handbook of Optoelectronic Device Modeling and Simulation. Volume 2, J. Piprek, ed. (CNC, 2018), pp. 187–210.

Azaña, J.

A. Pasquazi, M. Peccianti, Y. Park, B. E. Little, S. T. Chu, R. Morandotti, J. Azaña, and D. J. Moss, “Sub-picosecond phase-sensitive optical pulse characterization on a chip,” Nat. Photonics 5(10), 618–623 (2011).
[Crossref]

A. Pasquazi, Y. Park, J. Azaña, F. Légaré, R. Morandotti, B. E. Little, S. T. Chu, and D. J. Moss, “Efficient wavelength conversion and net parametric gain via Four Wave Mixing in a high index doped silica waveguide,” Opt. Express 18(8), 7634–7641 (2010).
[Crossref]

Bagley, B. G.

Bahloul, F.

Balle, S.

D. Chaparro, L. Furfaro, and S. Balle, “Subpicosecond pulses in a self-starting mode-locked semiconductor-based figure-of-eight fiber laser,” Photonics Res. 5(1), 37–40 (2017).
[Crossref]

M. Marconi, J. Javaloyes, S. Balle, and M. Giudici, “How lasing localized structures evolve out of passive mode locking,” Phys. Rev. Lett. 112(22), 223901 (2014).
[Crossref]

Braham, F. B.

Broderick, N. G.

Cao, W. J.

Z. B. Lin, A. P. Luo, S. K. Wang, H. Y. Wang, W. J. Cao, Z. C. Luo, and W. C. Xu, “Generation of dual-wavelength domain-wall rectangular shape pulses in HNLF-based fiber ring laser,” Opt. Laser Technol. 44(7), 2260–2264 (2012).
[Crossref]

Chang, W.

W. Chang, A. Ankiewicz, J. M. Soto-Crespo, and N. Akhmediev, “Dissipative soliton resonances,” Phys. Rev. A 78(2), 023830 (2008).
[Crossref]

Chaparro, D.

D. Chaparro, L. Furfaro, and S. Balle, “Subpicosecond pulses in a self-starting mode-locked semiconductor-based figure-of-eight fiber laser,” Photonics Res. 5(1), 37–40 (2017).
[Crossref]

Charles, E. L.

T. H. Cormen, E. L. Charles, R.L. Rivest, and C. Stein, “Introduction to algorithms” 2nd ed. (MIT, 2001).

Chen, C. H.

Chen, G.

Chen, H.

Chen, H. J.

Chen, H. R.

Chen, S.

Chen, Y.

Chi, Y. C.

Chu, S. T.

P. Roztocki, M. Kues, C. Reimer, B. Wetzel, S. Sciara, Y. Zhang, A. Cino, B. E. Little, S. T. Chu, D. J. Moss, and R. Morandotti, “Practical system for the generation of pulsed quantum frequency combs,” Opt. Express 25(16), 18940–18949 (2017).
[Crossref]

Y. Zhang, C. Reimer, J. Wu, P. Roztocki, B. Wetzel, B. E. Little, S. T. Chu, D. J. Moss, B. J. Eggleton, M. Kues, and R. Morandotti, “Multichannel phase-sensitive amplification in a low-loss CMOS-compatible spiral waveguide,” Opt. Lett. 42(21), 4391–4394 (2017).
[Crossref]

M. Kues, C. Reimer, B. Wetzel, P. Roztocki, B. E. Little, S. T. Chu, T. Hansson, E. A. Viktorov, D. J. Moss, and R. Morandotti, “Passively mode-locked laser with an ultra-narrow spectral width,” Nat. Photonics 11(3), 159–162 (2017).
[Crossref]

A. Pasquazi, M. Peccianti, Y. Park, B. E. Little, S. T. Chu, R. Morandotti, J. Azaña, and D. J. Moss, “Sub-picosecond phase-sensitive optical pulse characterization on a chip,” Nat. Photonics 5(10), 618–623 (2011).
[Crossref]

D. Duchesne, M. Peccianti, M. R. Lamont, M. Ferrera, L. Razzari, F. Légaré, R. Morandotti, S. T. Chu, B. E. Little, and D. J. Moss, “Supercontinuum generation in a high index doped silica glass spiral waveguide,” Opt. Express 18(2), 923–930 (2010).
[Crossref]

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Figures (7)

Fig. 1.
Fig. 1. Schematic of the laser system for variable pulse profile emissions: An integrated nonlinear waveguide, a bandpass filter (200 GHz at 1550 nm), and a semiconductor optical amplifier (SOA) were employed in the NALM stage. A beam splitter and an EDFA with a built-in optical isolator were used in the amplifier stage. The polarization controllers in both (NALM and amplifying) stages are used to manipulate the nonlinear phase via the control of both linear losses and effective nonlinearity, leading to tunability between different operational regimes.
Fig. 2.
Fig. 2. (a) Amplitude response of the NALM as a function of the field intensity for different SOA gain values: JSOA = 1.5 (black), JSOA = 2.25(green), JSOA = 3.0 (blue). (b) An illustration of the full system response function in the limit of a large filter bandwidth Γ as given by the right-hand side of Eq. (3) (black). The blue line demonstrates an example (for JSOA = 3.13) of a stable period-two orbit of the map which corresponds to a periodic switching between two intensity values (1.1→0.5→1.1→…; the grey line is |En|2 = |En+1|2). The dashed black line illustrates the right-hand side of Eq. (3) for JSOA = 1.5, when period-two orbits and therefore SWs do not exist. The other parameters are: κ = 0.3, SSOA = 1, $\gamma$ = 3, JEDFA = 1.5, SEDFA = 0.1.
Fig. 3.
Fig. 3. Numerical simulations proving the hybrid NALM laser reconfigurability. (a) Bifurcation diagram showing laser intensity extrema for different operation regimes obtained by varying the SOA gain parameter JSOA, ML – mode-locked regime; MSW – modulated square wave regime; SW – square wave regime; SSW – spike square wave regime; FO – fast oscillation regime. Color plots in (b-g) correspond to those of the areas in (a). (b) ML at JSOA = 2.1; (c) harmonic ML at JSOA = 2.1; (d) SW at JSOA = 3.528; (e) MSW at JSOA = 3.54; (f) SSW at JSOA= 3.131; (g) FO at JSOA = 3.055. The parameters are: Γ = 20, α = 0. The other parameters are the same as in Fig. 2.
Fig. 4.
Fig. 4. Numerically obtained harmonics of various square-wave regimes for Γ = 2000: (a)–(c) correspond to the regimes (d)–(f) in Fig. 3. The other parameters are the same as in Fig. 3.
Fig. 5.
Fig. 5. (a) Experimental time traces showing different passively mode-locked dynamical states obtained by varying the polarization controllers PC1 and PC2 for fixed EDFA and SOA gain levels of 11 dB and 2.3 dB, respectively. (a)–(f) correspond to the regimes obtained theoretically and shown in Fig. 3 (b)–(g).
Fig. 6.
Fig. 6. Experimental optical spectra for different dynamics: harmonic-ML, SW and FO with a central wavelength of ∼1550 nm (first column). The corresponding autocorrelation trace (second column). Experimental radio-frequency (RF) spectrum showing clear and narrow peaks at the repetition rate of the dynamical states, confirming stable lasing operation. RF spectrum recorded with a resolution bandwidth (RBW) of 30 Hz, centered at the carrier frequency and with a 1 MHz frequency span (third column).
Fig. 7.
Fig. 7. Schematics of the figure-eight laser based on a nonlinear amplifying loop mirror (NALM). SOA – semiconductor optical amplifier, NE – Kerr-nonlinear element, EDFA – erbium doped fiber amplifier. Propagation in the NALM is characterized by two counter propagating fields as indicated by color arrows. Black arrows show input/output fields at the NALM ports. The points in the scheme have been labeled so to correspond to the field indices in the main text, where further explanations can be found.

Equations (15)

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Γ 1 E ˙ ( τ ) + E ( τ ) = κ 2 exp 1 2 [ ( 1 i α ) G SOA ( E ( τ 1 ) ) + G EDFA ( E ( τ 1 ) ) ] Φ ( τ 1 ) E ( τ 1 ) ,
Φ ( τ ) = { 1 exp [ i γ | E ( τ ) | 2 2 ( exp G SOA ( E ( τ ) ) 1 ) ] } exp i γ | E ( τ ) | 2 2 ,
| E n + 1 | 2 = κ exp ( J SOA 1 + S SOA | E n | 2 + J EDFA 1 + S EDFA | E n | 2 ) × sin 2 ( 1 4 γ | E n | 2 ( 1 exp J SOA 1 + S SOA | E n | 2 ) ) | E n | 2 .
D ^ A ~ ( ω ) = 1 1 i ( ω ω F ) / Δ A ~ ( ω ) ,
K ^ ± A ( t ) = A ( t ) exp ( i γ ± | A ( t ) | 2 ) ,
G ^ SOA A ( t ) = A ( t ) exp ( 1 i α ) G SOA ( A ( t ) ) 2 ,
G ^ EDFA A ( t ) = A ( t ) exp G EDFA ( A ( t ) ) 2 ,
E + ( t ) = K ^ G ^ SOA E 0 ( t ) 2 ,
E ( t ) = i G ^ SOA K ^ E 0 ( t ) 2 ,
E 1 ( t ) = ( E + ( t ) i E ( t ) ) / 2 ,
E 2 ( t ) = κ D ^ G ^ EDFA E 1 ( t ) ,
E ( t ) = κ 2 D ^ G ^ EDFA [ K ^ , G ^ SOA ] E ( t T ) 2 ,
Δ 1 E ˙ ( t ) + E ( t ) = κ 2 G ^ EDFA [ K ^ , G ^ SOA ] E ( t T ) 2 ,
Γ 1 E ˙ ( τ ) + E ( τ ) = κ 2 exp 1 2 [ ( 1 i α ) G SOA ( E ( τ 1 ) ) + G EDFA ( E ( τ 1 ) ) ] Φ ( τ 1 ) E ( τ 1 ) ,
Φ ( τ ) = ( 1 exp [ 1 2 i γ | E ( τ ) | 2 ( exp G SOA ( E ( τ ) ) 1 ) ] ) × exp ( i γ | E ( τ ) | 2 / 2 ) .

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