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A solitary monolithic integrated semiconductor laser (MISL) chip with a size of 780 micrometer is designed and fabricated for broadband chaos generation. Such a MISL chip consists of a DFB section, a phase section and an amplification section. Test results indicate that under suitable operation conditions, this laser chip can be driven into broadband chaos. The generated chaos covers an RF frequency range, limited by our measurement device, of 26.5GHz, and possesses significant dimension and complexity. Moreover, the routes into and out of chaos are also characterized through extracting variety dynamical states of temporal waveforms, phase portraits, RF spectra and statistical indicators.
© 2013 Optical Society of America
1. Introduction
Chaos is of great interest owing its important roles in both basic science and applied technology. Chaos in semiconductor lasers (SLs) has drawn considerable attention because of its excellent features and many significant applications, such as secure communications [1], fast physical random number generation [2–4] and high performance radar and lidar [5, 6] etc. Since SLs belong to the class B laser [7], the chaos generated by SLs usually needs to introduce some external perturbations. In past years, many valuable techniques, such as optical feedback [8–12], electro-optical feedback [13], optical injection [14] and mutual coupling [15], have been proposed and implemented. However, in reality, most of experimental setups with external perturbations make use of discrete optical components, which are usually bulky, lack of long-term stability and reproducibility, and uneconomical for commercial use. Therefore, developing compact and miniature chaos generator is very attractive. One solution for compact chaos generation is to design specific photonic integrated circuits (PICs). Compared to those setups composed of discrete components, PICs devices own inherent mechanical stability and good reproducibility for mass production [16]. Ushakov et al. demonstrated the excitability of high-dimensional chaotic transients in an integrated SL with amplified optical feedback [17], which is introduced [18] and extensively characterized [19] by Bauer et al.. Schikora et al. proposed a chaotic system combining a multisection laser with an external Fabry-Perot etalon [20]. Yousefi et al. observed the complex chaos generated from an integrated colliding-pulse mode-locked SL chip [21]. Argyris et al. reported a four sections integrated laser chip consisting of a distributed feedback laser, a one centimeter straight-type passive resonator, and active elements that control the optical feedback properties [22]. Furthermore, these chaos laser chips have been applied in secure optical communication [23], and fast physical random number generation [24]. More recently, Sunada et al. reported a novel compact chaos laser chip contained a ring-type passive waveguide [25]. The size of this laser chip reaches within 3.5mm × 3.5mm, which is much smaller than those of setups with discrete components.
In this paper, a three-section monolithic integrated semiconductor laser (MISL) chip is specifically designed and fabricated for broadband chaos generation. The overall length of this chip is only 780 micrometer. Without any aid of external perturbations, this solitary MISL chip is able to generate ultra-broadband chaotic signals with RF spectra of beyond 26.5 GHz. Meanwhile, the routes into and out of chaos are confirmed through the observation of diverse nonlinear dynamics. Finally, chaos data analysis is also performed in order to quantify the dimension and complexity of observed various nonlinear dynamics.
2. MISL chip and experimental setup
Figures 1(a) and 1(b) show the photo and schematic diagram of the MISL, respectively. The epitaxial material of MISL chip is grown on an InP-substrate. Figure 1(b) shows the schematic diagram of the MISL, which consists of a distributed feedback (DFB) section, a phase section and an amplifier section with lengths of 220μm, 240μm and 320μm, respectively. Each section is separated by an electric isolation region. Here, the DFB section and the amplifier section have the same epitaxial structure, which contains seven compressively strained InGaAsP quantum wells and six lattice-matched InGaAsP barriers. Additionally, a gain-coupled Bragg grating has been applied to the DFB section. In the phase section, quantum wells intermixing (QWI) technique is used to make blue-shift of the band-gap to reduce the absorption loss as much as possible. Moreover, the processes of QWI require no additional material re-growth step. Therefore, the use of QWI ensures perfect alignment between different sections of MISL chip and results in a negligibly small interfacial reflection loss [26, 27]. Moreover, a high-reflection coating is applied to the face of amplifier section, and a precise cleavage plane forms the facet of DFB section for optical output. It should be pointed out that low absorption loss in the phase section induced by adopting QWI and high facet reflectivity resulted from coating a high-reflection film are two important factors for chaos generation since enough strong feedback level is needed for realizing chaotic output in such a short external cavity [7, 22]. Finally, three electrodes are welded to the top of MISL, and different injection currents, named as IDFB, IP and IA, can be applied to DFB section, phase section and amplifier section, respectively.
Fig. 1 (a) Photo of the MISL. (b) Schematic diagram of the MISL. (c) Measurement setup. ISO: isolator; BS: beam splitter; PD: photoelectric detector; OSA: optical spectrum analyzer; ESA: RF spectrum analyzer; OSC: wide-bandwidth oscilloscope. Dashed line: optical path; solid line: electrical path.
The measurement setup is shown in Fig. 1(c). In this setup, the MISL chip is driven by high-accuracy current sources (ILX-Lightwave, LDC-3724B), and stabled by a thermoelectric controller (ILX-Lightwave, LDT-5412). The temperature of the MISL chip is always stabilized at 25°C during the measurement process. An optical isolators (ISO) (isolation>55dB) is inserted into the optical path to prevent from unwanted external feedback disturbances. The output of MISL is divided into two parts by a beam splitter (BS). One part is injected into an optical spectrum analyzer (OSA, Ando AQ6317C), and the other part is firstly converted to an electrical signal by a fast photo-detector (PD, U2T-XPDV2150R, 47GHz bandwidth), and then analyzed by electronic equipments, such as a radio-frequency (RF) spectrum analyzer (ESA, Agilent E4407B with 26.5GHz bandwidth) and a wide-bandwidth oscilloscope (OSC, Agilent MSOX92504A with 25GHz bandwidth).
3. Experimental results
The P-I characteristic and optical spectrum of the MISL are shown in Fig. 2. The P-I curve is obtained when IDFB is altered while IP and IA are fixed as 0mA. Under this circumstance, the threshold current (Ith) of MISL is measured as about 39mA. In Fig. 2(b), the lasing optical spectrum is recorded under different IDFB values. For instance, the lasing wavelength is about 1541.96nm for IDFB = 87mA. It can be observed that the lasing wavelength moves toward longer wavelength along with the increase of IDFB, but always maintains a single mode oscillation. This phenomenon may originate from the fact that only DFB section of MISL is active, and the amplifier section and the phase section work as a passive waveguide since no injection current is applied to them. Therefore, the MISL behaves similar as a normal single mode DFB laser.
Fig. 2 (a) Measured P-I curve. (b) Lasing optical spectra of MISL under different IDFB values and IP = IA = 0mA.
To characterize comprehensively the chaos of the MISL, the outputs of the MISL are observed from multiple perspectives. Figure 3 shows the recorded temporal waveforms (a), phase portraits (b), RF spectrum (c) and optical spectrum (d). The phase portrait is plotted by the temporal waveform versus its derivative of the waveform. The red represents the output of the MISL under IDFB = 88mA, IA = 20.4mA and IP = 0mA, while the blue represents that for IDFB = 88mA, IA = 0mA and IP = 0mA. For the first case (red), the temporal waveform (Fig. 3(a)) exhibits large-amplitude oscillations and fluctuates dramatically in sub-nanosecond level, and the trajectories evolve complicated and the data points scatter over a wide area (Fig. 3(b)). Moreover, the recorded RF spectrum (Fig. 3(c)) shows a relatively flat distribution and continuously extends up to the cutoff frequency (26.5GHz) of the ESA. Additionally, the optical spectrum (Fig. 3(d)) also expands significantly. All these indicate that the MISL operate at a chaotic state. Comparatively, for IDFB = 88mA, IA = 0mA and IP = 0mA, the amplitude temporal waveform shrinks to almost zero, meanwhile the trajectories of phase portrait shrink as a small spot and the optical spectrum has typical single mode shape.
Fig. 3 (a) Temporal waveform of output from MISL. (b) Phase portraits of output from MISL. (c) RF spectra of output from MISL, where the gray line is the noise floor of RF spectrum. (d) Optical spectra of output from MISL. The red labels the chaotic output from MISL while the blue labels the stable output from MISL.
To further show how the MISL evolves into and out of chaos, a typical sequence of dynamics is given in Fig. 4. From the top to the bottom, different dynamical states are steady state (S), period-one state (P1), period-two state (P2), chaotic state (C), transition state (T) and S state, respectively. Generally, different dynamical states can be identified based on their unique characteristics. For the S state (Figs. 4(a) and 4(f)), the temporal waveform just has some tiny fluctuations mainly caused by the noise in system. Accordingly, the phase portrait shrinks as a small spot, and the RF spectrum almost coincides with the noise floor. But a very small bulge could still be observed in Fig. 4(a3) at about 9.4 GHz, which reveals the characteristic relaxation-oscillation frequency of the MISL chip. Next, as shown in the Fig. 4(b), P1 state is presented. In Fig. 4(b1), the temporal waveform shows a sequence of regular pulses with constant oscillation intensity, and the trajectories of phase portrait show clear limit cycle feature. In Fig. 4(b3), the fundamental frequency (about 9.4 GHz) and its harmonics also present sharply. In the Fig. 4(c), the temporal waveform shows irregular fluctuations, and the trajectories of phase portrait disperse within a certain range. This dispersion may be caused by the noise of the system and digitization errors from oscilloscope. In Fig. 4(c3), both the sub-harmonic frequency (about 4.7GHz) and fundamental frequency (about 9.4GHz) present clearly, which demonstrates the typical characteristics of doubled periodicity. Then, the dynamics shown in Fig. 4(c) could be identified as P2 state. Furthermore, in the Fig. 4(d), the temporal waveform fluctuates dramatically, and the phase portrait shows a widely scattered distribution in a large area. Meanwhile, the corresponding RF spectrum continuously covers a very broad frequency range. All these indicate the MISL operate at a broadband C state. Figure 4(e) presents a T state from C state to S state, and shows intermittent switching between C state and stationary emission. Figure 4(f) shows the final S state. In short, with the increase of IA from 17mA to 21mA, the MISL shows rich nonlinear dynamical states followed a route of S-P1-P2-C-T-S.
Fig. 4 Dynamical characteristics routes into and out of chaos for IDFB = 88mA, IP = 0mA, and IA varies from top to bottom as (a) 17mA, (b) 19mA, (c) 19.5mA, (d) 20.4mA, (e) 20.9mA and (f) 21mA, respectively. The first, second and third columns show the temporal waveforms, the phase portraits and the measured RF spectra, respectively, and the gray lines are the noise floor of RF spectrum. S: steady state; P1: period-one state; P2: period-two state; C: chaotic state; T: transition state.
Finally, the chaos data analysis is also performed in Fig. 5. The correlation dimension D2 and Kolmogorov entropy K2 are calculated by using the G-P algorithm [28–30], which is one of the main methods to measure the dimensions and complexity of dynamics. As shown in Fig. 5, four regions with different characteristics could be identified. Firstly, in the region “I” and “IV”, D2 is omitted in these two regions since the MISL is in a steady state and only contains noise fluctuations in temporal waveforms. Accordingly, K2 is very close to zero. In the region “II”, D2 and K2 are enhanced. After taking into account the noise contribution to the temporal waveforms, D2 (D2<2) and K2 (K2<1) are still not large enough to support the judgment of chaos dynamics. With the aid of Figs. 4(b)-4(c), the dynamics in region “II” are P1 or P2 states. Furthermore, in the region “III”, both D2 and K2 increase considerably. Specially, for the case of IA = 20.4 mA, D2 arrives at its maximum value of 4.6 meanwhile K2 achieves its maximum of 5.3ns−1. Combined with the above observations in Fig. 4(d), it can be reasonably determined that under this condition, high-dimensional broadband chaos is produced in the MISL chip. Meanwhile, it should be noted that for the region “III”, its range of IA for generating chaos is about 19.7mA~20.8mA, and its boundary is steep. If IA is located at the central region, the output of MISL chip can maintain chaos state. However, when the current IA is located at near the boundary, the output state of MISL chip may be unstable and experience intermittent switching between two different states due to the noise of MISL chip and the fluctuations of current IA.
Fig. 5 Variation of correlation dimension D2 and Kolmogorov entropy K2 for IDFB = 88mA, IP = 0mA and IA is changed from 14mA to 26mA. The red circles represent D2, while the blue squares represent K2. Four different regions are identified and labeled as I, II, III and IV, respectively.
5. Conclusions
In this paper, a three-section MISL chip is designed and fabricated for broadband chaos generation. The overall size of this chaos laser chip is less than 1 millimeter. Using this solitary laser chip, the chaos exceeding 26.5GHz frequency coverage is successfully produced. Moreover, various nonlinear dynamics are also observed and identified by acquiring temporal waveforms, phase portraits, RF spectra, and statistical indicators D2 and K2. Accordingly, a typical period doubling route into chaos and intermittent transition route out of chaos are defined. This highly integrated chaos generator is helpful for the exploitation of compact, robust and low cost optical chaotic source and has potential applications in ultra-fast physical random number generation and on-chip optical chaos communications.
Acknowledgments
This work was supported by the National Natural Science Foundation of China under Grant Nos. 61078003, 11004161, 61178011, 61274045, 61275116, 61201103 and 61021003, the National 973 Program under Grant 2011CB301702, and the Fundamental Research Funds for the Central Universities under Grant XDJK2013B037.
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