In-Phase and Anti-Phase Synchronization in a Laser Frequency Comb

Coupled clocks are a classic example of a synchronization system leading to periodic collective oscillations. Already in 1665, Christiaan Huygens described this phenomenon as a kind of “sympathy” among oscillators. In this work, we describe the formation of two types of laser frequency combs as a system of oscillators coupled through the beating of the lasing modes. We experimentally show two completely different types of synchronization in a quantum dot laser—in-phase and splay-phase states. Both states can be generated in the same device, just by varying the damping losses of the system. This modifies the coupling among the oscillators. The temporal laser output is characterized using both linear and quadratic autocorrelation techniques. Our results show that both pulses and frequency-modulated states can be generated on demand within the same device. These findings allow us to connect laser frequency combs produced by amplitude-modulated and frequency-modulated lasers and link these to pattern formation in coupled systems such as Josephson-junction arrays.

Figure 1

(a) Different synchronization states of intermode beatings. Every beating represents an oscillator illustrated by metronomes. These oscillators are coupled globally through their collective action—the laser beat note. Depending on the coupling, two distinct synchronization states are observed. In an AM comb, they are synchronized in-phase leading to strong amplitude modulation and pulses. In an FM comb, the phases are splayed uniformly across the unit circle. Hence, intermode beatings oscillating out of phase by $\pi$ mutually annihilate each other. This suppresses amplitude modulations and the beat note. (b) The same can be observed in a system of two coupled metronomes on a movable platform. Metronomes positioned on top of the platform will synchronize either in-phase or in antiphase, depending on the damping. Such damping can be added by placing the system in a water bath. (c) Illustrating the analogy to AM and FM comb generation with semiconductor lasers. AM combs can be generated through passive mode locking via fast saturable loss, while FM comb can even be realized in single section lasers. There, gain saturation dampens amplitude modulations and the beat note similarly to the water bath in (b).

Figure 2

(a) Schematic of the investigated 4 mm long QDL with two gain sections and two $200\mu \mathrm{m}$ long absorber sections. (b) First and second harmonic beat notes of the QDL operating in the AM (blue) and FM (red) regimes. The weaker beat note of the FM comb indicates the strong suppression of amplitude modulations in the FM regime. The beat note was measured using a fast photodiode. (c) Characterization of the AM and FM states by intensity autocorrelation measurements (blue lines). In the AM regime, the autocorrelation shows a FWHM of 14 ps, corresponding to 10 ps pulse width assuming a Gaussian shape. The red dotted line corresponds to the calculated autocorrelation using the SWIFTS time traces shown in Figs. 3 and 3, highlighting the good qualitative agreement between both experimental techniques.

Figure 3

(a) SWIFTS characterization of the AM comb. The spectrum (blue) spans over roughly $30{\mathrm{cm}}^{-1}$. The intermodal difference phases $\mathrm{\Delta }\varphi$ (green dots) cover a range of $0.43\pi$. (b) The reconstructed optical power yields optical pulses with 8.9 ps FWHM. The instantaneous frequency allows us to identify the spectral region responsible for the trailing edge of the pulses. (c) SWIFTS characterization of the FM comb. $\mathrm{\Delta }\varphi$ are now splayed across the full range of $2\pi$. (d) The reconstructed optical power shows almost no amplitude modulation while the instantaneous frequency is linearly chirped across one round-trip period. (e) Numerical simulations results, depicting the normalized power and instantaneous frequency in the case of both AM and FM combs. The instantaneous frequency and time are normalized to the cavity round-trip time. (f) Color-coded radio frequency (rf) spectrum of the QDL while a rectangular modulation between 0 and $-3.8\mathrm{V}$ is applied to the absorber sections, while the gain section remains unchanged.