1. Introduction

Femtosecond technology has enabled tremendous scientific advances in the past two decades [1–4]. However, a breakthrough of this technology into mass applications is yet to come. This is mainly because state of the art femtosecond laser sources are still too expensive and complex. Short pulse generation with cost-effective electrically pumped diode lasers is a promising alternative. In spite of extensive research in this field, challenges for commercial applications remain [5]. Most significantly, the available semiconductor gain bandwidth can often not be completely utilized [6], limiting pulse widths. Intra-cavity dispersion management [7–9], as well as spectral amplitude shaping [6] broaden the bandwidth, and have enabled sub-300 fs pulses. Both approaches usually require careful alignment, so that such systems can only be operated by a highly qualified operator. Here, we circumvent this by introducing the first computer-controlled intelligent femtosecond diode-laser system that self-optimizes intra-cavity dispersion and spectral amplitude shaping for femtosecond pulse generation.

Intra-cavity control of dispersion and spectral shaping is enabled by introducing a spatial light modulator (SLM) into the cavity [10]. Spectral phase- and amplitude masks can be applied to form arbitrary dispersion and loss filters. But finding the optimal shape for the filter masks required tedious optimization due to the complexity of the parameter space, especially since small deviations from the optimal form of the amplitude masks can cause big reductions in spectral bandwidth of the spectrum in passively mode-locked operation. Here, utilizing an evolutionary algorithm, the dispersion and spectral shape are optimized for maximum spectral width of the resulting pulses by the SLM. This leads to a self-optimizing laser system, substituting complex alignment and optimization procedures with an intelligent automatic optimization. As a result full widths at half maximum (FWHM) as high as 3.74 THz were obtained. After chirp compensation by external pulse compression, which is required due to self-phase modulation and ultrafast non-linear processes in the gain medium, Fourier limited pulse widths of 216 fs were obtained.

2. Experimental setup

The experimental setup, as shown in Fig. 1, is comprised of a multi-section laser diode configured for external cavity operation with a high-reflectivity (HR) coated back facet and an anti-reflection (AR) coated front facet, which is coupled to the cavity. The saturable absorber, which is needed for passive mode-locking, is realized by applying a reverse voltage to the segment next to the HR-coated facet. The external cavity is formed by a pulse shaper [11] consisting of a diffraction grating, a cylindrical focusing lens, SLM and end mirror. The SLM provides arbitrary intra-cavity control of dispersion and spectral shaping. After the output of the laser, a folded grating compressor [12] is used to compensate the chirp of the pulses in order to generate nearly transform-limited pulses.

 

Fig. 1 Experimental setup. The beam is coupled out of the AR-coated facet (AR) of a multi-section laser diode and collimated with an aspheric lens (L1). The spectral components are diffracted into the −1’st diffraction order by the reflection grating (RG), focused with the achromatic lens (L2) and modulated by the spatial light modulator (SLM). The cavity is formed by the back facet of the laser diode and the mirror (M) behind the SLM. The 0th diffraction order is used to couple the beam out into a folded transmission grating compressor (TG), the beam reflected back from the compressor is separated from the incoming beam with a pickoff-mirror (PM). Spectra and autocorrelations are measured behind the output.

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The active medium is a compressively strained InGaAsP triple quantum well structure in a super-large optical cavity based on a GaAs substrate [13]. The laser diode is a ridge-waveguide device with a metallization divided into 10 sections with a respective length of 100 µm. The 9 sections adjacent to the anti-reflection coated facet are used as the gain segment by applying an injection current, while the segment next to the high-reflectivity coated facet is used as an absorber. A reverse bias voltage of 6 V was applied to the absorber section. The temperature of the laser diode was regulated to ambient temperature (20 °C) with a Peltier element and a commercially available temperature controller. The laser was started by continuously increasing the gain current, beginning with a current below threshold, until an increase in absorber current was observed.

The SLM is a Cambridge Research and Instrumentation Inc. SLM-128, with two one-dimensional liquid crystal masks aligned at −45° and 45° with respect to the polarization of light travelling through the resonator. Combinations of extraordinary phase retardation of the first and second mask allow for independent control of phase and amplitude [14].

3. Intra-cavity self-optimization

In semiconductor diode lasers the strong self-phase modulation in the semiconductor as well as ultrafast nonlinear gain saturation effects complicate the direct generation of femtosecond pulses out of diode lasers. Thus, it is more favorable to optimize the system for a high spectral bandwidth with predominantly linearly chirped pulses that can be externally compressed [10].

In order to optimize the laser for broadband emission, we manipulate the intra-cavity dispersion and losses. For that purpose, phase- and amplitude masks for the intra-cavity SLM are manipulated by an evolutionary algorithm [15]. Evolutionary algorithms optimize a set of control parameters in order to maximize an evaluation criterion called the fitness function, in a process analogous to biological evolution. A set of potential solutions is subjected to processes equivalent to mutation, reproduction and natural selection. This is done over a set of iterations of the algorithm called generations [15], typically leading to convergence to an optimum fitness value after a number of generations. The fitness of each individual within a generation is determined by applying the corresponding masks and measuring the resulting optical spectrum. In order to reduce the convergence time, mask pixels were not addressed individually as control parameters. Rather, the phase and amplitude values of the pixels were represented by spline interpolations for the amplitude and phase values with a certain number of control points. These control points were varied for the different individuals of the algorithm.

For the runs presented in this work, 8 control points were used. The evolutionary algorithm has populations of 127 individuals. In the evolutionary step, 1 of the individuals is cloned, 10 are obtained by interpolation, 10 by single-point crossover, 10 by multiple-point crossover and 96 by mutation. Probability for parameter variation was 12.5%. For the individuals subject to mutation, the mutation length was determined with a Gaussian probability distribution with a standard deviation of 0.2 rad for the first 32 individuals and 2 rad for the next 32 individuals. Adaptive mutation with a variable standard deviation for each control point was used for the last 32 individuals. The variable deviation started with a value of 0.2 rad and was changed according to the mutation length of successful individuals in the previous generation. The first 32 individuals were most effective in the first 30 generations before convergence, while the individuals with wide mutation lengths keep the population out of local fitness maxima. The adaptive mutation effectively tends to smaller mutation lengths in the later stages of the run, providing fine adjustment of the masks. To ensure comparable conditions for each individual, the laser was switched off when the SLM masks were changed and operation close to threshold on the fundamental repetition frequency of 183.4 MHz was ensured after restarting it.

Before starting the optimization, we analyzed the laser operation without intra-cavity dispersion and loss manipulation. Figure 2(a) shows emission spectra of the laser in free running operation with a conventional external cavity using an output coupler as end mirror (red solid line) and with the cavity arrangement shown in Fig. 1, but with no voltage applied to the SLM (black solid line). While both spectra have similar width at half maximum, the latter one has additional spectral components at the short wavelength edge of the spectrum, resulting in a reduction of Fourier-transform limited pulse width from 534 fs to 324 fs. However, the spectral bandwidth of 1.1 THz FWHM is still rather small in comparison to the available net gain bandwidth, which is roughly estimated to about 6 THz around a maximum at 849 nm. The bandwidth was estimated from the blue rectangles in Fig. 2(a), which show the threshold currents as a function of center wavelength for mode-locked operation with a narrow Gaussian amplitude filter of 0.5 nm width. The threshold current was determined by the step-like increase of the absorber current at the onset of mode-locked lasing.

 

Fig. 2 Optimization using an evolutionary algorithm. (a), spectrum of the laser diode in a conventional external cavity using an output coupler as end mirror (red solid line); spectrum of the laser in the SLM system without an applied mask (black solid line); spectrally resolved threshold currents (blue rectangles). (b), evolution of the maximum fitness per generation for a run of the evolutionary algorithm over 100 generations. (c), optical spectra for the best individuals of generations 1, 15, 30, 45 and 60.

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No threshold was found up to 200 mA for filters centered at spectral components smaller than 842 nm and larger than 856.5 nm, suggesting these to be the limits for mode-locked operation of the material system investigated.

In the following, the evolutionary algorithm was used to optimize the laser emission for maximal FWHM of the optical spectrum. In Fig. 2(b), the fitness curve for a run of the evolutionary algorithm as described in the previous paragraph is presented. It is evident, that the algorithm converges after approximately 50 generations. Figure 2(c) shows spectra for the best individuals in generations 1, 15, 30, 45 and 60. The spectral width broadens equally to both sides of the spectrum over the course of the optimization and the shape of the spectra gets more rectangular. The masks found with the algorithm after 100 generations are depicted in Fig. 3.

 

Fig. 3 Comparison between masks, spectrum and spectrally resolved threshold after optimization. Phase mask applied to the SLM (green solid line); optical spectrum of the laser at threshold (grey solid line); amplitude mask applied to the SLM (red solid line); spectrally resolved threshold currents, also shown in Fig. 2(a) (blue rectangles).

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Figure 3 shows a comparison between the amplitude mask found by the optimization (red line) and the threshold spectrum already depicted in Fig. 2(a) (blue rectangles). The threshold curve was scaled so that the threshold minimum coincides with the minimum in transmission of the amplitude mask. It is evident, that both curves closely follow each other over much of the area where spectral components are found. The ratio between minimum threshold and threshold at the point where the amplitude mask reaches 100% was found to be 78%, closely matching the reduction in transmission introduced by the amplitude mask, which was 77% at 848.2 nm. The attenuation mask therefore compensates for the gain differences of the spectral components by attenuating the gain maximum. This confirms the prediction in [6], that an attenuation mask following an inversion of the gain profile should produce the broadest spectra. The phase mask is depicted as the green curve in Fig. 3. A second order polynomial fit of the part of the phase mask (blue) overlapping with the spectrum yields a dominant linear chirp of 3.12 × 10⁵ fs², the fit has a coefficient of determination of 0.995. The spectrum obtained after optimization is shown in the grey trace. A spectral width of 3.74 THz was achieved. This value demonstrates that a significant fraction of the total gain bandwidth of about 6 THz is utilized for the pulse formation. The pulses could be successfully compressed with an external compressor to an autocorrelation width of 293 fs, shown in Fig. 4. Assuming a sech² pulse as is typically done for passively mode-locked diode lasers, this would correspond to a pulse width of 184 fs with a non-Fourier-limited time-bandwidth product of 0.68. But a more careful analysis based on a fast Fourier transformation of the spectrum yields Fourier-limited 216 fs pulses.

 

Fig. 4 Autocorrelation trace and electrical spectrum for the optimized resonator. Intensity autocorrelation after external compression of the laser pulse found for the best individual of generation 100 of the evolutionary algorithm run depicted in Fig. 2(a) (black solid curve); autocorrelation of the Fourier transform of the optical spectrum (red solid curve). Inset: electrical spectrum taken by a fast photo-diode.

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This is demonstrated by the good agreement between measured autocorrelation and calculated autocorrelation trace (red solid line). The inset in Fig. 4 shows the electrical spectrum of the pulse train obtained with a fast photo-diode. It confirms proper mode-locked operation on the fundamental repetition frequency. The reduction in amplitude for frequencies above 700 MHz was due to the bandwidth of an amplifier between photo-diode and spectrum analyzer. The output power of the oscillator at the fundamental repetition rate, using the diffraction order 0 of the grating as output coupling was 0.8 mW. This value did not differ significantly for the laser with- or without amplitude mask applied.

As the fitness parameter used by the evolutionary algorithm was the spectral bandwidth of the emitted pulses, it was assumed that the laser would continue to generate linearly chirped pulses in passively mode-locked operation, even with arbitrary phase masks. While the autocorrelation width would be more obvious as a fitness parameter, being directly related to the pulse duration, it does not lead to successful optimization when starting with arbitrary masks, as the noise of the autocorrelation signal becomes bigger than the differences in pulse duration between individuals. This is caused by the nonlinear relationship between pulse duration and the intensity after second harmonic generation. Never the less, when starting with nearly optimal individuals from early parts of spectral FWHM optimization runs, a shortening in pulse durations is observed. Therefore, in order to ensure that no residual higher order chirp components were present in the pulses that were emitted by the laser after optimization for spectral FWHM, further runs of the evolutionary algorithm utilizing the autocorrelation FWHM as fitness parameter were performed. For these runs, the best masks from the optimization for spectral width were used as a starting point of the algorithm. No further reduction in observed pulse duration was observed over a duration of 100 generations, suggesting that spectral FWHM is indeed a good fitness parameter for the generation of Fourier-limited pulses. Overall, our results clearly demonstrate that the optimization strategy towards a large spectral bandwidth in combination with an external pulse compression was successful.

4. Conclusion

In summary, we demonstrate for the first time a self-optimizing femtosecond diode laser system. By implementing an SLM into the external laser cavity and optimizing it with an evolutionary algorithm, we achieve 216 fs pulses with a spectral bandwidth of 3.74 THz. Since this bandwidth already uses a significant fraction of the total bandwidth it would be desirable to use gain material with considerably larger bandwidth in order to achieve pulse widths shorter than 100 fs. Such large gain bandwidths could be obtained, for example, with quantum dot active media [16].

Our concept can be further developed towards the generation of specific pulse profiles exactly adapted to applications like, e.g. generation of THz transients in THz time domain spectroscopy systems [17]. For such applications, the algorithm can be operated with a fitness function adapted to the application requirements (e.g. generated THz intensity).

The laser presented in this work is a proof of principle. With a size of approximately 40 cm × 50 cm, it is not optimized for minimum footprint. However, we obtain unambiguous values for the intra-cavity dispersion and spectral losses after optimization by the algorithm. Consequently, for particular practical applications, the bulky SLM device can be replaced by compact intra-cavity chirped mirrors [18], providing values for dispersion and spectral losses that are exactly optimized for the application. A further step in order to increase competitiveness to conventional sources, is to increase the output power of the system. This can be done by amplifying the output of the oscillator in a compact master-oscillator power-amplifier geometry using tapered diode laser amplifiers [9]. Thus, one obtains an extremely compact, efficient, and cost-effective femtosecond diode laser source perfectly adapted to the application.