A 4-section semiconductor laser with integrated optical feedback has been shown experimentally to be capable of operating in either the short- or long-cavity regime, by controlling the device relaxation oscillation frequency relative to the external cavity frequency. Systematic increase of the laser injection current, and the resulting increase in relaxation oscillation frequency, allowed the transition between the two regimes of operation to be observed. The system displayed a gradual transition from a dynamic dominated by regular pulse packages in the short-cavity regime to one dominated by broadband chaotic output when operating in the long-cavity regime. This suggests that the “short cavity” regular pulse packages continue to co-exist with the “long cavity” broadband chaotic dynamic in the system studied. It is the relative power associated with each of these dynamics that changes. This may occur more generally in similar systems.
© 2015 Optical Society of America
Semiconductor lasers with external optical feedback continue to be a significant and much studied nonlinear system [1–4]. The rich dynamical behavior of these systems has found applications in, for example, secure communications , random number generation [6, 7] and reservoir computing .
In most cases these feedback systems are based on longer external fiber-based or free-space cavities. Whilst such systems are easily implemented in a laboratory environment, they are bulky and somewhat impractical for commercial use. A photonic integrated device, which consists of a laser section, a feedback control section, and a waveguide acting as the external cavity which provides the optical feedback; all on a single chip, is a minimal, compact and practical way to implement a delayed feedback system that can be deployed in real world environments [9–12].
One issue is that the photonic integrated devices are typically much shorter than semiconductor-laser-with-external-optical-feedback systems using fiber or bulk optics. In shorter devices the relative magnitude of the two main driving frequencies, the relaxation oscillation frequency (fRO) and the external cavity frequency (fext), can span both the short-cavity and long-cavity condition for such systems. A system is classified as being either short-cavity, when fRO is much less than fext, or long-cavity, when fRO is much larger than fext [13, 14]. Traditional delayed optical feedback systems typically have external cavities of more than a few centimeters and therefore fall into the long-cavity regime (LCR) with fext generally much less than the high frequency relaxation oscillations (several GHz to tens of GHz) which are characteristic of semiconductor lasers. Photonic integrated devices of appropriate design also fall into this category when operated at sufficiently high injection current. Achieving this informs the length of the passive waveguide section in their design [9, 10]. At low injection current, or in integrated devices of shorter total length, the photonic integrated chip (PIC) semiconductor lasers fext can be comparable to, or even higher than, the fRO. In such cases the system will be operating in the short-cavity regime (SCR).
Semiconductor lasers with short coupled cavities have been studied for decades . It was well into these studies that experiments were able to directly capture the temporal dynamics in high resolution [16, 17]. These studies demonstrated that, under certain conditions, laser diodes with delayed optical feedback in the short cavity regime would emit pulse packages made up of short regular pulses occurring at the external cavity round trip frequency under a much lower frequency envelope. It has been established that the phase of the optical feedback heavily influenced the type of output observed in the SCR [17–19]. Some detailed theoretical studies outline bifurcation scenarios by which these pulses arise  and also the form they take under varying conditions . Semiconductor lasers with integrated feedback cavities have also been investigated. The effects of feedback phase have been investigated in a 2-section device with a very short feedback cavity (200 µm) which showed transitions between CW and self-pulsation . A study of a 3-section device with integrated phase and amplifier sections also observed self-pulsations whilst tuning both the optical feedback phase and strength . No chaotic outputs were observed in these devices due to the requirement of very high feedback levels to push a short cavity system into coherence collapse . In order to target the growing number of applications of chaotic outputs, integrated devices with additional passive waveguides were developed to achieve longer cavity lengths suitable for producing chaotic signals . These 4-section integrated devices consisted of a DFB laser, passive waveguide resonator, and active sections for tuning the strength and phase of the feedback.
Here we present a systematic experimental investigation into the transition between short and long-cavity dynamics in such a 4-section photonic integrated laser. By adjusting the relaxation oscillation frequency relative to the external cavity, whilst monitoring the laser dynamics, a gradual transition between states is revealed.
2. Photonic integrated chip (PIC) laser
The type of device used here is the same as those used as transmitter/receiver pairs in a demonstration of chaotic secure communication over 100 km transmission path which achieved a bit error rate of 10-12 for bit rates up to 2.5Gb/s . It consists of a 300 μm DFB laser section with an operating wavelength of 1561 nm and a measured linewidth enhancement factor of α = 3.5; a 200 μm variable optical attenuation section, which can either be forward biased for gain or reverse biased for attenuation; a 150 μm phase control section and a high reflective coating on the end facet of a 1 cm long passive waveguide section. The latter section provides the necessary optical feedback for chaotic operation. A schematic of the device is shown in Fig. 1 and is described in detail in .
The laser output characteristics can be tuned by direct biasing of the 3 active sections. Applying a forward injection current to the DFB laser section (IDFB) provides the necessary gain for lasing. The other 2 active sections control the strength (IGAS or VGAS) and phase (IPH) of the feedback from the HR coated end facet. The laser output power dynamics were detected at the AR coated end facet of the DFB section. Experimental time series containing 80000 points were recorded on a 12GHz bandwidth real-time oscilloscope sampled at 40 GSa/s. A variety of complex dynamics can be observed over an extensive operating parameter space and are discussed elsewhere .
With a round trip time of ~0.25 ns, the external cavity frequency of this integrated device, fext ~4 GHz, can be close to the relaxation oscillation frequency of the free-running device, depending on the DFB section injection current. Typically, a study of the transition between SCR and LCR operation would involve changing the actual cavity length. The device studied here allows a detailed experimental investigation of the transition between these regimes by changing the relaxation oscillation frequency, via adjustment of the DFB laser section current. This transition is achieved while avoiding any complications due to possible changes in alignment that can occur in parallel when physically changing the external cavity length.
3. Short-cavity vs long-cavity regime operation
The relaxation oscillation frequency in a free-running semiconductor laser scales as the square root of the injection current above threshold . In order to determine the fRO curve for this device, a large reverse bias was applied to the gain/absorption (G/A) section to reduce the effective feedback level and to achieve an essentially free-running device. The phase section was left unbiased (IPH = 0 mA). At minimum feedback level (VGAS = −2 V), output power time series were recorded for DFB section current IDFB = 15 mA to 50 mA in 0.1 mA steps. A fast Fourier transform (FFT) was applied to the time series and an example of the broad fRO peak can be observed in Fig. 2(a). The frequency at which these peaks occur is plotted in Fig. 2(b) (note that the raw FFT has been smoothed to assist in peak identification). With this PIC device the value of fRO can be tuned from ~500 MHz up to ~6 GHz by changing the DFB section injection current. The linear relationship between the relaxation oscillation frequency and the square root of the difference between the injection current (IDFB) and the laser threshold current (Ith = 18.5 mA at VGAS = −2 V) is shown in Fig. 2(c).
The point at which the system transitions between short and long cavity regimes is governed by the injection current which sets fRO ≈fext ≈4 GHz. From Fig. 2(b) this can be seen to occur in the range of 30 – 35 mA. The spread of points seen in Figs. 2(b) and 2(c), especially at high injection currents, is due to the very broad nature of the FFT peaks and the smoothing procedure used so that the peaks could be identified.
When operating in a short cavity regime it has been demonstrated that semiconductor lasers display regular pulse packages (RPP) each consisting of a short train of pulses separated by the external cavity round trip time. The repetition frequency of the RRPs (fRPP) is much lower than the external cavity frequency . The phenomenon is quite similar to low frequency fluctuations (LFF) that have been observed and studied in long-cavity systems . The mechanism behind both types of dynamic is similar; as illustrated by theoretical studies using the laser rate equations. Both LFF and RPP power jumps occur when the state of the system wanders among the external-modes and anti-modes of the laser oscillations, a result of a saddle node instability caused by the optical feedback . The difference being that in the SCR the system tends to visit the same external cavity mode, thus displaying much more regular pulses, compared to the irregular trajectory observed for long cavity dynamics. The other significant differences relate to the time scale of the high frequency dynamics and the sensitivity to feedback phase. In the LCR, fast time scales are dominated by the undamped relaxation oscillations and the dynamics are largely insensitive to the phase of the optical feedback, In contrast, in the SCR, the external cavity frequency dictates the fast pulse period and the output can vary significantly with changes in the feedback phase .
Applying forward current to the G/A section of the device studied here provides amplification of the optical feedback which is guided by the passive waveguide forming the external cavity. A forward current of IGAS = 6.7 mA provides moderate level of feedback resulting in a reduction of the lasing threshold from 18.5 mA to 10.2 mA (approximately 45%). Using this feedback level and keeping the DFB laser section current low so as to operate within the SCR, regular pulse packages were observed as the dominant dynamic. An example of the output for the device operating in a short cavity regime where IDFB = 15 mA, IGAS = 6.7 mA, IPH = 0 mA is shown in Fig. 3.
The time series in Fig. 3(a) show regular pulses, with a period of the cavity round trip time (1/fext), modulated by a fairly regular envelope of lower frequency (fRPP). The RF spectra in Fig. 3(b) contain peaks at the RPP frequency and at the external cavity frequency (with more power) and higher harmonics (not shown on this scale). Previous studies on RPP’s describe the intensity behavior of the underlying pulses within each package as starting with a high intensity pulse, followed by almost monotonically decreasing intensity from pulse to pulse . Here we observed a more complex behavior in the intensity of the pulses within each package, typically with the highest intensity pulse towards the middle of the package, as seen in the inset of Fig. 3(a). This behavior has been predicted theoretically to be dependent on the external cavity length and is caused by a modification to the systems trajectory in phase space .
Increasing the DFB laser section current drives the fRO higher than fext and pushes the system into the long-cavity regime. An example of the LCR dynamics are shown in Fig. 4 where IDFB = 50 mA, IGAS = 6.7 mA, IPH = 0 mA. At this point the RPP dynamic becomes almost indistinguishable from a very broadband chaotic output.
Typically, the dynamics would change from a RPP to a LFF when transitioning from SCR to LCR in a system where just the external cavity length is changing [16, 17, 21]. However in this case the laser drive current is used to transition the system from short to long-cavity and so the LFF is not observed as IDFB is well above the solitary laser threshold where LFF usually occurs  (although it can be observed at higher injection currents, but only at much higher feedback levels ). As a result, in this particular device we are unable to experimentally confirm the theoretically predicted transition from RPP to LFF as in .
The transition between the SCR and LCR is best observed in Fig. 5(a) which shows the FFT of the time series for DFB section injection currents between IDFB = 10 and 50 mA. The lowest frequency peak corresponds to fRPP and the 3 peaks at higher frequencies are the external cavity frequency fext and its multiples, up to the detection bandwidth of 12 GHz where the spectra roll off.
The transition between short and long-cavity regime behavior is gradual. Consider the prominence of the RPP peak relative to the background level. This is measured as the peak height above the minimum value of the trough between 1.5 GHz and 3.5 GHz as an indicator and it is used to correlate with short-cavity and long-cavity regime operation. This difference is depicted by the red horizontal lines in Fig. 6. Once the laser is above threshold (Ith = 10.2 mA at IGAS = 6.7 mA) the relative amplitude of the RPP peak increases as the laser output power grows. At IDFB ~15 mA the background/chaotic power level begins to increase steadily and a gradual reduction in the relative amplitude of the RPP peak is observed. This amplitude difference is plotted in Fig. 5(b).
Previous studies on RPP dynamics showed a linear dependence of fRPP on the injection current, both experimentally and in simulations of the laser rate equations . For the integrated device studied here the dependence on injection current is displayed in Fig. 5(c). In general, the frequency of the RPP increases with DFB current. The exception is at lower injection currents where a jump to a lower value occurs at IDFB = 17.9 mA. Interestingly, subsidiary peaks occur within the broader envelope of the RPP peak and the jump observed in Fig. 5(c) represents the point at which the lower frequency sub-peak becomes the one with the highest amplitude. This jump can be observed in Visualization 1 which shows the evolution of the RF spectrum with increasing DFB section current. The animation starts at IDFB = 10.0 mA and each subsequent frame represents an increase of 0.1 mA up to IDFB = 50 mA. A single frame showing the sub-peaks within the RPP envelope just after the jump occurs is shown in Fig. 6. The right-hand plot in Visualization 1 and Fig. 6 shows the RF spectrum with the RPP frequency marked by the blue vertical line and the amplitude difference between the RPP peak and spectrum baseline marked by the 2 horizontal red lines. Both of these quantities are plotted in the left-hand plot with corresponding colors: the RPP frequency in blue (left axis) and the amplitude difference in red (right axis).
There is some suggestion that this jump occurs again for IDFB ~30 mA, though it is not definitive due to the difficulty in locating the precise location of the peak from the background level. The precise origin of the frequency spacing between the sub peaks is not known, but the spacings are of a similar magnitude to the spacing between strong discrete frequency features observed in the noise spectrum of the device and detection system at injection currents below and near threshold. It is possible that the laser system is picking up these RF signals from the environment and they are being nonlinearly enhanced by the feedback system as seen previously in a bulk semiconductor laser with optical feedback system . The frequency jump of ~110 MHz observed at 17.9 mA corresponds to a frequency spacing in the noise spectrum observed at low injection current. Additional frequencies from the noise spectrum are observed as peak spacings in the smoothed spectra as a function of injection current contained in the supplementary Visualization 1 data. Pushing and pulling between these additional noise frequencies in the system may be the cause or part of the cause of the scatter in the RPP frequency seen here in Fig. 5(c) (with 2% data smoothing window).
A laser system of the type studied here naturally tends towards a linear increase in RPP frequency with injection current as reported in . If we consider the center frequency of the broader RPP peak, detected by using a larger smoothing window, in this case 5% of the total FFT length - see red points in Fig. 5(c), the frequency increase with DFB current is much closer to linear, as observed in . There is some suggestion that this trend is more linear at IDFB > 30 mA (i.e. in the LCR) and “rolls-off” in the SCR for IDFB < 30 mA. This roll-off in fRPP at low injection currents, close to the laser threshold in the SCR, has also been observed in simulations , albeit without the multiple peaks seen experimentally in the present study.
This analysis shows there is no clear change from SCR behavior to LCR. Instead a gradual transition occurs where both short cavity RPP dynamics occur simultaneously with longer cavity chaotic dynamics with the relative prominence of each changing systematically. It is worth noting that it is when operating in the LCR, at higher DFB section currents, the output signal from this device has properties that are desirable for chaotic carriers in secure communication systems , i.e. a relatively flat, featureless, broadband RF spectrum and rapid drop off in correlations. The investigation presented in  identifies the SCR as a preferred region in which to operate to achieve this type of output. This is in contrast to the observations made with the integrated device studied here for which the LCR is preferable as a chaotic carrier.
In contrast to the LCR, a definitive characteristic of SCR operation is that the dynamics are sensitive to the phase of the optical feedback [17, 20]. Operating the PIC device with a low fixed injection current, chosen to place the device within the SCR operating space, the temporal dynamics were recorded whilst varying both the phase (IPH) and level (IGAS) of the optical feedback. A map depicting the RMS amplitude of the dynamics in SCR operation (IDFB = 15.5 mA) is shown in Fig. 7(a).
There are clear variations to the observed dynamics when varying the phase of the optical feedback. The output can transition between CW (low RMS amplitude) to RPP output (higher RMS amplitude), via an intermediate stage where the output switches between both.
In contrast, when the same map is produced for higher injection current IDFB = 50 mA, resulting in LCR type output, no feedback phase dependence is observed, see Fig. 8.
The slight trend to lower RMS amplitudes with increasing phase section current seen in both the SCR, in Fig. 7(a), and LCR, in Fig. 8, is likely due to slight current leakage between the device sections.
For a fixed feedback level of IGAS = 6.7 mA we note that phase dependencies only occur up to a DFB injection current of IDFB ~18 mA. This is noticeably less than the anticipated SCR/LCR boundary of IDFB ~30-35 mA which was based on the proximity of the free-running relaxation oscillation frequency to the external cavity frequency. This suggests that the feedback phase sensitivity of the dynamics is only significant when fRO is much less than fext, whereas the RPP dynamic persists even when fRO is comparable with fext. A more thorough stability analysis of the RPP over a wider parameter space is the focus of future work.
It has been experimentally demonstrated that a 4-section photonic integrated semiconductor laser can be operated in either the short- or long-cavity regime, by controlling the device relaxation oscillation frequency, as set by the laser section injection current. Systematic increase of the DFB laser bias, and the resulting increase in fRO, allowed the transition between the short and long cavity regimes of operation to be observed. The system displayed a gradual transition from regular pulse package output in the SCR operation to broadband chaotic output when operating in the LCR. The results support the simulations reported in previously modelled short cavity systems, including phase sensitivity , and nonlinear response of fRPP to injection current when operated close to the lasing threshold .
From an applications perspective, for the device to be utilized as a chaotic source it must be operated in the LCR. The long passive waveguide section was designed to achieve this. The DFB injection current needs to be above ~40 mA for this device to operate in the LCR. In this regime the laser output is highly unpredictable, has a rapid drop off in correlation, and has a very flat broadband spectrum, suitable for applications such as chaotic masking in secure communication schemes. In addition to masking the RPP frequency, higher DFB injection current results in increased output power which is also beneficial for applications.
This research was supported in parts by the Australian Research Council (Linkage Project LP100100312), Sirca Technology Pty Ltd, Macquarie University, the Science and Industry Endowment Fund (RP 04-174) and the Greek Secretariat of Research and Technology under program ARISTEIA II-CONECT-4750. The PIC device was fabricated by M. Hamacher and colleagues at the Fraunhofer Institute for Telecommunications, Heinrich-Hertz-Institute, Berlin, Germany, funded by the European Commission project PICASSO IST-2006-34551. Authors would like to thank Dr. A. Kapsalis for his contribution in supporting the data acquisition processes.
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