The timing jitter, optical phase noise, and carrier-envelope offset (CEO) noise of passively mode-locked lasers are closely related. New key results concern analytical calculations of the quantum noise limits for optical phase noise and CEO noise. Earlier results for the optical phase noise of actively mode-locked lasers are generalized, particularly for application to passively mode-locked lasers. It is found, for example, that mode locking with slow absorbers can lead to optical linewidths far above the Schawlow–Townes limit. Furthermore, mode-locked lasers can at the same time have nearly quantum-limited timing jitter and a strong optical excess phase noise. A feedback timing stabilization via cavity length control can, depending on the situation, reduce or greatly increase the optical phase noise, while not affecting the CEO noise. Besides presenting such findings, the paper also tries to clarify some basic aspects of phase noise in mode-locked lasers.

Optical phase noise and carrier-envelope offset noise of mode-locked lasers

Electric-field correlation measurements of fundamental and harmonic modelocked external cavity semiconductor lasers are presented. Based on these results, an empirical model of a harmonic modelocked pulsetrain is constructed. Using this model, the equivalence between the time-interleaved pulsetrains picture and the supermode picture of a harmonic modelocked pulsetrain is shown. Simulations based on the model are presented showing the key characteristics of modelocked pulsetrains in radio frequency (RF) and optical domains. The fundamental relationship between longitudinal mode linewidth and RF phase-noise corner frequency is delineated. The generated results point to fundamental limitations in timing jitter in modelocked lasers.

Noise in fundamental and harmonic modelocked semiconductor lasers: experiments and simulations

An analysis of the pulse-to-pulse timing jitter in an actively mode-locked laser is presented. The model includes spontaneous emission noise, mode-locker driver phase noise, and cavity length detuning. Analytical expressions for the laser pulse train phase noise spectrum, the intensity power spectrum, and the RMS timing jitter are given. The timing fluctuations are characterized by a time constant proportional to the cavity round-trip time times the number of locked modes squared divided by the modulation depth. The contribution from the mode-locker driver phase noise will dominate unless high-stability RF sources are used. The residual timing jitter due to spontaneous emission noise is very sensitive to cavity detuning. >

Theory of timing jitter in actively mode-locked lasers

We report a semiconductor-based, low-noise, 10.24 GHz actively mode-locked laser with 4.65 fs of relative timing jitter and a 0.0365% amplitude fluctuation (1 Hz to 100 MHz) of the optical pulse train. The keys to obtaining this result were the laser's high optical power and the low phase noise of the rf source used to mode lock the laser. The low phase noise of the rf source not only improves the absolute and relative timing jitter of the laser, but also prevents coupling of the rf source phase noise to the pulse amplitude fluctuations by the mode-locked laser.

Ultralow-jitter and -amplitude-noise semiconductor-based actively mode-locked laser

We experimentally compare the linewidth of the individual modes of an extended cavity semiconductor laser when it operates mode locked and when it operates single mode. We find that the linewidths under these two operating conditions have the same inverse dependence on the average power. Therefore, the coherence length of the mode-locked source is the same as that of the single-mode source despite lower power per mode, much broader total bandwidth, and much higher spontaneous emission noise level in the mode-locked source. It can be inferred from our data that the electric fields of over 1000 consecutive mode-locked pulses are correlated.

D. Rush

Papers

The linewidth of a mode-locked semiconductor laser caused by spontaneous emission: Experimental comparison to single-mode operation