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Passive harmonic mode locking of twin-pulse solitons in an erbium-doped fiber ring laser
Optics Communications 229 (2004) 363–370 www.elsevier.com/locate/optcom
Passive harmonic mode locking of twin-pulse solitons in an erbium-doped fiber ring laser B. Zhao a, D.Y. Tang a,*, P. Shum a, W.S. Man b, H.Y. Tam b, Y.D. Gong c, C. Lu c a
School of Electrical and Electronic Engineering, Nanyang Technological University, Nanyang Avenue, Singapore 639798, Singapore b Department of Electrical Engineering, Hong Kong Polytechnic University, Hong Kong c Institute for Infocomm Research, 18 Nanyang Drive, Singapore 637723, Singapore Received 2 April 2003; received in revised form 16 August 2003; accepted 5 November 2003
Abstract We report on the experimental observation of passive harmonic mode locking of twin-pulse solitons in an erbiumdoped fiber ring laser. Experimental investigations on the passive harmonic mode locking of both the single-pulse and the twin-pulse solitons revealed that, apart from the gain recovery and acoustically induced soliton interactions, the global soliton interaction mediated through an unstable CW lasing in the laser cavity also plays an important role in the formation of the state in the laser. Ó 2003 Elsevier B.V. All rights reserved. PACS: 42.81.Dp; 42.55.Wd; 42.60.Fc Keywords: Fiber laser; Solitons; Mode-locking
1. Introduction Passive harmonic mode locking is a well known phenomenon in the passively mode-locked fiber lasers and has been, intensively investigated previously [1–4]. Grudinin et al. [1] firstly reported the experimental observation of this phenomenon. They showed that, under certain conditions the
*
Corresponding author. Tel.: +6567904337; +6567920415. E-mail address: [email protected] (D.Y. Tang).
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multiple solitons in a passively mode-locked fiber laser could arrange themselves automatically to form a stable state, where all the soliton pulses are equally spaced in the cavity. As in such a state, the solitons in cavity have a similar distribution as the optical pulses of a harmonically mode-locked laser, they called the state the passive harmonic mode locking of a fiber soliton laser. The multiple soliton formation in a passively mode-locked fiber laser is a result of the soliton energy quantization, which is known as a typical characteristic of soliton operation in the laser cavity [2,5]. However, what mechanisms drive the multiple solitons to
0030-4018/$ - see front matter Ó 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2003.11.004
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equally distribute in the laser cavity has so far not been clearly explained. Philipetskii et al. [3] have numerically studied the effect of acoustically induced long-term soliton interaction in a fiber laser and found, that the effect could cause the multiple soliton in a laser cavity either to bunch or form harmonic mode locking. Kutz et al. [4] simulated the effect of laser gain depletion and recovery on the soliton distribution in the cavity. They demonstrated, that competition for gain between the solitons could results in equally spaced soliton distributions. Obviously these two effects always exist in a passively mode-locked fiber laser, but the passive harmonic mode locking does not always appear. It would be interesting to know under what conditions will the influence of the two effects on the solitons become significant, or if there are other mechanisms, which have played a even stronger role on the formation of the harmonic mode locking of the lasers. The single-pulse soliton operation is a generic property of the passively mode-locked ultrashort pulse fiber lasers, where the soliton pulse formation is a result of the balanced interaction between the cavity chromatic dispersion and the fiber nonlinearity [6–10]. Recently, we have also experimentally demonstrated, a state of twin-pulse form of soliton operation in passively mode-locked fiber lasers [11,12]. Compared with the single-pulse solitons, the twin-pulse solitons are characterized as that, their soliton profiles have double peaks and the separation between the peaks have discrete, fixed values. Experimental investigations, on the properties of the twin-pulse solitons, have also revealed their energy quantization and pump power hysteresis properties, which were found to be exactly the same as those of the single-pulse solitons [13]. In this paper, we further report on the experimental observation, of the passive harmonic mode locking of the twin-pulse solitons. We demonstrate, that under certain experimental conditions the multiple twin-pulse solitons can automatically arrange themselves in the laser cavity and form a harmonically mode-locked state. In addition, we have experimentally investigated the formation of the harmonic mode locking for both the single-pulse and the twin-pulse solitons in our laser. We show experimentally that, apart
from the gain depletion and recovery and the acoustically induced soliton interactions, an unstable CW lasing mediated global soliton interaction also plays an essential role on the formation of the harmonically mode-locked states.
2. Experimental setup and observations Our laser configuration is schematically shown in Fig. 1. It has a ring cavity of about 5.5 m long, which comprises of a 3.5 m 2000 ppm erbiumdoped fiber, a piece of 1 m long single-mode dispersion-shifted fiber and another piece of 1 m standard telecom fiber (SMF28). The nonlinear polarization rotation technique is used to achieve the self-started mode locking of the laser. For this purpose, a polarization dependent isolator together with two polarization controllers, one consists of two quarter-wavelength-plates and the other two-quarter-wavelength-plates and one halfwavelength-plate, is used to adjust the polarization of light in the cavity. The polarization dependent isolator and the polarization controllers are mounted on a 7 cm long fiber bench to easily and accurately control the polarization of the light. The laser is pumped by a pigtailed InGaAsP semiconductor diode of wavelength 1480 nm. The output of the fiber laser is taken via a 10% fiber coupler and analyzed with an optical spectrum analyzer (HP 70004A) and a commercial optical
Fig. 1. A schematic of the fiber laser setup. PI: polarization dependent isolator; PC: polarization controller; WDM: wavelength division multiplexer; EDF: erbium-doped fiber; DSF: dispersion-shifted fiber.
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autocorrelator (Inrad 5-14-LDA). A 50 GHz wide bandwidth sampling oscilloscope (Agilent 86100A) and a 25 GHz photo-detector (New Focus 1414FC) are used to study the soliton evolution in the laser cavity. As also reported by other authors, mode locking is self-started in the laser simply by increasing the pump power beyond a certain threshold and, adjusting the orientations of the wave-plates. When the polarization of the light is appropriately set, a multi-soliton operation state can be obtained immediately after the mode locking. In our experiment, depending on the setting of the waveplates, either the single-pulse soliton or the twin-pulse soliton operation can be obtained, respectively. Fig. 2 presents the respective optical
Fig. 2. Optical spectra of the single- and twin-pulse solitons of the laser. (a) Single-pulse soliton spectrum, (b) twin-pulse soliton spectrum.
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spectrum of the single- and twin-pulse solitons of the laser. Based on their distinctive optical spectra one can easily identified whether the laser is operating on a single-pulse soliton state or a twinpulse soliton state. The single-pulse solitons observed in our laser have a pulse width (FWHM) of about 340 fs when a sech-form pulse profile is assumed. The twin-pulse solitons has a profile of two bound single-pulse solitons with a pulse separation of about 930 fs. The evolution of multiple single-pulse solitons in passively mode-locked fiber lasers has been intensively investigated previously [6,9,10]. It can be summarized as several modes of operation: the soliton bunching mode, where several solitons tightly bunch and move together in the laser cavity; the stable irregular soliton distribution mode, where solitons are scattered randomly in the cavity with stable relative positions; and the complicated soliton motion mode, where solitons move randomly in the cavity. Under special conditions, the solitons can also automatically rearrange themselves and form the so-called harmonic modelocking state [1,2]. In our experiments, we can reproduce all these types of multiple single-pulse soliton operation modes. As an example, we have shown in Fig. 3 the oscilloscope traces of one stable irregularly distributed and one harmonically modelocked single-pulse soliton operation states. The cavity round trip time of our laser is about 26 ns. Multiple single-pulse solitons coexist in the cavity, either irregularly (Fig. 3(a)) or equally spaced (Fig. 3(b)). In both cases the soliton distributions are stable. However, in the case of Fig. 3(b) as the soliton pulses are equally spaced, the repetition rate of the laser emission becomes 6 times of its fundamental value. Fig. 4 gives the power spectrum of the laser output in the harmonically mode-locked state shown in Fig. 3(b). It is to see, that under the harmonic mode locking the fundamental repetition frequency is suppressed more than 40 dB. Exactly the same modes of multiple soliton evolution have been observed for the twin-pulse solitons, which supports again strongly that the twin-pulse solitons are another form of solitary waves in the laser. Depending on the experimental conditions, we have observed the twin-pulse soliton bunching, stable irregular twin-pulse soliton
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Fig. 3. Oscilloscope traces of multiple single-pulse soliton operations. (a) Stable irregular soliton distribution, (b) harmonic mode-locking. The cavity round trip time is 26 ns.
Fig. 5. Oscilloscope traces of twin-pulse soliton bunching. (a) Several solitons bunch together in the cavity, (b) three bunches of twin-pulse solitons coexist in the cavity.
Fig. 4. Power spectrum of the harmonic mode-locking state shown in Fig. 2(b). The repetition rate of this state is 226.8 MHz, which is 6 times large of the fundamental repetition rate of 37.8 MHz.
distributions, and complicated random twin-pulse soliton motions. Fig. 5(a) shows for example a case of the twin-pulse soliton bunching. Like the singlepulse solitons, several twin-pulse solitons can tightly bunch together. Within a bunch, the solitons have stable relative positions and the bunch moves as a whole with the fundamental repetition rate in the cavity. Several bunches could also coexist in the cavity with stable relative separations as shown in Fig. 5(b). Fig. 6(a) shows a case of the stable irregular twin-pulse soliton distributions. In the state the twin-pulse solitons are scattered in the whole cavity, each of them is well far apart from the other with stable relative positions. With the ex-
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the above-mentioned stable states. Under certain special conditions harmonically mode-locked twin-pulse soliton state have also been obtained. Fig. 6(b) shows one of the experimentally observed such states. In Fig. 6(b) fifteen twin-pulse solitons coexist in the cavity and are equally spaced. As a consequence, the pulse repetition rate becomes 15 times of the laser fundamental repetition rate. Harmonic mode locking of various numbers of twin-pulse solitons has been observed in our experiments. Empirically it was found that, the more the twin-pulse solitons in the cavity, the higher possibility they form harmonic mode locking.
3. Mechanisms of harmonic mode locking
Fig. 6. Oscilloscope traces of multiple twin-pulse soliton in cavity. (a) Stable irregular twin-pulse soliton distribution, (b) harmonic mode-locking of twin-pulse solitons. 15 twin-pulse solitons coexist and are equally distributed in the cavity.
perimental conditions fixed, the soliton distribution pattern is stable. However, if one twin-pulse soliton is destroyed or a new twin-pulse soliton is generated, the solitons will rearrange their positions until a new stable state with a different distribution pattern is reached. The soliton bunching and the stable irregular soliton distribution state, are two most frequently observed multiple soliton operation states in our laser. The complicated random relative soliton motion state is normally observed as a transient process. It occurs at the moment, when the laser operation condition is changed. Depending on the concrete situation, this transient process could take a longer time. But eventually solitons in the cavity will form one of
As mentioned above, theoretical studies have shown that, two mechanisms could contribute to the formation of the harmonic mode locking of solitons in passively mode-locked fiber lasers, one is the gain depletion and recovery and the other one is the acoustic effect. Obviously these two effects always exist in a passively mode-locked fiber soliton laser and affect details of the evolution of solitons in the cavity. However, as demonstrated in our experiments, the harmonic mode-locking states occur only as a special case of the soliton operation. In order to understand this experimental phenomenon, we have conducted experiments, to study the formation of the harmonic mode locking in our laser. It comes to our attention that, whenever, a harmonic mode-locking state occurs in our laser, the oscilloscope trace displays a strong noise background, which spreads over the whole laser cavity as can be clearly seen in Fig. 3(b) and 6(b). While in the other states of the soliton operation, there is no such noise background, e.g. the oscilloscope traces shown in Fig. 5 and 6(a). We have experimentally, identified the physical origin of the noisy background and found out that, it was a result of the unstable CW lasing in the laser. In passively mode-locked fiber soliton lasers depending on the laser parameter setting, the coexistence of CW lasing and soliton operation was frequently observed [14]. This effect is especially pronounced in the fiber lasers mode locked by using the nonlinear polarization rotation
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technique, where the soliton operation and CW lasing suppression is achieved by appropriately selecting the linear cavity birefringence and the orientation of the polarizer in the cavity. Here we present in Fig. 7, a typical optical spectrum of the laser output when, the CW lasing coexists with the single-pulse solitons in the cavity. The strength of the CW component is determined by the linear cavity transmission of the laser. Chen et al. [15] have derived an analytic formula to calculate the cavity transmission of such a laser. Based on the formula and also taking into account the cavity dispersion effect, it is to see that, the linear cavity loss is in fact a sinusoidal function of the wavelength. In a previous paper, we have also demonstrated numerically that the experimentally observed soliton sideband asymmetry is caused by this property of the linear cavity loss of the lasers [16]. Although ideally due to the existence of the saturable absorber effect in the laser, under an optimized soliton operation all CW components would experience negative effective gain and, therefore be suppressed, in practice if the minimum linear cavity loss position is not appropriately set and/or the pump power is strong, CW lasing can still be built up and coexist with the solitons. Also because of the soliton energy quantization, increasing the pump power can significantly increase the strength of the CW components.
Fig. 7. A typical optical spectrum of the laser output when the CW lasing coexists with the single-pulse solitons in the cavity.
Generally the existence of a weak CW wave will not affect the property of the solitons in the cavity. However, when the strength of the CW component becomes strong, as all linear waves are intrinsically unstable in the laser due to the modulation instability, it eventually becomes unstable. Experimentally we observed that, whenever, the CW components become unstable as characterized by the appearance of sidebands on the CW spectral component, a noisy background is observed in the oscilloscope traces as shown in Fig. 3(b) and Fig. 6(b). Under the influence of the noise background all solitons in the cavity start to move, suggesting that the unstable CW components could introduce a kind of global soliton interaction mechanism to the solitons. Under the global interaction of the solitons, eventually an equilibrium state where all the solitons are equally distributed over the whole cavity could be obtained. Actually all of our harmonically mode-locked states are obtained this way. By changing the pump power or the linear cavity loss, the strength of the CW components (the strength of their modulation instability) can be experimentally controlled. To demonstrate the effect of such unstable CW mediated global soliton interaction, we show in Fig. 8 a series of oscilloscope traces recorded at several different instants. In the state of laser operation five single-pulse solitons coexist in the cavity. Two solitons have very closed soliton separation (5 ps) and are bound together. Details about the properties and binding mechanism of this bound-soliton will be reported elsewhere. As our detection system cannot resolve the two bound-solitons, therefore it appears as a large pulse in the oscilloscope. We used the bound-soliton as a trigger signal (it therefore has a fixed position in the oscilloscope traces) and experimentally investigated the relative soliton movement in the cavity. Figs. 8(a) and (b) show the cases, when the noise background is clearly visible in the oscilloscope traces. In these cases, the three solitons moved with respect to each other in the cavity. On the oscilloscope screen the speed of the soliton movement is slow, so we can follow them and study their behavior in details. Even the solitons are very far apart from each other the move of one soliton affects all the others in the cavity. By reducing the CW component strength, the modu-
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shown in Fig. 8(c). Without the noise background the solitons then stay very stable in the cavity, forming an irregular distribution pattern. Exactly the same phenomenon has been observed for the twin-pulse solitons. Based on our experimental results, we strongly believe that the unstable CW lasing in the laser cavity, could be the real mechanism for the formation of the passive harmonic soliton mode locking in the fiber lasers. So far we do not have a concrete theory to describe the interaction between the solitons and the unstable CW components. Nevertheless, it is to point out that interaction between soliton and dispersive waves, have already been studied previously [17–20]. It has been shown that, the soliton interaction mediated through the dispersive waves could be either attractive or repulsive. When a CW component becomes unstable, due to the modulation instability, most probably a similar interaction between the unstable CW and the solitons could be resulted in. As the unstable CW fills in the whole laser cavity and is controlled by the cavity resonance condition, it could be imaged that the interaction of one soliton in the cavity with the unstable CW would affect the interaction of all the other solitons with it. Namely, it introduces a kind of global interaction between the solitons. Only when all the solitons in the cavity are in an equal position, a steady state soliton distribution could be built up. This steady state would be the harmonically mode-locked state. In this sense, one may understand qualitatively how the harmonically mode-locked state is formed.
4. Conclusions
Fig. 8. Oscilloscope traces demonstrating unstable CW lasing mediated soliton interaction. (a) and (b) Two consecutive instants under existence of noisy background. Solitons alter their positions in the cavity. (c) Noisy background is suppressed. Solitons form a stable irregular pattern.
lation instability of the CW component could be suppressed, and consequently the noise background disappears from the oscilloscope trace as
In conclusion, we have experimentally studied the evolution of multiple twin-pulse solitons in a passively mode-locked erbium-doped fiber ring laser and, firstly observed the passive harmonic mode locking of twin-pulse solitons. With the aid of a high-speed oscilloscope, we have experimentally investigated the mechanism of the passive harmonic mode locking in the laser and found that, apart from the gain recovery and the acoustic effect, the unstable CW lasing also plays an important role. Our experimental results also demonstrated
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that, a CW lasing in the passively mode-locked fiber soliton laser could become unstable due to the modulation instability and consequently, become interactive with the solitons in the cavity. As this unstable CW fills in the whole laser cavity, solitons in the laser cavity could become interactive with each other mediated through it, even that they are far apart separated. As a result of this unstable CW mediated soliton interaction, solitons automatically arrange their relative positions and form the harmonically mode-locked states. References [1] A.B. Grudinin, D.J. Richardson, D.N. Payne, Electron. Lett. 29 (1993) 1860. [2] A.B. Grudinin, S. Gray, J. Opt. Soc. Am. B 14 (1997) 144. [3] J.N. Kutz, B.C. Collings, K. Bergman, W.H. Knox, IEEE J. Quantum Electron. 34 (1998) 1749. [4] A.N. Pilipetskii, E.A. Golovchenko, C.R. Menyuk, Opt. Lett. 20 (1995) 907. [5] A.B. Grudinin, D.J. Richardson, D.N. Payne, Electron. Lett. 28 (1992) 67. [6] D.J. Richardson, R.I. Laming, P.N. Payne, M.W. Philips, V. Matsas, Electron. Lett. 27 (1991) 1451.
[7] I.N. Duking III, Electron. Lett. 27 (1991) 544. [8] K. Tamura, H.A. Haus, E.P. Ippen, Electron. Lett. 28 (1992) 2226. [9] D.J. Richardson, R.I. Laming, D.N. Payne, M.W. Phillips, V.J. Matsas, Electron. Lett. 27 (1991) 730. [10] M. Nakazawa, E. Yoshida, Y. Kimura, Appl. Phys. Lett. 21 (1991) 2073. [11] D.Y. Tang, W.S. Man, H.Y. Tam, P.D. Drummond, Phys. Rev. A 64 (2001) 033814/1. [12] D.Y. Tang, B. Zhao, D.Y. Shen, C. Lu, W.S. Man, H.Y. Tam, Phys. Rev. A 66 (2002) 033806/1. [13] B. Zhao, D.Y. Tang, P. Shum, Y.D. Gong, C. Lu, W.S. Man, H.Y. Tam, Appl. Phys. B, Lasers Opt. 77 (2003) 585. [14] S. Namiki, E.P. Ippen, H.A. Haus, K. Tamura, Appl. Phys. Lett. 69 (1996) 3969. [15] C.J. Chen, P.K.A. Wai, C.R. Menyuk, Opt. Lett. 17 (1992) 417. [16] W.S. Man, H.Y. Tam, M.S. Demokan, P.K.A. Wai, D.Y. Tang, J. Opt. Soc. B 17 (2000) 28. [17] L. Socci, M. Romagnoli, Opt. Soc. Am. B 16 (1999) 12. [18] K. Smith, L.F. Mollenauer, Opt. Lett. 14 (1989) 1284. [19] W.H. Loh, A.B. Grudinin, V.V. Afanasjev, D.N. Payne, Opt. Lett. 19 (1994) 698. [20] I. Cristiani, M. Romagnoli, P. Franco, A. Paoletti, L. Socci, IEEE Photonics Tech. Lett. 10 (1998) 1557.
Passive harmonic mode locking of twin-pulse solitons in an erbium-doped fiber ring laser B. Zhao a, D.Y. Tang a,*, P. Shum a, W.S. Man b, H.Y. Tam b, Y.D. Gong c, C. Lu c a
School of Electrical and Electronic Engineering, Nanyang Technological University, Nanyang Avenue, Singapore 639798, Singapore b Department of Electrical Engineering, Hong Kong Polytechnic University, Hong Kong c Institute for Infocomm Research, 18 Nanyang Drive, Singapore 637723, Singapore Received 2 April 2003; received in revised form 16 August 2003; accepted 5 November 2003
Abstract We report on the experimental observation of passive harmonic mode locking of twin-pulse solitons in an erbiumdoped fiber ring laser. Experimental investigations on the passive harmonic mode locking of both the single-pulse and the twin-pulse solitons revealed that, apart from the gain recovery and acoustically induced soliton interactions, the global soliton interaction mediated through an unstable CW lasing in the laser cavity also plays an important role in the formation of the state in the laser. Ó 2003 Elsevier B.V. All rights reserved. PACS: 42.81.Dp; 42.55.Wd; 42.60.Fc Keywords: Fiber laser; Solitons; Mode-locking
1. Introduction Passive harmonic mode locking is a well known phenomenon in the passively mode-locked fiber lasers and has been, intensively investigated previously [1–4]. Grudinin et al. [1] firstly reported the experimental observation of this phenomenon. They showed that, under certain conditions the
*
Corresponding author. Tel.: +6567904337; +6567920415. E-mail address: [email protected] (D.Y. Tang).
fax:
multiple solitons in a passively mode-locked fiber laser could arrange themselves automatically to form a stable state, where all the soliton pulses are equally spaced in the cavity. As in such a state, the solitons in cavity have a similar distribution as the optical pulses of a harmonically mode-locked laser, they called the state the passive harmonic mode locking of a fiber soliton laser. The multiple soliton formation in a passively mode-locked fiber laser is a result of the soliton energy quantization, which is known as a typical characteristic of soliton operation in the laser cavity [2,5]. However, what mechanisms drive the multiple solitons to
0030-4018/$ - see front matter Ó 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2003.11.004
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equally distribute in the laser cavity has so far not been clearly explained. Philipetskii et al. [3] have numerically studied the effect of acoustically induced long-term soliton interaction in a fiber laser and found, that the effect could cause the multiple soliton in a laser cavity either to bunch or form harmonic mode locking. Kutz et al. [4] simulated the effect of laser gain depletion and recovery on the soliton distribution in the cavity. They demonstrated, that competition for gain between the solitons could results in equally spaced soliton distributions. Obviously these two effects always exist in a passively mode-locked fiber laser, but the passive harmonic mode locking does not always appear. It would be interesting to know under what conditions will the influence of the two effects on the solitons become significant, or if there are other mechanisms, which have played a even stronger role on the formation of the harmonic mode locking of the lasers. The single-pulse soliton operation is a generic property of the passively mode-locked ultrashort pulse fiber lasers, where the soliton pulse formation is a result of the balanced interaction between the cavity chromatic dispersion and the fiber nonlinearity [6–10]. Recently, we have also experimentally demonstrated, a state of twin-pulse form of soliton operation in passively mode-locked fiber lasers [11,12]. Compared with the single-pulse solitons, the twin-pulse solitons are characterized as that, their soliton profiles have double peaks and the separation between the peaks have discrete, fixed values. Experimental investigations, on the properties of the twin-pulse solitons, have also revealed their energy quantization and pump power hysteresis properties, which were found to be exactly the same as those of the single-pulse solitons [13]. In this paper, we further report on the experimental observation, of the passive harmonic mode locking of the twin-pulse solitons. We demonstrate, that under certain experimental conditions the multiple twin-pulse solitons can automatically arrange themselves in the laser cavity and form a harmonically mode-locked state. In addition, we have experimentally investigated the formation of the harmonic mode locking for both the single-pulse and the twin-pulse solitons in our laser. We show experimentally that, apart
from the gain depletion and recovery and the acoustically induced soliton interactions, an unstable CW lasing mediated global soliton interaction also plays an essential role on the formation of the harmonically mode-locked states.
2. Experimental setup and observations Our laser configuration is schematically shown in Fig. 1. It has a ring cavity of about 5.5 m long, which comprises of a 3.5 m 2000 ppm erbiumdoped fiber, a piece of 1 m long single-mode dispersion-shifted fiber and another piece of 1 m standard telecom fiber (SMF28). The nonlinear polarization rotation technique is used to achieve the self-started mode locking of the laser. For this purpose, a polarization dependent isolator together with two polarization controllers, one consists of two quarter-wavelength-plates and the other two-quarter-wavelength-plates and one halfwavelength-plate, is used to adjust the polarization of light in the cavity. The polarization dependent isolator and the polarization controllers are mounted on a 7 cm long fiber bench to easily and accurately control the polarization of the light. The laser is pumped by a pigtailed InGaAsP semiconductor diode of wavelength 1480 nm. The output of the fiber laser is taken via a 10% fiber coupler and analyzed with an optical spectrum analyzer (HP 70004A) and a commercial optical
Fig. 1. A schematic of the fiber laser setup. PI: polarization dependent isolator; PC: polarization controller; WDM: wavelength division multiplexer; EDF: erbium-doped fiber; DSF: dispersion-shifted fiber.
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autocorrelator (Inrad 5-14-LDA). A 50 GHz wide bandwidth sampling oscilloscope (Agilent 86100A) and a 25 GHz photo-detector (New Focus 1414FC) are used to study the soliton evolution in the laser cavity. As also reported by other authors, mode locking is self-started in the laser simply by increasing the pump power beyond a certain threshold and, adjusting the orientations of the wave-plates. When the polarization of the light is appropriately set, a multi-soliton operation state can be obtained immediately after the mode locking. In our experiment, depending on the setting of the waveplates, either the single-pulse soliton or the twin-pulse soliton operation can be obtained, respectively. Fig. 2 presents the respective optical
Fig. 2. Optical spectra of the single- and twin-pulse solitons of the laser. (a) Single-pulse soliton spectrum, (b) twin-pulse soliton spectrum.
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spectrum of the single- and twin-pulse solitons of the laser. Based on their distinctive optical spectra one can easily identified whether the laser is operating on a single-pulse soliton state or a twinpulse soliton state. The single-pulse solitons observed in our laser have a pulse width (FWHM) of about 340 fs when a sech-form pulse profile is assumed. The twin-pulse solitons has a profile of two bound single-pulse solitons with a pulse separation of about 930 fs. The evolution of multiple single-pulse solitons in passively mode-locked fiber lasers has been intensively investigated previously [6,9,10]. It can be summarized as several modes of operation: the soliton bunching mode, where several solitons tightly bunch and move together in the laser cavity; the stable irregular soliton distribution mode, where solitons are scattered randomly in the cavity with stable relative positions; and the complicated soliton motion mode, where solitons move randomly in the cavity. Under special conditions, the solitons can also automatically rearrange themselves and form the so-called harmonic modelocking state [1,2]. In our experiments, we can reproduce all these types of multiple single-pulse soliton operation modes. As an example, we have shown in Fig. 3 the oscilloscope traces of one stable irregularly distributed and one harmonically modelocked single-pulse soliton operation states. The cavity round trip time of our laser is about 26 ns. Multiple single-pulse solitons coexist in the cavity, either irregularly (Fig. 3(a)) or equally spaced (Fig. 3(b)). In both cases the soliton distributions are stable. However, in the case of Fig. 3(b) as the soliton pulses are equally spaced, the repetition rate of the laser emission becomes 6 times of its fundamental value. Fig. 4 gives the power spectrum of the laser output in the harmonically mode-locked state shown in Fig. 3(b). It is to see, that under the harmonic mode locking the fundamental repetition frequency is suppressed more than 40 dB. Exactly the same modes of multiple soliton evolution have been observed for the twin-pulse solitons, which supports again strongly that the twin-pulse solitons are another form of solitary waves in the laser. Depending on the experimental conditions, we have observed the twin-pulse soliton bunching, stable irregular twin-pulse soliton
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Fig. 3. Oscilloscope traces of multiple single-pulse soliton operations. (a) Stable irregular soliton distribution, (b) harmonic mode-locking. The cavity round trip time is 26 ns.
Fig. 5. Oscilloscope traces of twin-pulse soliton bunching. (a) Several solitons bunch together in the cavity, (b) three bunches of twin-pulse solitons coexist in the cavity.
Fig. 4. Power spectrum of the harmonic mode-locking state shown in Fig. 2(b). The repetition rate of this state is 226.8 MHz, which is 6 times large of the fundamental repetition rate of 37.8 MHz.
distributions, and complicated random twin-pulse soliton motions. Fig. 5(a) shows for example a case of the twin-pulse soliton bunching. Like the singlepulse solitons, several twin-pulse solitons can tightly bunch together. Within a bunch, the solitons have stable relative positions and the bunch moves as a whole with the fundamental repetition rate in the cavity. Several bunches could also coexist in the cavity with stable relative separations as shown in Fig. 5(b). Fig. 6(a) shows a case of the stable irregular twin-pulse soliton distributions. In the state the twin-pulse solitons are scattered in the whole cavity, each of them is well far apart from the other with stable relative positions. With the ex-
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the above-mentioned stable states. Under certain special conditions harmonically mode-locked twin-pulse soliton state have also been obtained. Fig. 6(b) shows one of the experimentally observed such states. In Fig. 6(b) fifteen twin-pulse solitons coexist in the cavity and are equally spaced. As a consequence, the pulse repetition rate becomes 15 times of the laser fundamental repetition rate. Harmonic mode locking of various numbers of twin-pulse solitons has been observed in our experiments. Empirically it was found that, the more the twin-pulse solitons in the cavity, the higher possibility they form harmonic mode locking.
3. Mechanisms of harmonic mode locking
Fig. 6. Oscilloscope traces of multiple twin-pulse soliton in cavity. (a) Stable irregular twin-pulse soliton distribution, (b) harmonic mode-locking of twin-pulse solitons. 15 twin-pulse solitons coexist and are equally distributed in the cavity.
perimental conditions fixed, the soliton distribution pattern is stable. However, if one twin-pulse soliton is destroyed or a new twin-pulse soliton is generated, the solitons will rearrange their positions until a new stable state with a different distribution pattern is reached. The soliton bunching and the stable irregular soliton distribution state, are two most frequently observed multiple soliton operation states in our laser. The complicated random relative soliton motion state is normally observed as a transient process. It occurs at the moment, when the laser operation condition is changed. Depending on the concrete situation, this transient process could take a longer time. But eventually solitons in the cavity will form one of
As mentioned above, theoretical studies have shown that, two mechanisms could contribute to the formation of the harmonic mode locking of solitons in passively mode-locked fiber lasers, one is the gain depletion and recovery and the other one is the acoustic effect. Obviously these two effects always exist in a passively mode-locked fiber soliton laser and affect details of the evolution of solitons in the cavity. However, as demonstrated in our experiments, the harmonic mode-locking states occur only as a special case of the soliton operation. In order to understand this experimental phenomenon, we have conducted experiments, to study the formation of the harmonic mode locking in our laser. It comes to our attention that, whenever, a harmonic mode-locking state occurs in our laser, the oscilloscope trace displays a strong noise background, which spreads over the whole laser cavity as can be clearly seen in Fig. 3(b) and 6(b). While in the other states of the soliton operation, there is no such noise background, e.g. the oscilloscope traces shown in Fig. 5 and 6(a). We have experimentally, identified the physical origin of the noisy background and found out that, it was a result of the unstable CW lasing in the laser. In passively mode-locked fiber soliton lasers depending on the laser parameter setting, the coexistence of CW lasing and soliton operation was frequently observed [14]. This effect is especially pronounced in the fiber lasers mode locked by using the nonlinear polarization rotation
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technique, where the soliton operation and CW lasing suppression is achieved by appropriately selecting the linear cavity birefringence and the orientation of the polarizer in the cavity. Here we present in Fig. 7, a typical optical spectrum of the laser output when, the CW lasing coexists with the single-pulse solitons in the cavity. The strength of the CW component is determined by the linear cavity transmission of the laser. Chen et al. [15] have derived an analytic formula to calculate the cavity transmission of such a laser. Based on the formula and also taking into account the cavity dispersion effect, it is to see that, the linear cavity loss is in fact a sinusoidal function of the wavelength. In a previous paper, we have also demonstrated numerically that the experimentally observed soliton sideband asymmetry is caused by this property of the linear cavity loss of the lasers [16]. Although ideally due to the existence of the saturable absorber effect in the laser, under an optimized soliton operation all CW components would experience negative effective gain and, therefore be suppressed, in practice if the minimum linear cavity loss position is not appropriately set and/or the pump power is strong, CW lasing can still be built up and coexist with the solitons. Also because of the soliton energy quantization, increasing the pump power can significantly increase the strength of the CW components.
Fig. 7. A typical optical spectrum of the laser output when the CW lasing coexists with the single-pulse solitons in the cavity.
Generally the existence of a weak CW wave will not affect the property of the solitons in the cavity. However, when the strength of the CW component becomes strong, as all linear waves are intrinsically unstable in the laser due to the modulation instability, it eventually becomes unstable. Experimentally we observed that, whenever, the CW components become unstable as characterized by the appearance of sidebands on the CW spectral component, a noisy background is observed in the oscilloscope traces as shown in Fig. 3(b) and Fig. 6(b). Under the influence of the noise background all solitons in the cavity start to move, suggesting that the unstable CW components could introduce a kind of global soliton interaction mechanism to the solitons. Under the global interaction of the solitons, eventually an equilibrium state where all the solitons are equally distributed over the whole cavity could be obtained. Actually all of our harmonically mode-locked states are obtained this way. By changing the pump power or the linear cavity loss, the strength of the CW components (the strength of their modulation instability) can be experimentally controlled. To demonstrate the effect of such unstable CW mediated global soliton interaction, we show in Fig. 8 a series of oscilloscope traces recorded at several different instants. In the state of laser operation five single-pulse solitons coexist in the cavity. Two solitons have very closed soliton separation (5 ps) and are bound together. Details about the properties and binding mechanism of this bound-soliton will be reported elsewhere. As our detection system cannot resolve the two bound-solitons, therefore it appears as a large pulse in the oscilloscope. We used the bound-soliton as a trigger signal (it therefore has a fixed position in the oscilloscope traces) and experimentally investigated the relative soliton movement in the cavity. Figs. 8(a) and (b) show the cases, when the noise background is clearly visible in the oscilloscope traces. In these cases, the three solitons moved with respect to each other in the cavity. On the oscilloscope screen the speed of the soliton movement is slow, so we can follow them and study their behavior in details. Even the solitons are very far apart from each other the move of one soliton affects all the others in the cavity. By reducing the CW component strength, the modu-
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shown in Fig. 8(c). Without the noise background the solitons then stay very stable in the cavity, forming an irregular distribution pattern. Exactly the same phenomenon has been observed for the twin-pulse solitons. Based on our experimental results, we strongly believe that the unstable CW lasing in the laser cavity, could be the real mechanism for the formation of the passive harmonic soliton mode locking in the fiber lasers. So far we do not have a concrete theory to describe the interaction between the solitons and the unstable CW components. Nevertheless, it is to point out that interaction between soliton and dispersive waves, have already been studied previously [17–20]. It has been shown that, the soliton interaction mediated through the dispersive waves could be either attractive or repulsive. When a CW component becomes unstable, due to the modulation instability, most probably a similar interaction between the unstable CW and the solitons could be resulted in. As the unstable CW fills in the whole laser cavity and is controlled by the cavity resonance condition, it could be imaged that the interaction of one soliton in the cavity with the unstable CW would affect the interaction of all the other solitons with it. Namely, it introduces a kind of global interaction between the solitons. Only when all the solitons in the cavity are in an equal position, a steady state soliton distribution could be built up. This steady state would be the harmonically mode-locked state. In this sense, one may understand qualitatively how the harmonically mode-locked state is formed.
4. Conclusions
Fig. 8. Oscilloscope traces demonstrating unstable CW lasing mediated soliton interaction. (a) and (b) Two consecutive instants under existence of noisy background. Solitons alter their positions in the cavity. (c) Noisy background is suppressed. Solitons form a stable irregular pattern.
lation instability of the CW component could be suppressed, and consequently the noise background disappears from the oscilloscope trace as
In conclusion, we have experimentally studied the evolution of multiple twin-pulse solitons in a passively mode-locked erbium-doped fiber ring laser and, firstly observed the passive harmonic mode locking of twin-pulse solitons. With the aid of a high-speed oscilloscope, we have experimentally investigated the mechanism of the passive harmonic mode locking in the laser and found that, apart from the gain recovery and the acoustic effect, the unstable CW lasing also plays an important role. Our experimental results also demonstrated
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that, a CW lasing in the passively mode-locked fiber soliton laser could become unstable due to the modulation instability and consequently, become interactive with the solitons in the cavity. As this unstable CW fills in the whole laser cavity, solitons in the laser cavity could become interactive with each other mediated through it, even that they are far apart separated. As a result of this unstable CW mediated soliton interaction, solitons automatically arrange their relative positions and form the harmonically mode-locked states. References [1] A.B. Grudinin, D.J. Richardson, D.N. Payne, Electron. Lett. 29 (1993) 1860. [2] A.B. Grudinin, S. Gray, J. Opt. Soc. Am. B 14 (1997) 144. [3] J.N. Kutz, B.C. Collings, K. Bergman, W.H. Knox, IEEE J. Quantum Electron. 34 (1998) 1749. [4] A.N. Pilipetskii, E.A. Golovchenko, C.R. Menyuk, Opt. Lett. 20 (1995) 907. [5] A.B. Grudinin, D.J. Richardson, D.N. Payne, Electron. Lett. 28 (1992) 67. [6] D.J. Richardson, R.I. Laming, P.N. Payne, M.W. Philips, V. Matsas, Electron. Lett. 27 (1991) 1451.
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