Soliton Phenomena in Passively Mode-Locked Er-Fiber Lasers
2.5 Soliton Bound States
In this section, the experimental observations of soliton bound states in the passively mode-locked Er-fiber laser are shown. Instead of the equal time separations of several tens ns to several ns between the solitons in passive harmonic mode-locking, the time separations between the bound solitons are only several hundred femtoseconds to several picoseconds. Figure 2-7 shows the SHG autocorrelation trace of the soliton bound states with ps time separations, and the respective optical spectrum is shown in Fig. 2-8. In Fig. 2-7, a variety of soliton bound states has been observed, including two identical bound solitons, five identical bound solitons with equal spacing, and three bound solitons with unequal spacing. For the femtosecond soliton pulse, separation of several ps indicates that these solitons do not overlap and the long-range interaction exists to maintain the bound solitons stably. The long-range interaction may be resulted from the effects of dispersive waves, gain relaxation, and acoustic wave in fiber lasers [24-26].
Bound solitons with the time separation of a few hundred femtoseconds are also observed in the same passively mode-locked Er-fiber laser. In Fig. 2-9, the SHG autocorrelation trace shows the time separation between the bound soliton pair is less than 1 ps. Fig. 2-10 shows the optical spectrum of this closely bound soliton pair with the larger modulation period compared to Fig. 2-8. The closely bound solitons can
interact each other by the overlap of the tails of the pulses, and this soliton bound states can be modeled by Ginzberg-Landau equations within certain parameter regimes [11,27].
2.6 Summary
In this chapter, based on the master equation of passively mode-locked lasers, we introduce the concept of average soliton in the mode-locked Er-fiber laser. The experimental observations of soliton energy quantization and spectral sidebands show the main characteristics of P-APM Er-fiber lasers in soliton regime. Although in soliton regime the passively mode-locked Er-fiber lasers can not generation pulses as short as the pulses from stretched pulse regime, the occurrence of multiple pulses still exhibits exotic soliton phenomena, such as passive harmonic mode-locking and soliton bound states. The passive harmonic mode-locking shows the capability of increasing the repetition rates of femtosecond Er-fiber soliton lasers. However, the repetition rates of spontaneous multiplication are limited to several hundreds of MHz in our case. Besides, the harmonic of spontaneous multiplication is usually not easy to precisely control, and typically passive harmonic mode-locking does not own a very high supermode noise suppression ratio (SMSR). In order to solve these problems, we adopt the method of asynchronous soliton mode-locking to generate high repetition rate femtosecond pulses, and this part will be described in Chapter 3 and Chapter 4.
At the end of this chapter, the observations of various soliton bound states in the P-APM Er-fiber laser are shown. In the literature, soliton bound states in passively mode-locked fiber lasers have been intensely investigated, and a lot of efforts have been dedicated to explain and understand these soliton phenomena. However, it is still an academic interest to ask and explore the possibility of the existence of any other
soliton bound states from the different kinds of mode-locked fiber lasers. The works of the observations of the new soliton bound state in hybrid FM mode-locked Er-fiber laser will be presented in Chapter 5.
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Fig. 2-1 Left: schematic diagram of the P-APM fiber laser. Right: equivalent ring cavity of the P-APM fiber laser.
Fig. 2-2 Left: illustration of nonlinear rotation of elliptical polarization of P-APM. Right: the effect of saturable absorber achieved by P-APM.
Fig. 2-3 Schematic diagram of experimental setup.
(a)
(b)
Fig. 2-4 Optical spectra of the two different mode-locking regimes of a P-APM Er-fiber laser.
(a) Stretched pulse regime at fundamental repetition rate (b) Soliton regime at harmonic repetition rates.
(a)
(b)
(c)
Fig. 2-5 The RF spectra when the spontaneous pulse repetition rate multiplication occurs. (a) At beginning: fundamental repetition rate (b) Pulse bunching (c) Passive harmonic mode-locking.
(a)
(b)
Fig. 2-6 (a) RF spectra of laser output of different harmonics M at 4, 25, and 35 respectively.
(b) Harmonic number versus output power.
(a)
(b)
(c)
Fig. 2-7 SHG autocorrelation trace of the different soliton bound states with ps time separation. (a) Two identical bound solitons (b) Five identical bound solitons with the same time separation (c) Three bound solitons with the different time separations.
Fig. 2-8 Optical spectrum of the soliton bound states with ps time separation.
Fig. 2-9 SHG autocorrelation trace of the bound soliton pair with fs time separation.
Fig. 2-10 Optical spectrum of the bound soliton pair with fs time separation.