Discussion and Summary

We have also compared the behavior of our laser when operated with synchronous modulation. We find the asynchronous mode-locking shows superior performance than the synchronous mode-locking in two aspects. The first one is the higher SMSR which leads to more stable operation. The reason why the asynchronous mode-locking can achieve high SMSR is because the slow periodic timing position modulation of

the pulses caused by asynchronous modulation will also produce the slow periodic center-wavelength modulation of the pulses through the asynchronous phase modulation. The combination of the periodic center-wavelength drifting and the fixed filter can produce the equivalent sliding filter guiding-center soliton effects that have been extensively studied in soliton transmission. The combination of the periodic carrier frequency drift and the fixed optical filter in turns produces the equivalent sliding filter guiding-center soliton effects, with the difference that the optical filter is now fixed while the carrier frequency of the soliton is sliding. The solitons can survive with the presence of the sliding filtering effects due to their nonlinear-optic properties, while the noises will be filtered out due to their linear-optic properties. In this way, the supermode noises with asynchronous mode-locking can be lower than those with synchronous mode-locking. Another advantageous aspect of asynchronous mode-locking is that the pulse width is much shorter than that in synchronous mode-locking, since the pulse width of soliton is determined by the laser cavity parameters instead of the phase modulator. When the modulation frequency is exactly equal to the cavity harmonic frequency, the optical bandwidth is reduced to 0.5 nm and we can no longer observe sub-ps pulses.

The above mentioned results prove the advantages of the asynchronous modulation scheme.We believe the superior performance of our mode-locked fiber laser is due to the combination of APM, SPM with filtering, and asynchronous mode locking in a single fiber laser cavity. In addition, the effect additive-pulse limiting (APL)should also be helpful in stabilizing the laser [3,22]. By adjusting the bias point of additive-pulse interference through the adjustment of the two polarization controllers, either APM or APL or a combination of both effects can be achieved [3,22,23]. The APL effect will help to reduce the laser noises. Such a noise suppression effect is sensitive to the adjustment of the two polarization controllers. This is one of the

characteristics that indicate the presence of the APL effect. Even though all these mechanisms are included in the laser operation simultaneously, the structure of our hybrid mode-locked fiber laser is still rather simple.

We have found that the average cavity dispersion and the pump power are very crucial to the operation of asynchronous mode-locking. If the average cavity dispersion is unchanged, when the pulse repetition rate increases, the pump power should also be increased to keep the pulse energy close to that at the lower repetition rate. In this way the nonlinear effects in the laser cavity can be kept strong enough to support the stable operation of the mode-locked fiber laser at a higher repetition rate.

One can estimate the soliton energy by the siliton area theorem. Given the fact that the average cavity dispersion parameter β2 is -2.26 ps²/km, the nonlinear coefficient γ is 1.7 (km⋅W)⁻¹, and the pulsewidth is 816 fs, the soiltion energy inside the cavity is estimated to be 3.14 pJ, which is consistent with the pulse energy we observed experimentally.

To summarize, we have successfully demonstrated a 10 GHz femtosecond mode-locked Er-fiber soliton laser achieved by asynchronous phase modulation. The output of the laser exhibits unique and interesting characteristics of slow periodic timing-position and center-wavelength sweep, which may have the potential for developing interesting new applications. The slowly varying timing position should not cause problems for optical transmission applications since the synchronization circuit of the receiver can follow it. However, the optical-carrier-frequency sweep may make the laser not suitable for frequency metrology applications. On the other hand, the periodic variation of the timing position may find some new uses in optical sampling applications, in which the timing-sweep of the sampling pulses can be automatically achieved. In the future more investigation can be pursued along this direction.

References for Chapter 3:

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[9] M. Nakazawa, and E. Yoshida, “A 40GHz 850-fs regeneratively FM mode-locked

polarization-maintaining erbium fiber ring laser,” IEEE Photon. Technol. Lett. 12, 1613 (2000).

[10] M. Margalit, C. X. Yu, S. Namiki, E. P. Ippen, and H. A. Haus, “Harmonic mode locking using regenerative phase modulation,” IEEE Photon. Technol. Lett. 10, 337 (1998).

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[13] M.-F. Tie, W.-W. Hsiang and Y. Lai, “A femtosecond hybrid mode-locked Er-fiber soliton laser by asynchronous phase modulation,” in Proceedings of Pacific Rim Conference on Lasers and Electro-Optics( Taipei, Taiwan, 2003), Vol.

1, 34.

[14] W.-W. Hsiang, C.-Y. Lin, M.-F. Tien, and Y. Lai, “Direct generation of 10 GHz 816 fs pulse train from an erbium-fiber soliton laser with asynchronous phase modulation,” Opt. Lett. 30, 2493 (2005).

[15] D. Kuizenga and A. E. Siegaman, “FM and AM Mode Locking of Homogeneous Laser─Part I: Thoery,” IEEE J. Quantum Electron. 6, 694 (1970).

[16] D. Kuizenga and A. E. Siegaman, “FM and AM Mode Locking of Homogeneous Laser─Part II: Experimental results in a Nd-YAG Laser With Internal FM Modulator,” IEEE J. Quantum Electron. 6, 709 (1970).

[17] 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).

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guiding filters,” J. Opt. Soc. Am. B 14, 627 (1997)

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[21] M. Nakazawa, K. Tamura, and E. Yoshida, “Supermode noise suppression in a harmonically modelocked fiber laser by self phase modulation and spectral filtering,” Electron. Lett. 32, 461 (1996).

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(a)

(b)

(c)

Fig. 3-1 (a) Laser cavity with the gain, the filter, GVD, SPM and the phase modulation driven asynchronously (b) Slow modulation in asynchronous soliton mode-locking (c) Noise clean-up effect in asynchronous soliton mode-locking.

Fig. 3-2 Schematic of the asynchronously mode-locked Er-fiber laser.

1540 1545 1550 1555 1560

-80 -60 -40 -20 0

Power [dBm]

Wavelength [nm]

1544 1552 1560 0

5

Intensity [a.u.]

Wavelength [nm]

Fig. 3-3 (a)

Fig. 3-3 Optical characteristics of the pulse train from asynchronous mode-locking: (a) the optical spectrum with measurement resolution=0.07nm (inset: on a linear scale).

-10 -5 0 5 10

Fig. 3-3(b) Optical characteristics of the pulse train from asynchronous mode-locking: (b) the autocorrelation trace (the solid curve) and the fitting curve (the empty circles) assuming sech^2 pulse shape.

Fig. 3-4(a) RF spectra of the pulse train from asynchronous mode-locking: (a) 20 MHz span, SMSR>70 dB.

9.997650 9.997700 9.997750 9.997800 -80

-60 -40 -20 0

Power [dBm]

Frequency [GHz]

1204th cavity harmonic

modulation frequency

36kHz

Fig. 3-4(b)

Fig. 3-4(b) RF spectra of the pulse train from asynchronous mode-locking: (b) 200 kHz span, detuning frequency = 36 kHz.

Chapter 4

Long-Term Stabilization of Asynchronously