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Harmonic Mode Locking

Definition: mode locking of a laser where multiple pulses are circulating in the laser resonator with equal temporal spacing

More general term: mode locking

Opposite term: fundamental mode locking

German: harmonisches Modenkoppeln

Categories: light pulses, methods

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Pulse trains with high pulse repetition rate are sometimes obtained with the technique of harmonic mode locking, where multiple ultrashort pulses are circulating in the laser resonator with a constant temporal spacing (see Figure 1). This technique is often applied in high (multi-gigahertz) pulse repetition rate fiber lasers, since their resonators can not be made short enough to achieve a high repetition rate with a single pulse (→ fundamental mode locking).

Harmonic mode locking is associated with some technical challenges:

harmonically mode-locked fiber ring laser
Figure 1: Schematic of a harmonically mode- locked fiber ring laser.
  • Additional means may be required for achieving a constant pulse energy. Without special measures, there may be fluctuating pulse energies, or even pulse drop-out (missing pulses).
  • The circulating pulses are not always mutually phase-coherent, which can matter under certain circumstances.
  • In the case of passively mode-locked lasers, it can also be difficult to obtain a stable pulse spacing, i.e. a low timing jitter.

Various kinds of instabilities are related to so-called supermode noise. If N identical pulses are circulating in the resonator with equal phase, only every Nth resonator mode is excited. Supermode noise means that stable oscillation on such a subset of resonator modes is not achieved; the laser may hop to different sets of modes, or exhibit simultaneous oscillation on different mode sets over longer times. The beat notes involved are associated with increased high-frequency laser noise, e.g. in the form of increased timing jitter.

There are a variety of methods for suppressing supermode noise. These involve measures such as inserting various types of intracavity spectral filters and/or using electronic feedback systems, or exploit nonlinear and dispersive effects. In many cases, the setup of a harmonically mode-locked laser becomes more sophisticated due to such requirements. On the other hand, once supermode noise is effectively suppressed, harmonically mode-locked lasers have the potential for substantially lower laser noise (e.g. timing jitter and phase noise), compared with fundamentally mode-locked lasers. This is essentially because they tentatively require less laser gain per unit time, and gain is what mostly introduces timing jitter.

A variation of harmonic mode locking is called rational harmonic mode locking. Here, the modulation frequency is the round-trip frequency times the ratio of two integers. This also enforces a higher pulse repetition rate. In some cases, very high repetition rates have been achieved, but often with a non-constant pulse energy.

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Bibliography

[1]M. Becker and D. J. Kuizenga, “Harmonic mode locking of the Nd:YAG laser”, IEEE J. Quantum Electron. 8 (8), 687 (1972), doi:10.1109/JQE.1972.1077271
[2]S. Longhi et al., “Third-order-harmonic mode locking of a bulk erbium:ytterbium:glass laser at a 2.5-GHz repetition rate”, Opt. Lett. 19 (23), 1985 (1994), doi:10.1364/OL.19.001985
[3]K. Tamura and M. Nakazawa, “Pulse energy equalization in harmonically FM mode-locked lasers with slow gain”, Opt. Lett. 21 (23), 1930 (1996), doi:10.1364/OL.21.001930
[4]S. Arahira et al., “Mode-locking at very high repetition rates more than terahertz in passively mode-locked distributed-Bragg-reflector laser diodes”, IEEE J. Quantum Electron. 32 (7), 1211 (1996), doi:10.1109/3.517021
[5]A. B. Grudinin and S. Gray, “Passive harmonic mode locking in soliton fiber lasers”, J. Opt. Soc. Am. B 14 (1), 144 (1997), doi:10.1364/JOSAB.14.000144
[6]B. C. Collings et al., “Stable multigigahertz pulse-train formation in a short-cavity passively harmonic mode-locked erbium/ytterbium fiber laser”, Opt. Lett. 23 (2), 123 (1998), doi:10.1364/OL.23.000123
[7]O. G. Okhotnikov and M. Guina, “Colliding-pulse harmonically mode-locked fiber laser”, Appl. Phys. B 72, 381 (2001), doi:10.1007/s003400100529
[8]O. Pottiez et al., “Supermode noise of harmonically mode-locked erbium fiber lasers with composite cavity”, IEEE J. Quantum Electron. 38 (3), 252 (2002), doi:10.1109/3.985565
[9]T. Yilmaz et al., “Supermode suppression to below −130 dBc/Hz in a 10 GHz harmonically mode-locked external sigma cavity semiconductor laser”, Opt. Express 11 (9), 1090 (2003), doi:10.1364/OE.11.001090
 [10]Y. Deng and W. H. Knox, “Self-starting passive harmonic mode-locked femtosecond Yb3+-doped fiber laser at 1030 nm”, Opt. Lett. 29 (18), 2121 (2004), doi:10.1364/OL.29.002121
[11]Y. Deng et al., “Colliding-pulse passive harmonic mode-locking in a femtosecond Yb-doped fiber laser with a semiconductor saturable absorber”, Opt. Express 12 (16), 3872 (2004), doi:10.1364/OPEX.12.003872
[12]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. 30 (17), 2212 (2005), doi:10.1364/OL.30.002212
[13]D. Panasenko et al., “Er-Yb femtosecond ring fiber oscillator with 1.1-W average power and GHz repetition rates”, IEEE Photon. Technol. Lett. 18 (7), 853 (2006), doi:10.1109/LPT.2006.871821
[14]S. Zhou et al., “Passive harmonic mode-locking of a soliton Yb fiber laser at repetition rates to 1.5 GHz”, Opt. Lett. 31 (8), 1041 (2006), doi:10.1364/OL.31.001041
[15]S. Gee et al., “Correlation of supermode noise of harmonically mode-locked lasers”, J. Opt. Soc. Am. B 24 (7), 1490 (2007), doi:10.1364/JOSAB.24.001490
[16]Li Zhan et al., “Critical behavior of a passively mode-locked laser: rational harmonic mode locking”, Opt. Lett. 32 (16), 2276 (2007), doi:10.1364/OL.32.002276
[17]G. Sobon et al., “10 GHz passive harmonic mode-locking in Er-Yb double-clad fiber laser”, Opt. Commun. 284 (18), 4203 (2011), doi:10.1016/j.optcom.2011.04.050

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See also: mode locking, active mode locking, mode-locked lasers, fundamental mode locking
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