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Regimes of operation states in passively mode-locked fiber soliton ring laser
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Optics & Laser Technology 36 (2004) 299 – 307 www.elsevier.com/locate/optlastec
Regimes of operation states in passively mode-locked 'ber soliton ring laser Y.D. Gonga;∗ , P. Shumb , D.Y. Tangb , C. Lua , X. Guoa , V. Paulosea , W.S. Manc , H.Y. Tamc a Institute
for Infocomm Research, Innovation Center Block 2, 18 Nanyang Drive, Singapore 637723, Singapore of Electrical & Electronic Engineering, Nanyang Technological University, Singapore 639798, Singapore c Department of Electrical Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong b School
Received 13 May 2003; received in revised form 18 August 2003; accepted 12 September 2003
Abstract The principal of passively mode-locked 'ber soliton ring lasers is summarized, including its three output operation states: normal soliton, bound–solitons and noise-like pulse. The experimental results of the passively mode-locked 'ber soliton ring lasers developed by us are given. Bound–solitons with di>erent discrete separations and three-bound–solitons state have been observed in our 'ber laser for the 'rst time. The relationship among three operation states in 'ber soliton laser is analyzed. ? 2003 Elsevier Ltd. All rights reserved. PACS: 42.55W; 42.81D; 42.65R Keywords: Optical 'ber lasers; Optical 'ber solitons; Optical pulse generation and pulse compression
1. Introduction Ultra-short 'ber soliton pulse sources have attracted great attention of scientists recently due to their potential in the next generation optical 'ber communication systems. Passively mode-locking technique is used to generate ultra-short pulses. Since 1990s, passively mode-locked 'ber soliton laser at 1550 nm wavelength has made great progress due to the breakthrough of Erbium-doped 'ber. Several techniques including nonlinear polarization rotation (NPR) [1], stretched pulse [2], additive pulse mode locking [3], Figure-8 'ber laser [4,5] which uses the nonlinear amplifying loop mirror technique (NOLM) and the dispersion-imbalanced NOLM (DI-NOLM) [6–8] have been used to achieve this objective. Further to these techniques, single-soliton, multi-solitons, and bound–solitons and noise-like pulses have been observed and reported in those con'gurations [9–12]. To date the shortest soliton pulse from 'ber laser at 1550 nm wavelength is 77 fs [13], and the shortest bound pulse is 326 fs with separation of 938 s [11]. But those results are reported and analyzed separately [14–18]. To date, no paper has been published to summarize the existence of these output states: normal ∗
Corresponding author. Tel.: +65-631-60495; fax:+65-679-59842. E-mail address: [email protected] (Y.D. Gong).
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soliton, bound–solitons and noise-like pulse in one given 'ber laser. Is there any relationship among these states? Then how to design a soliton laser generating the best pulses? Hence, our main focus in this paper is to report our experimental results and establish a relationship between the con'gurations and working principle of a soliton laser that can generate the best pulses. 2. Dierent congurations of passively mode-locked ber soliton ring lasers Fiber lasers can be designed by choosing the right kind of laser cavity. These can be classi'ed into two groups: Fabry– Perot cavities and ring cavity. The simplest type of laser cavity known is the Fabry–Perot cavity and is realized by placing the gain medium between two high-reLecting mirrors that can be replaced by nonlinear optical loop mirror (NOLM). Ring cavities are often used for lasers since they can be designed to operate unidirectionally. In the case of 'ber ring lasers, an additional advantage is that a ring cavity can be made without using mirrors, which results in an all-'ber cavity. So 'ber soliton ring laser is becoming a very attractive research area. In the following part of this section, we will focus on di>erent ring cavity con'gurations and their operation. They are mainly further divided into
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Pump LD
Output
Er-fiber
1480nm Pump 10/90 Output 1
WDM Coupler
DSF
10/90 Coupler
Er-doped fiber
Pol PC
Fiber bench
Fiber
50/50 Coupler
bench
PC1
λ/4
λ/4 λ/2
P-I
λ/4 λ/4
Isolator 10/90 Output 2
PC2
Fig. 1. Con'guration of typical NPR 'ber laser.
SMF
Output2
Pump LD WDM Coupler
Isolator
λ/4
λ/2
λ/4
PBS
λ/4
λ/4
Fiber bench
Er-doped fiber
DCF Output1
Fig. 2. Con'guration of typical stretched 'ber laser.
nonlinear polarization rotation 'ber laser and 'gure-8 'ber laser. We have set all of above types of 'ber lasers up in our experiment. 2.1. Nonlinear polarization rotation (NPR) Fig. 1 shows the con'guration of this kind of 'ber soliton ring laser. There are two polarization controllers, one polarizer and one isolator in the cavity. The 'ber in the cavity should have a low dispersion. Nonlinearity in the 'ber balances the dispersion and forms the soliton pulse. NPR uses the e>ect of nonlinearity in the 'ber, because di>erent parts of a pulse accumulates di>erent phase in one round trip in the laser cavity. Thus, the pulse peak has large nonlinear phase shift which leads to a large rotation of polarization direction. When the polarization controller and polarizer are at a bias, which allow higher intensities peak experience lower loss, the polarizer lets pass the central intense part of the pulse but blocks (absorbs) low intensity pulse wings. The net result is that the pulse is slightly shortened after one round trip inside the ring cavity. In theory, for an isotropic Kerr medium, only the 'rst polarization controller is necessary. However, for the experimental system, a second controller was inserted to counteract the e>ects of residual birefringence in the 'bers. The stretched pulse NPR 'ber laser, as shown in Fig. 2, is one special kind of 'ber ring laser in NPR laser group. Because ultra-short soliton laser usually has lower pulse energy, one way to increase the pulse energy is to use a longer
PC
Fig. 3. The con'guration of typical Figure-8 'ber laser.
cavity to accumulate the dispersion, but this will lower the pulse repetition rate. So the pulse that is stretched due to dispersion before ampli'cation and recompressed afterwards, is a good idea. Actually this kind of laser is very similar to the above NPR design with the same principle, except for the di>erent dispersive 'ber in the di>erent locations. A piece of high dispersion 'ber is placed before Erbium 'ber. The pulse will broaden before ampli'cation, therefore can obtain the larger ampli'cation. At this point the soliton pulses have higher energy. Another reverse dispersion 'ber is placed after the Erbium 'ber to compress the soliton pulse to original shape and stabilize the soliton operation. If we choose the output1 point, where is just after the ampli'cation in Fig. 2, as the output point. In this way, the output1 pulse will have higher energy; it always corresponds to pulses of higher chirp and stretching factor. Output2 always has a narrower width than the output1. Of course, the total dispersion in the cavity should be around zero. 2.2. Figure-8
Y.D. Gong et al. / Optics & Laser Technology 36 (2004) 299 – 307 1480nm Pump
Er-fiber
Pol PC
10/90 Output 1
301
DCF
50/50 Coupler
Fiber bench Isolator 10/90 Output 2
SMF
PC
DSF
Fig. 4. The con'guration of typical DI-NOLM Figure-8 'ber laser.
intensity dependent. It is important to note that the nonreciprocal phase shift exists only for pulsed inputs. DI-NOLM only allows the pulse to pass through and blocks the continuous wave (CW) components. Further tuning of the polarization controller, until higher intensities of the pulse experience lower loss and let light pass, but blocks (absorbs) low intensity pulse wings. Therefore, the net result of DI-NOLM is that the pulse is shortened without any CW background, it is much better than the NOLM made of DSF. Of course, there is need to insert one piece of SMF in the main cavity to compensate the normal dispersion of DCF. 3. Theory of laser The equation that describes the 'ber laser operation is given by modi'ed coupled nonlinear Schrodinger equations [19]: @u @v @2 u i = iv − + 2 @z @t 2 @t 1 2 2 2 g |u| u + |v| u + u; + i2 3 3 2 @v @2 v @u i = iv − + 2 @z @t 2 @t 1 2 2 2 g + i2 |v| v + |u| v + v; 3 3 2
(1)
where u and v are the normalized envelopes of the optical pulses along the two circularly polarized modes of a birefringent optical 'ber. 2 = 2 Tn= is the wave number difference between the modes ( = is the 'ber’s beat length). 2 = 2=2 c is the inverse group velocity di>erence. is the second-order dispersion and is the nonlinearity of the 'ber. g is the gain of the erbium-doped 'ber. For undoped 'ber, g = 0. With above equations, simulations have been carried out. No matter what techniques are used to achieve mode locking for a passively mode-locked 'ber laser, the repetition rate of output pulses is very low and it can be calculated using the equation: fc = ne> Lc =c;
(2)
Fig. 5. Optical Spectrum of 'ber soliton laser (pump power is 12 mW, single-soliton operation).
where ne> is e>ective refractive index in the 'ber, Lc is cavity length of one round trip, c is the speed of light in vacuum. fc is usually below than 100 MHz for a typical passively mode-locked 'ber laser. In order to generate a ultra-short normal soliton, a net anomalous dispersion around zero in the cavity is needed. Regardless of the cavity con'guration, the minimum pulse width is approximately given by [16] |; min ∼ Lc |avg (3) where avg is the average dispersion coeUcient in the cavity. The total dispersion should be as small as possible in order to obtain the narrow pulse output. Hence reducing the cavity length and the use of DSF is two ways of approaching the objective. In order to realize the soliton operation, another mechanism limiting the pulse duration has been revealed in recent studies on the periodic perturbation of solitons [20]. It has shown that periodic ampli'cation of solitons leads to large Luctuations in the pulse energy and shape when the ampli'cation period is approximately 8Z0 . (Z0 is soliton period.) The shortest soliton that can be supported stably must have L ¡ 8Z0 . In practice, the shortest observed pulse typically have L=1, or 2Z0 . Since Z0 ˙ 1= , one may increase Z0 to a manageable length by lowering in the 'ber. However, this comes at the expense of lower pulse energies because soliton peak power P ˙ . Thus to guarantee high-energy ultra-short pulses in the soliton regime appears diUcult. A typical output spectrum of single soliton is shown in Fig. 5, which has many sidelobes, and this is due to the interference between dispersion waves.
4. Three states of operation It has been proved that, irrespective of which cavity design, a soliton pulse can be obtained only if the cavity parameters are suitable. Pump power is increased beyond the threshold and mode locking is achieved by careful tuning
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Table 1 Operation states of passively mode-locked 'ber soliton ring laser
Output states Operation states of passively mode-locking
Special state
Normal soliton state
Single-soliton Multi-solitons Bunch state
Bound–solitons state
Single–bound–solitons pair Multi–bound–solitons pairs Bunch of bound–solitons pairs
Noise-like pulse state
Noise-like single pulse state Noise-like bound–soliton state
Fig. 6. Autocorrelation trace of 'ber soliton laser with 3 dB width of 503 fs.
of the polarization controllers. There are three soliton operation states in any one given 'ber laser, which is mainly based on the polarizations and cavity parameters: normal soliton, bound–solitons and noise-like pulse state, and each of them can be further divided, as shown in Table 1. 4.1. Normal soliton output By careful adjustment of the wave plates, self-started mode locking of the laser is obtained above self-start threshold (usually at a pump power of tens of mW) suddenly. Soliton operation of the laser is 'rstly characterized by the simultaneous generation of multiple soliton pulses in the cavity. Once soliton operation is achieved, the pump power can be reduced to a low value which is much lower than the mode-locking threshold, while still maintaining the soliton operation. Below this value, mode locking cannot be maintained and soliton pulse suddenly disappears and remains in CW operation. This is called pump power hysteresis. Figs. 5 and 6 show single-soliton spectrum (Anritsu MS97204 WDM Network Tester) and autocorrelator (APE PulseScope 50 Autocorrelator) from our NPR 'ber soliton laser using a pump power of 12 mW. The spectrum is almost symmetrical and its 3 dB spectral width is 8:76 nm. The 3 dB width of autocorrelation trace is 503 fs, which is corresponding to 326 fs if Sech2 pulse pro'le is assumed.
Harmonic state
Harmonic state of bound–solitons
Fig. 7. Optical spectrum of multi-solitons state with bunches.
The time-bandwidth product is about 0.37. Therefore, our laser is nearly transform limited. For pump power above the mode-locking self-start threshold, many pulses exist within the laser resonator. This is usually called multi-solitons operation or bunches states, in which solitons are separated by tens of picoseconds. Fig. 7 shows the spectrum from our NPR 'ber laser, where soliton bunches exist in the output. It leads to a small modulation, which corresponding to the separation of pulses inside bunch, on the spectral envelope. Owing to the random nature of the laser pulsing, the pulse patterns and motions vary with time and the detailed features of the laser characteristics similarly di>er for each sweep of the pump power. In some cavities, CW component is also apparent. A change in pump power and the polarization state can change multi-solitons operation or bunches operation; it means the spectrum will change together. The separations between multi-solitons and bunches is related to the acoustic e>ect and gain recovery [24,29,33]. Further tuning the PC and under suitable polarizations bias, if the multiple solitons are spaced uniformly in the cavity, then a special regime of passive harmonic mode locking operation can be observed. As the pump power is lowered below the self-starting threshold, the pulse motions become progressively less chaotic. Pulse quantization was observed too [6,13]. Further theory [24] and measurements indicate that the soliton
Y.D. Gong et al. / Optics & Laser Technology 36 (2004) 299 – 307
Fig. 8. Spectral output of normal soliton from our stretched 'ber laser.
Fig. 9. Optical spectrum of bound–solitons.
pulses exhibit a small pulse to pulse energy variation, which is of the order of a few percent (in our experiment is around 5%). Further reduction in pump power below the losing-mode–locking threshold will result in stoppage of soliton operation. If the pump power is kept just above it, laser will keep the single-solitons operation stable. As the pump power is further reduced, abrupt changes in output power are observed and are associated with the disappearance of individual pulses from the pulse train. Only CW laser can be observed. We have also established another stretched NPR 'ber soliton laser, as shown in Fig. 2. Fig. 8 is its typical optical spectrum of normal soliton from output1 port, and the pulse width is 351 fs.
Fig. 10. Autocorrelation trace of the bound–solitons.
4.2. Bound–solitons output In 1992, Malomed theoretically predicted the existence of bound states of solitons in the dissipatively perturbed nonlinear SchrWodinger equation [25–28,30–32], and Afanasjev has developed the theoretical solution of stable bound solitons [28]. It showed that the interaction of slightly overlapped soliton pulses in the system could lead to the formation of bound solitons with a discrete and 'xed separation. We are the 'rst group to report the experimental observation of the bound–solitons [11,12]. In our NPR laser, with further careful tuning of the polarization controllers, bound– solitons state can be achieved. Bound–solitons behave as a unit and have properties same as single-pulse soliton. They never damage their bindings or alter their pulse separations. Usually their separation is around 1 ps. It is the balance, between dispersion with SPM and XPM, which lead to the 'xed separation. For a given laser, this separation can be several discrete values, which are multiples of the fundamental separation. In the bound–solitons regime, the pulse and its separation are very stable for hours even in the presence of small perturbations such as pump power changes and small linear polarization and temperature drifts. This also indicates that the phase di>erence between the bound–solitons is stable and is of value according to the theory of soliton
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interaction. This feature is di>erent in the case of closed spaced multi-solitons operation mentioned in last subsection. Its output would change due to soliton interaction when the pump and other conditions changed. The threshold of bound state is higher than the single-soliton operation mode. We feel that the increased value is the same as the pump power for the single-soliton pulse energy, since we 'nd that the threshold of bound–solitons is the same as the pump power with two single-soliton pulses existing in the cavity. Further increase in pump power will enter into multi-bound–solitons operation, and even bunch of bound–solitons. Fig. 9 is the spectrum of bound–solitons and Fig. 10 is the output autocorrelation trace, where the height of side peak is only half of the main peak. This means that the two bound– solitons pulses are symmetrical. The spectrum is strongly modulated which is a direct consequence of a very close pulse separation in the time domain according to Fourier transform. The pro'le of the spectrum has a very symmetric structure with a dip in the center. The soliton pulse duration in our laser was around 326 fs measured from the main peak autocorrelation function in Fig. 10. The spectral average modulation period was 8:88 nm (this corresponds to 911 fs according to Fourier transform) from Fig. 9, and the soliton separation between bound–solitons is about 938 fs from its
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Fig. 12. A typical optical spectrum of bunched bound–solitons pairs. Fig. 11. Oscilloscope output under 40 mW pump power.
autocorrelation trace (Fig. 10). This separation seems 'xed in every self-started mode-locking sweep for our laser. Fig. 11 shows the oscilloscope output of multi-bound– solitons. Due to its slow detector rise time, we can only 'nd it works in multi-solitons regime. Bound states need to be veri'ed by autocorrelation trace (Fig. 10) and optical spectrum (Fig. 9). Fig. 12 is the typical optical spectrum that indicates the existence of bunches of bound–solitons in the cavity, it overlaps a very small modulation, and corresponds to the separation of pulses inside bunch. The separation of multi-solitons and bunches is related to the acoustic e>ect and gain recovery too [21–24,29,33]. Harmonic mode-locking of bound solitons has been observed too.
Fig. 13(a) – (d) are the output spectra of di>erent states of bound–solitons from our-made another NPR laser (almost same as the former NPR laser). In this laser, we observed the existence of several discrete separations for bound–solitons, and these are integral multiples of the fundamental base separation, from 982 fs to 1:96 ps, 2:94 ps and 3:92 ps. It is evident from Fig. 13(a) – (d) that the periodicity of modulation progressively decreases in the wavelength space with varying polarization states, which is indeed veri'ed by the experimental results from the autocorrelation. This is 'rst experimental report of existing 4 di>erent bound states with discrete separations in one 'ber soliton laser. In addition, from our stretched NPR 'ber soliton laser, not only two-bound–solitons output with separation of 3:78 ps
Fig. 13. Optical spectra of di>erent bound–solitons with discrete separations. From (a) to (d) the separation increased accordingly.
Y.D. Gong et al. / Optics & Laser Technology 36 (2004) 299 – 307
Fig. 14. Typical optical spectrum of two-bound–solitons from our stretched 'ber laser.
Fig. 15. Optical spectrum of three-bound–solitons.
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Fig. 17. Autocorrelation trace of a noise-like pulse.
Fig. 18. A typical optical spectrum of a noise-like pulse from our 'ber laser.
4.3. Noise-like pulse output
Fig. 16. Autocorrelation trace of three-bound–solitons.
are observed, as shown in Fig. 14, but also the states of three-bound–solitons are observed, which is a signi'cant improvement over the last reported [12]. The separation of three-bound–solitons is 1:15 ps. Figs. 15 and 16 are the traces of autocorrelation and the corresponding output spectrum. In order to produce bound solitons, we found that low birefringence in the laser cavity is necessary. A CW is also a necessity for two-bound–solitons.
If further continue with tuning the polarization bias, then we can obtain noise-like pulse output. The feature of the noise-like pulse is that it has a very wide and smooth optical spectrum without any side lobes. The noise-like output from our made 'ber laser is shown in Fig. 17, the SHG autocorrelation output gives a very narrow pulse. If Sech2 pro'le is assumed, the pulse width is 72 fs. Fig. 18 shows its optical spectrum; sometimes it is a little asymmetrical. This may let you think that you had obtained a very good soliton pulse. But when you use an optical oscilloscope, you will 'nd that the pulse is very wide, usually in the order of nanosecond, as shown in Fig. 19. This is because the noise-like ultrashort pulse has a very rapidly varying timing jitter which smearing out the oscilloscope, hence there show a wide pulse due to the limitation of photodetector’s rise time (around 12 ps). In noise-like pulses operation, the pulses are less stable and the system operates entirely in the regime in which the soliton pulses are seemingly randomly spaced and repeat at the cavity round-trip frequency. The lower the pump power, the more unstable the pulse. We had also measured it by autocorrelator at maximum 50 ps scan range, but this range is too small, so could not catch the whole pro'le. Anyway there always is only one peak with broad pedestal. From the voltage level, the
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5. Summary and discussion
Fig. 19. Noise-like “square pulse” output from oscilloscope.
Fig. 20. Typical optical spectrum of noise-like state from our stretched NPR 'ber laser.
ratio between the peak and the shoulder of the autocorrelation trace is about 2:1, same as the one reported by Ref. [8]. So we think it is noise-like pulse with the 'ne structure of a very narrow pulse, and this 'ne structure has a very rapidly varying timing jitter. For 'gure-8 'ber laser, changing the NOLM bias readily induces the transition from the noise-like pulse to the normal soliton regime of operation. As the polarization is slowly altered, the “square pulse” is seen to break up into tightly packed bunches of solitons, with bunches repeating at the cavity round-trip frequency. As the bias is adjusted close to the point at which the transition from “square pulse” to soliton behavior occurs, large deviation from the expected 2:1 aspect ratio of the coherent spike to the pulse shoulder in the background-free autocorrelation traces of the “square pulses”, are observed. This indicates that the 'ne substructure on a femtosecond timescale develops within the “square pulse”. Fig. 20 is the typical optical spectrum of noise-like state from our stretched NPR 'ber soliton laser, and its “square pulse” width reading from oscilloscope depends on the pump power, it is around 100 ps–2 ns. The higher the pump power, the broader the spectrum. From autocorrelator, the pulse width of its 'ne pulse structure is 278 fs.
Exactly what factors determine which of the three regimes of soliton generation is encountered is not yet fully understood. One possibility is that, under di>erent polarizations, the dispersion and birefringence in the laser cavity, leads to di>erent cross phase modulations between counter-propagating pulse bunches. Then, di>erent transmittivity of nonlinear-cavity allows di>erent operation modes. Of course, low birefringence in the cavity is necessary for bound–solitons operation. Too higher birefringence will not lead bound–solitons operation. Perhaps a CW laser centered at soliton spectrum is another necessity for inducing the bound states. All kinds of 'ber lasers can support three operation states under suitable cavity and polarization parameters. Of course, the threshold of single normal soliton is the lowest, then bound–solitons, and the threshold of noise-like pulses are the highest. The threshold of Figure-8 'ber laser is much higher than that of NPR laser, because of its long cavity and switching e>ect. Both in single-soliton and in bound–solitons state, energy quantization exists. We think that there are some links among these three states. In single-soliton operation, further increasing pump power leads to multi-solitons operation with separation of many picoseconds. Continuing to tune polarization controller, when certain conditions match, bound–solitons were observed. Bound–solitons with di>erent discrete separations and three-bound–solitons state also have been observed in our 'ber laser for the 'rst time. Further increase of pump power can lead to multi-bound– solitons and bunches operation. It seems that low birefringence and CW component are necessary for generating bound–solitons. Further tuning of the polarization controller, noise-like pulse operation can be observed. It is not suitable for the telecommunication. All these three operation states have been observed in our stretched 'ber soliton laser. We think that, for a given 'ber soliton laser, there usually exist three operation states: normal soliton, bound– solitons and noise-like pulse under the di>erent polarization settings. And bound–soliton is a transition state between normal single-soliton state and noise-like pulse state.
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Optics & Laser Technology 36 (2004) 299 – 307 www.elsevier.com/locate/optlastec
Regimes of operation states in passively mode-locked 'ber soliton ring laser Y.D. Gonga;∗ , P. Shumb , D.Y. Tangb , C. Lua , X. Guoa , V. Paulosea , W.S. Manc , H.Y. Tamc a Institute
for Infocomm Research, Innovation Center Block 2, 18 Nanyang Drive, Singapore 637723, Singapore of Electrical & Electronic Engineering, Nanyang Technological University, Singapore 639798, Singapore c Department of Electrical Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong b School
Received 13 May 2003; received in revised form 18 August 2003; accepted 12 September 2003
Abstract The principal of passively mode-locked 'ber soliton ring lasers is summarized, including its three output operation states: normal soliton, bound–solitons and noise-like pulse. The experimental results of the passively mode-locked 'ber soliton ring lasers developed by us are given. Bound–solitons with di>erent discrete separations and three-bound–solitons state have been observed in our 'ber laser for the 'rst time. The relationship among three operation states in 'ber soliton laser is analyzed. ? 2003 Elsevier Ltd. All rights reserved. PACS: 42.55W; 42.81D; 42.65R Keywords: Optical 'ber lasers; Optical 'ber solitons; Optical pulse generation and pulse compression
1. Introduction Ultra-short 'ber soliton pulse sources have attracted great attention of scientists recently due to their potential in the next generation optical 'ber communication systems. Passively mode-locking technique is used to generate ultra-short pulses. Since 1990s, passively mode-locked 'ber soliton laser at 1550 nm wavelength has made great progress due to the breakthrough of Erbium-doped 'ber. Several techniques including nonlinear polarization rotation (NPR) [1], stretched pulse [2], additive pulse mode locking [3], Figure-8 'ber laser [4,5] which uses the nonlinear amplifying loop mirror technique (NOLM) and the dispersion-imbalanced NOLM (DI-NOLM) [6–8] have been used to achieve this objective. Further to these techniques, single-soliton, multi-solitons, and bound–solitons and noise-like pulses have been observed and reported in those con'gurations [9–12]. To date the shortest soliton pulse from 'ber laser at 1550 nm wavelength is 77 fs [13], and the shortest bound pulse is 326 fs with separation of 938 s [11]. But those results are reported and analyzed separately [14–18]. To date, no paper has been published to summarize the existence of these output states: normal ∗
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0030-3992/$ - see front matter ? 2003 Elsevier Ltd. All rights reserved. doi:10.1016/j.optlastec.2003.09.013
soliton, bound–solitons and noise-like pulse in one given 'ber laser. Is there any relationship among these states? Then how to design a soliton laser generating the best pulses? Hence, our main focus in this paper is to report our experimental results and establish a relationship between the con'gurations and working principle of a soliton laser that can generate the best pulses. 2. Dierent congurations of passively mode-locked ber soliton ring lasers Fiber lasers can be designed by choosing the right kind of laser cavity. These can be classi'ed into two groups: Fabry– Perot cavities and ring cavity. The simplest type of laser cavity known is the Fabry–Perot cavity and is realized by placing the gain medium between two high-reLecting mirrors that can be replaced by nonlinear optical loop mirror (NOLM). Ring cavities are often used for lasers since they can be designed to operate unidirectionally. In the case of 'ber ring lasers, an additional advantage is that a ring cavity can be made without using mirrors, which results in an all-'ber cavity. So 'ber soliton ring laser is becoming a very attractive research area. In the following part of this section, we will focus on di>erent ring cavity con'gurations and their operation. They are mainly further divided into
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Pump LD
Output
Er-fiber
1480nm Pump 10/90 Output 1
WDM Coupler
DSF
10/90 Coupler
Er-doped fiber
Pol PC
Fiber bench
Fiber
50/50 Coupler
bench
PC1
λ/4
λ/4 λ/2
P-I
λ/4 λ/4
Isolator 10/90 Output 2
PC2
Fig. 1. Con'guration of typical NPR 'ber laser.
SMF
Output2
Pump LD WDM Coupler
Isolator
λ/4
λ/2
λ/4
PBS
λ/4
λ/4
Fiber bench
Er-doped fiber
DCF Output1
Fig. 2. Con'guration of typical stretched 'ber laser.
nonlinear polarization rotation 'ber laser and 'gure-8 'ber laser. We have set all of above types of 'ber lasers up in our experiment. 2.1. Nonlinear polarization rotation (NPR) Fig. 1 shows the con'guration of this kind of 'ber soliton ring laser. There are two polarization controllers, one polarizer and one isolator in the cavity. The 'ber in the cavity should have a low dispersion. Nonlinearity in the 'ber balances the dispersion and forms the soliton pulse. NPR uses the e>ect of nonlinearity in the 'ber, because di>erent parts of a pulse accumulates di>erent phase in one round trip in the laser cavity. Thus, the pulse peak has large nonlinear phase shift which leads to a large rotation of polarization direction. When the polarization controller and polarizer are at a bias, which allow higher intensities peak experience lower loss, the polarizer lets pass the central intense part of the pulse but blocks (absorbs) low intensity pulse wings. The net result is that the pulse is slightly shortened after one round trip inside the ring cavity. In theory, for an isotropic Kerr medium, only the 'rst polarization controller is necessary. However, for the experimental system, a second controller was inserted to counteract the e>ects of residual birefringence in the 'bers. The stretched pulse NPR 'ber laser, as shown in Fig. 2, is one special kind of 'ber ring laser in NPR laser group. Because ultra-short soliton laser usually has lower pulse energy, one way to increase the pulse energy is to use a longer
PC
Fig. 3. The con'guration of typical Figure-8 'ber laser.
cavity to accumulate the dispersion, but this will lower the pulse repetition rate. So the pulse that is stretched due to dispersion before ampli'cation and recompressed afterwards, is a good idea. Actually this kind of laser is very similar to the above NPR design with the same principle, except for the di>erent dispersive 'ber in the di>erent locations. A piece of high dispersion 'ber is placed before Erbium 'ber. The pulse will broaden before ampli'cation, therefore can obtain the larger ampli'cation. At this point the soliton pulses have higher energy. Another reverse dispersion 'ber is placed after the Erbium 'ber to compress the soliton pulse to original shape and stabilize the soliton operation. If we choose the output1 point, where is just after the ampli'cation in Fig. 2, as the output point. In this way, the output1 pulse will have higher energy; it always corresponds to pulses of higher chirp and stretching factor. Output2 always has a narrower width than the output1. Of course, the total dispersion in the cavity should be around zero. 2.2. Figure-8
Y.D. Gong et al. / Optics & Laser Technology 36 (2004) 299 – 307 1480nm Pump
Er-fiber
Pol PC
10/90 Output 1
301
DCF
50/50 Coupler
Fiber bench Isolator 10/90 Output 2
SMF
PC
DSF
Fig. 4. The con'guration of typical DI-NOLM Figure-8 'ber laser.
intensity dependent. It is important to note that the nonreciprocal phase shift exists only for pulsed inputs. DI-NOLM only allows the pulse to pass through and blocks the continuous wave (CW) components. Further tuning of the polarization controller, until higher intensities of the pulse experience lower loss and let light pass, but blocks (absorbs) low intensity pulse wings. Therefore, the net result of DI-NOLM is that the pulse is shortened without any CW background, it is much better than the NOLM made of DSF. Of course, there is need to insert one piece of SMF in the main cavity to compensate the normal dispersion of DCF. 3. Theory of laser The equation that describes the 'ber laser operation is given by modi'ed coupled nonlinear Schrodinger equations [19]: @u @v @2 u i = iv − + 2 @z @t 2 @t 1 2 2 2 g |u| u + |v| u + u; + i2 3 3 2 @v @2 v @u i = iv − + 2 @z @t 2 @t 1 2 2 2 g + i2 |v| v + |u| v + v; 3 3 2
(1)
where u and v are the normalized envelopes of the optical pulses along the two circularly polarized modes of a birefringent optical 'ber. 2 = 2 Tn= is the wave number difference between the modes ( = is the 'ber’s beat length). 2 = 2=2 c is the inverse group velocity di>erence. is the second-order dispersion and is the nonlinearity of the 'ber. g is the gain of the erbium-doped 'ber. For undoped 'ber, g = 0. With above equations, simulations have been carried out. No matter what techniques are used to achieve mode locking for a passively mode-locked 'ber laser, the repetition rate of output pulses is very low and it can be calculated using the equation: fc = ne> Lc =c;
(2)
Fig. 5. Optical Spectrum of 'ber soliton laser (pump power is 12 mW, single-soliton operation).
where ne> is e>ective refractive index in the 'ber, Lc is cavity length of one round trip, c is the speed of light in vacuum. fc is usually below than 100 MHz for a typical passively mode-locked 'ber laser. In order to generate a ultra-short normal soliton, a net anomalous dispersion around zero in the cavity is needed. Regardless of the cavity con'guration, the minimum pulse width is approximately given by [16] |; min ∼ Lc |avg (3) where avg is the average dispersion coeUcient in the cavity. The total dispersion should be as small as possible in order to obtain the narrow pulse output. Hence reducing the cavity length and the use of DSF is two ways of approaching the objective. In order to realize the soliton operation, another mechanism limiting the pulse duration has been revealed in recent studies on the periodic perturbation of solitons [20]. It has shown that periodic ampli'cation of solitons leads to large Luctuations in the pulse energy and shape when the ampli'cation period is approximately 8Z0 . (Z0 is soliton period.) The shortest soliton that can be supported stably must have L ¡ 8Z0 . In practice, the shortest observed pulse typically have L=1, or 2Z0 . Since Z0 ˙ 1= , one may increase Z0 to a manageable length by lowering in the 'ber. However, this comes at the expense of lower pulse energies because soliton peak power P ˙ . Thus to guarantee high-energy ultra-short pulses in the soliton regime appears diUcult. A typical output spectrum of single soliton is shown in Fig. 5, which has many sidelobes, and this is due to the interference between dispersion waves.
4. Three states of operation It has been proved that, irrespective of which cavity design, a soliton pulse can be obtained only if the cavity parameters are suitable. Pump power is increased beyond the threshold and mode locking is achieved by careful tuning
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Table 1 Operation states of passively mode-locked 'ber soliton ring laser
Output states Operation states of passively mode-locking
Special state
Normal soliton state
Single-soliton Multi-solitons Bunch state
Bound–solitons state
Single–bound–solitons pair Multi–bound–solitons pairs Bunch of bound–solitons pairs
Noise-like pulse state
Noise-like single pulse state Noise-like bound–soliton state
Fig. 6. Autocorrelation trace of 'ber soliton laser with 3 dB width of 503 fs.
of the polarization controllers. There are three soliton operation states in any one given 'ber laser, which is mainly based on the polarizations and cavity parameters: normal soliton, bound–solitons and noise-like pulse state, and each of them can be further divided, as shown in Table 1. 4.1. Normal soliton output By careful adjustment of the wave plates, self-started mode locking of the laser is obtained above self-start threshold (usually at a pump power of tens of mW) suddenly. Soliton operation of the laser is 'rstly characterized by the simultaneous generation of multiple soliton pulses in the cavity. Once soliton operation is achieved, the pump power can be reduced to a low value which is much lower than the mode-locking threshold, while still maintaining the soliton operation. Below this value, mode locking cannot be maintained and soliton pulse suddenly disappears and remains in CW operation. This is called pump power hysteresis. Figs. 5 and 6 show single-soliton spectrum (Anritsu MS97204 WDM Network Tester) and autocorrelator (APE PulseScope 50 Autocorrelator) from our NPR 'ber soliton laser using a pump power of 12 mW. The spectrum is almost symmetrical and its 3 dB spectral width is 8:76 nm. The 3 dB width of autocorrelation trace is 503 fs, which is corresponding to 326 fs if Sech2 pulse pro'le is assumed.
Harmonic state
Harmonic state of bound–solitons
Fig. 7. Optical spectrum of multi-solitons state with bunches.
The time-bandwidth product is about 0.37. Therefore, our laser is nearly transform limited. For pump power above the mode-locking self-start threshold, many pulses exist within the laser resonator. This is usually called multi-solitons operation or bunches states, in which solitons are separated by tens of picoseconds. Fig. 7 shows the spectrum from our NPR 'ber laser, where soliton bunches exist in the output. It leads to a small modulation, which corresponding to the separation of pulses inside bunch, on the spectral envelope. Owing to the random nature of the laser pulsing, the pulse patterns and motions vary with time and the detailed features of the laser characteristics similarly di>er for each sweep of the pump power. In some cavities, CW component is also apparent. A change in pump power and the polarization state can change multi-solitons operation or bunches operation; it means the spectrum will change together. The separations between multi-solitons and bunches is related to the acoustic e>ect and gain recovery [24,29,33]. Further tuning the PC and under suitable polarizations bias, if the multiple solitons are spaced uniformly in the cavity, then a special regime of passive harmonic mode locking operation can be observed. As the pump power is lowered below the self-starting threshold, the pulse motions become progressively less chaotic. Pulse quantization was observed too [6,13]. Further theory [24] and measurements indicate that the soliton
Y.D. Gong et al. / Optics & Laser Technology 36 (2004) 299 – 307
Fig. 8. Spectral output of normal soliton from our stretched 'ber laser.
Fig. 9. Optical spectrum of bound–solitons.
pulses exhibit a small pulse to pulse energy variation, which is of the order of a few percent (in our experiment is around 5%). Further reduction in pump power below the losing-mode–locking threshold will result in stoppage of soliton operation. If the pump power is kept just above it, laser will keep the single-solitons operation stable. As the pump power is further reduced, abrupt changes in output power are observed and are associated with the disappearance of individual pulses from the pulse train. Only CW laser can be observed. We have also established another stretched NPR 'ber soliton laser, as shown in Fig. 2. Fig. 8 is its typical optical spectrum of normal soliton from output1 port, and the pulse width is 351 fs.
Fig. 10. Autocorrelation trace of the bound–solitons.
4.2. Bound–solitons output In 1992, Malomed theoretically predicted the existence of bound states of solitons in the dissipatively perturbed nonlinear SchrWodinger equation [25–28,30–32], and Afanasjev has developed the theoretical solution of stable bound solitons [28]. It showed that the interaction of slightly overlapped soliton pulses in the system could lead to the formation of bound solitons with a discrete and 'xed separation. We are the 'rst group to report the experimental observation of the bound–solitons [11,12]. In our NPR laser, with further careful tuning of the polarization controllers, bound– solitons state can be achieved. Bound–solitons behave as a unit and have properties same as single-pulse soliton. They never damage their bindings or alter their pulse separations. Usually their separation is around 1 ps. It is the balance, between dispersion with SPM and XPM, which lead to the 'xed separation. For a given laser, this separation can be several discrete values, which are multiples of the fundamental separation. In the bound–solitons regime, the pulse and its separation are very stable for hours even in the presence of small perturbations such as pump power changes and small linear polarization and temperature drifts. This also indicates that the phase di>erence between the bound–solitons is stable and is of value according to the theory of soliton
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interaction. This feature is di>erent in the case of closed spaced multi-solitons operation mentioned in last subsection. Its output would change due to soliton interaction when the pump and other conditions changed. The threshold of bound state is higher than the single-soliton operation mode. We feel that the increased value is the same as the pump power for the single-soliton pulse energy, since we 'nd that the threshold of bound–solitons is the same as the pump power with two single-soliton pulses existing in the cavity. Further increase in pump power will enter into multi-bound–solitons operation, and even bunch of bound–solitons. Fig. 9 is the spectrum of bound–solitons and Fig. 10 is the output autocorrelation trace, where the height of side peak is only half of the main peak. This means that the two bound– solitons pulses are symmetrical. The spectrum is strongly modulated which is a direct consequence of a very close pulse separation in the time domain according to Fourier transform. The pro'le of the spectrum has a very symmetric structure with a dip in the center. The soliton pulse duration in our laser was around 326 fs measured from the main peak autocorrelation function in Fig. 10. The spectral average modulation period was 8:88 nm (this corresponds to 911 fs according to Fourier transform) from Fig. 9, and the soliton separation between bound–solitons is about 938 fs from its
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Fig. 12. A typical optical spectrum of bunched bound–solitons pairs. Fig. 11. Oscilloscope output under 40 mW pump power.
autocorrelation trace (Fig. 10). This separation seems 'xed in every self-started mode-locking sweep for our laser. Fig. 11 shows the oscilloscope output of multi-bound– solitons. Due to its slow detector rise time, we can only 'nd it works in multi-solitons regime. Bound states need to be veri'ed by autocorrelation trace (Fig. 10) and optical spectrum (Fig. 9). Fig. 12 is the typical optical spectrum that indicates the existence of bunches of bound–solitons in the cavity, it overlaps a very small modulation, and corresponds to the separation of pulses inside bunch. The separation of multi-solitons and bunches is related to the acoustic e>ect and gain recovery too [21–24,29,33]. Harmonic mode-locking of bound solitons has been observed too.
Fig. 13(a) – (d) are the output spectra of di>erent states of bound–solitons from our-made another NPR laser (almost same as the former NPR laser). In this laser, we observed the existence of several discrete separations for bound–solitons, and these are integral multiples of the fundamental base separation, from 982 fs to 1:96 ps, 2:94 ps and 3:92 ps. It is evident from Fig. 13(a) – (d) that the periodicity of modulation progressively decreases in the wavelength space with varying polarization states, which is indeed veri'ed by the experimental results from the autocorrelation. This is 'rst experimental report of existing 4 di>erent bound states with discrete separations in one 'ber soliton laser. In addition, from our stretched NPR 'ber soliton laser, not only two-bound–solitons output with separation of 3:78 ps
Fig. 13. Optical spectra of di>erent bound–solitons with discrete separations. From (a) to (d) the separation increased accordingly.
Y.D. Gong et al. / Optics & Laser Technology 36 (2004) 299 – 307
Fig. 14. Typical optical spectrum of two-bound–solitons from our stretched 'ber laser.
Fig. 15. Optical spectrum of three-bound–solitons.
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Fig. 17. Autocorrelation trace of a noise-like pulse.
Fig. 18. A typical optical spectrum of a noise-like pulse from our 'ber laser.
4.3. Noise-like pulse output
Fig. 16. Autocorrelation trace of three-bound–solitons.
are observed, as shown in Fig. 14, but also the states of three-bound–solitons are observed, which is a signi'cant improvement over the last reported [12]. The separation of three-bound–solitons is 1:15 ps. Figs. 15 and 16 are the traces of autocorrelation and the corresponding output spectrum. In order to produce bound solitons, we found that low birefringence in the laser cavity is necessary. A CW is also a necessity for two-bound–solitons.
If further continue with tuning the polarization bias, then we can obtain noise-like pulse output. The feature of the noise-like pulse is that it has a very wide and smooth optical spectrum without any side lobes. The noise-like output from our made 'ber laser is shown in Fig. 17, the SHG autocorrelation output gives a very narrow pulse. If Sech2 pro'le is assumed, the pulse width is 72 fs. Fig. 18 shows its optical spectrum; sometimes it is a little asymmetrical. This may let you think that you had obtained a very good soliton pulse. But when you use an optical oscilloscope, you will 'nd that the pulse is very wide, usually in the order of nanosecond, as shown in Fig. 19. This is because the noise-like ultrashort pulse has a very rapidly varying timing jitter which smearing out the oscilloscope, hence there show a wide pulse due to the limitation of photodetector’s rise time (around 12 ps). In noise-like pulses operation, the pulses are less stable and the system operates entirely in the regime in which the soliton pulses are seemingly randomly spaced and repeat at the cavity round-trip frequency. The lower the pump power, the more unstable the pulse. We had also measured it by autocorrelator at maximum 50 ps scan range, but this range is too small, so could not catch the whole pro'le. Anyway there always is only one peak with broad pedestal. From the voltage level, the
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5. Summary and discussion
Fig. 19. Noise-like “square pulse” output from oscilloscope.
Fig. 20. Typical optical spectrum of noise-like state from our stretched NPR 'ber laser.
ratio between the peak and the shoulder of the autocorrelation trace is about 2:1, same as the one reported by Ref. [8]. So we think it is noise-like pulse with the 'ne structure of a very narrow pulse, and this 'ne structure has a very rapidly varying timing jitter. For 'gure-8 'ber laser, changing the NOLM bias readily induces the transition from the noise-like pulse to the normal soliton regime of operation. As the polarization is slowly altered, the “square pulse” is seen to break up into tightly packed bunches of solitons, with bunches repeating at the cavity round-trip frequency. As the bias is adjusted close to the point at which the transition from “square pulse” to soliton behavior occurs, large deviation from the expected 2:1 aspect ratio of the coherent spike to the pulse shoulder in the background-free autocorrelation traces of the “square pulses”, are observed. This indicates that the 'ne substructure on a femtosecond timescale develops within the “square pulse”. Fig. 20 is the typical optical spectrum of noise-like state from our stretched NPR 'ber soliton laser, and its “square pulse” width reading from oscilloscope depends on the pump power, it is around 100 ps–2 ns. The higher the pump power, the broader the spectrum. From autocorrelator, the pulse width of its 'ne pulse structure is 278 fs.
Exactly what factors determine which of the three regimes of soliton generation is encountered is not yet fully understood. One possibility is that, under di>erent polarizations, the dispersion and birefringence in the laser cavity, leads to di>erent cross phase modulations between counter-propagating pulse bunches. Then, di>erent transmittivity of nonlinear-cavity allows di>erent operation modes. Of course, low birefringence in the cavity is necessary for bound–solitons operation. Too higher birefringence will not lead bound–solitons operation. Perhaps a CW laser centered at soliton spectrum is another necessity for inducing the bound states. All kinds of 'ber lasers can support three operation states under suitable cavity and polarization parameters. Of course, the threshold of single normal soliton is the lowest, then bound–solitons, and the threshold of noise-like pulses are the highest. The threshold of Figure-8 'ber laser is much higher than that of NPR laser, because of its long cavity and switching e>ect. Both in single-soliton and in bound–solitons state, energy quantization exists. We think that there are some links among these three states. In single-soliton operation, further increasing pump power leads to multi-solitons operation with separation of many picoseconds. Continuing to tune polarization controller, when certain conditions match, bound–solitons were observed. Bound–solitons with di>erent discrete separations and three-bound–solitons state also have been observed in our 'ber laser for the 'rst time. Further increase of pump power can lead to multi-bound– solitons and bunches operation. It seems that low birefringence and CW component are necessary for generating bound–solitons. Further tuning of the polarization controller, noise-like pulse operation can be observed. It is not suitable for the telecommunication. All these three operation states have been observed in our stretched 'ber soliton laser. We think that, for a given 'ber soliton laser, there usually exist three operation states: normal soliton, bound– solitons and noise-like pulse under the di>erent polarization settings. And bound–soliton is a transition state between normal single-soliton state and noise-like pulse state.
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