Non-Linear Dynamics of Semiconductor Lasers

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Mode-locked Lasers

Mode-locking of lasers is a means of generating very short pulses, typically on the order of picoseconds or femtoseconds, by enforcing a fixed phase relationship between the many modes of the laser cavity. The laser then only emits when all these modes interfere constructively, resulting in a regular train of ultrashort pulses. Applications for mode-locked lasers include telecommunications (signal encoding), exploration of fast chemical and physical processes, optical data storage, production of THz radiation, and the generation and extraction of clock signals.

There are several different methods for controlling the phase relation between the modes, using either active elements such as acousto-optic or electro-optic modulators, or passive elements such as saturable absorbers. The arrangement studied here (see Fig. 1) consists of a ridge waveguide laser with the ridge divided into two sections. This allows one section to be forward biased as normal and thus act as the gain section, while the second section can be reverse biased so that it behaves as an absorber. Careful control of the bias voltages determines the saturation level of the absorber section, and can induce mode-locking. This approach has the advantage that it is very compact, relatively inexpensive,and easily integrated with existing technologies. Fig. 2 shows a typical map of the behaviour of the devices as the gain and absorber section voltages are varied. Above threshold, different regions of mode-locking are observed, with different pulse repetition rates in each region.


Two section mode-locked laser

Mode-locking map

Fig. 1: Two-section monolithic mode-locked laser with InAs/GaAs quantum dot active layer. Fig. 2: Map of the mode-locking behaviour as the gain and absorber section voltages are varied, showing the different mode-locking regions.


Frequency Resolved Electro-Absorption Gating (FREAG)

The Frequency Resolved Electro-Absorption Gating (FREAG) technique gives complete recovery of spectral and temporal information on ultrafast laser pulses in real time, and is similar to, but far more sensitive than, Frequency Resolved Optical Gating (FROG). FREAG pulse analysers work on the same principle as a Second Harmonic Generation (SHG) autocorrelator, but use linear transmission through a modulated gate, contrasting with the non-linear crystal required for SHG autocorrelators. The result is the same, accurate recovery of real and imaginary parts of the electric field but without requiring high intensity input.

FREAG data
Fig. 3: FREAG measurements on quantum dot mode-locked lasers. (a) Pre-sampled spectrogram, (b) recovered spectrogram. (c) Measured (black) and recovered (red) optical spectrum – injection frequency is shown by the arrow.

FREAG is very sensitive and can resolve sub-picosecond pulses since it is not limited by the response time of the detector. In addition to this, at each delay position of the gate a complete spectrum is measured, so that both the spectral and temporal characteristics of the pulse are captured simultaneously. So, while a 10Gb/s data stream may look perfectly normal on a conventional oscilloscope, the FREAG will show all the changes in the underlying carrier phase in real-time, allowing complete and rapid optimisation of the system.

Semiconductor mode-locked lasers can spontaneously emit picosecond light pulses at high rates, making them valuable candidates for applications such as optical time division multiplexing. Traditional methods of pulse characterisation such as autocorrelation require high laser intensities and often lose critical pulse information. For example, autocorrelation always returns symmetric traces, regardless of the true pulse shape. With FREAG, a trigger is derived from the laser pulses and used to open and shut an optical gate. The remaining laser light is passed through this gate and a set of laser spectra gathered as a function of pulse delay with respect to the gate. This spectrogram can then be inverted and the full laser intensity and phase information recovered. With this tool several pulse stabilisation techniques such as dual-tone optical injection have been proven and outstanding pulse jitter performance achieved.

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Our research

Laser Dynamics Lab

Master-slave experiment

Optical Injection

Injection Locking Experiment
Fig. 4: Schematic diagram of the experimental setup for injection locking of a semiconductor laser. Click on the image for a larger view.
Injection map
Fig. 5: Evolution of the slave power spectrum as a function of the master-slave detuning. Master power is 4 mW and slave current is 45 mA.
Single and double pulses
Fig. 6: Excitable pulses observed in the slave laser time series; single pulses for low master powers and detuning, double pulses at higher master powers and detuning.

The synchronisation of two oscillators has been widely studied since the observations of Huygens in 1600, who noticed that two wall clocks of different natural frequencies synchronised when attached to the same wall. In a similar fashion, when the light from a semiconductor laser (the master laser) is injected into a second laser (the slave laser), the emission frequency of the slave may synchronise with that of the master. Injection locking a semiconductor laser has been shown to lead to a reduction in the relative intensity noise, spectral narrowing, as well as a significant enhancement of the modulation bandwidth.

Additionally, the possibility of excitability in injection locked semiconductor lasers has been predicted by Wieczorek et al. [1]. A dynamical system is called excitable if it produces a large nonlinear response to a small but sufficiently large perturbation from its steady state. Perturbations of the steady state above a threshold cause a large excursion in phase space leading to a large amplitude pulse. This excursion is followed by a refractory period of time before another can be induced. The CAPPA group conducts an ongoing analysis of the dynamical properties of Quantum Dot (QD) lasers under the influence of external injection, and have demonstrated that such a system is excitable.

In the experimental setup shown in Fig. 4, the slave laser is a QD laser consisting of 6 InAs QD layers, embedded in an InGaAs quantum well on a GaAs substrate. The slave is biased above threshold and the tunable master laser is set to a wavelength close to a Fabry-Perot mode of the slave, at a fixed master power. It is then varied across resonance with the slave laser. The master laser is a narrow linewidth (100 kHz) commercial tunable source, with a wavelength of approximately 1320 nm. Fig. 5 gives a typical example of how the slave laser behaves as the detuning is varied, for particular fixed values of the master and slave power. Three distinct regions of behavior are evident: (i) in regions far from zero for both positive and negative detuning, a beating frequency indicates that the slave laser is unlocked from the master laser; (ii) a stable locking region, where the slave laser synchronizes with the master and operates single mode; (iii) a region of complex dynamics that occurs on only the positive detuning unlocking boundary. In this region, as the master power increases, we observed single and double excitable pulses, random switching between a locked state and complex multipulse transient, random switching between locked and unlocked states, and random switching between two locked states.

Clearly, there is a plethora of interesting physics at work in this third region. In order to better understand it, we have modelled the system using quantum dot rate equations, further details of which can be found in [2]. Our theoretical analysis shows a clear and simple bifurcation scenario which enables the observation of single and double excitable pulses.

[1] S. Wieczorek, B. Krauskopf, and D. Lenstra, Phys. Rev. Lett., 88, 063901 (2002)

[2] D. Goulding, S. P. Hegarty. O. Rasskazov, et al., Phys. Rev. Lett. 98, 153903 (2007)


Dual mode injection

Quantum Dot Mode-Locked Lasers

One of the major drawbacks with semiconductor passively mode-locked lasers is that they often exhibit worse timing jitter than their larger, actively mode-locked counterparts. Timing jitter is the variation in the time between pulses, and can be particularly detrimental in clock signal and communications applications. MLLs based on quantum dots (QDs) are expected to exhibit lower timing jitter and more robust operating regimes compared with quantum well devices as a result of the reduced amplified spontaneous emission in three-dimensional quantum confinement and a lower linewidth enhancement factor with respect to less confined structures. The high repetition rates of MLLs means it is difficult to measure the timing jitter with an electrical spectrum analyser, and instead we use a time-domain optical cross-correlation technique [3]. We have demonstrated a record combination of 2 ps pulses and 25 fs/cycle timing jitter (500 fs, 1-100 MHz), with 1 mW average output power per facet [4].

We have also investigated dual-mode injection of QD-MLLs, using frequency resolved Mach- Zehnder gating (FRMZG) to characterise the pulse intensity, phase and chirp. FRMZG is a linear technique based on the same principle as FREAG, except using a Mach-Zehnder modulator as the gate. Dual-mode injection close to a pair of slave laser modes resulted in significant narrowing of the optical spectrum and tunability of the slave laser spectrum, with low timing jitter and significantly improved pulse time-bandwidth product (TBP) [5]. Figs. 7 and 8 show how the slave output spectral shape was remarkably consistent at the different injection wavelengths, with very little laser power at wavelengths below the injection wavelength and the peak output approximately 1.5 nm longer than the injection.

[3] J. P. Tourrenc, S. O'Donoghue, M. T. Todaro, et al., Photon. Techn. Lett., 18, 2317 (2006)

[4] M. T. Todaro, J. P. Tourrenc, S. P. Hegarty, et al., Opt. Lett., 31, 3107 (2006)

[5] T. Habruseva, S. O'Donoghue, N. Rebrova, et al., IEEE Photon. Tech. Lett., 22, 359 (2010).

Fig. 7: Optical spectra of the free-running (black) and injection locked QD-MLL with 17% absorber section for a number of master wavelengths (shown with arrow).

Dual mode injection

Fig. 8: RF signals of the slave laser with 12% absorbance section for the free-running case (black) and with dual injection (red).







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Dr. Stephen Hegarty

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