We analyze the influence of second and third order intracavity dispersion on a passively mode-locked diode laser by introducing a spatial light modulator (SLM) into the external cavity. The dispersion is optimized for chirped pulses with highest possible spectral bandwidth that can be externally compressed to the sub picosecond range. We demonstrate that the highest spectral bandwidth is achieved for a combination of second and third order dispersion. With subsequent external compression pulses with a duration of 437 fs are generated.
© 2014 Optical Society of America
For several decades, semiconductor lasers have been the focus of research as a possible source for ultrashort light pulses. They have unique features, which no other gain media can offer. They can be pumped electrically, which allows for a compact design and good wall-plug efficiency. This, combined with the possibility of semiconductor mass production, leads to a cost-effective alternative to established solid state fs-laser systems . The emission wavelength depends on the band gap of the semiconductor compound and can be adapted for the desired application. This is an advantage over fiber lasers, which are strongly restricted in the emission wavelength . In addition, it has recently been shown that diode laser systems can be easily expanded by a pulse picking device to generate high power pulses with a variable repetition rate . A wide gain spectrum makes mode-locked semiconductor lasers to a suitable choice to generate ultrashort light pulses. It has been predicted that the gain spectrum is wide enough to support sub-50 fs pulses .
However, the shortest pulse obtained directly from an injection mode-locked semiconductor laser had a duration of 390 fs . The difference between the predicted pulse durations and the experimentally obtained pulse durations originates from another property specific to semiconductors. Semiconductor gain media have large gain per unit length and an α-factor, which is unequal to zero. The linewidth broadening factor α describes the coupling between the carrier-induced variation of real and imaginary parts of the susceptibility . This means, that a change of the gain is connected to a change of the refractive index and leads to nonlinearities. A strong self-phase modulation (SPM) is the result, which leads to a nonlinear chirp of the propagating pulse and limits the minimal pulse duration .
There are different approaches to solve this problem. The first one is to reduce the interaction length of the pulse with the gain medium in order to minimize the effect of SPM. This is done with the concept of the vertical external cavity surface emitting laser (VCSEL). The light incident to the cavity is perpendicular to the growth direction of the active medium, which is a multi-quantum well (MQW) structure. Hence the interaction length of the pulse with the gain media is reduced below 100 nm. With this concept pulses as short as 107 fs were generated . While these pulses had only 3 mW average output power, the VECSEL concept can be used to generate pulses with a high average power. Wilcox et al. reported on a VECSEL with 3.3 W average output power and a pulse duration of 400 fs, which leads to 4.35 kW peak power . Despite these impressive results, the VECSEL concept has drawbacks. The results above were achieved by optical pumping of the gain media. This makes the setup more complex, expensive and inefficient and hence the gain chip needs sophisticated cooling. Another disadvantage is the need for a semiconductor saturable absorber mirror (SESAM) for passive mode locking, which further increases the complexity of the system.
In edge emitting diode lasers, the use of quantum dots (QD) instead of QWs as the active region may be promising because QDs are supposed to have a broader gain spectrum and shorter carrier lifetimes then QWs . A saturable absorber (SA) can be integrated into the laser chip by separating the laser into two segments. The longer segment acts as the gain section by applying an injection current. By applying a reverse voltage to the shorter section a SA is realized, which provides passive mode locking . The two facets are forming the resonator in the case of a monolithic laser diode. From such a device pulses with a duration of 390 fs were obtained directly from the oscillator . By using a standard single mode fiber as a compressor, another group obtained 374 fs pulses from a mode-locked QD laser diode .
Independent of the active region in use, intracavity dispersion management (IDM) seems to be highly recommended in semiconductor lasers as well as in most other ultrashort pulse lasers. Thus, a dispersive element is introduced into the cavity in order to compensate the chirp due to SPM. An MQW structure can be used as the active medium. Resan et al. built a ring cavity with two dispersion elements, a SESAM and a semiconductor optical amplifier (SOA) and generated 185 fs by employing an external compressor . Kono et al. demonstrated 200 fs pulses from a dispersion optimized external cavity laser with an edge-emitting GaInN MQW gain chip with an integrated saturable absorber and subsequent spectral filtering . In 2013 our group demonstrated the generation of 158 fs with an edge-emitting multi-section MQW laser diode with a dispersion optimized external cavity and subsequent pulse compression . An advantage of our concept, which is described in detail in , is the fact that pulses from the oscillator exhibit a strong linear chirp and can be hence easily amplified by a SOA. This allowed us to generate pulses with an average power of 805 mW, 358 fs and a peak power of 6.5 kW .
Overall, it seems to be obvious that the use of IDM is highly recommended if ultrashort pulses shall be generated with mode-locked external cavity semiconductor diode lasers. Thus, we present here a consequent analysis of the influences of second and third order intracavity dipersion in passively mode-locked diode lasers. The use of a SLM enables unambiguous intracavity dispersion management without introducing of spatial chirp and undesired amplitude modulations as in our earlier work .
2. Experimental setup
The following section describes the experimental setup. To enable IDM an external cavity is needed. Therefore, the laser diode has an anti-reflection coating () on one facet and a high-reflection coating () on the other facet. The laser structure used is based on an InGaAsP triple quantum well active region with a design wavelength of 850 nm embedded in a super large AlGaAs optical waveguide layer of 3.4 µm to realize a narrow vertical divergence of 20 degrees to reach a good collimation of the output beam. The 1 mm long device is divided into 10 sections of equal length. For passive mode locking the section adjacent to the high reflective facet is reverse biased to act as a saturable absorber. The other nine sections are used as the gain section by applying an injection current. The laser diode is stabilized to 20 °C by a thermoelectric cooler (TEC). The configuration of the cavity is called Fourier-transform external cavity laser (FTECAL)  and is depicted in Fig. 1.
The light emitted from the laser diode is collimated by an aspheric lens with a focal length of 11 mm. The resulting spot size is relatively large in order to illuminate most lines of the diffraction grating to yield a high spectral resolution of the diffraction order. We used a gold coated sinus grating with 1800 lines per mm to get high spectral resolution and high angular dispersion. The 1st diffraction order is collimated by a cylindrical lens with a focal length of 200 mm, while the spectral components are focused in the Fourier plane. For optimal focusing the plane side of the lens is orientated into the direction of the Fourier plane, where a folding mirror is placed, which reflects the light back into the laser diode. The 0th order of the diffraction grating is used to couple light out of the cavity. The ratio of output coupling can be changed by rotating the HWP, because the diffraction efficiency of the grating is highly polarization dependent. For horizontal polarization, a maximum diffraction efficiency of 90% is achieved.
The described setup is basically a single pass folded Martinez compressor. If the grating and the folding mirror are in the focal plane of the cylindrical lens the setup is in the zero dispersion position. Hence no group delay dispersion (GDD) is introduced. In our previous work [15,16] we introduced negative GDD into the cavity, by moving the lens away from the grating, while keeping the folding mirror in the focal plane of the lens. This approach to introduce GDD into the cavity has two drawbacks. First, spatial chirp  is introduced into the cavity. This leads to unspecified spectral amplitude filtering. The second drawback arises from the fact that only GDD can be controlled, but no higher order dispersion.
These two drawbacks can be avoided by using a SLM. The SLM, which is manufactured by Cambridge Research and Instrumentation (Cri SLM-128-D-VN), consists of two liquid crystal panels forming masks shaped as linear arrays with 128 pixels, respectively. Each pixel is 98 µm wide with a 2 µm gap between adjacent pixels. The extra-ordinary axes of the liquid-crystal molecules of both arrays are aligned at 45° and −45° with respect to the polarization of the incident light. The orientation of the liquid-crystal molecules is a function of an electric field, which is applied by transparent electrodes. If an identical electrical field is applied to both arrays, the polarization of the light is unaffected, while the refractive index is changed. Hence, the phase is changed. If two different electrical fields are applied to the arrays a change in the polarization is the result. Since the diffraction grating and the laser diode are highly sensitive to the polarization, the SLM also changes the amplitude. Hence the SLM allows for independent control of spectral phase and amplitude without misalignment of the cavity if it is placed in the Fourier plane of the FTECAL.
3. Experimental results
In this section we describe and discuss the results achieved for IDM with an SLM as dispersive element. The SLM is able to manipulate phase and amplitude independent from each other. However, here we restrict our interests to phase manipulation. As the first step we reproduced the trends obtained with conventional IDM techniques . All results were achieved for passive mode-locking with a fixed reverse voltage bias of 6 V to the SA. The average output power was measured with a Thorlabs PM100D power meter in combination with a S142C detector. The spectra were recorded with a USB HR4000 spectrometer from Ocean Optics, with a resolution better then 0.05 nm. For the estimation of the temporal pulse duration, an autocorrelator (APE Berlin Pulse Check) was used. All parameters were measured simultaneously. To ensure reproducibility of the measurements, the laser was switched off before each new data point. The injection current was then slowly raised until the threshold was reached. We monitored the photo current generated in the SA as the indicator for the onset of lasing operation.
From mode-locking theory, it is known that pulses from a passively mode-locked semiconductor laser have a positive, mostly linear, chirp due to the different α-factors of the gain and the absorber sections . The pulse shaping mechanism of a passively mode-locked semiconductor laser is based on a temporal net gain window . The temporal net gain window is created by the interplay of absorber saturation and gain saturation . Under the assumption of a constant duration, we suggested that IDM leads to a greater spectral bandwidth , because more spectral components fit into the temporal net gain window, if the chirp is compensated. Hence the aim of IDM is to increase the spectral bandwidth and exploit the property that the emitted pulses are mainly linearly chirped and can be compressed with a grating compressor.
In order to obtain a larger spectral bandwidth we introduce as a first step negative GDD to compensate the positive chirp of the passively mode-locked semiconductor laser. The temporal behavior as a function of intracavity GDD is depicted in Fig. 2. A sech2 pulse shape is assumed. It can be seen that there is a slight dependency of the GDD on the temporal duration. The pulse duration changes from a maximum of 5.8 ps (−4.6 x 104 fs2) to a minimum of 4.7 ps (−6.1 x 104 fs2). This corresponds to a change of 1 ps or of about 20%. After reaching this point, the mode-locking became instable. Hence, we concentrate in the following on the stable region.
The development of the spectral bandwidth (black curve), the photo current generated in the SA (red curve) and the average output power (blue curve) is shown in Fig. 3(a). As an indicator for the spectral bandwidth we took the full width at a value of 1/e2 of the maximum. This is done because the full width half maximum (FWHM) is not representative for the complex shaped spectra, because a slight decrease of spectral intensity in certain parts of the spectrum can lead to a strong decrease in the calculated FWHM. It can be seen that additional negative GDD leads to a larger spectral bandwidth. This is in good agreement with our previous results from the FTECAL without SLM . The spectral broadening is equivalent to an increase of the time-bandwidth product and accompanied by an increase of the average output power. The increased output power explains the slight decrease of the temporal duration .
This is also in good agreement with the theoretical prediction that the shortest pulses with the highest peak power are obtained in the case for equal α-factors in the gain and the absorber section . From this point of view the IDM compensates the difference of the α-factors in both sections and increases the peak power. With the increased peak power the pulses are able to saturate the SA at higher energy levels, where the unsaturated losses are higher . Without the IDM the peak power is too low to saturate these spectral regions and hence the laser is spectrally restricted to operate near the band gap of the SA. The spectral broadening can be seen with a look at the spectral behavior of the mode-locked laser, which is depicted in Fig. 3(b). It can be seen that the red edge of the spectrum shows a slight dependence of the introduced GDD, while the blue edge is showing a strong blue shift. Hence, the spectral bandwidth is increased, because the laser is able to saturate the SA over a wider spectral range. The maximum bandwidth was reached for −5.9 x 104 fs2. The average output power was 4 mW and the photo current generated in the SA was 0.94 mA.
The instability and break down in average power output power after reaching the maximum is predicted by  for the case that the α-factor in the SA is greater then the α-factor in the gain section. Figure 3 shows that the setup with the SLM is capable to reproduce the trend from our previous work without SLM . However, the usage of the SLM enables measurements with a higher resolution of the intracavity dispersion in a shorter period of time, which further increases the significance, because temporal instabilities are neglected. In addition no moving parts are used in the cavity.
So far only the linear chirp was compensated. But as mentioned before, the setup is capable to generate higher order dispersion. As the next step we examine if the spectral bandwidth can be increased further by adding third order dispersion (TOD) in addition to the GDD. As a starting point for the GDD we took the value −5.9 x 104 fs2 and varied the TOD. The results can be seen in Fig. 4.
It can be seen that the broadest spectrum is achieved for a TOD value of 2.5 x 10−5 fs3. Hence the broadest spectra can only be achieved for a combination of GDD and TOD. A difference to the case of pure GDD is that the increase of the average output power and the increase of spectral bandwidth not have the same normalized slope. Another difference is the spectral behavior as a function of TOD. The red spectral edge is shifting slightly further into the red, while there is again a strong blue shift of the blue edge. After reaching the maximum of spectral bandwidth for 2.5 x 10−5 fs3, there is again a strong breakdown in average output power and spectral bandwidth.
After demonstrating that a combination of GDD and TOD leads to broader spectra than GDD alone, the question is whether the increased bandwidth can be used to generate shorter pulses by using a standard grating compressor. As discussed before, a grating compressor is only capable to generate GDD, hence to use the additional bandwidth the chirp has to be mainly linear. The external compressor we used is a folded grating compressor as described in .
The results are depicted in Fig. 5. It can be seen that the spectrum without any IDM is the narrowest one with 1.63 nm (black curve). By applying a GDD of −5.9 x 104 fs2 (red curve) the spectrum is blue shifted and significantly broader (5.05 nm). By adding 2.5 x 10−5 fs3 TOD the spectrum (blue curve) gets more blue shifted and broader (5.27 nm). It follows that an optimization of TOD leads to an increase of the spectral bandwidth of about 4.3%. In Fig. 5(b) the corresponding normalized autocorrelation traces are depicted. There is only a slight difference in the temporal duration, while no change in the pulse shape can be observed. The deconvoluted temporal durations are 4.6 ps without dispersion (black trace), 4.3 ps for GDD only and 4.0 ps for the combination of GDD and TOD. This means that the temporal duration is reduced by about 7% for optimized TOD.
From Fig. 5(b) it can be seen that he TOD has no obvious impact on the pulse shape. This is an indicator that the gained bandwidth can be used for a further shortening of the pulse if a subsequent external compressor is used. The normalized autocorrelation traces with subsequent compression are depicted in Fig. 6. In the case of no extra dispersion the shortest obtainable pulse has a duration of 1.6 ps (black curve). The pulse with pure linear chirp compensation can be compressed down to 483 fs (red curve). The combination of GDD and TOD leads with subsequent compression to a duration of 437 fs, which correspond to a reduction of the temporal duration of 10.5%.
4. Summary and conclusion
We present an analysis of second order and third order intracavity dispersion management (IDM) for passively mode-locked semiconductor lasers in an external resonator. The dispersive element is an SLM, which allows the generation of arbitrary phase and amplitude masks. Here we restrict ourselves to phase manipulation. Our results confirm our results from previous experiments : The passively mode-locked laser generates strongly chirped pulses due to self phase modulation in the semiconductor and optimized IDM increases the spectral bandwidth of the pulses and thus enables external compression to sub-picosecond pulses with a standard grating compressor. Here we show that the most important influence of IDM is for GDD but further improvement can be with additional TOD. Our experimental concept with an intracavity SLM enables precisely controlled introduction of dispersion and thus a well suited basis for comparing experimental results with theoretical models of mode-locked diode lasers with variable dispersion [19,22]. For future work, we are planning to expand our IDM with amplitude filtering. We except that even shorter pulses may be generated, because the benefits from amplitude shaping of other mode-locked lasers are well known . For semiconductor lasers it has already been shown that spectral amplitude shaping is beneficial for the increase of spectral bandwidth . With a combination of IDM and amplitude shaping the generation of sub-150 fs with subsequent external pulse compression should become feasible from an edge emitting laser diode.
We thank the German Research Foundation (HO1973/15-1) for financial support.
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