Asynchronous mode-locked fiber soliton lasers have been attractive due to the low cost stabilization method and the high supermode suppression ratio (SMSR). It is natural to expect that by combining the asynchronous mode-locking mechanism and the rational harmonica mode-locking mechanism, one may be able to generate high repetition rate pulse trains without being limited by the synthesizer frequency and without suffering from the environmental perturbations. However, the laser dynamics of asynchronous rational harmonic mode-locked Er-doped
5
fiber soliton lasers have not been well studied. It will be important to understand more about their laser dynamics before one can actually develop their applications.
1.3 Organization of this thesis
This thesis consists of four chapters. Chapter 1 is an overview of the fiber laser development and the motivation for carrying out this research.
Chapter 2 describes the methods of active mode-lockingand discusses the issues of rational harmonic mode-locking, asynchronous mode-locking, and long-term stabilization of mode-locked fiber lasers.
Chapter 3 presents the experimental setup and analyzes the results of experiments. Finally, Chapter 4 gives a summary about our achievements and possible future work.
6
Reference
[1.1] M. Yoshida, K. Kasai and M. Nakazawa, “Mode-hop-free optical frequency tunable 40 GHz mode-locked fiber laser,” IEEE J.
Quantum Electron. 8, 704 (2007).
[1.2] W. W. Hsiang, C. Y. Lin, M. F. Then and Y. Lai, “Direct generation of a 10 GHz 816 fs pulse train from an erbium-fiber soliton laser with asynchronous phase modulation,” Opt. Lett. 18, 2493 (2005).
[1.3] W. W. Hsiang, C. Y. Lin, N. Sooi and Y. Lai, “Long-term stabilization of a 10 GHz 0.8 ps asynchronously mode-locked Er-fiber soliton laser by deviation-frequency locking,” Opt.
Express 5, 1822 (2006).
[1.4] C. Wu and N. K. Dutta, “High-repetition-rate optical pulse generation using high-repetition-rate optical pulse generation using,” IEEE J. Quantum Electron. 2, 145 (2000).
[1.5] J. P. Wang, B. S. Robinson, S. A. Hamilton, and E. P. Ippen,
“Demonstration of 40-Gb/s packet routing using all-optical header processing,” IEEE Photon. Technol. Lett. 21, 2275 (2006).
7
Chapter 2
Theories of mode-locked fiber lasers 2.1 Active mode-locking
The active mode-locking mechanism is based on the active modulation which induces the loss or phase modulation in the laser cavity.
The utilized active modulators may be either the acousto-optic or the electro-optic modulators. If the modulation frequency is synchronized with the resonator round trip time, the optical pulse trains in the cavity will continue to grow and finally achieve stable mode-locking (Fig. 2.1).
In general, active mode-locked fiber lasers can use two different methods for optical modulation. One is the amplitude modulation (AM) mode-locking, and the other is the phase modulation (PM) mode-locking.
Detailed introduction for the two general methods of modulation will be given in the following section.
Fig. 2.1 Schematic of an active mode-locked laser
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2.1.1 Amplitude modulation mode-locking
Amplitude modulation mode-locking is a way in which the optical amplitude is modulated directly to produce a short pulse train. This mechanism can be analyzed both in the frequency domain and the time domain [2.1].
In frequency domain, as the net gain of the system is greater than zero, longitudinal modes will start to lase. The longitudinal modes are separated equally in the frequency domain and the frequency interval is , where is the round trip time. Denoting the center frequency to be , the sidebands which center on will grow together as explained below if the lasers carry out mode-locking by the method of amplitude modulation.
Fig. 2.2 Actively mode-locked modes in the frequency domain
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Assuming the optical signal in the resonator is , then the amplitude modulated optical signal can be expressed as below:
(2-1)
Here we have denoted the modulation depth and modulation frequency to be M and respectively. According to above results, the center frequency produces two inphase sidebands after the modulation. If one applies the amplitude modulation again other two inphase sidebands can be produced. After repeating the process of modulation, the longitudinal modes in the gain profile will be all phase-locked and the mode-locking can be achieved finally.
ν
0-2f
mν
0-f
mν
0ν
0+f
mν
0+2f
mFig. 2.3 Diagram of the amplitude modulation mode-locking in the frequency domain.
In the time domain analysis, the modulator produces a periodic loss in the cavity. Pulse trains builds up when the gain is greater than the
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loss. If the optical signal passes through the maximum transmission point every roundtrip, then the optical signal will be amplified again and again until it reaches the steady state. The pulsewidth become shorter after passing through the amplitude modulator repeatedly. The pulse shortening strength caused by modulation balances the pulse broadening strength caused by the dispersion/filtering effects of the cavity in the steady state.
The modulation time period must be either equal to the roundtrip time of the laser cavity or equal to the integer fractional of the roundtrip time for the cases of harmonic mode-locking.
Fig. 2.4 Actively mode-locked pulses in the time domain and the time dependence of the net gain.
The master equation of amplitude modulation mode-locked lasers can be written as:
(2-2)
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where g is the gain per pass, l is the loss, is the gain bandwidth and M is the modulation index.
2.1.2 Phase modulation mode-locking
Phase modulation mode-locking is a way in which the optical signal is phase modulated directly to produce short pulse trains. This mechanism again can be analyzed both in the frequency domain and the time domain.
In the frequency domain, we assume the center frequency is as before. When the longitudinal mode is modulated by passing through the phase modulator, the optical signal can be written as below:
(2-3)
(2-4)
where M is the modulation index, is the modulation frequency and is the n-th order Bessel function.
It can be seen that the optical signal consist of unlimited sidebands when (2-3) is expanded into (2-4). The periodic pulse trains are formed when the phases of different modes are mode-locked. The pulse trains diagram is shown in Fig. 2.5
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Fig. 2.5 Formulation of pulse trains in the time domain.
In the time domain, the phase of the optical pulse will be changed by the phase modulator. In the beginning, we can set the constant phase without modulation effect is . Then the optical phase changed by the phase modulator can be expressed by a Taylor series and the result is written as below:
+… (2-5)
where means the immediate frequency. When , the modulation will cause the frequency shift of the optical pulse. Central frequency will continue to be shifted when passing through the phase modulator per round trip, until the optical pulse is shifted out of the gain bandwidth and disappears. As a result, only the synchronized pulses can survive in the laser cavity and then reach the steady state. However, has two solutions (positive 2nd order derivative and negative 2nd order derivative). There will be only one stable solution depending on the
13
sign of and the sign of the cavity dispersion.
2.2 Rational Harmonic mode-locked fiber laser
The high repetition rate mode-locked fiber laser may be useful for high bit rate optical communication systems. The active mode-locking of Er-doped fiber lasers is an attractive way for achieving mode-locking because it can offer transform-limited, sub-picosecond pulse trains with a repetition rate of 10 GHz or higher [2.2] [2.3]. However, the repetition rate of fiber laser is limited by the bandwidths of the electro-optic modulator, synthesizer and RF power amplifier. Rational harmonic mode-locked (RHML) technique can overcome this problem and thus it has attracted a great deal of interest. The method is to detune the modulation frequency away from the longitudinal mode of harmonic mode-locking (HML) to generate high repetition rate pulse trains [2.4].
In this mode-locked mechanism, the final repetition rate can be
(2-6)
when the modulation frequency is set at
(2-7)
Note that is the fundamental frequency of the cavity
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(2-8)
Here n and p are integrals, c is the optical speed in the vacuum and is the effective index of the cavity and L is the cavity length.
By using the RHML laser configuration, Nakazawa and Yoshida have achieved high repetition rate rational harmonic mode-locked fiber laser up to 80-200GHz [2.5]. L. R. Chen hasdemonstrated wavelength-tunable, 30-GHz pulse train generation from a rational harmonic mode-locked fiber optical parametric oscillator (FOPO) by using a 10-GHz driving source [2.6].
If the fiber laser is applied to practical systems, the stability of the optical pulse trains from a fiber laser needs to be improved. The instability may originally come from three main causes:
1) Polarization fluctuations in the long fiber cavity due to fiber vibrations,
2) Cavity length drifts due to the temperature fluctuations.
3) Supermode noises which frequencies could be any integral multiples of the cavity fundamental frequency.
Several approaches have been developed to overcome these problems.
Nakazawa and Yoshida constructed the fiber lasers with an
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all-polarization-maintaining ring cavity [2.3] [2.7]. The issues about how to stabilize the fiber cavity length from not being suffered from the fluctuations in the temperature will be given in Chapter 2.4.
However, the most important problem in the rational harmonic mode-locking is the pulse amplitude variation. Considering a simple example when , the diagram of light modulation in the ring cavity is shown in Fig. 2.6.
Fig. 2.6. Sketch of light modulation in the cavity after T, 2T, 3T, 4T respectively
When light is modulated in the cavity after T, 2T, 3T, 4T respectively,
16
this process will continue to go through repeatedly. The lights in the cavity are amplified and eventually form the pulse trains in the particular position of time domain as shown in the Fig. 2.7 (a).
Fig. 2.7 (a) Pulse train in the particular position of time domain. (b) Pulse in the modulation transmission curve at immediate time
In Fig. 2.7 (b), the pulse forms and gets modulated at I, II, II sequentially in three time periods. So for the , the pulse can be generated in the three points of the modulation curve, but their transmission ratios are different in different time periods. That is the reason why the amplitude variation usually occurs in the rational harmonic mode-locked fiber lasers.
To solve this problem, several researches have been reported for amplitude equalization. By properly adjusting the bias level of the
17
modulator one can equalize the amplitude [2.8]. N.K. Dutta has applied this equalized technique to demonstrate a rational harmonic mode-locked fiber laser with amplitude-equalized output operating at 80 Gbits/s [2.9].
Another main technique for equalizing the pulse amplitude is by using the SOA [2.10].
Rational harmonic mode-locking can be carried out by an amplitude modulator or a phase modulator [2.11]. X. Bao gave a conclusion that rational harmonic mode-locking can be achieved by using the phase modulation and better performance than the counterpart with amplitude modulation can be expected [2.12].
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2.3 Asynchronously mode-locked fiber laser
In active harmonic mode-locked lasers, the modulation frequency must exactly be equal to the cavity harmonic frequency, since otherwise the pulse trains cannot build up in the cavity. This is because the optical pulses will be shifted by a frequency if not synchronized. In the presence of finite bandwidth filter and gain, the pulse train cannot achieve stable mode-locking. However, in the asynchronous mode-locking mechanism [2.13], the modulation frequency is detuned from the cavity harmonic frequency by several kHz to tens kHz and stable mode-locking still can be achieved [2.14]. For the explanation of asynchronously mode-locking mechanism, it is not difficult to know from the simple diagram shown in the Fig. 2.8
Fig. 2.8 Laser cavity with the gain, filter, group velocity dispersion (GVD), self phase
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modulation (SPM) and the phase modulation driven asynchronously.
The fiber laser of Fig. 2.8 is consisted of the optical bandpass filter, group velocity dispersion (GVD), self phase modulation (SPM), gain medium and the phase modulator. Under this laser configuration, the pulse does not disappear in the cavity. On the contrary, stable pulse trains can be realized and compressed to sub-picosecond pulse-width with the 10GHz repetition rate [2.15]. The noise clean up mechanism is similar to the effects of sliding-frequency guiding filters in soliton communication systems [2.16]. The soliton effects induced by the fiber nonlinearity in the asynchronous mode-locked fiber laser can help the mode-locked pulses to survive the asynchronous phase modulation. As a result, the solitons can exist steadily in the cavity, as is shown in Fig. 2.9.
Fig.2.9 The noise-cleanup effect in the asynchronous mode-locked soliton laser.
The central frequency of the solitons varies in the fiber cavity during
20
propagation, but the central frequency of the linear noises keep fixed and will be filtered out by the optical filter. So the asynchronous mode-locking mechanism can provide high SMSR performance without requiring additional intracavity optical devices [2.17].
Applying asynchronous mode-locking in fiber lasers to generate ultra-short pulses provides other advantages. One is to utilize the deviation frequency for feedback use. The other is to take advantages of the laser dynamics of asynchronous mode-locked fiber lasers for special applications [2.18]. These two aspects will be discussed in Chapter 2.4 and Chapter 3.
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2.4 Long-Term Stabilization of Mode-Locked fiber laser
The generation of ultrashort optical pulses in the GHz level is very important for high bit rate optical communication and optical metrology [2.19]. The most common way to produce high speed optical pulse trains is through active mode-locking. In the literature, many techniques have been carried out. These techniques include synchronous mode-locking, asynchronous mode-locking, rational harmonic mode-locking and regenerative mode-locking [2.20].
When the laser speed is improved to the GHz level, applications in practical systems still require enhancing the stability of optical pulse trains. There are many researches to reduce the noises for achieving long-term stabilization of the mode-locked fiber laser. They are as given in the below:
A) PZT
The main cause for laser instability is the cavity length drift due to the temperature fluctuations. This perturbation causes the repetition rate to shift and then the mode-locking cannot be maintained. The supermodes may also oscillate simultaneously and compete with each other. Thus the
22
fluctuations of pulse amplitude are generated, which appear as noises in the RF spectrum.
As said above, controlling the cavity length is a direct way to enhance the stability. It can use the error signal from the mixing of the modulation frequency signal and the pulse repetition rate signal to control the voltage of PZT. The PZT is lengthened or shorted by the applied voltage. The length of fiber winded around the PZT is thus also changed by the error signal. Finally, the cavity length fluctuations caused by temperature perturbations can be compensated and a fixed cavity length can be kept [2.21].
Fig. 2.10 Schematic setup of PZT feedback control
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B) Regenerative mode-locking [2.3]
As shown in Fig. 2.11, the 40GHz clock extraction circuit is used to extract the 40 GHz clock from the laser output. The clock is then amplified and applied to the phase modulator. Finally, mode-locking is carried out. The laser operation continued stably for a long time because the modulation frequency (i.e. clock signal) always follows the changes in the cavity length. This means the modulation frequency and the cavity harmonic frequency always keep synchronous.
Fig. 2.11 Diagram of regenerative mode-locked fiber laser
Recently, the mode-locked fiber laser stabilization techniques are improved to a more advanced level. Base on the regenerative
24
mode-locked technique, Nakazawa and Yoshida have successfully demonstrated the mode-hop-free optical frequency tunable mode-locked fiber laser [2.22].The wavelength reference of C2H2 is employed to absolutely stabilize the optical frequency of the mode-locked fiber laser [2.23]. It is also possible to independently stabilize the repetition rate and the optical frequency [2.24].
Base on controlling the cavity length to lock the deviation frequency at a suitable value, there is a stabilization technique by taking advantages of the unique characteristics of asynchronous mode-locking [2.25]. It provides an advantage that the feedback module does not require high frequency electronics and in principle the cost can be much less.
25
Reference
[2.1] H. A. Haus, “Mode-locking of lasers,” IEEE J. Quantum Electron. 6, 117 (2000).
[2.2] B. Bakhshi, P. A. Andrekson, “40 GHz actively modelocked polarization maintaining erbium fiber ring laser”, Electronics Lett. 5, 411 (2000).
[2.3] E. Yoshida and M. Nakazawa, “A 40-GHz 850-fs regeneratively FM mode-locked polarization-maintaining Erbium fiber ring laser”, IEEE Photon. Technol. Lett. 12, 1613 (2000).
[2.4] C. Wu and N. K. Dutta, “High-repetition-rate optical pulse generation using a rational harmonic mode-locked fiber laser,”
IEEE J. Quantum Electron. 2, 145 (2000).
[2.5] E. Yoshida and M. Nakazawa, “80~200 GHz erbium doped fiber laser using a rational harmonic mode-locking technique,”
Electron. Lett. 15, 1370 (1996).
[2.6] J. Li, T. Huang, and L. R. Chen, “Rational harmonic mode-locking of a fiber optical parametric oscillator at 30 GHz,” IEEE J. Photon. 3, 468 (2011).
[2.7] E. Yoshida and M. Nakazawa, “Ultrastable harmonically and
26
regeneratively mode-locked polarization-maintaining erbium fiber ring laser,” IEEE Electronics Lett. 19, 1603 (1994).
[2.8] X. Feng, Y. Liu, S. Yuan, G. Kai, W. Zhang, and X. Dong,
“Pulse-amplitude equalization in a rational harmonic mode-locked fiber laser using nonlinear modulation,” IEEE Photon. Technol. Lett. 8, 1813 (2004).
[2.9] G. Zhu and N. K. Dutta, “Eighth-order rational harmonic mode-locked fiber laser with amplitude-equalized output
operating at 80 Gbits/s,” Opt. Lett. 17, 2212 (2005).
[2.10] X. Feng, Y. Liu, S. Yuan, G. Kai, W. Zhang, and X. Dong,
“Pulse-amplitude equalization in a rational harmonic mode-locked fiber laser using nonlinear modulation,” IEEE Photon. Technol. Lett. 8, 1813 (2004).
[2.11] S. Yang and X. Bao, “Rational harmonic mode-locking in a phase modulated fiber laser,” IEEE Photon. Technol. Lett. 12, 1332 (2006).
[2.12] S. Yang, J. Cameron, and X. Bao, “Stabilized Phase-Modulated Rational Harmonic Mode-Locking Soliton Fiber Laser,” IEEE Photon. Technol. Lett. 19, 393 (2007).
27
[2.13] C. R. Doerr, H. A. Haus, and E. P. Ippen, “Asychronous soliton mode locking”, Opt. Lett. 19, 1958 (1994).
[2.14] H. A. Haus, D. J. Jones, E. P. Ippen, and W. S. Wong, “Theory of soliton stability in asynchronous modelocking,” IEEE J.
Lightwave Technol. 14, 622 (1996).
[2.15] W. W. Hsiang, C. Y. Lin, M. F. Tien, and Y. C. Lai, “Direct generation of a 10 GHz 816 fs pulse train from an erbium-fiber soliton laser with asynchronous phase modulation,” Opt. Lett. 30, 2493 (2005).
[2.16] L. F. Mollenauer, J. P. Gordon, and S. G. Evangelides, ‘‘The sliding frequency guiding filter: an improved form of soliton jitter control,’’ Opt. Lett. 17, 1575 (1992).
[2.17] G. T. Harvey and L. F. Mollenauer, “Harmonically mode-locked fiber ring laser with an internal Fabry-Perot stabilizer for soliton transmission,” Opt. Lett. 2, 107 (1993).
[2.18] W. W. Hsiang, H. C. Chang, and Y. Lai, “Laser dynamics of a 10 GHz 0.55 ps asynchronously harmonic modelocked Er-doped fiber soliton Laser”, IEEE J. Quantum Electron. 3, 292 (2010).
[2.19] H. G. Weber and M. Nakazawa, “Ultrahigh-Speed Optical
28
Transmission Technology,” (2007).
[2.20] M. Nakazawa, E. Yoshida, and Y. Kimura, “Ultrastable harmonically and regeneratively mode-locked polarization maintaining erbium fiber ring laser,” Electron. Lett. 19, 1603 (1994).
[2.21] H. Takara, S. Kawanishi, and M. Sarawatari, “Stabilization of a modelocked Er-doped fiber laser by suppressing the relaxation oscillation frequency component,” Electron. Lett. 4, 292 (1995).
[2.22] M. Yoshida, K. Kasai, and M. Nakazawa, “Mode-hop-free, optical frequency tunable 40-GHz mode-locked fiber laser,”
IEEE J. Quantum Electron. 9, 704 (2007).
[2.23] M. Nakazawa, K. Kasai, and M. Yoshida, “C2h2 absolutely optical frequency-stabilized and 40 GHz repetition rate stabilized regeneratively mode-locked picosecond erbium fiber laser at 1.53 μm,” Opt. Lett. 22, 2641 (2008).
[2.24] M. Nakazawa and M. Yoshida, “Scheme for independently stabilizing the repetition rate and optical frequency of a laser using a regenerative mode-locking technique”, Opt. Lett. 33, 1059 (2008).
29
[2.25] W. W. Hsiang, C. Lin, N. Sooi, and Y. Lai, “Long-term stabilization of a 10 GHz 0.8 ps asynchronously mode-locked Er-fiber soliton laser by deviation-frequency locking,” Opt. Exp.
5, 1822 (2006).
30
Chapter 3
Experimental setup and results
3.1 21GHz asynchronous rational mode-locked Er-fiber soliton laser with stabilization
3.1.1 Experimental setup and component parameters
The system setup of our rational asynchronous mode-locked Er-fiber laser with the feedback control is shown in Fig. 3.1Fig. 3.1 The experimental setup
The schematic diagram of experimental setup consists of two main systems. One is the laser cavity and the other is the feedback control
31
system. The Er-doped fiber is pumped by two 980 nm laser diodes respectively. The 20/80 coupler divides 80% optical signal into the cavity and 20% into the feedback control system. The feedback control system consists of an optical delay line, a low bandwidth photodetector, a
system. The Er-doped fiber is pumped by two 980 nm laser diodes respectively. The 20/80 coupler divides 80% optical signal into the cavity and 20% into the feedback control system. The feedback control system consists of an optical delay line, a low bandwidth photodetector, a